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| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
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| date | Thu, 02 May 2013 11:08:12 +0200 |
| parents | 22d6a63640c6 |
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<?xml version="1.0"?> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink" > <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"></pb><p type="head"> <s>MATHEMATICAL <lb></lb>Collections <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Tranſlations: <lb></lb><emph type="italics"></emph>In two<emph.end type="italics"></emph.end><lb></lb>TOMES.</s></p><pb xlink:href="040/01/002.jpg"></pb><pb xlink:href="040/01/003.jpg"></pb><p type="head"> <s>MATHEMATICAL <lb></lb>COLLECTIONS <lb></lb>AND <lb></lb>TRANSLATIONS: <lb></lb>THE FIRST <lb></lb>TOME. <lb></lb><emph type="italics"></emph>IN TWO PARTS.<emph.end type="italics"></emph.end></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"></emph>I.<emph.end type="italics"></emph.end> GALILEUS GALILEUS <emph type="italics"></emph>His SYSTEM of the <lb></lb>WORLD.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>II.<emph.end type="italics"></emph.end> GALILEUS <emph type="italics"></emph>His EPISTLE to the GRAND <lb></lb>DUTCHESSE MOTHER, concerning the Au<lb></lb>thority of Holy SCRIPTURE in Philoſophical <lb></lb>Controverſies.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>III.<emph.end type="italics"></emph.end> JOHANNES KEPLERUS <emph type="italics"></emph>His Reconcilings of SCRI<lb></lb>PTURE Texts, &c.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>IV.<emph.end type="italics"></emph.end> DIDACUS à STUNICA <emph type="italics"></emph>His Reconcilings of SCRI<lb></lb>PTURE Texts, &c.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>V.<emph.end type="italics"></emph.end> P. A. FOSCARINUS <emph type="italics"></emph>His Epiſtle to Father FANTONUS, <lb></lb>reconciling the Authority of SCRIPTURE, and Judg<lb></lb>ments of Divines alledged againſt this SYSTEM.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>By <emph type="italics"></emph>THOMAS SALUSBURY, <expan abbr="Eſq.">Eſque</expan><emph.end type="italics"></emph.end></s></p><p type="head"> <s>LONDON, <lb></lb>Printed by WILLIAM LEYBOURN, MDCLXI.</s></p><pb xlink:href="040/01/004.jpg"></pb><pb xlink:href="040/01/005.jpg"></pb></section><section><p type="head"> <s>To the Noble and moſt perfectly Accompliſhed <lb></lb>S^{t.} JOHN DENHAM <lb></lb>Knight of the Noble Order of the <lb></lb>BATH, <lb></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></lb>bringing this Book under your Pro<lb></lb>tection. </s> <s>Were it a Work of my <lb></lb>own, or I any thing but the Tranſla<lb></lb>tour, I should maſter my Thoughts to a meaner <lb></lb>Dedication; But being a Collection of ſome of <lb></lb>the greateſt Maſters in the World, and never <lb></lb>made English till now, I conceived I might <lb></lb>ſooner procure their Welcome to a perſon ſo <lb></lb>eminent for Noble Candor, as well as for all <lb></lb>thoſe Intellectual Excellencies wherewith <lb></lb>Your Rich Soulis known to be furnished. </s> <s>I <lb></lb>reſolv'd to be as kind to this Book as I could, <pb xlink:href="040/01/006.jpg"></pb>and ſeriouſly conſidering which way to effect <lb></lb>it, I at laſt concluded to prefix Your Name, <lb></lb>whom His Majeſty and all his Subjects, (who <lb></lb>have a higher Senſe and Judgement of Excel<lb></lb>lent Parts) know beſt able to defend my Im<lb></lb>perfections. </s> <s>And yet I confeſs there's one <lb></lb>thing makes againſt me, which is your eminent <lb></lb>Integrity and great Affection to Truth, where<lb></lb>by my Lapſesin a Work of this Nature might <lb></lb>juſtly deſpair of Shelter, but that the Excel<lb></lb>lency of Your Native Candor ſtrives for Pre<lb></lb>dominancy over all Your great Abilities. </s> <s>For <lb></lb>'tis all-moſt impoſſible to think what Your <lb></lb>Matchleſs Wit is not able to Conquer, would <lb></lb>Your known Modeſty but give leave: there<lb></lb>fore <emph type="italics"></emph>Galileus, Kepler,<emph.end type="italics"></emph.end> and thoſe other worthies <lb></lb>in Learning are now brought before You in <lb></lb>English Habit, having chang'd their Latine, <lb></lb>Italian and French, whereby they were almoſt <lb></lb>Strangers to our Nation, unleſs to ſuch as You, <lb></lb>who ſo perfectly maſter the Originals. </s> <s>I know <lb></lb>you have ſo much and great imployment for <lb></lb>His Majeſty, and his good Subjects that I shall <lb></lb>not robb you of another Minutes loſs; beſides <lb></lb>the liberty of ſubſcribing my Self;</s></p><p type="main"> <s>SIR,</s></p><p type="main"> <s><emph type="italics"></emph>Your Honours<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Moſt Humble <lb></lb>and <lb></lb>Moſt obedient Servant</s></p><p type="main"> <s>THOMAS SALUSBURY.</s></p><pb xlink:href="040/01/007.jpg"></pb></section><section><p type="main"> <s>READER,</s></p><p type="main"> <s>Mathematical Learning <emph type="italics"></emph>(to ſpeak nothing touching the neceſsity & delight thereof) hath bin ſo ſparing<lb></lb>ly imparted to our Countrymen in their native Engliſh, eſpecially the nobler and ſublimer part, <lb></lb>that in Compliance with the<emph.end type="italics"></emph.end> Solicitations <emph type="italics"></emph>of ſeveral of my noble and learned Friends, and the<emph.end type="italics"></emph.end> Incli<lb></lb>nations <emph type="italics"></emph>of ſuch as are Mathematically diſpoſed, more eſpecially thoſe, who either want Time or <lb></lb>Patience to look into the vulgar and unſtudied Languages, I did adventure upon this Work of Collecting & Tranſ<lb></lb>lating from amongſt the excellent Pieces that are ſo abounding in the Italian and French Tongues, ſome of thoſe <lb></lb>that my own obſervation and the intimation of Friends were moſt uſefull and deſired, and with all moſt wanting <lb></lb>in their Own.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>I was, indeed, at firſt ſeriouſly Conſcious, and am now, by experience, fully convinced how diſproportionate the <lb></lb>weight of the Enterprize is to the weakneſs of the Vndertaker, but yet the Paſsion I ever had to be ſubſervient to <lb></lb>my Friends and Compatriots in their Inquiſition after theſe Sublime Studies, and a Patience which I owe to the <lb></lb>Flegme that is predominant in my Conſtitution, joyned with a nine-years converſence in theſe Languages, as alſo an <lb></lb>unhappy and long Vacation that the perſecutions of the late Tyrants gave me from more advantagious employ<lb></lb>ments ſo prevailed with me, that I reſolved to improve even my very Confinement to ſerve thoſe Friends, whom, as <lb></lb>the Times then ſtood, I could not ſee.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>The Book being for Subject and Deſign intended chiefly for Gentlemen, I have hin as careleſs of uſing a ſtudied <lb></lb>Pedantry in my Style; as careful in contriving a pleaſant and beautiful Impreſſion. </s> <s>And when I had conſidered <lb></lb>the hazard, and computed the charge of the undertaking, I found it to exceed the ability of a private Purſe, eſpe<lb></lb>cially of mine, that had bin ſo lately emptied by the hand of violent enemies, and perfidious friends; not to <lb></lb>make mention here of the Sums that a Loyal Reflexion upon my Princes Affairs had at the ſame time drawn <lb></lb>from me; and judg'd that the most ſafe, eaſy, and reaſonable way was to invite thoſe Perſons who had appeared <lb></lb>deſirous of the Book, to be contributary to their own Contentment, by ſubſcribing towards the charge of this Pu<lb></lb>blication.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>And for the better management of the Work, I joyned to my ſelf a Printer, whoſe Genius having rendered <lb></lb>him Mathematical, and my overtures of profit having intereſſed his diligence, I was induced to promiſe my ſelf a <lb></lb>more than common Aſſiſtance from him: and at his door I with reaſon lay all miſcarriages that concerns his <lb></lb>Profeſſion in the Buſineſs.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>In this Work I found more than ordinary Encouragement from that publick ſpirited Perſon the Reverend and <lb></lb>Learned Dr.<emph.end type="italics"></emph.end> Thomas Barlow, <emph type="italics"></emph>Provoſt of Queens Colledge Oxford, and<emph.end type="italics"></emph.end> Margaret <emph type="italics"></emph>Profeſſor in that Vniver<lb></lb>ſity, as alſo from thoſe two able Mathematicians and my Reall Friends Major<emph.end type="italics"></emph.end> Miles Symner, <emph type="italics"></emph>and Mr.<emph.end type="italics"></emph.end> Robert <lb></lb>Wood <emph type="italics"></emph>of Trinity Colledge<emph.end type="italics"></emph.end> Dublin, <emph type="italics"></emph>and ſome few others whoſe Modeſty hath expreſly enjoin'd me a concealment <lb></lb>of their Names.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Well, at length I have got to the end of my firſt Stage; and if I have not rid Poſt, let my excuſe be that my long <lb></lb>ſtay for my Warrant cauſed me to ſet out late; and being ill mounted, and in a road full of rubbs, I could not with <lb></lb>any ſafety go faſter; but hope to get it up in the next Stage, for in that I intend to ſhift my Horſes.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>The names of thoſe Authors and Treatices which I judged would moſt grace our Language, and gratify Stu<lb></lb>dents, are particularly expreſt in the General Title of the two Tomes. </s> <s>Diſtinct Tomes they are as conſiſting of <lb></lb>ſeverat Pieces: Collections I call them, becauſe they have bin ſo publiſhed, diſperſt, and worn out of Print, that <lb></lb>they very rarely meet in one hand: and Tranſlations I own them to be, as not pretending to any thing more than <lb></lb>the diſpoſure and converſion of them: thoſe Tracts only excepted which compoſe the ſecond Part of the ſecond <lb></lb>Tome.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>The firſt Book which offers it ſelf to your view in this Tome is that ſingular and unimitable Piece of Reaſon <lb></lb>and Demonſtration the Syſteme of<emph.end type="italics"></emph.end> Galilco. <emph type="italics"></emph>The ſubject of it is a new and Noble port of Aſtronomy, to wit the <lb></lb>Doctrine and Hypotheſis of the Mobility of the carth and the Stability of the Sun; the Hiſtory whereof I ſhall <lb></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></lb>why theſe Dialogues found ſo various entertainment in Italy (for he cannot but have heard that though they have <lb></lb>been with all veneration valued, read & applauded by the Iudicious yet they were with much deteſtation perſecuted, <lb></lb>ſuppreſſed & exploded by the Superſtitious) I am to tell him that our Author having aſſigned his intimate Friends<emph.end type="italics"></emph.end><lb></lb>Salviati <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Sagredo <emph type="italics"></emph>the more ſucceßfull Parts of the Challenger, and Moderater, he made the famous Commen<lb></lb>tator<emph.end type="italics"></emph.end> Simplicius <emph type="italics"></emph>to perſonate the Peripatetick. </s> <s>The Book coming out, and Pope<emph.end type="italics"></emph.end> Urban <emph type="italics"></emph>the<emph.end type="italics"></emph.end> VIII. <emph type="italics"></emph>taking his Ho<lb></lb>nour to be concern'd as having in his private Capacity bin very poſitive in declaiming against the Samian Philo<lb></lb>ſophy, and now (as he ſuppoſed) being ill delt with by<emph.end type="italics"></emph.end> Galilco <emph type="italics"></emph>who had ſummed up all his Arguments, and pur <lb></lb>them into the mouth of<emph.end type="italics"></emph.end> Simplicius; <emph type="italics"></emph>his Holineſs thereupon conceived an implacable Diſpleaſure against our Au<lb></lb>thor, and thinking no other revenge ſufficient, he employed his Apoſtolical Authority, and deals with the Conſiſtory <lb></lb>to condemn him and proſcribe his Book as Heretical; proſtituting the Cenſure of the Church to his private revenge. <lb></lb></s> <s>This was<emph.end type="italics"></emph.end> Galilco's <emph type="italics"></emph>fortune in<emph.end type="italics"></emph.end> Italy: <emph type="italics"></emph>but had I not reaſon to hope that the Engliſh will be more hoſpitable, on the <lb></lb>account of that Principle which induceth them to be civil to (I ſay not to dote on) Strangers, I ſhould fear to be <lb></lb>charged with imprudence for appearing an Interpreter to that great Philoſopher. </s> <s>And in this confidence I ſhall <lb></lb>forbear to make any large Exordium concerning him or his Book: & the rather in regard that ſuch kind of Gau<lb></lb>deries become not the Gravity of the Subject; as alſo knowing how much (coming from me) they must fall ſhort of <lb></lb>the Merits of it, or him: but principally becauſe I court only perſons of Judgement & Candor, that can diſtinguiſh <lb></lb>between a Native Beauty, and ſpurious Verniſh. </s> <s>This only let me premiſe, though more to excuſe my weakneſs in <lb></lb>the menaging, than to inſinuate my ability in accompliſhing this ſo arduous a Task, that theſe profound Dialogues <lb></lb>have bin found ſo uneaſy to Tranſlate, that neither affectation of Novelty could induce the French, nor the <lb></lb>Tranſlating humour perſwade the Germans to undertake them. </s> <s>This difficulty, as I conceived, was charged either <lb></lb>upon the Intricacy of this manner of Writing, or upon the ſingular Elegance in the ſtile of<emph.end type="italics"></emph.end> Galilco, <emph type="italics"></emph>or elſe upon the<emph.end type="italics"></emph.end><pb xlink:href="040/01/008.jpg"></pb><emph type="italics"></emph>miſcarriage of the unfortunate<emph.end type="italics"></emph.end> Mathias Berneggeius <emph type="italics"></emph>who firſt attempted to turn them into Latine for the benefit <lb></lb>of the Learned World.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>I ſhall not preſume to Cenſure the Cenſure which the Church of Rome paſt upon this Doctrine and its Aſſectors. <lb></lb></s> <s>But, on the contrary, my Author having bin indefinite in his diſcourſe, I ſhall forbear to exaſperate, and attempt <lb></lb>to reconcile ſuch perſons to this Hypotheſis as devout eſteem for Holy Scripture, and dutifull Reſpect to Canonical <lb></lb>Injunctions hath made to ſtand off from this Opinion: and therefore for their ſakes I have at the end of the Dia<lb></lb>logues by way of ſupplement added an Epiſtle of<emph.end type="italics"></emph.end> Galilco <emph type="italics"></emph>to Her Most Serene Highneſs<emph.end type="italics"></emph.end> Chriſtina Lotharinga <emph type="italics"></emph>the <lb></lb>Grand Dutcheſſe Mother of<emph.end type="italics"></emph.end> Tuſcany; <emph type="italics"></emph>as alſo certain Abſtracts of<emph.end type="italics"></emph.end> John Kepler, <emph type="italics"></emph>Mathematician to two Empe<lb></lb>rours, and<emph.end type="italics"></emph.end> Didacus à Stunica <emph type="italics"></emph>a famous Divine of Salamanca, with an Epiſtle of<emph.end type="italics"></emph.end> Paulo Antonio Foſcarini <emph type="italics"></emph>a learn<lb></lb>ed Carmelite of Naples, that ſhew the Authority of Sacred Scripture in determining of Philoſophical and Natu<lb></lb>ral Controverſies: hoping that the ingenious & impartial Reader will meet with full ſatisfaction in the ſame. <lb></lb></s> <s>And leaſt what I have ſpoken of the prohibiting of theſe Pieces by the Inquiſition may deterre any ſcrupulous <lb></lb>perſon from reading of them, I have purpoſely inſerted the Imprimatur by which that Office licenced them. </s> <s>And <lb></lb>for a larger account of the Book or Author, I refer you to the Relation of his Life, which ſhall bring up the Reare <lb></lb>in the Second Tome.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>What remains of this, is that Excellent Diſcourſe of D.<emph.end type="italics"></emph.end> Benedetto Caſtelli Abbate di San Benedetto Aloyſio, <lb></lb><emph type="italics"></emph>concerning the Menſuration of Running waters, with other Treatiſes of that Learned Prelate, & of the Superin<lb></lb>tendent<emph.end type="italics"></emph.end> Corſini. <emph type="italics"></emph>Some may alledge, and I doe confeſs that I promiſed to publiſh the Life of<emph.end type="italics"></emph.end> Galilco <emph type="italics"></emph>in this place: <lb></lb>But the great miſcarriages of Letters from ſome Friends in Italy and elſe where, to whom I am a Debtor for ſe<lb></lb>veral Remarques, & from whom I daily expect yet greater Helps concerning the Hiſtory of that famous Perſonage: <lb></lb>theſe diſappointments, I ſay, joyned with the undeniable Requeſt of ſome Friends, who were impatient to ſee<emph.end type="italics"></emph.end> Caſtelli <lb></lb><emph type="italics"></emph>in Engliſh, together with a conſideration of the diſproportionate Bulk that would otherwiſe have bin betwixt the <lb></lb>two Volumes, perſwaded me to this exchange. </s> <s>This deviation from my Promiſe I hope is Venial, and for the ex<lb></lb>plating of it I plead Supererrogation: having in each Tome made ſo large Aditions (though to my great ex<lb></lb>penſe) that they make neer a third part more than I ſtood by promiſe bound to Publiſh. </s> <s>That this is ſo will appearby <lb></lb>comparing the Contents I here prefix with the Advertiſment I formerly Printed. </s> <s>For not to mention thoſe Epitomes <lb></lb>of<emph.end type="italics"></emph.end> Kepler <emph type="italics"></emph>and<emph.end type="italics"></emph.end> à Stunica, <emph type="italics"></emph>the whole ſecond and following Books of<emph.end type="italics"></emph.end> Caſtclli, <emph type="italics"></emph>were not come to my hands at the time of <lb></lb>my penning that Paper; yet knowing how imperfect the Volume would be without them, they being partly a ſup<lb></lb>plement to the Theoremes and Problemes which the Abbot had formerly Printed, and partly experiments that <lb></lb>had procured him and his Doctrine a very great Reputation, knowing this I ſay, I apprehended a neceſſity of pu<lb></lb>bliſhing them with the reſt: and hope that if you think not the ſervice I have done therein worth your acknowledge<lb></lb>ment, you will yet at leaſt account the encreaſe of my expence a ſufficient extenuation of the Treſpaſs that thoſe <lb></lb>Additions have forced me to commit upon your Patience in point of Time.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>As for the ſecond Tome, I have only this to aſſure the Generous Readers; 1 that I am very confident I ſhall <lb></lb>be much more punctual in publiſhing that, than (for the reaſons above related.) I was able to be in ſetting forth <lb></lb>this: 2 that they ſhall not be abuſed in advancing of their moneys, (as hath bin uſed in the like caſe) by ſelling <lb></lb>the remaining Copyes at an under rate; and 2 that I have a very great care that no diſeſteem may by my means a<lb></lb>riſe unto this way of publiſhing Books, for that it is of excellent uſe in uſhering Great and Coſtly Volumes into <lb></lb>the World.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>To ſay nothing of the diſadvantages of Tranſlations in general, this of mine doubtleſs is not without it's Er<lb></lb>rours, and overſights: but thoſe of the Printer diſcounted, I hope the reſt may be allowed me upon the ſcore of<emph.end type="italics"></emph.end> Hu<lb></lb>man Imbecilitic. <emph type="italics"></emph>The truth is, I have aſſumed the Liberty to note the Miſtakes in the Florid Verſion of<emph.end type="italics"></emph.end> Bernegge<lb></lb>rus <emph type="italics"></emph>in the Margent, not ſo much to reproach him, as to convince thoſe who told me that they accounted my pains <lb></lb>needleſs, having his Latine Tranſlation by them. </s> <s>The like they ſaid of the whole two Tomes: but they thereby cauſed <lb></lb>me to question their Underſtanding or Veracity. </s> <s>For ſome of the Books were yet never extant: As for inſtance; <lb></lb>the Mcchanicks of Monſieur<emph.end type="italics"></emph.end> Des Cartes, <emph type="italics"></emph>a Manuſcript which I found amongſt the many other Rarities that en<lb></lb>rich the well-choſen Library of my Learned and Worthy Friend Dr.<emph.end type="italics"></emph.end> Charles Scarburgh; <emph type="italics"></emph>the Experiments of Gra<lb></lb>vity, and the Life of<emph.end type="italics"></emph.end> Galileo, <emph type="italics"></emph>both my own: Others were included in Volumes of great price, or ſo diſperſed that <lb></lb>they were not to be purchaſed for any money; as thoſe of<emph.end type="italics"></emph.end> Kepler, à Stunica, Archimedes, Tartaglia, <emph type="italics"></emph>and the Mecha<lb></lb>nicks of<emph.end type="italics"></emph.end> Galileo: <emph type="italics"></emph>And the remainder, though eaſyer to procure, were harder to be underſtood; as<emph.end type="italics"></emph.end> Tartaglia <emph type="italics"></emph>his notes <lb></lb>on<emph.end type="italics"></emph.end> Archimedes, Torricellio <emph type="italics"></emph>his Doctrine of Projects,<emph.end type="italics"></emph.end> Galileo <emph type="italics"></emph>his Epiſtle to the Dutcheſſe of<emph.end type="italics"></emph.end> Tuſcany, <emph type="italics"></emph>and above all <lb></lb>his Dialogues<emph.end type="italics"></emph.end> de Motu; <emph type="italics"></emph>(never till now done into any Language) which were ſo intermixt of Latine and Italian, <lb></lb>that the difficulty of the Stile, joyned with the intricatneſſe of the Subject rendered them Unpleaſant, if not wholly <lb></lb>Vnintelligible, to ſuch as were not abſolute Maſters of both the Tongues.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>To conclude; according to the entertainment that you pleaſe to afford theſe Collections, I ſhall be encouraged to <lb></lb>proceed with the Publication of a large Body of Hydrography; declaring the Hiſtory, Art, Lawes, and Apendages <lb></lb>of that Princely Study of Navigation, wherein I have omitted nothing of note that can be found either in<emph.end type="italics"></emph.end> Dud<lb></lb>ley, Fournier, Aurigarius, Nonius, Snellus, Marſennus, Bayſius, Moriſetus, Blondus, Wagoner, <emph type="italics"></emph>abroad, or learnt <lb></lb>amongst our Mariners at home, touching the Office of an Admiral, Commander, Pilot, Modelliſt, Shipwright, <lb></lb>Gunner, &c.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>But order requiring that I ſhould diſcharge my firſt Obligation before I contract a ſecond; I ſhall detein you no <lb></lb>longer in the Portall, but put you into poſſeſſion of the Premiſes,<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Novemb. </s> <s>20, 1661.</s></p><p type="main"> <s><emph type="italics"></emph>T. S.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/009.jpg"></pb></section><section><p type="head"> <s>The CONTENTS of the FIRST <lb></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"></emph>Treatiſe<emph.end type="italics"></emph.end></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></lb>GRAND DUTCHESSE of TUSCANY, touching the Ancient and Modern <lb></lb>DOCTRINE of HOLY FATHERS, and JUDICIOUS DIVINES, concerning <lb></lb>the AUTHORITY of SACRED SCRIPTURE in PHYLOSOPHICAL <lb></lb>CONTROVERSIES.</s></p><p type="main"> <s>III. JOHANNES KEPLERUS, his RECONCILINGS of TEXTS of SACRED <lb></lb>SCRIPTURE that ſeem to oppoſe the DOCTRINE of the EARTHS MOBILI<lb></lb>TY: abſtracted from his INTRODUCTION unto his LEARNED COMMEN<lb></lb>TARIES upon the PLANET MARS.</s></p><p type="main"> <s>IV. DIDACUS A STUNICA, a learned SPANISH DIVINE, his RECONCILINGS of <lb></lb>the ſaid DOCTRINE with the TEXTS of SACRED SCRIPTURE; abſtracted <lb></lb>from his COMMENTARIE upon JOB.</s></p><p type="main"> <s>V. PAULUS ANTONIUS FOSCARINUS, a CARMELITE, his EPISTLE to <lb></lb>SEBASTIANUS FANTONUS, the GENERAL of his ORDER, concerning <lb></lb>the PYTHAGOREAN and COPERNICAN OPINION of the MOBILITY OF <lb></lb>THE EARTH, and STABILITY OF THE SUN; and of the NEW SYSTEME <lb></lb>or CONSTITUTION of the WORLD: in which he reconcileth the TEXTS <lb></lb>OF SACRED SCRIPTURE, and ASSERTIONS of DIVINES, commonly <lb></lb>alledged against this OPINION.</s></p><p type="main"> <s><emph type="italics"></emph>A<emph.end type="italics"></emph.end> Table <emph type="italics"></emph>of the most obſervable<emph.end type="italics"></emph.end> Perſons <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Matters <emph type="italics"></emph>mentioned in the<emph.end type="italics"></emph.end> Firſt 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></lb>DISCOURSE of the MENSURATION OF RUNNING WATERS: The Firſt <lb></lb>BOOK.</s></p><p type="main"> <s>II. HIS LETTER to GALILEUS, repreſenting the ſtate of the Lake of PERUGIA in <lb></lb>TUSCANY.</s></p><p type="main"> <s>III. HIS GEOMETRICAL DEMONSTRATIONS of the MEASURE of RUNNING <lb></lb>WATERS.</s></p><p type="main"> <s>IV. HIS DISCOURSE of the MENSURATION OF RUNNING WATERS: The Second <lb></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></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 inſtance <lb></lb>of PRINCE LEOPALDO, he delivereth his judgment concerning the turning <lb></lb>FIUME MORTO (a River near PISA in TUSCANY) into the SEA, and into <lb></lb>the River SERCHIO.</s></p><p type="main"> <s>VIII. HIS ſecond LETTER in anfwer to certain OBJECTIONS propoſed, and DIFFICUL<lb></lb>TIES obſerved by SIGNORE BARTOLOTTI, in that affair of the <lb></lb>DIVERSION of FIUME MORTO.</s></p><p type="main"> <s>IX. HIS CONSIDERATION upon the DRAINING of the PONTINE FENNS in CALA<lb></lb>BRIA.</s></p><p type="main"> <s>X. HIS CONSIDERATION upon the DRAINING of the TERRITORIES of BOLOG<lb></lb>NA, FERRARA, and ROMAGNA.</s></p><p type="main"> <s>XI. HIS LETTER to D. FERRANTE CESARINI, applying his DOCTRINE to the <lb></lb>MENSURATION of the LENGTH, and DISTRIBUTION of the QUANTITY <lb></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></lb>of ROMAGNA, his RELATION of the ſtate of the WATERS in the <lb></lb>TERRITORIES of BOLOGNA and FERRARA.</s></p><p type="main"> <s><emph type="italics"></emph>A<emph.end type="italics"></emph.end> Table <emph type="italics"></emph>of the moſt obſervable<emph.end type="italics"></emph.end> Perſons <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Matters <emph type="italics"></emph>mentioned in the<emph.end type="italics"></emph.end> Second Part.</s></p><pb xlink:href="040/01/010.jpg"></pb><p type="head"> <s>The CONTENTS of the SECOND <lb></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"></emph>Treatiſe<emph.end type="italics"></emph.end></s></p><p type="main"> <s>I. GALILEUS GALILEUS, his MATHEMATICAL DISCOURSES and DEMON<lb></lb>STRATIOMS touching two NEVV SCIENCES, pertaining to the MECHA<lb></lb>NICKS, and LOCAL MOTION: with an APPENDIX of the CENTRE of <lb></lb>GRAVITY of ſome 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; tranſlated from his FRENCM <lb></lb>MANUSCRIPT; a New PEICE.</s></p><p type="main"> <s>IV. ARCHIMEDES, his Tract DE INSIDENTIBUS HUMIDO; with the NOTES and <lb></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></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></lb>of the RANGES of GREAT GUNNS of all ſorts; wherein he detects ſundry <lb></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></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"></emph>Chap.<emph.end type="italics"></emph.end> 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 firſt Education.</s></p><p type="main"> <s>5. His Maſters.</s></p><p type="main"> <s>II. </s> <s>Containing Three Chapters.</s></p><p type="main"> <s><emph type="italics"></emph>Chap.<emph.end type="italics"></emph.end> 1. His judgment in ſeveral 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"></emph>Chap.<emph.end type="italics"></emph.end> 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"></emph>Chap.<emph.end type="italics"></emph.end> 1. His perſon deſcribed.</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 Syſteme in particular, containing <emph type="italics"></emph>Nine Sections.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Section<emph.end type="italics"></emph.end> 1. Of Aſtronomy in General; its Definition, Praiſe, Original.</s></p><p type="main"> <s>2. Of Aſtronomers: a Chronological Catalogue of the <lb></lb>moſt famous of them.</s></p><p type="main"> <s>3. Of the Doctrine of the Earths Mobility, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> its Antiquity, <lb></lb>and Progreſſe from <emph type="italics"></emph>Pythagoras<emph.end type="italics"></emph.end> to the time of <emph type="italics"></emph>Copernicus.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>4. Of the Followers of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> unto the time of <emph type="italics"></emph>Galileus.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>5. Of the ſeverall Syſtemes amongſt Aſtronomers.</s></p><p type="main"> <s>6. Of the Allegations againſt the <emph type="italics"></emph>Copern.<emph.end type="italics"></emph.end> Syſteme, in 77 <lb></lb>Arguments taken out of <emph type="italics"></emph>Ricciolo,<emph.end type="italics"></emph.end> with Anſwers to them.</s></p><p type="main"> <s>7. Of the Allegations for the <emph type="italics"></emph>Copern.<emph.end type="italics"></emph.end> Syſteme in so Arguments.</s></p><p type="main"> <s>8. Of the Scriptures Authorities produced againſt and for the <lb></lb>Earths mobility.</s></p><p type="main"> <s>9. The Concluſion 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"></emph>Chap.<emph.end type="italics"></emph.end> 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 againſt him.</s></p><p type="main"> <s>4. A Concluſion in certain Reflections upon his whole Life.</s></p><p type="main"> <s><emph type="italics"></emph>A<emph.end type="italics"></emph.end> Table <emph type="italics"></emph>of the whole<emph.end type="italics"></emph.end> Second TOME.</s></p> </section> </front> <pb xlink:href="040/01/011.jpg"></pb> <body> <chap> <p type="head"> <s>THE <lb></lb> SYSTEME <lb></lb>OF THE <lb></lb>WORLD: <lb></lb>IN FOUR <lb></lb>DIALOGUES. <lb></lb></s><s>Wherein the Two <lb></lb>GRAND SYSTEMES</s></p><p type="head"><s>Of <emph type="italics"></emph>PTOLOMY<emph.end type="italics"></emph.end> and <emph type="italics"></emph>COPERNICUS<emph.end type="italics"></emph.end> <lb></lb>are largely diſcourſed of:</s></p><p type="head"><s>And the <emph type="italics"></emph>REASONS,<emph.end type="italics"></emph.end> both <emph type="italics"></emph>Phyloſophical<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Phyſical,<emph.end type="italics"></emph.end> <lb></lb>as well on the one ſide as the other, <emph type="italics"></emph>impartially<emph.end type="italics"></emph.end> <lb></lb>and <emph type="italics"></emph>indefinitely<emph.end type="italics"></emph.end> propounded:</s></p><p type="head"><s>By <emph type="italics"></emph>GALILEUS GALILEUS LINCEUS,<emph.end type="italics"></emph.end> <lb></lb>A <emph type="italics"></emph>Gentleman<emph.end type="italics"></emph.end> of <emph type="italics"></emph>FLORENCE:<emph.end type="italics"></emph.end> Extraordinary <emph type="italics"></emph>Profeſſor<emph.end type="italics"></emph.end> of <lb></lb>the <emph type="italics"></emph>Mathematicks<emph.end type="italics"></emph.end> in the UNIVERSITY of <emph type="italics"></emph>PISA<emph.end type="italics"></emph.end>; and <lb></lb>Chief <emph type="italics"></emph>Mathematician<emph.end type="italics"></emph.end> to the GRAND DUKE of <emph type="italics"></emph>TVSCANY.<emph.end type="italics"></emph.end></s></p><p type="head"><s><emph type="italics"></emph>Ingliſhed from the<emph.end type="italics"></emph.end> Original <emph type="italics"></emph>Italián<emph.end type="italics"></emph.end> Copy, <emph type="italics"></emph>by<emph.end type="italics"></emph.end> THOMAS SALUSBURY.</s></p><p type="head"><s>ALCINOUS, <lb></lb><foreign lang="grc">Δεῑ δ̓ ἐλευγέριον εἰ̄ναι τῃ̄ γνωμῃ̄ ρ̀ν μέλλοντα φιλοσοφεῑν.</foreign></s></p><p type="head"><s>SENECA, <lb></lb><emph type="italics"></emph>Inter nullos magis quam inter PHILOSOPHOS eſſe debet aqua LIBERTAS.<emph.end type="italics"></emph.end></s></p><p type="head"><s><emph type="italics"></emph>LONDON,<emph.end type="italics"></emph.end> <lb></lb>Printed by WILLIAM LEYBOURNE. MDCLXI.</s></p><pb xlink:href="040/01/012.jpg"></pb><pb xlink:href="040/01/013.jpg"></pb></chap><chap><p type="head"><s>To the moſt Serene Grand DUKE <lb></lb>OF <lb></lb>TUSCANY.</s></p><p type="main"><s>Though the difference between Men and other <lb></lb>living Creatures be very great, yet happly he that <lb></lb>ſhould ſay that he could ſhew little leſs between <lb></lb>Man and Man would not ſpeak more than he <lb></lb>might prove. </s><s>What proportion doth one bear to <lb></lb>athouſand? </s><s>and yet it is a common Proverb, <emph type="italics"></emph>One Man is <lb></lb>worth athouſand, when as a thouſand are not worth one.<emph.end type="italics"></emph.end> This difference <lb></lb>hath dependence upon the different abilities of their Intelle <lb></lb>ctuals; which I reduce to the being, or not being a Philoſo <lb></lb>pher; in regard that Philoſophy as being the proper food of <lb></lb>ſuch as live by it, diſtinguiſheth a Man from the common Eſ <lb></lb>ſence of the Vulgar in a more or leſs honourable degree accord <lb></lb>ing to the variety of that diet. </s><s>In this ſence he that hath the <lb></lb>higheſt looks, is of higheſt quality; and the turning over of <lb></lb>the great Volume of Nature, which is the proper Object of <lb></lb>Philoſophy is the way to make one look high: in which Book, <lb></lb>although whatſoever we read, as being the Work of Al <lb></lb>mighty God, is therefore moſt proportionate; yet notwith <lb></lb>ſtanding that is more abſolute and noble wherein we more <lb></lb>plainly deſerne his art and skill. </s><s>The <emph type="italics"></emph>Conſtitution<emph.end type="italics"></emph.end> of the <emph type="italics"></emph>Vnivers,<emph.end type="italics"></emph.end> <lb></lb>among all Phyſical points that fall within Humane Compre <lb></lb>henſion, may, in my opinion, be preferred to the Precedency: <lb></lb>for if that in regard of univerſal extent it excell all others, it <lb></lb>ought as the Rule and Standard of the reſt to goe before <lb></lb>them in Nobility. </s><s>Now if ever any perſons might challenge <lb></lb>to be ſignally diſtinguiſhed for Intellectuals from other men; <pb xlink:href="040/01/014.jpg"></pb><emph type="italics"></emph>Ptolomey<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> were they that have had the honour to <lb></lb>ſee fartheſt into, and diſcourſe moſt profoundly of the <emph type="italics"></emph>Worlds <lb></lb>Syſteme.<emph.end type="italics"></emph.end> About the Works of which famous Men theſe Dia <lb></lb>lous being chiefly converſant, I conceived it my duty to De <lb></lb>dicate them only to <emph type="italics"></emph>Your Highneſs.<emph.end type="italics"></emph.end> For laying all the weight <lb></lb>upon theſe two, whom I hold to be the Ableſt Wits that <lb></lb>have left us their Works upon theſe Subjects; to avoid a Sole <lb></lb>ciſmein Manners, I was obliged to addreſs them to Him, who <lb></lb>with me, is the Greateſt of all Men, from whom they can re <lb></lb>ceive either Glory or Patrociny. </s><s>And if theſe two perſons <lb></lb>have ſo farre illuminated my Underſtanding as that this my <lb></lb>Book may in a great part be confeſſed to belong to them, well <lb></lb>may it alſo be acknowledged to belong to <emph type="italics"></emph>Your Highneſs,<emph.end type="italics"></emph.end> unto <lb></lb>whoſe Bounteous Magnificence I owe the time and leaſure I <lb></lb>had to write it, as alſo unto Your Powerful Aſſiſtance, (never <lb></lb>weary of honouring me) the means that at length I have had <lb></lb>to publiſh it. </s><s>May <emph type="italics"></emph>Your Highneſs<emph.end type="italics"></emph.end> therefore be pleaſed to accept <lb></lb>of it according to Your accuſtomed Goodneſs; and if any <lb></lb>thing ſhall be found therein, that may be ſubſervient towards <lb></lb>the information or ſatisfaction of thoſe that are Lovers of <lb></lb>Truth; let them acknowledge it to be due to <emph type="italics"></emph>Your Self,<emph.end type="italics"></emph.end> who are <lb></lb>ſo expert in doing good, that Your Happy Dominion cannot <lb></lb>ſhew the man that is concerned in any of thoſe general Cala <lb></lb>mities that diſturb the World; ſo that Praying for Your Proſpe <lb></lb>rity, and continuance in this Your Pious and Laudable Cu <lb></lb>ſtome, I humbly kiſs Your Hands;</s></p><p type="main"><s><emph type="italics"></emph>Your Moſt Serene Highneſſes<emph.end type="italics"></emph.end></s></p><p type="main"><s>Moſt Humble and moſt 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"></pb><p type="head"><s>THE AUTHOR'S <lb></lb>INTRODUCTION.</s></p><p type="main"><s>Judicious Reader,</s></p><p type="main"><emph type="italics"></emph><s>There was publiſhed ſome years ſince in<emph.end type="italics"></emph.end> Rome <emph type="italics"></emph>a ſalutiferous Edict, that, for <lb></lb>the obviating of the dangerous Scandals of the preſent Age, impoſed a ſea <lb></lb>ſonable Silence upon the Pythagorean Opinion of the Mobility of the Earth. <lb></lb></s><s>There want not ſuch as unadviſedly affirm, that that Decree was not the produ <lb></lb>ction of a ſober Scrutiny, but of an ill informed Paſsion; & one may hear ſome mut <lb></lb>ter that Conſultors altogether ignorant of Aſtronomical Obſervations ought not <lb></lb>to clipp the Wings of Speculative Wits with raſh Prohibitions. </s><s>My zeale can <lb></lb>not keep ſilence when I hear theſe inconſiderate complaints. </s><s>I thought fit, as being thoroughly ac <lb></lb>quainted with that prudent Determination, to appear openly upon the Theatre of the World as a Wit <lb></lb>neſs of the naked Truth. </s><s>I was at that time in<emph.end type="italics"></emph.end> Rome; <emph type="italics"></emph>and had not only the audiences, but applauds of <lb></lb>the moſt Eminent Prelates of that Court; nor was that Decree Publiſhed without Previous Notice given <lb></lb>me thereof. </s><s>Therefore it is my reſolution in the preſent caſe to give Foraign Nations to ſee that this <lb></lb>point is as well under stood in<emph.end type="italics"></emph.end> Italy, <emph type="italics"></emph>and particularly in<emph.end type="italics"></emph.end> Rome, <emph type="italics"></emph>as Tranſalpine Diligence can imagine <lb></lb>it to be: and collecting together all the proper Speculations that concern the<emph.end type="italics"></emph.end> Copernican Syſteme, <lb></lb><emph type="italics"></emph>to let them know, that the notice of all preceded the Cenſure of the<emph.end type="italics"></emph.end> Roman Court; <emph type="italics"></emph>and that there <lb></lb>proceed from this Climate not only Doctrines for the health of the Soul, but alſo ingenious Diſcoveries <lb></lb>for the recreating of the Mind.<emph.end type="italics"></emph.end></s></p><p type="main"><s><emph type="italics"></emph>To this end I have perſonated the<emph.end type="italics"></emph.end> Copernican <emph type="italics"></emph>in this Diſcourſe; proceeding upon an Hypotheſis <lb></lb>purely Mathematical; ſtriving by all artificial wayes to repreſent it Superiour, not to that of the Im <lb></lb>mobility of the Earth abſolutely, but according as it is mentioned by ſome, that retein no more, but the <lb></lb>name of<emph.end type="italics"></emph.end> Peripateticks, <emph type="italics"></emph>and are content, without going farther, to adore Shadows, not philoſophizing <lb></lb>with requiſit caution, but with the ſole remembrance of four<emph.end type="italics"></emph.end> Principles, <emph type="italics"></emph>but badly under ſtood.<emph.end type="italics"></emph.end></s></p><p type="main"><s><emph type="italics"></emph>We ſhall treat of three principall heads. </s><s>Firſt I will endeavour to ſhew that all Experiments that can <lb></lb>be made upon the Earth are inſufficient means to conclude it's Mobility, but are indifferently applicable <lb></lb>to the Earth moveable or immoveable: and I hope that on this occaſion we ſhall diſcover many obſer <lb></lb>vable paſſages unknown to the Ancients. </s><s>Secondly we will examine the Cœleſtiall<emph.end type="italics"></emph.end> Phœnomena <lb></lb><emph type="italics"></emph>that make for the<emph.end type="italics"></emph.end> Copernican Hypotheſis, <emph type="italics"></emph>as if it were to prove abſolutely victorious; adding by the <lb></lb>way certain new Obſervations, which yet ſerve only for the Aſtronomical Facility, not for Natural <lb></lb>Neceßity. </s><s>In the third place I will propoſe an ingenuous Fancy. </s><s>I remember that I have ſaid many <lb></lb>years ſince, that the unknown Probleme of the Tide might receive ſome light, admitting the Earths <lb></lb>Motion. </s><s>This Poſition of mine paſsing from one to another had found charitable Fathers that <lb></lb>adopted it for the Iſſue of their own wit. </s><s>Now, becauſe no ſtranger may ever appear that defending him <lb></lb>ſelf with our armes ſhall charge us with want of caution in ſo principal an Accident, I have thought <lb></lb>good to lay down thoſe probabilities that would render it credible, admitting that the Earth did <lb></lb>move. </s><s>I hope, that by theſe Conſider ations the World will come to know, that if other Nations have <lb></lb>Navigated more than we, we have not ſtudied leſs than they; & that our returning to aſſert the Earths <lb></lb>Stability, and to take the contrary only for a Mathematical<emph.end type="italics"></emph.end> Capriccio, <emph type="italics"></emph>proceeds not from inadvertency <lb></lb>of what others have thought thereof, but (had we no other inducements) from thoſe Reaſons that Pic <lb></lb>ty, Religion, the Knowledge of the Divine Omnipotency, and a conſciouſneſs of the incapacity of mans <lb></lb>Vnderſtanding dictate unto us.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/016.jpg"></pb><p type="main"><s><emph type="italics"></emph>With all I conceived it very proper to expreſs theſe conceits by way of Dialogue, which, as not being <lb></lb>bound up to the riggid obſervance of Mathematical Laws, gives place alſo to Digreſsions that are <lb></lb>ſometimes no leſs curious than the principal Argument.<emph.end type="italics"></emph.end></s></p><p type="main"><s><emph type="italics"></emph>I chanced to be ſeveral years ſince, at ſeveral times, in the Stupendious Citty of<emph.end type="italics"></emph.end> Venice, <emph type="italics"></emph>where I <lb></lb>converſed with<emph.end type="italics"></emph.end> Signore Giovan Franceſco Sagredo <emph type="italics"></emph>of a Noble Extraction, and piercing wit. </s><s>There <lb></lb>came thither from<emph.end type="italics"></emph.end> Florence <emph type="italics"></emph>at the ſame time<emph.end type="italics"></emph.end> Signore Filippo Salviati, <emph type="italics"></emph>whoſe leaſt glory was the Emi <lb></lb>nence of his Blood, and Magnificence of his Eſtate: a ſublime Wit that fed not more hungerly upon <lb></lb>any pleaſure than on elevated Speculations. </s><s>In the company of theſe two I often diſcourſed of theſe <lb></lb>matters before a certain Peripatetick Philoſopher who ſeemed to have no geater obſtacle in underſtand <lb></lb>ing of the Truth, than the Fame he had acquired by Ariſtotelical Interpretations.<emph.end type="italics"></emph.end></s></p><p type="main"><s><emph type="italics"></emph>Now, ſeeing that inexorable Death hath deprived<emph.end type="italics"></emph.end> Venice <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Florence <emph type="italics"></emph>of thoſe two great Lights in <lb></lb>the very Meridian of their years, I did reſolve, as far as my poor ability would permit, to perpetuate <lb></lb>their lives to their honour in theſe leaves, bringing them in as Interlocutors in the preſent Controverſy. <lb></lb></s><s>Nor ſhall the Honest Peripatetick want his place, to whom for his exceſsive affection to wards the Com <lb></lb>mentaries of<emph.end type="italics"></emph.end> Simplicius, <emph type="italics"></emph>I thought fit, without mentioning his own Name, to leave that of the Author <lb></lb>he ſo much reſpected. </s><s>Let thoſe two great Souls, ever venerable to my heart, pleaſe to accept this pu <lb></lb>blick Monument of my never dying Love; and let the remembr ance of their Eloquence aſsiſt me in <lb></lb>delivering to Poſterity the Conſider ations that I have promiſed.<emph.end type="italics"></emph.end></s></p><p type="main"><s><emph type="italics"></emph>There caſually happened (as was uſuall) ſeveral diſcourſes at times between theſe Gentlemen, the <lb></lb>which had rather inflamed than ſatisfied in their wits the thirſt they had to be learning; whereupon <lb></lb>they took a diſcreet reſolution to meet together for certain dayes, in which all other buſineſs ſet aſide, <lb></lb>they might betake themſelves more methodically to contemplate the Wonders of God in Heaven, and in <lb></lb>the Earth: the place appointed for their meeting being in the Palace of the Noble<emph.end type="italics"></emph.end> Sagredo, <emph type="italics"></emph>after the <lb></lb>due, but very ſhort complements<emph.end type="italics"></emph.end>; Signore Salviati <emph type="italics"></emph>began in this manner.<emph.end type="italics"></emph.end></s></p></chap> <chap> <pb xlink:href="040/01/017.jpg" pagenum="1"></pb><p type="head"><s>GALILÆUS <lb></lb>Galilæus Lyncæus, <lb></lb>HIS <lb></lb>SYSTEME <lb></lb>OF THE <lb></lb>WORLD.</s></p> <p type="head"><s>The Firſt Dialogue.</s></p><p type="head"><s><emph type="italics"></emph>INTERLOCVTORS.<emph.end type="italics"></emph.end></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 yeſterdayes reſolution, and a <lb></lb>greement, that we ſhould to day diſcourſe <lb></lb>the moſt diſtinctly, and particularly we <lb></lb>could poſſible, of the natural reaſons, and <lb></lb>their efficacy that have been hitherto al <lb></lb>ledged on the one or other part, by the <lb></lb>maintainers of the Poſitions, <emph type="italics"></emph>Aristotelian,<emph.end type="italics"></emph.end> <lb></lb>and <emph type="italics"></emph>Ptolomaique<emph.end type="italics"></emph.end>; and by the followers </s></p><p type="main"><s><arrow.to.target n="marg3"></arrow.to.target> <lb></lb>of the <emph type="italics"></emph>Copernican Syſteme<emph.end type="italics"></emph.end>: And becauſe <lb></lb><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> placing the Earth among the moveable Bodies of Hea <lb></lb>ven, comes to conſtitute a Globe for the ſame like to a Planet; it <lb></lb>would be good that we began our diſputation with the examina <lb></lb>tion of what, and how great the energy of the <emph type="italics"></emph>Peripateticks<emph.end type="italics"></emph.end> ar <lb></lb>guments is, when they demonſtrate, that this <emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> is impoſ <pb xlink:href="040/01/018.jpg" pagenum="2"></pb>ſible: Since that it is neceſſary to introduce in Nature, ſubſtances <lb></lb><arrow.to.target n="marg4"></arrow.to.target> <lb></lb>different betwixt themſelves, that is, the Cœleſtial, and Elementa <lb></lb>ry; that impaſſible and immortal, this alterable and corruptible. <lb></lb></s><s>Which argument <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> handleth in his book <emph type="italics"></emph>De Cœlo,<emph.end type="italics"></emph.end> inſinu <lb></lb>ating it firſt, by ſome diſcourſes dependent on certain general aſ <lb></lb>ſumptions, and afterwards confirming it with experiments and per <lb></lb>ticular demonſtrations: following the ſame method, I will pro <lb></lb>pound, and freely ſpeak my judgement, ſubmitting my ſelf to <lb></lb>your cenſure, and particularly to <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> a Stout Champion <lb></lb>and contender for the <emph type="italics"></emph>Ariſtotelian<emph.end type="italics"></emph.end> Doctrine. <lb></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"></emph>repu <lb></lb>teth the earth œ <lb></lb>Globe like to a Pla <lb></lb>net.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg4"></margin.target><emph type="italics"></emph>Cœleſtial ſubſtan <lb></lb>ces that are inalte <lb></lb>rable, and Elemen <lb></lb>tary that be alte <lb></lb>rable, are neceſſary <lb></lb>in the opinion of<emph.end type="italics"></emph.end> <lb></lb>Ariſtotle.</s></p><p type="margin"><s><margin.target id="marg5"></margin.target>Ariſtotle <emph type="italics"></emph>maketh <lb></lb>the World perfect, <lb></lb>becauſe it hath the <lb></lb>threefold demenſi <lb></lb>on.<emph.end type="italics"></emph.end></s></p><p type="main"><s>And the firſt Step of the <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> arguments is that, where <emph type="italics"></emph>A <lb></lb>riſtotle<emph.end type="italics"></emph.end> proveth the integrity and perfection of the World, telling <lb></lb>us, that it is not a ſimple line, nor a bare ſuperficies, but a body <lb></lb>adorned with Longitude, Latitude, and Profundity; and becauſe <lb></lb>there are no more dimenſions but theſe three; The World having <lb></lb>them, hath all, and having all, is to be concluded perfect. </s><s>And <lb></lb>again, that by ſimple length, that magnitude is conſtituted, which <lb></lb>is called a Line, to which adding breadth, there is framed the Su <lb></lb>perficies, and yet further adding the altitude or profoundity, there <lb></lb>reſults the Body, and after theſe three dimenſions there is no <lb></lb>paſſing farther, ſo that in theſe three the integrity, and to ſo ſpeak, <lb></lb>totality is terminated, which I might but with juſtice have requi <lb></lb>red <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> to have proved to me by neceſſary conſequences, the <lb></lb>rather in regard he was able to do it very plainly, and ſpeedily.</s></p><p type="main"><s>SIMPL. </s><s>What ſay you to the excellent demonſtrations in the </s></p><p type="main"><s><arrow.to.target n="marg6"></arrow.to.target> <lb></lb>2. 3. and 4. Texts, after the definition of <emph type="italics"></emph>Continual<emph.end type="italics"></emph.end>? </s><s>have you it <lb></lb>not firſt there proved, that there is no more but three dimenſions, <lb></lb>for that thoſe three are all things, and that they are every where? <lb></lb></s><s>And is not this confirmed by the Doctrine and Authority of the <lb></lb><arrow.to.target n="marg7"></arrow.to.target> <lb></lb><emph type="italics"></emph>Pythagorians,<emph.end type="italics"></emph.end> who ſay that all things are determined by three, be <lb></lb>ginning, middle, and end, which is the number of All? </s><s>And where <lb></lb>leave you that reaſon, namely, that as it were by the law of Na <lb></lb>ture, this number is uſed in the ſacrifices of the Gods? </s><s>And why <lb></lb>being ſo dictated by nature, do we atribute to thoſe things that <lb></lb>are three, and not to leſſe, the title of all? </s><s>why of two is it ſaid <lb></lb>both, and not all, unleſs they be three? </s><s>And all this Doctrine you <lb></lb>have in the ſecond Text. </s><s>Afterwards in the third, <emph type="italics"></emph>Ad pleniorem<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg8"></arrow.to.target> <lb></lb><emph type="italics"></emph>ſcientiam,<emph.end type="italics"></emph.end> we read that <emph type="italics"></emph>All,<emph.end type="italics"></emph.end> the <emph type="italics"></emph>Whole,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Perfect,<emph.end type="italics"></emph.end> are formally <lb></lb>one and the ſame; and that therefore onely the <emph type="italics"></emph>Body,<emph.end type="italics"></emph.end> amongſt <lb></lb>magnitudes is perfect: becauſe it is determined by three, which is <lb></lb>All, and being diviſible three manner of waies, it is every way di <lb></lb>viſible; but of the others, ſome are dividible in one manner, and <lb></lb>ſome in two, becauſe according to the number aſſixed, they have <lb></lb>their diviſion and continuity, and thus one magnitude is continu <lb></lb><arrow.to.target n="marg9"></arrow.to.target> <lb></lb>ate one way, another two, a third, namely the Body, every way. <pb xlink:href="040/01/019.jpg" pagenum="3"></pb>Moreover in the fourth Text; doth he not after ſome other Do <lb></lb>ctrines, prove it by another demonſtration? <emph type="italics"></emph>Scilicet,<emph.end type="italics"></emph.end> That no tran <lb></lb>ſition is made but according to ſome defect (and ſo there is a tran <lb></lb>ſition or paſſing from the line to the ſuperficies, becauſe the line is <lb></lb>defective in breadth) and that it is impoſſible for the perfect to <lb></lb>want any thing, it being every way ſo; therefore there is no tran <lb></lb>ſition from the Solid or Body to any other magnitude. </s><s>Now <lb></lb>think you not that by all theſe places he hath ſufficiently proved, <lb></lb>how that there's no going beyond the three dimenſions, Length, <lb></lb>Breadth, and Thickneſs, and that therefore the body or ſolid, <lb></lb>which hath them all, is perfect?</s></p><p type="margin"><s><margin.target id="marg6"></margin.target>Ariſtotles <emph type="italics"></emph>demon <lb></lb>ſtrations to prove <lb></lb>the dimenſions to be <lb></lb>three and no more.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg7"></margin.target><emph type="italics"></emph>The number three <lb></lb>celebrated among ſt <lb></lb>the<emph.end type="italics"></emph.end> Pythagorians</s></p><p type="margin"><s><margin.target id="marg8"></margin.target>Omne, Totum & <lb></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 ſelf bound by all theſe <lb></lb>reaſons to grant any more but onely this, That that which hath <lb></lb>beginning, middle, and end, may, and ought to be called perfect: But <lb></lb>that then, becauſe beginning, middle, and end, are Three, the num <lb></lb>ber Three is a perfect number, and hath a faculty of conferring <lb></lb><emph type="italics"></emph>Perfection<emph.end type="italics"></emph.end> on thoſe things that have the ſame, I find no inducement <lb></lb>to grant; neither do I underſtand, nor believe that, for example, <lb></lb>of feet, the number three is more perfect then four or two, nor do <lb></lb>I conceive the number four to be any imperfection to the Ele <lb></lb>ments: and that they would be more perfect if they were three. <lb></lb></s><s>Better therefore it had been to have left theſe ſubtleties to the <lb></lb><emph type="italics"></emph>Rhetoricians,<emph.end type="italics"></emph.end> and to have proved his intent, by neceſſary demonſtra <lb></lb>tion; for ſo it behoves to do in demonſtrative ſciences.</s></p><p type="main"><s>SIMPL. </s><s>You ſeem to ſcorn theſe reaſons, and yet it is all the <lb></lb>Doctrine of the <emph type="italics"></emph>Pythagorians,<emph.end type="italics"></emph.end> who attribute ſo much to numbers; <lb></lb>and you that be a <emph type="italics"></emph>Mathematician,<emph.end type="italics"></emph.end> and believe many opinions in <lb></lb>the <emph type="italics"></emph>Pythagorick<emph.end type="italics"></emph.end> Philoſophy, ſeem now to contemn their My <lb></lb>ſteries.</s></p><p type="main"><s>SALV. </s><s>That the <emph type="italics"></emph>Pythagorians<emph.end type="italics"></emph.end> had the ſcience of numbers in <lb></lb>high eſteem, and that <emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> himſelf admired humane underſtand <lb></lb>ing, and thought that it pertook of Divinity, for that it under <lb></lb><arrow.to.target n="marg10"></arrow.to.target> <lb></lb>ſtood the nature of numbers, I know very well, nor ſhould I be <lb></lb>far from being of the ſame opinion: But that the Myſteries for <lb></lb>which <emph type="italics"></emph>Pythagoras<emph.end type="italics"></emph.end> and his ſect, had the Science of numbers in ſuch <lb></lb>veneration, are the follies that abound in the mouths and writings <lb></lb><arrow.to.target n="marg11"></arrow.to.target> <lb></lb>of the vulgar, I no waies credit: but rather becauſe I know that they, <lb></lb>to the end admirable things might not be expoſed to the con <lb></lb>tempt, and ſcorne of the vulgar, cenſured as ſacrilegious, the pub <lb></lb><arrow.to.target n="marg12"></arrow.to.target> <lb></lb>liſhing of the abſtruce properties of Numbers, and incommen <lb></lb>ſurable and irrational quantities, by them inveſtigated; and di <lb></lb>vulged, that he who diſcovered them, was tormented in the other <lb></lb>World: I believe that ſome one of them to deter the common <lb></lb>ſort, and free himſelf from their inquiſitiveneſs, told them that the <lb></lb>myſteries of numbers were thoſe trifles, which afterwards did ſo <pb xlink:href="040/01/020.jpg" pagenum="4"></pb>ſpread amongſt the vulgar; and this with a diſcretion and ſubtlety <lb></lb>reſembling that of the prudent young man, that to be freed <lb></lb>from the importunity of his inquiſitive Mother or Wife, I know <lb></lb>not whether, who preſſed him to impart the ſecrets of the Senate, <lb></lb>contrived that ſtory, which afterwards brought her and many o <lb></lb>ther women to be derided and laught at by the ſame Senate.</s></p><p type="margin"><s><margin.target id="marg10"></margin.target>Plato <emph type="italics"></emph>held that <lb></lb>humane under <lb></lb>ſtanding partook <lb></lb>of divinity, becauſe <lb></lb>it understood num <lb></lb>bers.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg11"></margin.target><emph type="italics"></emph>The Myſtery of<emph.end type="italics"></emph.end> <lb></lb>Pythagorick <emph type="italics"></emph>num <lb></lb>bers fabulous.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg12"></margin.target>De Papyrio præ <lb></lb>textato, <emph type="italics"></emph>Gellius<emph.end type="italics"></emph.end> I: <lb></lb>2. 3.</s></p><p type="main"><s>SIMPL. </s><s>I will not be of the number of thoſe who are over curi <lb></lb>ous about the <emph type="italics"></emph>Pythagorick<emph.end type="italics"></emph.end> myſteries; but adhering to the point <lb></lb>in hand; I reply, that the reaſons produced by <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> to prove <lb></lb>the dimenſions to be no more than three, ſeem to me conclu <lb></lb>dent, and I believe, That had there been any more evident demon <lb></lb>ſtrations thereof, <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> would not have omitted them.</s></p><p type="main"><s>SAGR. </s><s>Put in at leaſt, if he had known, or remembred any more. <lb></lb></s><s>But you <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> would do me a great pleaſure to alledge unto <lb></lb>me ſome arguments that may be evident, and clear enough for me <lb></lb>to comprehend.</s></p><p type="main"><s>SALV. </s><s>I will; and they ſhall be ſuch as are not onely to be ap <lb></lb>prehended by you, but even by <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> himſelf: nor onely <lb></lb>to be comprehended, but are alſo already known, although hap <lb></lb>ly unobſerved; and for the more eaſie underſtanding thereof, <lb></lb>we will take this Pen and Ink, which I ſee already prepared for <lb></lb><arrow.to.target n="marg13"></arrow.to.target> <lb></lb>ſuch occaſions, and deſcribe a few figures. </s><s>And firſt we will note <lb></lb>[Fig. </s><s>1. <emph type="italics"></emph>at the end of this Dialog.<emph.end type="italics"></emph.end>] theſe two points AB, and draw <lb></lb>from the one to the other the curved lines, ACB, and ADB, and the <lb></lb>right line A B, I demand of you which of them, in your mind, is <lb></lb>that which determines the diſtance between the terms AB, & why?</s></p><p type="margin"><s><margin.target id="marg13"></margin.target><emph type="italics"></emph>A Geometrical de <lb></lb>monſtration of the <lb></lb>triple dimenſion.<emph.end type="italics"></emph.end></s></p><p type="main"><s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>AGR. </s><s>I ſhould ſay the right line, and not the crooked, as well <lb></lb>becauſe the right is ſhorter, as becauſe it is one, ſole, and deter <lb></lb>minate, whereas the others are infinit, unequal, and longer; and my <lb></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></lb>tween the two terms; let us add another right line and parallel to <lb></lb>AB, which let be CD, [<emph type="italics"></emph>Fig.<emph.end type="italics"></emph.end> 2.] ſo that there is put between them a <lb></lb>ſuperficies, of which I deſire you to aſſign me the breadth, therefore <lb></lb>departing from the point A, tell me how, and which way you will <lb></lb>go, to end in the line C D, and ſo to point me out the breadth com <lb></lb>prehended between thoſe lines; let me know whether you will <lb></lb>terminate it according to the quantity of the curved line A E, or <lb></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></lb>crooked, that being already excluded from ſuch an uſe.</s></p><p type="main"><s>SAGR. </s><s>But I would take neither of them, ſeeing the right line <lb></lb>A F runs obliquely; But would draw a line, perpendicular to C <lb></lb>D, for this ſhould ſeem to me the ſhorteſt, and the propereſt of <lb></lb>infinite that are greater, and unequal to one another, which may be <pb xlink:href="040/01/021.jpg" pagenum="5"></pb>produced from the term A to any other part of the oppoſite line <lb></lb>C D.</s></p><p type="main"><s>SALV. </s><s>Your choice, and the reaſon you bring for it in my judg <lb></lb>ment is moſt excellent; ſo that by this time we have proved that <lb></lb>the firſt dimenſion is determined by a right line, the ſecond name <lb></lb>ly the breadth with another line right alſo, and not onely right, <lb></lb>but withall, at right-angles to the other that determineth the <lb></lb>length, and thus we have the two dimenſions of length and <lb></lb>breadth, definite and certain. </s><s>But were you to bound or termi <lb></lb>nate a height, as for example, how high this Roof is from the pave <lb></lb>ment, that we tread on, being that from any point in the Roof, <lb></lb>we may draw infinite lines, both curved, and right, and all of di <lb></lb>verſe lengths to infinite points of the pavement, which of all theſe <lb></lb>lines would you make uſe of?</s></p><p type="main"><s>SAGR. </s><s>I would faſten a line to the Seeling, and with a plummet <lb></lb>that ſhould hang at it, would let it freely diſtend it ſelf till it <lb></lb>ſhould reach well near to the pavement, and the length of ſuch a <lb></lb>thread being the ſtreighteſt and ſhorteſt of all the lines, that could <lb></lb>poſsibly be drawn from the ſame point to the pavement, I would <lb></lb>ſay 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></lb>ment by this pendent thread (taking the pavement to be levell <lb></lb>and not declining) you ſhould produce two other right lines, one <lb></lb>for the length, and the other for the breadth of the ſuperficies of <lb></lb>theſaid pavement, what angles ſhould they make with the ſaid <lb></lb>thread?</s></p><p type="main"><s>SAGR. </s><s>They would doubtleſs meet at right angles, the ſaid <lb></lb>lines falling perpendicular, and the pavement being very plain and <lb></lb>levell.</s></p><p type="main"><s>SALV. </s><s>Therefore if you aſſign any point, for the term from whence <lb></lb>to begin your meaſure; and from thence do draw a right line, as <lb></lb>the terminator of the firſt meaſure, namely of the length, it will <lb></lb>follow of neceſſity, that that which is to deſign out the largeneſs <lb></lb>or breadth, toucheth the firſt at right-angles, and that that which is <lb></lb>to denote the altitude, which is the third dimenſion, going from the <lb></lb>ſame point formeth alſo with the other two, not oblique but right <lb></lb>angles, and thus by the three perpendiculars, as by three lines, one, <lb></lb>certain, and as ſhort as is poſſible, you have the three dimenſions <lb></lb>A B length, A C breadth, and A D height; and becauſe, clear it <lb></lb>is, that there cannot concurre any more lines in the ſaid point, ſo <lb></lb>as to make therewith right-angles, and the dimenſions ought to <lb></lb>be determined by the ſole right lines, which make between them <lb></lb>ſelves right-angles; therefore the dimenſions are no more but <lb></lb>three, and that which hath three hath all, and that which hath all, <lb></lb>is diviſible on all ſides, and that which is ſo, is perfect, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/022.jpg" pagenum="6"></pb><p type="main"><s>SIMPL. </s><s>And who ſaith that I cannot draw other lines? </s><s>why <lb></lb>may not I protract another line underneath, unto the point A, <lb></lb>that may be perpendicular to the reſt?</s></p><p type="main"><s>SALV. </s><s>You can doubtleſs, at one and the ſame point, make no <lb></lb>more than three right lines concurre, that conſtitute right angles <lb></lb>between themſelves.</s></p><p type="main"><s>SAGR. </s><s>I ſee what <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> means, namely, that ſhould the <lb></lb>ſaid D A be prolonged downward, then by that means there might <lb></lb>be drawn two others, but they would be the ſame with the firſt <lb></lb>three, differing onely in this, that whereas now they onely touch, <lb></lb>then they would interſect, but not produce new dimenſions. <lb></lb><arrow.to.target n="marg14"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg14"></margin.target><emph type="italics"></emph>In phyfical proofs <lb></lb>geometrical exact <lb></lb>neſs is not neceſſa <lb></lb>ry.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>I will not ſay that this your argument may not be con <lb></lb>cludent; but yet this I ſay with <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> that in things natural <lb></lb>it is not alwaies neceſſary, to bring <emph type="italics"></emph>Mathematical<emph.end type="italics"></emph.end> demonſtrations.</s></p><p type="main"><s>SAGR. </s><s>Grant that it were ſo where ſuch proofs cannot be had, <lb></lb>yet if this caſe admit of them, why do not you uſe them? </s><s>But it <lb></lb>would be good we ſpent no more words on this particular, for I <lb></lb>think that <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> will yield, both to <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> and you, with <lb></lb>out farther demonſtration, that the World is a body, and perfect, <lb></lb>yea moſt perfect, as being the greateſt 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></lb>tion of the whole, let us deſcend to the conſideration of its parts, <lb></lb>which <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> in his firſt diviſion, makes two, and they very diffe <lb></lb>rent and almoſt contrary to one another; namely the Cœleſtial, <lb></lb>and Elementary: that ingenerable, incorruptible, unalterable, un <lb></lb>paſſible, &c. </s><s>and this expoſed to a continual alteration, mutati <lb></lb>on, &c. </s><s>Which difference, as from its original principle, he de <lb></lb>rives from the diverſity of local motions, and in this method he <lb></lb>proceeds.</s></p><p type="margin"><s><margin.target id="marg15"></margin.target><emph type="italics"></emph>Parts of the world <lb></lb>are two, according <lb></lb>to<emph.end type="italics"></emph.end> Ariſtotle, <emph type="italics"></emph>Cœle <lb></lb>ſtial and Elemen <lb></lb>tary contrary to <lb></lb>one another.<emph.end type="italics"></emph.end></s></p><p type="main"><s>Leaving the ſenſible, if I may ſo ſpeak, and retiring into the <lb></lb>Ideal world, he begins Architectonically to conſider that nature <lb></lb>being the principle of motion, it followeth that natural bodies be <lb></lb><arrow.to.target n="marg16"></arrow.to.target> <lb></lb>indued with local motion. </s><s>Next he declares local motion to be <lb></lb>of three kinds, namely, circular, right, and mixt of right and cir <lb></lb>cular: and the two firſt he calleth ſimple, for that of all lines the <lb></lb><arrow.to.target n="marg17"></arrow.to.target> <lb></lb>circular, and right are onely ſimple; and here ſomewhat re <lb></lb>ſtraining himſelf, he defineth anew, of ſimple motions, one to be <lb></lb>circular, namely that which is made about the <emph type="italics"></emph>medium,<emph.end type="italics"></emph.end> and the <lb></lb>other namely the right, upwards, and downwards; upwards, that <lb></lb>which moveth from the <emph type="italics"></emph>medium<emph.end type="italics"></emph.end>; downwards, that which goeth to <lb></lb>wards the <emph type="italics"></emph>medium.<emph.end type="italics"></emph.end> And from hence he infers, as he may by and ne <lb></lb><arrow.to.target n="marg18"></arrow.to.target> <lb></lb>ceſſary conſequence, that all ſimple motions are confined to theſe <lb></lb>three kinds, namely, to the <emph type="italics"></emph>medium,<emph.end type="italics"></emph.end> from the <emph type="italics"></emph>medium,<emph.end type="italics"></emph.end> and about <lb></lb>the <emph type="italics"></emph>medium<emph.end type="italics"></emph.end>; the which correſponds ſaith he, with what hath been <lb></lb>ſaid before of a body, that it alſo is perfected by three things, and ſo <pb xlink:href="040/01/023.jpg" pagenum="7"></pb>is its motion. </s><s>Having confirmed theſe motions, he proceeds ſaying, <lb></lb>that of natural bodies ſome being ſimple, and ſome compoſed of <lb></lb>them (and he calleth ſimple bodies thoſe, that have a principle <lb></lb>of motion from nature, as the Fire and Earth) it follows that <lb></lb>ſimple motions belong to ſimple bodies, and mixt to the com <lb></lb>pound; yet in ſuch ſort, that the compounded incline to the part <lb></lb>predominant in the compoſition.</s></p><p type="margin"><s><margin.target id="marg16"></margin.target><emph type="italics"></emph>Local motion of <lb></lb>three kinds, right, <lb></lb>circular, & mixt.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg17"></margin.target><emph type="italics"></emph>Circular, and <lb></lb>ſtreight motions <lb></lb>are ſimple, as pro <lb></lb>ceeding by ſimple <lb></lb>lines.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg18"></margin.target><emph type="italics"></emph>Ad medium, à me <lb></lb>dio, & circa medi <lb></lb>um.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Pray you hold a little <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> for I find ſo many <lb></lb>doubts to ſpring up on all ſides in this diſcourſe, that I ſhall be <lb></lb>conſtrained, either to communicate them if I would attentively <lb></lb>hearken to what you ſhall add, or to take off my attention from <lb></lb>the things ſpoken, if I would remember objections.</s></p><p type="main"><s>SALV. </s><s>I will very willingly ſtay, for that I alſo run the ſame <lb></lb>hazard, and am ready at every ſtep to loſe my ſelf whilſt I ſail be <lb></lb>tween Rocks, and boiſterous Waves, that make me, as they ſay, to <lb></lb>loſe my <emph type="italics"></emph>Compaſs<emph.end type="italics"></emph.end>; therefore before I make them more, propound <lb></lb>your difficulties. <lb></lb><arrow.to.target n="marg19"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg19"></margin.target><emph type="italics"></emph>The definition of <lb></lb>Nature, either im <lb></lb>perfect, or unſeaſo <lb></lb>nable, produced by<emph.end type="italics"></emph.end> <lb></lb>Ariſtotle.</s></p><p type="main"><s>SAGR. </s><s>You and <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> together would at firſt take me a <lb></lb>little out of the ſenſible World, to tell me of the <emph type="italics"></emph>Architecture,<emph.end type="italics"></emph.end> <lb></lb>wherewith it ought to be fabricated; and very appoſitly begin to <lb></lb>tell me, that a natural body is by nature moveable, nature being <lb></lb>(as elſewhere it is defined) the principle of motion. </s><s>But here I <lb></lb>am ſomewhat doubtfull why <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſaid not that of natural bo <lb></lb>dies, ſome are moveable by nature, and others immoveable, for <lb></lb>that in the definition, nature is ſaid to be the principle of Motion, <lb></lb>and Reſt; for if natural bodies have all a principle of motion, <lb></lb>either he might have omitted the mention of Reſt, in the definiti <lb></lb>on of nature: or not have introduced ſuch a definition in this place. <lb></lb></s><s>Next, as to the declaration of what <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> intends by ſimple <lb></lb>motions, and how by Spaces he determines them, calling thoſe ſim <lb></lb>ple, that are made by ſimple lines, which are onely the right, and </s></p><p type="main"><s><arrow.to.target n="marg20"></arrow.to.target> <lb></lb>circular, I entertain it willingly; nor do I deſire to tenter the <lb></lb>inſtance of the Helix, about the Cylinder; which in that it is in e <lb></lb>very part like to it ſelf, might ſeemingly be numbred among ſim <lb></lb>ple lines. </s><s>But herein I cannot concurre, that he ſhould ſo re <lb></lb>ſtrain ſimple motions (whilſt he ſeems to go about to repeat the <lb></lb>ſame definition in other words) as to call one of them the motion <lb></lb>about the <emph type="italics"></emph>medium,<emph.end type="italics"></emph.end> the others <emph type="italics"></emph>Surſum & Deorſum,<emph.end type="italics"></emph.end> namely up <lb></lb>wards and downward; which terms are not to be uſed, out of the <lb></lb>World fabricated, but imply it not onely made, but already in <lb></lb>habited by us; for if the right motion be ſimple, by the ſimplicity <lb></lb>of the right line, and if the ſimple motion be natural, it is made on <lb></lb>every ſide, to wit, upwards, downwards, backwards, forwards, to <lb></lb>the right, to the left, and if any other way can be imagined, pro <lb></lb>vided it be ſtraight, it ſhall agree to any ſimple natural body; or <pb xlink:href="040/01/024.jpg" pagenum="8"></pb>if not ſo, then the ſuppoſion of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> is defective. </s><s>It appears <lb></lb><arrow.to.target n="marg21"></arrow.to.target> <lb></lb>moreover that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> hinteth but one circular motion alone to <lb></lb>be in the World, and conſequently but one onely Center, to <lb></lb>which alone the motions of upwards and downwards, refer. </s><s>All <lb></lb>which are apparent proofs, that <emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> aim is, to make white <lb></lb>black, and to accommodate <emph type="italics"></emph>Architectur<emph.end type="italics"></emph.end> to the building, and not <lb></lb>to modle the building according to the precepts of <emph type="italics"></emph>Arthitecture:<emph.end type="italics"></emph.end> <lb></lb>for if I ſhould ſay that Nature in Univerſal may have a thou <lb></lb>ſand Circular Motions, and by conſequence a thouſand Cen <lb></lb>ters, there would be alſo a thouſand motions upwards, and <lb></lb>downwards. </s><s>Again he makes as hath been ſaid, a ſimple motion, <lb></lb>and a mixt motion, calling ſimple, the circular and right; and <lb></lb>mixt, the compound of them two: of natural bodies he calls ſome <lb></lb>ſimple (namely thoſe that have a natural principle to ſimple mo <lb></lb>tion) and others compound: and ſimple motions he attributes <lb></lb>to ſimple bodies, and the compounded to the compound; but by <lb></lb>compound motion he doth no longer underſtand the mixt of right <lb></lb>and circular, which may be in the World; but introduceth a mixt <lb></lb>motion as impoſſible, as it is impoſſible to mixe oppoſite motions <lb></lb>made in the ſame right line, ſo as to produce from them a motion <lb></lb>partly upwards, partly downwards; and, to moderate ſuch an ab <lb></lb>ſurdity, and impoſſibility, he aſſerts that ſuch mixt bodies move <lb></lb><arrow.to.target n="marg22"></arrow.to.target> <lb></lb>according to the ſimple part predominant: which neceſſitates <lb></lb>others to ſay, that even the motion made by the ſame right line is <lb></lb>ſometimes ſimple, and ſometimes alſo compound: ſo that the ſim <lb></lb>plicity of the motion, is no longer dependent onely on the ſim <lb></lb>plicity of the line.</s></p><p type="margin"><s><margin.target id="marg20"></margin.target><emph type="italics"></emph>The Helix about <lb></lb>the Cylinder may <lb></lb>be ſaid to be a ſim <lb></lb>ple line.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg21"></margin.target>Ariſtotle <emph type="italics"></emph>accom <lb></lb>modates the rules of<emph.end type="italics"></emph.end> <lb></lb>Architecture <emph type="italics"></emph>to <lb></lb>the frame of the <lb></lb>World, and not the <lb></lb>frame to the rules.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg22"></margin.target><emph type="italics"></emph>Right motion, ſome <lb></lb>times ſimple, ard <lb></lb>ſometimes mixt ac <lb></lb>cording to<emph.end type="italics"></emph.end> Ariſt.</s></p><p type="main"><s>SIMPL. How? </s><s>Is it not difference ſufficient, that the ſimple and <lb></lb>abſolute are more ſwift than that which proceeds from predomi <lb></lb>nion? </s><s>and how much faſter doth a piece of pure Earth deſcend, <lb></lb>than a piece of Wood?</s></p><p type="main"><s>SAGR. Well, <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end>; But put caſe the ſimplicity for this <lb></lb>cauſe was changed, beſides that there would be a hundred thou <lb></lb>ſand mixt motions, you would not be able to determine the ſim <lb></lb>ple; nay farther, if the greater or leſſe velocity be able to alter <lb></lb>the ſimplicity of the motion, no ſimple body ſhould move with a <lb></lb>ſimple motion; ſince that in all natural right motions, the veloci <lb></lb>ty is ever encreaſing, and by conſequence ſtill changing the ſimpli <lb></lb>city, which as it is ſimplicity, ought of conſequence to be immu <lb></lb>table, and that which more importeth, you charge <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> with <lb></lb>another thing, that in the definition of motions compounded, he <lb></lb>hath not made mention of tardity nor velocity, which you now <lb></lb>inſert for a neceſſary and eſſential point. </s><s>Again you can draw <lb></lb>no advantage from this rule, for that there will be amongſt the <lb></lb>mixt bodies ſome, (and that not a few) that will move ſwiftly, <pb xlink:href="040/01/025.jpg" pagenum="9"></pb>and others more ſlowly than the ſimple; as for example, Lead, and <lb></lb>Wood, in compariſon of earth; and therefore amongſt theſe mo <lb></lb>tions, which call you the ſimple, and which the mixt?</s></p><p type="main"><s>SIMPL. </s><s>I would call that ſimple motion, which is made by a <lb></lb>ſimple body, and mixt, that of a compound body.</s></p><p type="main"><s>SAGR. </s><s>Very well, and yet <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> a little before you ſaid, <lb></lb>that the ſimple, and compound motions, diſcovered which were <lb></lb>mixt, and which were ſimple bodies; now you will have me by <lb></lb>ſimple and mixt bodies, come to know which is the ſimple, and <lb></lb>which is the compound motion: an excellent way to keep us igno <lb></lb>rant, both of motions and bodies. </s><s>Moreover you have alſo a little <lb></lb>above declared, how that a greater velocity did not ſuffice, but <lb></lb>you ſeek a third condition for the definement of ſimple motion, for <lb></lb>which <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> contented himſelf with one alone, namely, of the <lb></lb>ſimplicity of the Space, or <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end>: But now according to you, <lb></lb>the ſimple motion, ſhall be that which is made upon a ſimple line, <lb></lb>with a certain determinate velocity, by a body ſimply moveable. <lb></lb></s><s>Now be it as you pleaſe, and let us return to <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> who defi <lb></lb>neth the mixt motion to be that compounded of the right, and cir <lb></lb>cular, but produceth not any body, which naturally moveth with <lb></lb>ſuch a motion.</s></p><p type="main"><s>SALV. </s><s>I come again to <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> who having very well, and <lb></lb>Methodically begun his diſcourſe, but having a greater aim to <lb></lb>reſt at, and hit a marke, predefigned in his minde, then that to <lb></lb>which his method lead him, digreſſing from the purpoſe, he comes <lb></lb>to aſſert, as a thing known and manifeſt, that as to the motions <lb></lb>directly upwards or downwards, they naturally agree to Fire, and <lb></lb>Earth; and that therefore it is neceſſary, that beſides theſe bodies, <lb></lb>which are neer unto us, there muſt be in nature another, to which <lb></lb>the circular motion may agree: which ſhall be ſo much the more <lb></lb>excellent by how much the circular motion is more perfect, then the <lb></lb>ſtreight, but how much more perfect that is than this, he deter <lb></lb>mines from the greatneſs of the circular lines perfection above the <lb></lb><arrow.to.target n="marg23"></arrow.to.target> <lb></lb>right line; calling that perfect, and this imperfect; imperfect, be <lb></lb>cauſe if infinite it wanteth a termination, and end: and if it be fi <lb></lb>nite, there is yet ſomething beyond which it may be prolonged. <lb></lb></s><s>This is the baſis, ground work, and maſter-ſtone of all the Fabrick <lb></lb>of the <emph type="italics"></emph>Aristotelian<emph.end type="italics"></emph.end> World, upon which they ſuperſtruct all their <lb></lb>other properties, of neither heavy nor light, of ingenerable incor <lb></lb>ruptible, exemption from all motions, ſome onely the local, &c. <lb></lb></s><s>And all theſe paſſions he affirmeth to be proper to a ſimple body <lb></lb>that is moved circularly; and the contrary qualities of gravity, <lb></lb>levity, corruptibility, &c. </s><s>he aſſigns to bodies naturally moveable <lb></lb>in a ſtreight line, for that if we have already diſcovered defects in <lb></lb>the foundation, we may rationally queſtion what ſoever may far <pb xlink:href="040/01/026.jpg" pagenum="10"></pb>ther built thereon. </s><s>I deny not, that this which <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> hitherto <lb></lb>hath introduced, with a general diſcourſe dependent upon univer <lb></lb>ſal primary principles, hathbeen ſince in proceſs of time, re-inforced <lb></lb>with particular reaſons, and experiments; all which it would be <lb></lb>neceſſary diſtinctly to conſider and weigh; but becauſe what hath <lb></lb>been ſaid hitherto preſents to ſuch as conſider the ſame many and <lb></lb>no ſmall difficulties, (and yet it would be neceſſary, that the pri <lb></lb>mary principles and fundamentals, were certain, firm, and eſtabliſh <lb></lb>ed, that ſo they might with more confidence be built upon) it <lb></lb>would not be amiſs, before we farther multiply doubts, to ſee if <lb></lb>haply (as I conjecture) betaking our ſelves to other waies, we may <lb></lb>not light upon a more direct and ſecure method; and with better <lb></lb>conſidered principles of Architecture lay our primary fundamen <lb></lb>tals. </s><s>Therefore ſuſpending for the preſent the method of <emph type="italics"></emph>Ariſto <lb></lb>tle,<emph.end type="italics"></emph.end> (which we will re-aſſume again in its proper place, and parti <lb></lb>cularly examine;) I ſay, that in the things hitherto affirmed by <lb></lb><arrow.to.target n="marg24"></arrow.to.target> <lb></lb>him, I agree with him, and admit that the World is a body enjoy <lb></lb>ing all dimenſions, and therefore moſt perfect; and I add, that as <lb></lb>ſuch, it is neceſſarily moſt ordinate, that is, having parts between <lb></lb>themſelves, with exquiſite and moſt perfect order diſpoſed; which <lb></lb>aſſumption I think is not to be denied, neither by you or any <lb></lb>other.</s></p><p type="margin"><s><margin.target id="marg23"></margin.target><emph type="italics"></emph>The circular line <lb></lb>perfect, according <lb></lb>to<emph.end type="italics"></emph.end> Ariſtotle, <emph type="italics"></emph>and <lb></lb>but the right im <lb></lb>perfect, and why.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg24"></margin.target><emph type="italics"></emph>The world is ſup <lb></lb>poſed by the Au <lb></lb>thor to be perfectly <lb></lb>ordinate.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>Who can deny it? </s><s>the firſt particular (of the worlds <lb></lb>dimenſions) is taken from <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> himſelf, and its denominati <lb></lb>on of ordinate ſeems onely to be aſſumed from the order which it <lb></lb>moſt exactly keeps. <lb></lb><arrow.to.target n="marg25"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg25"></margin.target><emph type="italics"></emph>Streight motion <lb></lb>impoſſible in the <lb></lb>world exactly or <lb></lb>dinate.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>This principle then eſtabliſhed, one may immediately <lb></lb>conclude, that if the entire parts of the World ſhould be by their <lb></lb>nature moveable, it is impoſſible that their motions ſhould be <lb></lb>right, or other than circular; and the reaſon is ſufficiently eaſie, <lb></lb>and manifeſt; for that whatſoever moveth with a right motion, <lb></lb>changeth place; and continuing to move, doth by degrees more <lb></lb>and more remove from the term from whence it departed, and <lb></lb>from all the places thorow which it ſucceſſively paſſed; and if <lb></lb>ſuch motion naturally ſuited with it, then it was not at the be <lb></lb>ginning in its proper place; and ſo the parts of the World were <lb></lb>not diſpoſed with perfect order. </s><s>But we ſuppoſe them to be per <lb></lb>fectly ordinate, therefore as ſuch, it is impoſſible that they ſhould <lb></lb>by nature change place, and conſequently move in a right moti</s></p><p type="main"><s><arrow.to.target n="marg26"></arrow.to.target> <lb></lb>on. </s><s>Again, the right motion being by nature infinite, for that <lb></lb>the right line is infinite and indeterminate, it is impoſſible that <lb></lb><arrow.to.target n="marg27"></arrow.to.target> <lb></lb>any moveable can have a natural principle of moving in a right <lb></lb>line; namely toward the place whither it is impoſſible to arrive, <lb></lb><arrow.to.target n="marg28"></arrow.to.target> <lb></lb>there being no præ-ſinite term; and nature, as <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> himſelf <lb></lb>ſaith well, never attempts to do that which can never be done, <pb xlink:href="040/01/027.jpg" pagenum="11"></pb>nor eſſaies to move whither it is impoſſible to arrive. </s><s>And if any <lb></lb>one ſhould yet object, that albeit the right line, and conſequent <lb></lb>ly the motion by it is producible <emph type="italics"></emph>in infinitum,<emph.end type="italics"></emph.end> that is to ſay, is in <lb></lb>terminate; yet nevertheleſs Nature, as one may ſay, arbitrarily <lb></lb>hath aſſigned them ſome terms, and given natural inſtincts to <lb></lb>its natural bodies to move unto the ſame; I will reply, that this <lb></lb><arrow.to.target n="marg29"></arrow.to.target> <lb></lb>might perhaps be fabled to have come to paſs in the firſt Chaos, <lb></lb>where indiſtinct matters confuſedly and inordinately wandered; <lb></lb>to regulate which, Nature very appoſitely made uſe of right mo <lb></lb><arrow.to.target n="marg30"></arrow.to.target> <lb></lb>tions, by which, like as the well-conſtituted, moving, diſdorder <lb></lb>themſelves, ſo were they which were before depravedly diſpoſed <lb></lb>by this motion ranged in order: but after their exquiſite diſtribu <lb></lb>tion and collocation, it is impoſſible that there ſhould remain na <lb></lb>tural inclinations in them of longer moving in a right motion, <lb></lb>from which now would enſue their removal from their proper and <lb></lb>natural place, that is to ſay, their diſordination; we may there <lb></lb>fore ſay that the right motion ſerves to conduct the matter to erect <lb></lb>the work; but once erected, that it is to reſt immoveable, or if <lb></lb><arrow.to.target n="marg31"></arrow.to.target> <lb></lb>moveable, to move it ſelf onely circularly. </s><s>Unleſs we will ſay <lb></lb>with <emph type="italics"></emph>Plato,<emph.end type="italics"></emph.end> that theſe mundane bodies, after they had been made <lb></lb>and finiſhed, were for a certain time moved by their Maker, in a <lb></lb>right motion, but that after their attainment to certain and de <lb></lb>terminate places, they were revolved one by one in Spheres, paſ <lb></lb>ſing from the right to the circular motion, wherein they have <lb></lb>been ever ſince kept and maintained. </s><s>A ſublime conceipt, and <lb></lb><arrow.to.target n="marg32"></arrow.to.target> <lb></lb>worthy indeed of <emph type="italics"></emph>Plato<emph.end type="italics"></emph.end>: upon which, I remember to have heard <lb></lb>our common friend the ^{*}<emph type="italics"></emph>Lyncean Academick<emph.end type="italics"></emph.end> diſcourſe in this man <lb></lb>ner, if I have not forgot it. </s><s>Every body for any reaſon conſtitu <lb></lb>ted in a ſtate of reſt, but which is by nature moveable, being ſet <lb></lb><arrow.to.target n="marg33"></arrow.to.target> <lb></lb>at liberty doth move; provided withal, that it have an inclina <lb></lb>tion to ſome particular place; for ſhould it ſtand indifferently af <lb></lb>fected to all, it would remain in its reſt, not having greater in <lb></lb>ducement to move one way than another. </s><s>From the having of <lb></lb>this inclination neceſſarily proceeds, that it in its moving ſhall con <lb></lb><arrow.to.target n="marg34"></arrow.to.target> <lb></lb>tinually increaſe its acceleration, and beginning with a moſt ſlow <lb></lb>motion, it ſhall not acquire any degree of velocity, before it <lb></lb>ſhall have paſſed thorow all the degrees of leſs velocity, or grea <lb></lb>ter tardity: for paſſing from the ſtate of quiet (which is the in <lb></lb><arrow.to.target n="marg35"></arrow.to.target> <lb></lb>finite degree of tardity of motion) there is no reaſon by which <lb></lb>it ſhould enter into ſuch a determinate degree of velocity, before <lb></lb>it ſhall have entred into a leſs, and into yet a leſs, before it entred <lb></lb>into that: but rather it ſtands with reaſon, to paſs firſt by thoſe <lb></lb>degrees neareſt to that from which it departed, and from thoſe to <lb></lb>the more remote; but the degree from whence the moveable <lb></lb><arrow.to.target n="marg36"></arrow.to.target> <lb></lb>began to move, is that of extreme tardity, namely of reſt. <pb xlink:href="040/01/028.jpg" pagenum="12"></pb><arrow.to.target n="marg37"></arrow.to.target> <lb></lb>Now this acceleration of motion is never made, but when the <lb></lb>moveable in moving acquireth it; nor is its acquiſt other than an <lb></lb>approaching to the place deſired, to wit, whither its natural in <lb></lb>clination attracts it, and thither it tendeth by the ſhorteſt way; <lb></lb>namely, by a right line. </s><s>We may upon good grounds therefore <lb></lb>ſay, That Nature, to confer upon a moveable firſt conſtituted in <lb></lb>reſt a determinate velocity, uſeth to make it move according to <lb></lb><arrow.to.target n="marg38"></arrow.to.target> <lb></lb>a certain time and ſpace with a right motion. </s><s>This preſuppoſed, <lb></lb>let us imagine God to have created the Orb <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> on <lb></lb>which he had determined to confer ſuch a certain velocity, which <lb></lb>it ought afterwards to retain perpetually uniform; we may with <lb></lb><emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> ſay, that he gave it at the beginning a right and accelerate <lb></lb>motion, and that it afterwards being arrived to that intended de <lb></lb><arrow.to.target n="marg39"></arrow.to.target> <lb></lb>gree of velocity, he converted its right, into a circular motion, <lb></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"></emph>Right motion by <lb></lb>nature infinite.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg27"></margin.target><emph type="italics"></emph>Motion by a right <lb></lb>line naturally im <lb></lb>poſſible.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg28"></margin.target><emph type="italics"></emph>Nature attempts <lb></lb>not things impoſſi <lb></lb>ble to be effected.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg29"></margin.target><emph type="italics"></emph>Right motion might <lb></lb>perhaps be in the <lb></lb>firſt Chaos.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg30"></margin.target><emph type="italics"></emph>Right motion is <lb></lb>commodious to <lb></lb>range in order, <lb></lb>things ous of or <lb></lb>der.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg31"></margin.target><emph type="italics"></emph>Mundane bodies <lb></lb>moved in the be <lb></lb>ginning in a right <lb></lb>line, and after <lb></lb>wards circularly? <lb></lb></s><s>according to<emph.end type="italics"></emph.end> Plato.</s></p><p type="margin"><s><margin.target id="marg32"></margin.target>* Thus doth he co <lb></lb>vertly and modeſt <lb></lb>ly ſtile himſelfe <lb></lb>throughout this <lb></lb>work.</s></p><p type="margin"><s><margin.target id="marg33"></margin.target><emph type="italics"></emph>A moveable be <lb></lb>ing in a ſtate of <lb></lb>reſt, ſhall not move <lb></lb>unleſs it have an <lb></lb>inclination to ſome <lb></lb>particular place.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg34"></margin.target><emph type="italics"></emph>The moveable ac <lb></lb>celerates its moti <lb></lb>on, going towards <lb></lb>the place whither <lb></lb>it hath an inclina <lb></lb>tion.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg35"></margin.target><emph type="italics"></emph>The moveable paſ <lb></lb>ſing from reſt, go <lb></lb>eth thorow all the <lb></lb>degrees of tardity.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg36"></margin.target><emph type="italics"></emph>Reſt the inſinioe <lb></lb>degree of tardity.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg37"></margin.target><emph type="italics"></emph>The moveable doth <lb></lb>not accelerate, ſave <lb></lb>only as it approach <lb></lb>eth nearer to its <lb></lb>term.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg38"></margin.target><emph type="italics"></emph>Nature, to intro <lb></lb>duce in the move <lb></lb>able a certain de <lb></lb>gree of velocity, <lb></lb>made it move in a <lb></lb>right line.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg39"></margin.target><emph type="italics"></emph>Vniform velocity <lb></lb>convenient to the <lb></lb>circular motion.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I hearken to this Diſcourſe with great delight; and I <lb></lb>believe the content I take therein will be greater, when you have <lb></lb>ſatisfied me in a doubt: that is, (which I do not very well com <lb></lb>prehend) how it of neceſſity enſues, that a moveable departing <lb></lb><arrow.to.target n="marg40"></arrow.to.target> <lb></lb>from its reſt, and entring into a motion to which it had a natural <lb></lb>inclination, it paſſeth thorow all the precedent degrees oſ tardity, <lb></lb>comprehended between any aſſigned degree of velocity, and the <lb></lb>ſtate of reſt, which degrees are infinite? </s><s>ſo that Nature was not <lb></lb>able to confer them upon the body of <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> his circular moti <lb></lb>on being inſtantly created with ſuch and ſuch velocity. <lb></lb><arrow.to.target n="marg41"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg40"></margin.target><emph type="italics"></emph>Betwixt reſt, and <lb></lb>any aſſigned degree <lb></lb>of velocity, infinite <lb></lb>degrees of leſs ve <lb></lb>locity interpoſe.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg41"></margin.target><emph type="italics"></emph>Nature doth not <lb></lb>immediately con <lb></lb>fer a determinate <lb></lb>degree of velocity, <lb></lb>howbeit ſhe could.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>I neither did, nor dare ſay, that it was impoſſible for <lb></lb>God or Nature to confer that velocity which you ſpeak of, imme <lb></lb>diately; but this I ſay, that <emph type="italics"></emph>de facto<emph.end type="italics"></emph.end> ſhe did not doit; ſo that the <lb></lb>doing it would be a work extra-natural, and by confequence mi <lb></lb>raculous.</s></p><p type="main"><s>SAGR. </s><s>Then you believe, that a ſtone leaving its reſt, and en <lb></lb>tring into its natural motion towards the centre of the Earth, paſ <lb></lb>ſeth thorow all the degrees of tardity inferiour to any degree of <lb></lb>velocity?</s></p><p type="main"><s>SALV. </s><s>I do believe it, nay am certain of it; and ſo certain, <lb></lb>that I am able to make you alſo very well ſatisfied with the truth <lb></lb>thereof.</s></p><p type="main"><s>SAGR. </s><s>Though by all this daies diſcourſe I ſhould gain no <lb></lb>more but ſuch a knowledge, I ſhould think my time very well <lb></lb>beſtowed.</s></p><p type="main"><s>SALV. </s><s>By what I collect from our diſcourſe, a great part of <lb></lb>your ſcruple lieth in that it ſhould in a time, and that very ſhort, <lb></lb>paſs thorow thoſe infinite degrees of tardity precedent to any ve <lb></lb>locity, acquired by the moveable in that time: and therefore be <lb></lb>fore we go any farther, I will ſeek to remove this difficulty, which <pb xlink:href="040/01/029.jpg" pagenum="13"></pb>ſhall be an eaſie task; for I reply, that the moveable paſſeth by <lb></lb>the aforeſaid degrees, but the paſſage is made without ſtaying in </s></p><p type="main"><s><arrow.to.target n="marg42"></arrow.to.target> <lb></lb>any of them; ſo that the paſſage requiring but one ſole inſtant <lb></lb>of time, and every ſmall time containing infinite inſtants, we ſhall <lb></lb>not want enough of them to aſſign its own to each of the infinite <lb></lb>degrees of tardity; although the time were never ſo ſhort.</s></p><p type="margin"><s><margin.target id="marg42"></margin.target><emph type="italics"></emph>The moveable de <lb></lb>parting from reſv <lb></lb>paſſeth thorow all <lb></lb>degrees of velocity <lb></lb>without ſtaying in <lb></lb>any.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Hitherto I apprehend you; nevertheleſs it is very much <lb></lb>that that Ball ſhot from a Cannon (for ſuch I conceive the ca <lb></lb>dent moveable) which yet we ſee to fall with ſuch a precipice, <lb></lb>that in leſs than ten pulſes it will paſs two hundred yards of al <lb></lb>titude; ſhould in its motion be found conjoyned with ſo ſmall a <lb></lb>degree of velocity, that, ſhould it have continued to have moved <lb></lb>at that rate without farther acceleration, it would not have paſt <lb></lb>the ſame in a day.</s></p><p type="main"><s>SALV. </s><s>You may ſay, nor yet in a year, nor in ten, no nor in a <lb></lb>thouſand; as I will endeavour to ſhew you, and alſo happily with <lb></lb>out your contradiction, to ſome ſufficiently ſimple queſtions that <lb></lb>I will propound to you. </s><s>Therefore tell me if you make any que <lb></lb>ſtion of granting that, that that ball in deſcending goeth increa <lb></lb>ſing its <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> and velocity.</s></p><p type="main"><s>SAGR. </s><s>I am moſt certain it doth.</s></p><p type="main"><s>SALV. </s><s>And if I ſhould ſay that the <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> acquired in any <lb></lb>place of its motion, is ſo much, that it would ſuffice to re-carry <lb></lb>it to that place from which it came, would you grant it?</s></p><p type="main"><s>SAGR. </s><s>I ſhould conſent to it without contradiction, provided al <lb></lb>waies, that it might imploy without impediment its whole <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> <lb></lb>in that ſole work of re-conducting it ſelf, or another equal toit, to <lb></lb><arrow.to.target n="marg43"></arrow.to.target> <lb></lb>that ſelf-ſame height as it would do, in caſe the Earth were bored <lb></lb>thorow the centre, and the Bullet fell a thouſand yards from the <lb></lb>ſaid centre, for I verily believe it would paſs beyond the centre, <lb></lb>aſcending as much as it had deſcended; and this I ſee plainly in <lb></lb>the experiment of a plummet hanging at a line, which removed <lb></lb>from the perpendicular, which is its ſtate of reſt, and afterwards <lb></lb>let go, falleth towards the ſaid perpendicular, and goes as far be <lb></lb>yond it; or onely ſo much leſs, as the oppoſition of the air, and <lb></lb>line, or other accidents have hindred it. </s><s>The like I ſee in the wa <lb></lb>ter, which deſcending thorow a pipe, re-mounts as much as it had <lb></lb>deſcended.</s></p><p type="margin"><s><margin.target id="marg43"></margin.target><emph type="italics"></emph>The ponderous mo <lb></lb>ver deſcending ac <lb></lb>quireth<emph.end type="italics"></emph.end> impetus <lb></lb><emph type="italics"></emph>ſufficient to re <lb></lb>carry it to the like <lb></lb>height.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>You argue very well. </s><s>And for that I know you will not <lb></lb>ſcruple to grant that the acquiſt of the <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> is by means of the <lb></lb>receding from the term whence the moveable departed, and its ap <lb></lb>proach to the centre, whither its motion tendeth; will you ſtick <lb></lb>to yeeld, that two equal moveables, though deſcending by divers <lb></lb>lines, without any impediment, acquire equal <emph type="italics"></emph>impetus,<emph.end type="italics"></emph.end> provided <lb></lb>that the approaches to the centre be equal?</s></p> <pb xlink:href="040/01/030.jpg" pagenum="14"></pb><p type="main"><s>SAGR. </s><s>I do not very well underſtand the queſtion.</s></p><p type="main"><s>SALV. </s><s>I will expreſs it better by drawing a Figure: therefore <lb></lb>I will ſuppoſe the line A B [in <emph type="italics"></emph>Fig.<emph.end type="italics"></emph.end> 3.] parallel to the Horizon, <lb></lb>and upon the point B, I will erect a perpendicular B C; and after <lb></lb>that I adde this ſlaunt line C A. </s><s>Underſtanding now the line C <lb></lb>A to be an inclining plain exquiſitely poliſhed, and hard, upon <lb></lb>which deſcendeth a ball perfectly round and of very hard matter, <lb></lb>and ſuch another I ſuppoſe freely to deſcend by the perpendicular <lb></lb>C B: will you now confeſs that the <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> of that which de <lb></lb>ſcends by the plain C A, being arrived to the point A, may be <lb></lb>equal to the <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> acquired by the other in the point B, after <lb></lb>the deſcent by the perpendicular C B? <lb></lb><arrow.to.target n="marg44"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg44"></margin.target><emph type="italics"></emph>The impetuoſity of <lb></lb>moveables equally <lb></lb>approaching to the <lb></lb>centre, are equal.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I reſolutely believe ſo: for in effect they have both the <lb></lb>ſame proximity to the centre, and by that, which I have already <lb></lb>granted, their impetuoſities would be equally ſufficient to re-carry <lb></lb>them to the ſame height.</s></p><p type="main"><s>SALV. </s><s>Tell me now what you believe the ſame ball would do <lb></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"></emph>Vpon an horizon <lb></lb>tall plane the move <lb></lb>able lieth ſtill.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>It would lie ſtill, the ſaid plane having no declination.</s></p><p type="main"><s>SALV. </s><s>But on the inclining plane C A it would deſcend, but <lb></lb>with a gentler motion than by the perpendicular C B?</s></p><p type="main"><s>SAGR. </s><s>I may confidently anſwer in the affirmative, it ſeem <lb></lb>ing to me neceſſary that the motion by the perpendicular C B <lb></lb>ſhould be more ſwift, than by the inclining plane C A; yet ne <lb></lb>vertheleſs, iſ this be, how can the Cadent by the inclination ar <lb></lb>rived to the point A, have as much <emph type="italics"></emph>impetus,<emph.end type="italics"></emph.end> that is, the ſame de <lb></lb>gree of velocity, that the Cadent by the perpendicular ſhall have <lb></lb>in the point B? theſe two Propoſitions ſeem 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"></emph>The veloeity by the <lb></lb>inclining plane e <lb></lb>qual to the veloci <lb></lb>ty by the perpendi <lb></lb>oular, and the mo <lb></lb>tion by the perpen <lb></lb>dicular ſwifter <lb></lb>than by the incli <lb></lb>nation.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Then you would think it much more falſe, ſhould I <lb></lb>ſay, that the velocity of the Cadents by the perpendicular, and <lb></lb>inclination, are abſolutely equal: and yet this is a Propoſition <lb></lb>moſt true, as is alſo this that the Cadent moveth more ſwiftly by <lb></lb>the perpendicular, than by the inclination.</s></p><p type="main"><s>SAGR. </s><s>Theſe Propoſitions to my ears ſound very harſh: and <lb></lb>I believe to yours <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end>?</s></p><p type="main"><s>SIMPL. </s><s>I have the ſame ſenſe of them.</s></p><p type="main"><s>SALV. </s><s>I conceit you jeſt with me, pretending not to compre <lb></lb>hend what you know better than my ſelf: therefore tell me <emph type="italics"></emph>Sim <lb></lb>plicius,<emph.end type="italics"></emph.end> when you imagine a moveable more ſwift than ano <lb></lb>ther, what conceit do you fancy in your mind?</s></p><p type="main"><s>SIMPL. </s><s>I fancie one to paſs in the ſame time a greater ſpace <lb></lb>than the other, or to move equal ſpaces, but in leſſer time.</s></p><p type="main"><s>SALV. </s><s>Very well: and for moveables equally ſwift, what's <lb></lb>your conceit of them?</s></p><p type="main"><s>SIMPL. </s><s>I fancie that they paſs equal ſpaces in equal times.</s></p> <pb xlink:href="040/01/031.jpg" pagenum="15"></pb><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></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"></emph>Velocities are ſaid <lb></lb>to be equal, when <lb></lb>the ſpaces paſſed <lb></lb>are proportionate to <lb></lb>their time.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>We will add moreover this other: and call that equal <lb></lb>velocity, when the ſpaces paſſed have the ſame proportion, as the <lb></lb>times wherein they are paſt, and it is a more univerſal definition.</s></p><p type="main"><s>SALV. </s><s>It is ſo: for it comprehendeth the equal ſpaces paſt in <lb></lb>equal times, and alſo the unequal paſt in times unequal, but pro <lb></lb>portionate to thoſe ſpaces. </s><s>Take now the ſame Figure, and apply <lb></lb>ing the conceipt that you had of the more haſtie motion, tell me <lb></lb>why you think the velocity of the Cadent by C B, is greater <lb></lb>than the velocity of the Deſcendent by C A?</s></p><p type="main"><s>SIMPL. </s><s>I think ſo; becauſe in the ſame time that the Cadent <lb></lb>ſhall paſs all C B, the Deſcendent ſhall paſs in C A, a part leſs <lb></lb>than C B.</s></p><p type="main"><s>SALV. True; and thus it is proved, that the moveable moves <lb></lb>more ſwiftly by the perpendicular, than by the inclination. </s><s>Now <lb></lb>conſider, if in this ſame Figure one may any way evince the o <lb></lb>ther conceipt, and finde that the moveables were equally ſwift <lb></lb>by both the lines C A and C B.</s></p><p type="main"><s>SIMPL. </s><s>I ſee no ſuch thing; nay rather it ſeems to contradict <lb></lb>what was ſaid before.</s></p><p type="main"><s>SALV. </s><s>And what ſay you, <emph type="italics"></emph>Sagredus<emph.end type="italics"></emph.end>? </s><s>I would not teach you <lb></lb>what you knew before, and that of which but juſt now you pro <lb></lb>duced me the definition.</s></p><p type="main"><s>SAGR. </s><s>The definition I gave you, was, that moveables may <lb></lb>be called equally ſwift, when the ſpaces paſſed are proportional <lb></lb>to the times in which they paſſed; therefore to apply the defini <lb></lb>tion to the preſent caſe, it will be requiſite, that the time of de <lb></lb>ſcent by C A, to the time of falling by C B, ſhould have the <lb></lb>ſame proportion that the line C A hath to the line C B; but I <lb></lb>underſtand not how that can be, for that the motion by C B is <lb></lb>ſwifter than by C A.</s></p><p type="main"><s>SALV. </s><s>And yet you muſt of neceſſity know it. </s><s>Tell me a little, <lb></lb>do not theſe motions go continually accelerating?</s></p><p type="main"><s>SAGR. </s><s>They do; but more in the perpendicular than in the <lb></lb>inclination.</s></p><p type="main"><s>SALV. </s><s>But this acceleration in the perpendicular, is it yet not <lb></lb>withſtanding ſuch in compariſon of that of the inclined, that <lb></lb>two equal parts being taken in any place of the ſaid perpendicu <lb></lb>lar and inclining lines, the motion in the parts of the perpendicu <lb></lb>lar is alwaies more ſwift, than in the part of the inclination?</s></p><p type="main"><s>SAGR. </s><s>I ſay not ſo: but I could take a ſpace in the inclinati <lb></lb>on, in which the velocity ſhall be far greater than in the like ſpace <lb></lb>taken in the perpendicular; and this ſhall be, if the ſpace in the <pb xlink:href="040/01/032.jpg" pagenum="16"></pb>perpendicular ſhould be taken near to the end C, and in the in <lb></lb>clination, far from it.</s></p><p type="main"><s>SALV. </s><s>You ſee then, that the Propoſition which ſaith, that <lb></lb>the motion by the perpendicular is more ſwift than by the incli <lb></lb>nation, holds not true univerſally, but onely of the motions, <lb></lb>which begin from the extremity, namely from the point of reſt: <lb></lb>without which reſtriction, the Propoſition would be ſo deficient, <lb></lb>that its very direct contrary might be true; namely, that the mo <lb></lb>tion in the inclining plane is ſwifter than in the perpendicular: <lb></lb>for it is certain, that in the ſaid inclination, we may take a ſpace <lb></lb>paſt by the moveable in leſs time, than the like ſpace paſt in the <lb></lb>perpendicular. </s><s>Now becauſe the motion in the inclination is in <lb></lb>ſome places more, in ſome leſs, than in the perpendicular; there <lb></lb>fore in ſome places of the inclination, the time of motion of the <lb></lb>moveable, ſhall have a greater proportion to the time of the motion <lb></lb>of the moveable, by ſome places of the perpendicular, than the <lb></lb>ſpace paſſed, to the ſpace paſſed: and in other places, the pro <lb></lb>portion of the time to the time, ſhall be leſs than that of the <lb></lb>ſpace to the ſpace. </s><s>As for example: two moveables departing <lb></lb>from their quieſcence, namely, from the point C, one by the per <lb></lb>pendicular C B, [in <emph type="italics"></emph>Fig.<emph.end type="italics"></emph.end> 4.] and the other by the inclination C A, <lb></lb>in the time that, in the perpendicular, the moveable ſhall have <lb></lb>paſt all C B, the other ſhall have paſt C T leſſer. </s><s>And therefore <lb></lb>the time by C T, to the time by C B (which is equal) ſhall have <lb></lb>a greater proportion than the line C T to C B, being that the <lb></lb><emph type="italics"></emph>ſame<emph.end type="italics"></emph.end> to the <emph type="italics"></emph>leſs,<emph.end type="italics"></emph.end> hath a greater proportion than to the <emph type="italics"></emph>greater.<emph.end type="italics"></emph.end> <lb></lb>And on the contrary, if in C A, prolonged as much as is requi <lb></lb>ſite, one ſhould take a part equal to C B, but paſt in a ſhorter <lb></lb>time; the time in the inclination ſhall have a leſs proportion to <lb></lb>the time in the perpendicular, than the ſpace to the ſpace. </s><s>If <lb></lb>therefore in the inclination and perpendicular, we may ſuppoſe <lb></lb>ſuch ſpaces and velocities, that the proportion between the ſaid <lb></lb>ſpaces be greater and leſs than the proportion of the times; we <lb></lb>may eaſily grant, that there are alſo ſpaces, by which the times <lb></lb>of the motions retain the ſame proportion as the ſpaces.</s></p><p type="main"><s>SAGR. </s><s>I am already freed from my greateſt doubt, and con <lb></lb>ceive that to be not onely poſſible, but neceſſary, which I but <lb></lb>now thought a contradiction: but nevertheleſs I underſtand not <lb></lb>as yet, that this whereof we now are ſpeaking, is one of theſe <lb></lb>poſſible or neceſſary caſes; ſo as that it ſhould be true, that the <lb></lb>time of deſcent by C A, to the time of the fall by C B, hath the <lb></lb>ſame proportion that the line C A hath to C B; whence it may <lb></lb>without contradiction be affirmed, that the velocity by the incli <lb></lb>nation C A, and by the perpendicular C B, are equal.</s></p><p type="main"><s>SALV. </s><s>Content your ſelf for this time, that I have removed <pb xlink:href="040/01/033.jpg" pagenum="17"></pb>your incredulity; but for the knowledge of this, expect it at <lb></lb>ſome other time, namely, when you ſhall ſee the matters concer <lb></lb>ning local motion demonſtrated by our <emph type="italics"></emph>Academick<emph.end type="italics"></emph.end>; at which <lb></lb>time you ſhall find it proved, that in the time that the one movea <lb></lb>ble falls all the ſpace C B, the other deſcendeth by C A as far <lb></lb>as the point T, in which falls the perpendicular drawn from the <lb></lb>point B: and to find where the ſame Cadent by the perpendi <lb></lb>cular would be when the other arriveth at the point A, draw from <lb></lb>A the perpendicular unto C A, continuing it, and C B unto the <lb></lb>interfection, and that ſhall be the point ſought. </s><s>Whereby you <lb></lb>ſee how it is true, that the motion by C B is ſwifter than by the <lb></lb>inclination C A (ſuppoſing the term C for the beginning of the <lb></lb>motions compared) becauſe the line C B is greater than C T, <lb></lb>and the other from C unto the interſection of the perpendicular <lb></lb>drawn from A, unto the line C A, is greater than C A, and <lb></lb>therefore the motion by it is ſwifter than by C A But when we <lb></lb>compare the motion made by all C A, not with all the motion <lb></lb>made in the ſame time by the perpendicular continued, but with <lb></lb>that made in part of the time, by the ſole part C B, it hinders <lb></lb>not, that the motion by C A, continuing to deſcend beyond, may <lb></lb>arrive to A in ſuch a time as is in proportion to the other time, <lb></lb>as the line C A is to the line C B. </s><s>Now returning to our firſt <lb></lb>purpoſe; which was to ſhew, that the grave moveable leaving <lb></lb>its quieſcence, paſſeth defcending by all the degrees of tardity, <lb></lb>precedent to any whatſoever degree of velocity that it aequireth, <lb></lb>re-aſſuming the ſame Figure which we uſed before, let us remem <lb></lb>ber that we did agree, that the Deſcendent by the inclination C <lb></lb>A, and the Cadent by the perpendicular C B, were found to have <lb></lb>acquired equal degrees of velocity in the terms B and A: now to <lb></lb>proceed, I ſuppoſe you will not ſcruple to grant, that upon ano <lb></lb>ther plane leſs ſteep than A C; as for example, A D [in <emph type="italics"></emph>Fig.<emph.end type="italics"></emph.end> 5.] <lb></lb>the motion of the deſcendent would be yet more ſlow than in the <lb></lb>plane A C. </s><s>So that it is not any whit dubitable, but that there <lb></lb>may be planes ſo little elevated above the Horizon A B, that the <lb></lb>moveable, namely the ſame ball, in any the longeſt time may <lb></lb>reach the point A, which being to move by the plane A B, an infi <lb></lb>nite time would not ſuffice: and the motion is made always more <lb></lb>ſlowly, by how much the declination is leſs. </s><s>It muſt be therefore <lb></lb>confeſt, that there may be a point taken upon the term B, ſo near <lb></lb>to the ſaid B, that drawing from thence to the point A a plane, <lb></lb>the ball would not paſs it in a whole year. </s><s>It is requiſite next <lb></lb>for you to know, that the <emph type="italics"></emph>impetus,<emph.end type="italics"></emph.end> namely the degree of velo <lb></lb>city the ball is found to have acquired when it arriveth at the <lb></lb>point A, is ſuch, that ſhould it continue to move with this ſelf-ſame <lb></lb>degree uniformly, that is to ſay, without accelerating or retarding; <pb xlink:href="040/01/034.jpg" pagenum="18"></pb>in as much more time as it was in coming by the inclining plane, it <lb></lb>would paſs double the ſpace of the plane inclined: namely (for <lb></lb>example) if the ball had paſt the plane D A in an hour, con <lb></lb>tinuing to move uniformly with that degree of velocity which it <lb></lb>is found to have in its arriving at the term A, it ſhall paſs in an <lb></lb>hour a ſpace double the length D A; and becauſe (as we have <lb></lb>ſaid) the degrees of velocity acquired in the points B and A, by <lb></lb>the moveables that depart from any point taken in the perpendicu <lb></lb>lar C B, and that deſcend, the one by the inclined plane, the o <lb></lb>ther by the ſaid perpendicular, are always equal: therefore the <lb></lb>cadent by the perpendicular may depart from a term ſo near to B, <lb></lb>that the degree of velocity acquired in B, would not ſuffice (ſtill <lb></lb>maintaining the ſame) to conduct the moveable by a ſpace dou <lb></lb>ble the length of the plane inclined in a year, nor in ten, no nor <lb></lb>in a hundred. </s><s>We may therefore conclude, that if it be true, <lb></lb>that according to the ordinary courſe of nature a moveable, all <lb></lb>external and accidental impediments removed, moves upon an in <lb></lb>clining plane with greater and greater tardity, according as the <lb></lb>inclination ſhall be leſs; ſo that in the end the tardity comes to be <lb></lb>infinite, which is, when the inclination concludeth in, and joyneth <lb></lb>to the horizontal plane; and if it be true likewiſe, that the de <lb></lb>gree of velocity acquired in ſome point of the inclined plane, is <lb></lb>equal to that degree of velocity which is found to be in the move <lb></lb>able that deſcends by the perpendicular, in the point cut by a <lb></lb>parallel to the Horizon, which paſſeth by that point of the incli <lb></lb>ning plane; it muſt of neceſſity be granted, that the cadent de <lb></lb>parting from reſt, paſſeth thorow all the infinite degrees of tar <lb></lb>dity, and that conſequently, to acquire a determinate degree of <lb></lb>velocity, it is neceſſary that it move firſt by right lines, deſcend <lb></lb>ing by a ſhort or long ſpace, according as the velocity to be acqui <lb></lb>red, ought to be either leſs or greater, and according as the plane <lb></lb>on which it deſcendeth is more or leſs inclined; ſo that a plane <lb></lb>may be given with ſo ſmall inclination, that to acquire in it the <lb></lb>aſſigned degree of velocity, it muſt firſt move in a very great ſpace, <lb></lb>and take a very long time; whereupon in the horizontal plane, any <lb></lb>how little ſoever velocity, would never be naturally acquired, <lb></lb>ſince that the moveable in this caſe will never move: but the </s></p><p type="main"><s><arrow.to.target n="marg48"></arrow.to.target> <lb></lb>motion by the horizontal line, which is neither declined or incli <lb></lb>ned, is a circular motion about the centre: therefore the circu <lb></lb>lar motion is never acquired naturally, without the right motion <lb></lb>precede it; but being once acquired, it will continue perpetually <lb></lb>with uniform velocity. </s><s>I could with other diſcourſes evince and <lb></lb>demonſtrate the ſame truth, but I will not by ſo great a digreſ <lb></lb>fion interrupt our principal argument: but rather will return to <lb></lb>it upon ſome other occaſion; eſpecially ſince we now aſſumed the <pb xlink:href="040/01/035.jpg" pagenum="19"></pb>ſame, not to ſerve for a neceſſary demonſtration, but to adorn a <lb></lb><emph type="italics"></emph>Platonick<emph.end type="italics"></emph.end> Conceit; to which I will add another particular obſer <lb></lb>vation of our <emph type="italics"></emph>Academick,<emph.end type="italics"></emph.end> which hath in it ſomething of admira <lb></lb>ble. </s><s>Let us ſuppoſe amongſt the decrees of the divine <emph type="italics"></emph>Architect,<emph.end type="italics"></emph.end> <lb></lb>a purpoſe of creating in the World theſe Globes, which we be <lb></lb>hold continually moving round, and of aſſigning the centre of <lb></lb>their converſions; and that in it he had placed the Sun immoveable, <lb></lb>and had afterwards made all the ſaid Globes in the ſame place, <lb></lb>and with the intended inclinations of moving towards the Centre, <lb></lb>till they had acquired thoſe degrees of velocity, which at firſt ſee <lb></lb>med good to the ſame Divine Minde; the which being acquired, <lb></lb>we laſtly ſuppoſe that they were turned round, each in his Sphere <lb></lb>retaining the ſaid acquired velocity: it is now demanded, in <lb></lb>what altitude and diſtance from the Sun the place was where the <lb></lb>ſaid Orbs were primarily created; and whether it be poſſible that <lb></lb>they might all be created in the ſame place? </s><s>To make this inve <lb></lb>ſtigation, we muſt take from the moſt skilfull Aſtronomers the <lb></lb>magnitude of the Spheres in which the Planets revolve, and like <lb></lb>wiſe the time of their revolutions: from which two cognitions is <lb></lb>gathered how much (for example) <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> is ſwifter than <emph type="italics"></emph>Sa <lb></lb>turne<emph.end type="italics"></emph.end>; and being found (as indeed it is) that <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> moves more <lb></lb>ſwiftly, it is requiſite, that departing from the ſame altitude, <emph type="italics"></emph>Ju <lb></lb>piter<emph.end type="italics"></emph.end> be deſcended more than <emph type="italics"></emph>Saturne,<emph.end type="italics"></emph.end> as we really know it is, its <lb></lb>Orbe being inferiour to that of <emph type="italics"></emph>Saturne.<emph.end type="italics"></emph.end> But by proceeding for <lb></lb>wards, from the proportions of the two velocities of <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> and <lb></lb><emph type="italics"></emph>Saturne,<emph.end type="italics"></emph.end> and from the diſtance between their Orbs, and from the <lb></lb>proportion of acceleration of natural motion, one may finde in <lb></lb>what altitude and diſtance from the centre of their revolutions, <lb></lb><arrow.to.target n="marg49"></arrow.to.target> <lb></lb>was the place from whence they firſt departed. </s><s>This found out, <lb></lb>and agreed upon, it is to be ſought, whether <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> deſcending <lb></lb>from thence to his Orb, the magnitude of the Orb, and the ve <lb></lb>locity of the motion, agree with that which is found by calcula <lb></lb>tion; and let the like be done of the <emph type="italics"></emph>Eartb,<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> and of <lb></lb><emph type="italics"></emph>Mercury<emph.end type="italics"></emph.end>; the greatneſs of which Spheres, and the velocity of <lb></lb>their motions, agree ſo nearly to what computation gives, that it <lb></lb>is very admirable.</s></p><p type="margin"><s><margin.target id="marg48"></margin.target><emph type="italics"></emph>The circular mo <lb></lb>tion is never ac <lb></lb>quired naturally, <lb></lb>without right mo <lb></lb>tion precede it. <lb></lb></s><s>Circular motion <lb></lb>perpetually uni <lb></lb>form.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg49"></margin.target><emph type="italics"></emph>The magnitude of <lb></lb>the Orbs, and the <lb></lb>velocity of the mo <lb></lb>tion of the Planets, <lb></lb>anſwer proportion <lb></lb>ably, as if deſcend <lb></lb>ed from the ſame <lb></lb>place.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I have hearkened to this conceit with extreme delight; <lb></lb>and, but that I believe the making of theſe calculations truly <lb></lb>would be a long and painfull task, and perhaps too hard for me <lb></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></lb>I be certain to finde it ſo readily; therefore we ſhall refer it to an <lb></lb>other time, and for the preſent we will return to our firſt propo <lb></lb>ſal, going on there where we made digreſſion; which, if I well <lb></lb>remember, was about the proving the motion by a right line of no <pb xlink:href="040/01/036.jpg" pagenum="20"></pb>uſe, in the ordinate parts of the World; and we did proceed to <lb></lb>ſay, that it was not ſo in circular motions, of which that which is <lb></lb>made by the moveable in it ſelf, ſtill retains it in the ſame place, <lb></lb><arrow.to.target n="marg50"></arrow.to.target> <lb></lb>and that which carrieth the moveable by the circumference of a <lb></lb>circle about its fixed centre, neither puts it ſelf, nor thoſe about it <lb></lb>in diſorder; for that ſuch a motion primarily is finite and terminate <lb></lb>(though not yet finiſhed and determined) but there is no point <lb></lb><arrow.to.target n="marg51"></arrow.to.target> <lb></lb>in the circumference, that is not the firſt and laſt term in the cir <lb></lb>culation; and continuing it in the circumference aſſigned it, it <lb></lb>leaveth all the reſt, within and without that, free for the uſe of <lb></lb>others, without ever impeding or diſordering them. </s><s>This being <lb></lb>a motion that makes the moveable continually leave, and con <lb></lb><arrow.to.target n="marg52"></arrow.to.target> <lb></lb>tinually arrive at the end; it alone therefore can primarily be u <lb></lb>niform; for that acceleration of motion is made in the moveable, <lb></lb>when it goeth towards the term, to which it hath inclination; <lb></lb>and the retardation happens by the repugnance that it hath to <lb></lb>leave and part from the ſame term; and becauſe in circular mo <lb></lb>tion, the moveable continually leaves the natural term, and con <lb></lb>tinually moveth towards the ſame, therefore, in it, the repug <lb></lb>nance and inclination are always of equal force: from which e <lb></lb>quality reſults a velocity, neither retarded nor accelerated, <emph type="italics"></emph>i. </s><s>e.<emph.end type="italics"></emph.end> an <lb></lb>uniformity in motion. </s><s>From this conformity, and from the being <lb></lb><arrow.to.target n="marg53"></arrow.to.target> <lb></lb>terminate, may follow the perpetual continuation by ſucceſſively <lb></lb>reiterating the circulations; which in an undeterminated line, <lb></lb>and in a motion continually retarded or accelerated, cannot na <lb></lb><arrow.to.target n="marg54"></arrow.to.target> <lb></lb>turally be. </s><s>I ſay, naturally; becauſe the right motion which is <lb></lb>retarded, is the violent, which cannot be perpetual; and the ac <lb></lb>celerate arriveth neceſſarily at the term, if one there be; and if <lb></lb>there be none, it cannot be moved to it, becauſe nature moves <lb></lb>not whether it is impoſſible to attain. </s><s>I conclude therefore, that <lb></lb>the circular motion can onely naturally conſiſt with natural bo <lb></lb>dies, parts of the univerſe, and conſtituted in an excellent diſpo <lb></lb>ſure; and that the right, at the moſt that can be ſaid for it, is <lb></lb><arrow.to.target n="marg55"></arrow.to.target> <lb></lb>aſſigned by nature to its bodies, and their parts, at ſuch time as <lb></lb>they ſhall be out of their proper places, conſtituted in a depraved <lb></lb>diſpoſition, and for that cauſe needing to be redured by the ſhort <lb></lb>eſt way to their natural ſtate. </s><s>Hence, me thinks, it may ratio <lb></lb>nally be concluded, that for maintenance of perfect order among ſt <lb></lb>the parts of the World, it is neceſſary to ſay, that moveables are <lb></lb>moveable onely circularly; and if there be any that move not <lb></lb><arrow.to.target n="marg56"></arrow.to.target> <lb></lb>circularly, theſe of neceſſity are immoveable: there being no <lb></lb>thing but reſt and circular motion apt to the conſervation of or <lb></lb>der. </s><s>And I do not a little wonder with my ſelf, that <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> <lb></lb>who held that the Terreſtrial globe was placed in the centre of <lb></lb>the World, and there remained immoveable, ſhould not ſay, that <pb xlink:href="040/01/037.jpg" pagenum="21"></pb>of natural bodies ſome are moveable by nature, and others immo <lb></lb>veable; eſpecially having before defined Nature, to be the prin <lb></lb>ciple of Motion and Reſt.</s></p><p type="margin"><s><margin.target id="marg50"></margin.target><emph type="italics"></emph>Finite and termi <lb></lb>nate circular mo <lb></lb>tions diſorder not <lb></lb>the parts of the <lb></lb>World.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg51"></margin.target><emph type="italics"></emph>In the circular mo <lb></lb>tion, every point in <lb></lb>the circumference <lb></lb>is the begining and <lb></lb>end.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg52"></margin.target><emph type="italics"></emph>Circular motion <lb></lb>onely is uniform.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg53"></margin.target><emph type="italics"></emph>Circular motion <lb></lb>may be continued <lb></lb>perpetually.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg54"></margin.target><emph type="italics"></emph>Right motion can <lb></lb>not naturally be <lb></lb>perpetual.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg55"></margin.target><emph type="italics"></emph>Right motion aſ <lb></lb>ſigned to natural <lb></lb>bodies, to reduce <lb></lb>them to perfect or <lb></lb>der, when removed <lb></lb>from their places.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg56"></margin.target><emph type="italics"></emph>Reſt onely, and <lb></lb>circular motion are <lb></lb>apt to conſerve or <lb></lb>der.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> though of a very perſpicacious wit, would <lb></lb>not ſtrain it further than needed: holding in all his argumen <lb></lb><arrow.to.target n="marg57"></arrow.to.target> <lb></lb>tations, that ſenſible experiments were to be preferred before <lb></lb>any reaſons founded upon ſtrength of wit, and ſaid thoſe which <lb></lb>ſhould deny the teſtimony of ſenſe deſerved to be puniſhed with <lb></lb><arrow.to.target n="marg58"></arrow.to.target> <lb></lb>the loſs of that ſenſe; now who is ſo blind, that ſees not the <lb></lb>parts of the Earth and Water to move, as being grave, natural <lb></lb>ly downwards, namely, towards the centre of the Univerſe, aſ <lb></lb>ſigned by nature her ſelf for the end and term of right motion <lb></lb><emph type="italics"></emph>deorſùm<emph.end type="italics"></emph.end>; and doth not likewiſe ſee the Fire and Air to move <lb></lb>right upwards towards the Concave of the Lunar Orb, as to the <lb></lb>natural end of motion <emph type="italics"></emph>ſurſùm<emph.end type="italics"></emph.end>? </s><s>And this being ſo manifeſtly ſeen, <lb></lb>and we being certain, that <emph type="italics"></emph>eadem est ratio totius & partium,<emph.end type="italics"></emph.end> why <lb></lb>may we not aſſert it for a true and manifeſt propoſition, that the <lb></lb>natural motion of the Earth is the right motion <emph type="italics"></emph>ad medium,<emph.end type="italics"></emph.end> and <lb></lb>that of the Fire, the right <emph type="italics"></emph>à medio<emph.end type="italics"></emph.end>?</s></p><p type="margin"><s><margin.target id="marg57"></margin.target><emph type="italics"></emph>Senſible experi <lb></lb>ments are to be pre <lb></lb>ferred before hu <lb></lb>mane argument a <lb></lb>tions.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg58"></margin.target><emph type="italics"></emph>He who denies <lb></lb>ſenſe, deſerves to <lb></lb>be deprived of it. <lb></lb></s><s>Senſe ſheweth that <lb></lb>things grave move <lb></lb>to the<emph.end type="italics"></emph.end> medium, <emph type="italics"></emph>and <lb></lb>the light to the <lb></lb>concave.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>The moſt that you can pretend from this your Diſ <lb></lb>courſe, were it granted to be true, is that, like as the parts of the <lb></lb>Earth removed from the whole, namely, from the place where <lb></lb>they naturally reſt, that is in ſhort reduced to a depraved and diſ <lb></lb>ordered diſpoſure, return to their place ſpontaneouſly, and there <lb></lb>fore naturally in a right motion, (it being granted, that <emph type="italics"></emph>eadem <lb></lb>ſit ratio totius & partium<emph.end type="italics"></emph.end>) ſo it may be inferred, that the <lb></lb>Terreſtrial Globe removed violently from the place aſſigned <lb></lb><arrow.to.target n="marg59"></arrow.to.target> <lb></lb>it by nature, it would return by a right line. </s><s>This, as I have <lb></lb>ſaid, is the moſt that can be granted you, and that onely for want <lb></lb>of examination; but he that ſhall with exactneſs reviſe theſe <lb></lb>things, will firſt deny, that the parts of the Earth, in returning to <lb></lb>its whole, move in a right line, and not by a circular or mixt; and <lb></lb>really you would have enough to do to demonſtrate the contra <lb></lb>ry, as you ſhall plainly ſee in the anſwers to the particular reaſons <lb></lb>and experiments alledged by <emph type="italics"></emph>Ptolomey<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ariſtotle.<emph.end type="italics"></emph.end> Secondly, <lb></lb>If another ſhould ſay that the <emph type="italics"></emph>parts<emph.end type="italics"></emph.end> of the Earth, go not in their <lb></lb>motion towards the Centre of the World, but to unite with its <lb></lb><emph type="italics"></emph>Whole,<emph.end type="italics"></emph.end> and that for that reaſon they naturally incline towards the <lb></lb>centre of the Terreſtrial Globe, by which inclination they con <lb></lb>ſpire to form and preſerve it, what other <emph type="italics"></emph>All,<emph.end type="italics"></emph.end> or what other Centre <lb></lb>would you find for the World, to which the whole Terrene <lb></lb><arrow.to.target n="marg60"></arrow.to.target> <lb></lb>Globe, being thence removed, would ſeek to return, that ſo the <lb></lb>reaſon of the <emph type="italics"></emph>Whole<emph.end type="italics"></emph.end> might be like to that of its <emph type="italics"></emph>parts<emph.end type="italics"></emph.end>? </s><s>It may be <lb></lb>added, That neither <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> nor you can ever prove, that the <lb></lb>Earth <emph type="italics"></emph>de facto<emph.end type="italics"></emph.end> is in the centre of the Univerſe; but if any Centre <pb xlink:href="040/01/038.jpg" pagenum="22"></pb><arrow.to.target n="marg61"></arrow.to.target> <lb></lb>may be aſligned to the Univerſe, we ſhall rather find the Sun <lb></lb>placed in it, as by the ſequel you ſhall underſtand.</s></p><p type="margin"><s><margin.target id="marg59"></margin.target><emph type="italics"></emph>It is queſtionable <lb></lb>whether deſcending <lb></lb>weights move in a <lb></lb>right line.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg60"></margin.target><emph type="italics"></emph>The Earth speri <lb></lb>cal by the conſpi <lb></lb>ration of its parts <lb></lb>to its Centre.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg61"></margin.target><emph type="italics"></emph>The Sun more pro <lb></lb>bably in the centre <lb></lb>of the Vniverſe, <lb></lb>than the Earth.<emph.end type="italics"></emph.end></s></p><p type="main"><s>Now, like as from the conſentaneous conſpiration of all the <lb></lb>parts of the Earth to form its whole, doth follow, that they with <lb></lb><arrow.to.target n="marg62"></arrow.to.target> <lb></lb>equal inclination concurr thither from all parts; and to unite <lb></lb>themſelves as much as is poſſible together, they there ſphelically <lb></lb>adapt themſelves; why may we not believe that the Sun, Moon, <lb></lb>and other mundane Bodies, be alſo of a round figure, not by o <lb></lb>ther than a concordant inſtinct, and natural concourſe of all the <lb></lb>parts compoſing them? </s><s>Of which, if any, at any time, by any <lb></lb>violence were ſeparated from the whole, is it not reaſonable to <lb></lb>think, that they would ſpontaneouſly and by natural inſtinct re <lb></lb>turn? </s><s>and in this manner to infer, that the right motion agreeth <lb></lb>with all mundane bodies alike.</s></p><p type="margin"><s><margin.target id="marg62"></margin.target><emph type="italics"></emph>Natural inclina <lb></lb>tion of the parts of <lb></lb>all the globes of <lb></lb>the World to go to <lb></lb>their centre.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. Certainly, if you in this manner deny not onely the <lb></lb>Principles of Sciences, but manifeſt Experience, and the Senſes <lb></lb>themſelves, you can never be convinced or removed from any o <lb></lb>pinion which you once conceit, therefore I will chooſe rather to <lb></lb>be ſilent (for, <emph type="italics"></emph>contra negantes principia non eſt diſputandum<emph.end type="italics"></emph.end>) <lb></lb>than contend with you. </s><s>And inſiſting on the things alledged by <lb></lb>you even now (ſince you queſtion ſo much as whether grave move <lb></lb>ables have a right motion or no) how can you ever rationally de <lb></lb><arrow.to.target n="marg63"></arrow.to.target> <lb></lb>ny, that the parts of the Earth; or, if you will, that ponderous <lb></lb>matters deſcend towards the Centre, with a right motion; when <lb></lb>as, if from a very high Tower, whoſe walls are vcry upright and <lb></lb>perpendicular, you let them fall, they ſhall deſcend gliding and <lb></lb>ſliding by the Tower to the Earth, exactly in that very place <lb></lb>where a plummet would fall, being hanged by a line faſtned above, <lb></lb>juſt there, whence the ſaid weights were let fall? </s><s>is not this a <lb></lb>more than evident argument of the motions being right, and to <lb></lb><arrow.to.target n="marg64"></arrow.to.target> <lb></lb>wards the Centre? </s><s>In the ſecond place you call in doubt, whe <lb></lb>ther the parts of the Earth are moved, as <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> affirms, to <lb></lb>wards the Centre of the World; as if he had not rationally de <lb></lb>monſtrated it by contrary motions, whilſt he thus argueth; The <lb></lb>motion of heavie bodies is contrary to that of the light: but the <lb></lb>motion of the light is manifeſt to be directly upwards, namely, <lb></lb>towards the circumference of the World, therefore the motion of <lb></lb>the heavie is directly towards the Centre of the World: and it <lb></lb><arrow.to.target n="marg65"></arrow.to.target> <lb></lb>happens <emph type="italics"></emph>per accidens,<emph.end type="italics"></emph.end> that it be towards the centre of the Earth, <lb></lb>for that this ſtriveth to be united to that. </s><s>The ſeeking in the <lb></lb>next place, what a part of the Globe of the Sun or Moon would <lb></lb>do, were it ſeparated from its whole, is vanity; becauſe that there <lb></lb><arrow.to.target n="marg66"></arrow.to.target> <lb></lb>by that is ſought, which would be the conſequence of an impoſſi <lb></lb>bility; in regard that, as <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> alſo demonſtrates, the cœleſtial <lb></lb>bodies are impaſſible, impenetrable, and infrangible; ſo that ſuch <pb xlink:href="040/01/039.jpg" pagenum="23"></pb>a caſe can never happen: and though it ſhould, and that the ſe <lb></lb><arrow.to.target n="marg67"></arrow.to.target> <lb></lb>parated part ſhould return to its whole, it would not return as <lb></lb>grave or light, for that the ſame <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> proveth, that the Cœ <lb></lb>leſtial Bodies are neither heavie nor light.</s></p><p type="margin"><s><margin.target id="marg63"></margin.target><emph type="italics"></emph>The right motion <lb></lb>of grave bodies <lb></lb>manifeſt to ſenſe.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg64"></margin.target><emph type="italics"></emph>Arguments of<emph.end type="italics"></emph.end> A <lb></lb>riſtotle, <emph type="italics"></emph>to prove <lb></lb>that grave bodies <lb></lb>move with an in <lb></lb>clination to arrive <lb></lb>at the centre of the <lb></lb>Vniverſe.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg65"></margin.target><emph type="italics"></emph>Heavie bodies <lb></lb>move towards the <lb></lb>centre of the Earth<emph.end type="italics"></emph.end> <lb></lb>per accidens.</s></p><p type="margin"><s><margin.target id="marg66"></margin.target><emph type="italics"></emph>To ſeek what <lb></lb>would follow upon <lb></lb>an impoſſibility, is <lb></lb>folly.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg67"></margin.target><emph type="italics"></emph>Cœleſtial bodies <lb></lb>neither heavie nor <lb></lb>light, according to<emph.end type="italics"></emph.end> <lb></lb>Ariſtotle.</s></p><p type="main"><s>SALV. </s><s>With what reaſon I doubt, whether grave bodies move <lb></lb>by a right and perpendicular line, you ſhall hear, as I ſaid be <lb></lb>fore, when I ſhall examine this particular argument. </s><s>Touching <lb></lb>the ſecond point, I wonder that you ſhould need to diſcover the <lb></lb><emph type="italics"></emph>Paralogiſm<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> being of it ſelf ſo manifeſt; and that <lb></lb>you perceive not, that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſuppoſeth that which is in queſti <lb></lb>on: therefore take notice.</s></p><p type="main"><s>SIMPL. </s><s>Pray <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> ſpeak with more reſpect of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end>: <lb></lb>for who can you ever perſwade, that he who was the firſt, only, <lb></lb>and admirable explainer of the <emph type="italics"></emph>Syllogiſtick<emph.end type="italics"></emph.end> forms of demonſtration, <lb></lb><arrow.to.target n="marg68"></arrow.to.target> <lb></lb>of <emph type="italics"></emph>Elenchs,<emph.end type="italics"></emph.end> of the manner of diſcovering <emph type="italics"></emph>Sophiſms, Paralogiſms,<emph.end type="italics"></emph.end> and <lb></lb>in ſhort, of all the parts of <emph type="italics"></emph>Logick,<emph.end type="italics"></emph.end> ſhould afterwards ſo notoriouſly <lb></lb>equivocate in impoſing that for known, which is in queſtion? </s><s>It <lb></lb>would be better, my Maſters, firſt perfectly to underſtand him, <lb></lb>and then to try, if you have a minde, to oppoſe him.</s></p><p type="margin"><s><margin.target id="marg68"></margin.target>Ariſtotle <emph type="italics"></emph>cannot e <lb></lb>quivocate, being <lb></lb>the inventer of<emph.end type="italics"></emph.end> Lo <lb></lb>gick.</s></p><p type="main"><s>SALV. <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> we are here familiarly diſcourſing among <lb></lb>our ſelves, to inveſtigate ſome truth; I ſhall not be diſpleaſed <lb></lb>that you diſcover my errors; and if I do not follow the mind of <lb></lb><emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> freely reprehend me, and I ſhall take it in good part. <lb></lb></s><s>Onely give me leave to expound my doubts, and to reply ſome <lb></lb>thing to your laſt words, telling you, that <emph type="italics"></emph>Logick,<emph.end type="italics"></emph.end> as it is well <lb></lb>underſtood, is the Organe with which we philoſophate; but as it <lb></lb>may be poſſible, that an Artiſt may be excellent in making Or <lb></lb>gans, but unlearned in playing on them, thus he might be a great <lb></lb>Logician, but unexpert in making uſe of <emph type="italics"></emph>Logick<emph.end type="italics"></emph.end>; like as we have <lb></lb>many that theorically underſtand the whole Art of Poetry, and <lb></lb>yet are unfortunate in compoſing but meer four Verſes; others <lb></lb><arrow.to.target n="marg69"></arrow.to.target> <lb></lb>enjoy all the precepts of <emph type="italics"></emph>Vinci<emph.end type="italics"></emph.end>^{*}, and yet know not how to paint <lb></lb>a Stoole. </s><s>The playing on the Organs is not taught by them who <lb></lb>know how to make Organs, but by him that knows how to play <lb></lb>on them: Poetry is learnt by continual reading of Poets: Limn <lb></lb>ing is learnt by continual painting and deſigning: Demonſtration <lb></lb>from the reading of Books full of demonſtrations, which are the <lb></lb>Mathematical onely, and not the Logical. </s><s>Now returning to our <lb></lb>purpoſe, I ſay, that that which <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſeeth of the motion of <lb></lb>light bodies, is the departing of the Fire from any part of the <lb></lb>Superficies of the Terreſtrial Globe, and directly retreating from <lb></lb>it, mounting upwards; and this indeed is to move towards a <lb></lb>circumference greater than that of the Earth; yea, the ſame <emph type="italics"></emph>A <lb></lb>riſtotle<emph.end type="italics"></emph.end> makes it to move to the concave of the Moon, but that <lb></lb>this circumference is that of the World, or concentrick to it, ſo <pb xlink:href="040/01/040.jpg" pagenum="24"></pb>that to move towards this, is a moving towards that of the World, <lb></lb>that he cannot affirm, unleſs he ſuppoſeth, That the Centre of the <lb></lb><arrow.to.target n="marg70"></arrow.to.target> <lb></lb>Earth, from which we ſee theſe light aſcendent bodies to depart, <lb></lb>be the ſame with the Centre of the World; which is as much as <lb></lb>to ſay, that the terreſtrial Globe is conſtituted in the midſt of the <lb></lb>World: which is yet that of which we were in doubt, and which <lb></lb><emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> intended to prove. </s><s>And do you ſay that this is not a <lb></lb><arrow.to.target n="marg71"></arrow.to.target> <lb></lb>manifeſt <emph type="italics"></emph>Paralogiſm<emph.end type="italics"></emph.end>?</s></p><p type="margin"><s><margin.target id="marg69"></margin.target>* A famous <emph type="italics"></emph>Italian<emph.end type="italics"></emph.end> <lb></lb>Painter.</s></p><p type="margin"><s><margin.target id="marg70"></margin.target><emph type="italics"></emph>Paralogiſm of<emph.end type="italics"></emph.end> A <lb></lb>riſtotle, <emph type="italics"></emph>in proving <lb></lb>the Earth to be in <lb></lb>the Centre of the <lb></lb>World.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg71"></margin.target><emph type="italics"></emph>The Paralogiſme <lb></lb>of<emph.end type="italics"></emph.end> Ariſtotle <emph type="italics"></emph>another <lb></lb>way diſcovered.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>This Argument of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> appeared to me deficient <lb></lb>alſo, and <emph type="italics"></emph>non<emph.end type="italics"></emph.end>-concludent for another reſpect; though it were <lb></lb>granted, that that Circumference, to which the Fire directly mo <lb></lb>veth, be that which includeth the World: for that in a circle, <lb></lb>not onely the centre, but any other point being taken, every move <lb></lb>able which departing thence, ſhall move in a right line, and to <lb></lb>wards any whatſoever part, ſhall without any doubt go towards <lb></lb>the circumference, and continuing the motion, ſhall alſo arrive <lb></lb>thither; ſo that we may truly ſay, that it moveth towards the <lb></lb>circumference: but yet it doth not follow, that that which mo <lb></lb>veth by the ſame line with a contrary motion, would go towards <lb></lb>the centre, unleſs when the point taken were the centre it ſelf, <lb></lb>or that the motion were made by that onely line, which produced <lb></lb>from the point aſſigned, paſſeth thorow the centre. </s><s>So that to <lb></lb>ſay, that Fire moving in a right line, goeth towards the circumfe <lb></lb>rence of the World, therefore the parts of the Earth which by <lb></lb>the ſame lines move with a contrary motion, go towards the cen <lb></lb>tre of the World, concludeth not, unleſs then when it is pre <lb></lb>ſuppoſed, that the lines of the Fire prolonged paſs by the centre <lb></lb>of the World; and becauſe we know certainly of them, that they <lb></lb>paſs by the centre of the Terreſtrial Globe (being perpendicu <lb></lb>lar to its ſuperficies, and not inclined) therefore to conclude, it <lb></lb>muſt be ſuppoſed, that the centre of the Earth is the ſame with <lb></lb>the centre of the World; or at leaſt, that the parts of the Fire <lb></lb>and Earth deſcend not, ſave onely by one ſole line which paſſeth <lb></lb>by the centre of the World. </s><s>Which nevertheleſs is falſe, and re <lb></lb>pugnant to experience, which ſheweth us, that the parts of <lb></lb>Fire, not by one line onely, but by infinite, produced from the <lb></lb>centre of the Earth towards all the parts of the World, aſcend <lb></lb>always by lines perpendicular to the Superficies of the Terreſtri <lb></lb>al Globe.</s></p><p type="main"><s>SALV. </s><s>You do very ingeniouſly lead <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> to the ſame in <lb></lb>convenience, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> ſhewing his manifeſt equivoke; but <lb></lb>withal you add another inconſiſtency. </s><s>We ſee the Earth to be <lb></lb>ſpherical, and therefore are certain that it hath its centre, to which <lb></lb>we ſee all its parts are moved; for ſo we muſt ſay, whilſt their <lb></lb>motions are all perpendicular to the Superficies of the Earth; we <pb xlink:href="040/01/041.jpg" pagenum="25"></pb>mean, that as they move to the centre of the Earth, they move to <lb></lb>their <emph type="italics"></emph>Whole,<emph.end type="italics"></emph.end> and to their Univerſal Mother: and we are ſtill far <lb></lb>ther ſo free, that we will ſuffer our ſelves to be perſwaded, that <lb></lb><arrow.to.target n="marg72"></arrow.to.target> <lb></lb>their natural inſtinct is, not to go towards the centre of the Earth, <lb></lb>but towards that of the Univerſe; which we know not where to <lb></lb>find, or whether it be or no; and were it granted to be, it is but <lb></lb>an imaginary point, and a nothing without any quality. </s><s>As to <lb></lb>what <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> ſaid laſt, that the contending whether the parts <lb></lb>of the Sun, Moon, or other cœleſtial Body, ſeparated from their <lb></lb><emph type="italics"></emph>Whole,<emph.end type="italics"></emph.end> ſhould naturally return to it, is a vanity, for that the caſe <lb></lb>is impoſſible; it being clear by the Demonſtrations of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> <lb></lb>that the cœleſtial Bodies are impaſſible, impenetrable, unparta <lb></lb><arrow.to.target n="marg73"></arrow.to.target> <lb></lb>ble, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> I anſwer, that none of the conditions, whereby <emph type="italics"></emph>Aristo <lb></lb>tle<emph.end type="italics"></emph.end> diſtinguiſheth the Cœleſtial Bodies from Elementary, hath o <lb></lb>ther foundation than what he deduceth from the diverſity of the <lb></lb>natural motion of thoſe and theſe; inſomuch that it being deni <lb></lb>ed, that the circular motion is peculiar to Cœleſtial Bodies, and <lb></lb>affirmed, that it is agreeable to all Bodies naturally moveable, it <lb></lb>is behoofull upon neceſſary conſequence to ſay, either that the <lb></lb>attributes of generable, or ingenerable, alterable, or unalterable, <lb></lb>partable, or unpartable, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> equally and commonly agree with <lb></lb>all worldly bodies, namely, as well to the Cœleſtial as to the E <lb></lb>lementary; or that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> hath badly and erroneouſly dedu <lb></lb>ced thoſe from the circular motion, which he hath aſſigned to Cœ <lb></lb>leſtial Bodies.</s></p><p type="margin"><s><margin.target id="marg72"></margin.target><emph type="italics"></emph>Grave bodies may <lb></lb>more rationally be <lb></lb>affirmed to tend to <lb></lb>the Centre of the <lb></lb>Earth, than of the <lb></lb>Vniverſe.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg73"></margin.target><emph type="italics"></emph>The conditions and <lb></lb>attributes which <lb></lb>differ the cœleſtial <lb></lb>bodies from Ele <lb></lb>mentary, depend on <lb></lb>the motions aſſign <lb></lb>ed them by<emph.end type="italics"></emph.end> Ariſt.</s></p><p type="main"><s>SIMPL. </s><s>This manner of argumentation tends to the ſubverſi <lb></lb>on of all Natural Philoſophy, and to the diſorder and ſubverſion <lb></lb>of Heaven and Earth, and the whole Univerſe; but I believe the <lb></lb>Fundamentals of the <emph type="italics"></emph>Peripateticks<emph.end type="italics"></emph.end> are ſuch, that we need not <lb></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></lb>neither fear their ſubverſion, or the ruine of Philoſophy. </s><s>As to <lb></lb>Heaven, your fears are vain for that which you your ſelf hold <lb></lb>unalterable and impaſſible; as for the Earth, we ſtrive to enoble <lb></lb>and perfect it, whilſt we make it like to the Cœleſtial Bodies, <lb></lb>and as it were place it in Heaven, whence your Philoſophers have <lb></lb>exiled it. </s><s>Philoſophy it ſelf cannot but receive benefit from our <lb></lb><arrow.to.target n="marg74"></arrow.to.target> <lb></lb>Diſputes, for if our conceptions prove true, new Diſcoveries will <lb></lb>be made; if falſe, the firſt Doctrine will be more confirmed. <lb></lb></s><s>Rather beſtow your care upon ſome Philoſophers, and help and <lb></lb>defend them; for as to the Science it ſelf, it cannot but improve. <lb></lb></s><s>And that we may return to our purpoſe, be pleaſed freely to pro <lb></lb>duce what preſents it ſelf to you in confirmation of that great dif <lb></lb>ference which <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> puts between the Cœleſtial Bodies, and <lb></lb>the Elementary parts of the World, in making thoſe ingenerable, <pb xlink:href="040/01/042.jpg" pagenum="26"></pb>incorruptible, unalterable, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> and this corruptible, alterable, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg74"></margin.target><emph type="italics"></emph>The diſputes and <lb></lb>contradictions of <lb></lb>Philoſophers may <lb></lb>conduce to the <lb></lb>benefit of Philoſo <lb></lb>phy.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>I ſee not yet any need that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> hath of help, <lb></lb>ſtanding as he doth ſtoutly and ſtrongly on his feet; yea not be <lb></lb>ing yet aſſaulted, much leſs foiled by you. </s><s>And what ward will <lb></lb>you chooſe in this combate for this firſt blow? <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> writeth, <lb></lb><arrow.to.target n="marg75"></arrow.to.target> <lb></lb>that whatever is generated, is made out of a contrary in ſome <lb></lb>ſubject, and likewiſe is corrupted in ſome certain ſubject from a <lb></lb><arrow.to.target n="marg76"></arrow.to.target> <lb></lb>contrary into a contrary; ſo that (obſerve) corruption and ge <lb></lb>neration is never but onely in contraries; If therefore to a Cœ <lb></lb>leſtial Body no contrary can be aſſigned, for that to the circular <lb></lb><arrow.to.target n="marg77"></arrow.to.target> <lb></lb>motion no other motion is contrary, then Nature hath done very <lb></lb>well to make that exempt from contraries, which was to be in <lb></lb>generable and incorruptible, This fundamental firſt confirmed, <lb></lb>it immediately followeth of conſequence, that it is inaugmenta <lb></lb>ble, inalterable, impaſſible, and finally eternal, and a propor <lb></lb><arrow.to.target n="marg78"></arrow.to.target> <lb></lb>tionate habitation to the immortal Deities, conformable to the <lb></lb>opinion even of all men that have any conceit of the Gods. </s><s>He <lb></lb><arrow.to.target n="marg79"></arrow.to.target> <lb></lb>afterwards confirmeth the ſame by ſenſe; in regard, that in all <lb></lb>times paſt, according to memory or tradition, we ſee nothing re <lb></lb>moved, according to the whole outward Heaven, nor any of its <lb></lb><arrow.to.target n="marg80"></arrow.to.target> <lb></lb>proper parts. </s><s>Next, as to the circular motion, that no other is <lb></lb>contrary to it, <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> proveth many ways; but without reci <lb></lb>ting them all, it is ſufficiently demonſtrated, ſince fimple motions <lb></lb>are but three, to the <emph type="italics"></emph>medium,<emph.end type="italics"></emph.end> from the <emph type="italics"></emph>medium,<emph.end type="italics"></emph.end> and about the <lb></lb><emph type="italics"></emph>medium,<emph.end type="italics"></emph.end> of which the two right, <emph type="italics"></emph>ſurſum<emph.end type="italics"></emph.end> and <emph type="italics"></emph>deorſum,<emph.end type="italics"></emph.end> are mani <lb></lb>feſtly contrary; and becauſe one onely hath onely one for con <lb></lb>trary, therefore there reſts no other motion which may be contra <lb></lb>ry to the circular. </s><s>You ſee the ſubtle and moſt concluding diſ <lb></lb>courſe of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> whereby he proveth the incorruptibility of <lb></lb>Heaven.</s></p><p type="margin"><s><margin.target id="marg75"></margin.target>Ariſtotles <emph type="italics"></emph>diſcourſe <lb></lb>to prove the incor <lb></lb>ruptibility of Hea <lb></lb>ven.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg76"></margin.target><emph type="italics"></emph>Generation & cor <lb></lb>ruption is onely a <lb></lb>mongſt contraries, <lb></lb>according to<emph.end type="italics"></emph.end> Ariſt.</s></p><p type="margin"><s><margin.target id="marg77"></margin.target><emph type="italics"></emph>To the circular <lb></lb>motion no other <lb></lb>motion is contrary.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg78"></margin.target><emph type="italics"></emph>Heaven an habi <lb></lb>tation for the imm <lb></lb>ortal Gods.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg79"></margin.target><emph type="italics"></emph>Immutability of <lb></lb>Heaven evident to <lb></lb>ſexſe.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg80"></margin.target><emph type="italics"></emph>He proveth that <lb></lb>the circular motion <lb></lb>hath no contrary.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>This is nothing more, ſave the pure progreſs of <emph type="italics"></emph>Ariſto <lb></lb>tle,<emph.end type="italics"></emph.end> by me hinted before; wherein, beſides that I affirm, that the <lb></lb>motion which you attribute to the Cœleſtial Bodies agreeth alſo <lb></lb>to the Earth, its illation proves nothing. </s><s>I tell you therefore, <lb></lb>that that circular motion which you aſſign to Cœleſtial Bodies, <lb></lb>ſuiteth alſo to the Earth, from which, ſuppoſing that the reſt of <lb></lb>your diſcourſe were concludent, will follow one of theſe three <lb></lb>things, as I told you a little before, and ſhall repeat; namely, <lb></lb>either that the Earth it ſelf is alſo ingenerable, and incorruptible, <lb></lb>as the Cœleſtial bodies; or that the Cœleſtial bodies are, like as <lb></lb>the Elementary generable, alterable &c. </s><s>or that this difference of <lb></lb>motion hath nothing to do with Generation and Corruption. <lb></lb></s><s>The diſcourſe of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> and yours alſo contain many Propoſi <lb></lb>tions not to be lightly admitted, and the better to examine them, <lb></lb>it will be convenient to reduce them to the moſt abſtracted and <pb xlink:href="040/01/043.jpg" pagenum="27"></pb>diſtinct that can be poſſible; and excuſe me <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> if haply <lb></lb>with ſome tediouſneſs you hear me oft repeat the ſame things, <lb></lb>and fancie that you ſee me reaſſume my argument in the pub <lb></lb>lick circle of Diſputations. </s><s>You ſay Generation and Corrupti <lb></lb>on are onely made where there are contraries; contraries <lb></lb>are onely amongſt ſimple natural bodies, moveable with contrary <lb></lb>motions; contrary motions are onely thoſe which are made by <lb></lb>a right line between contrary terms; and theſe are onely two, <lb></lb>that is to ſay, from the <emph type="italics"></emph>medium,<emph.end type="italics"></emph.end> and towards the <emph type="italics"></emph>medium<emph.end type="italics"></emph.end>; and <lb></lb>ſuch motions belong to no other natural bodies, but to the <emph type="italics"></emph>Earth,<emph.end type="italics"></emph.end> <lb></lb>the <emph type="italics"></emph>Fire,<emph.end type="italics"></emph.end> and the other two Elements: therefore Generation <lb></lb>and Corruption is onely amongſt the Elements. </s><s>And becauſe <lb></lb>the third ſimple motion, namely, the circular about the <emph type="italics"></emph>medium,<emph.end type="italics"></emph.end> <lb></lb>hath no contrary, (for that the other two are contraries, and one <lb></lb>onely, hath but onely one contrary) therefore that natural body <lb></lb>with which ſuch motion agreeth, wants a contrary; and having <lb></lb>no contrary is ingenerable and incorruptible, &c. </s><s>Becauſe where <lb></lb>there is no contrariety, there is no generation or corruption, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> <lb></lb>But ſuch motion agreeth onely with the Cœleſtial bodies; there <lb></lb><arrow.to.target n="marg81"></arrow.to.target> <lb></lb>fore onely theſe are ingenerable, incorruptible, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> And to <lb></lb>begin, I think it a more eaſie thing, and ſooner done to reſolve, <lb></lb>whether the Earth (a moſt vaſt Body, and for its vicinity to us, <lb></lb>moſt tractable) moveth with a ſpeedy motion, ſuch as its revo <lb></lb>lution about its own axis in twenty four hours would be, than it <lb></lb>is to underſtand and reſolve, whether Generation and Corruption <lb></lb>ariſeth from contrariety, or elſe whether there be ſuch things as <lb></lb>generation, corruption and contrariety in nature. </s><s>And if you, <lb></lb><emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> can tell me what method Nature obſerves in working, <lb></lb>when ſhe in a very ſhort time begets an infinite number of flies <lb></lb>from a little vapour of the Muſt of wine, and can ſhew me which <lb></lb>are there the contraries you ſpeak of, what it is that corrupteth, <lb></lb>and how; I ſhould think you would do more than I can; for I <lb></lb>profeſs I cannot comprehend theſe things. </s><s>Beſides, I would ve <lb></lb>ry gladly underſtand how, and why theſe corruptive contraries are <lb></lb>ſo favourable to Daws, and ſo cruel to Doves; ſo indulgent to <lb></lb>Stags, and ſo haſty to Horſes, that they do grant to them many <lb></lb>more years of life, that is, of incorruptibility, than weeks to theſe. <lb></lb></s><s>Peaches and Olives are planted in the ſame ſoil, expoſed to the <lb></lb>ſame heat and cold, to the ſame wind and rains, and, in a word, <lb></lb>to the ſame contrarieties; and yet thoſe decay in a ſhort time, <lb></lb>and theſe live many hundred years. </s><s>Furthermore, I never was <lb></lb>thorowly ſatisfied about this ſubſtantial tranſmutation (ſtill keep <lb></lb>ing within pure natural bounds) whereby a matter becometh ſo <lb></lb>transform'd, that it ſhould be neceſſarily ſaid to be deſtroy'd, ſo <lb></lb>that nothing remaineth of its firſt being, and that another body <pb xlink:href="040/01/044.jpg" pagenum="28"></pb><arrow.to.target n="marg82"></arrow.to.target> <lb></lb>quite differing there-from ſhould be thence produced; and if I <lb></lb>fancy to my ſelf a body under one aſpect, and by and by under <lb></lb>another very different, I cannot think it impoſſible but that it may <lb></lb>happen by a ſimple tranſpoſition of parts, without corrupting or <lb></lb>ingendring any thing a-new; for we ſee ſuch kinds of Metamor <lb></lb>phoſes dayly: ſo that to return to my purpoſe, I anſwer you, <lb></lb>that inaſmuch as you go about to perſwade me that the Earth can <lb></lb>not move circularly by way of corruptibility and generability, <lb></lb>you have undertook a much harder task than I, that with argu <lb></lb>ments more difficult indeed, but no leſs concluding, will prove <lb></lb>the contrary.</s></p><p type="margin"><s><margin.target id="marg81"></margin.target><emph type="italics"></emph>Its eaſier to prove <lb></lb>the Earth to move, <lb></lb>than that corrupti <lb></lb>on is made by con <lb></lb>traries.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg82"></margin.target><emph type="italics"></emph>Bare tranſpoſition <lb></lb>of parts may repre <lb></lb>ſent bodies under <lb></lb>diverſe asp cts.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Pardon me, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> if I interrupt your diſcourſe, <lb></lb>which, as it delights me much, for that I alſo am gravel'd with <lb></lb>the ſame doubts; ſo I fear that you can never conclude the ſame, <lb></lb>without altogether digreſſing from your chief deſign: therefore <lb></lb>if it be permitted to proceed in our firſt argument, I ſhould think <lb></lb>that it were convenient to remit this queſtion of generation and <lb></lb>corruption to another diſtinct and ſingle conference; as alſo, if <lb></lb>it ſhall pleaſe you and <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> we may do by other particular <lb></lb>queſtions which may fall in the way of our diſcourſe; which I <lb></lb>will keep in my mind to propoſe, and exactly diſcuſs them ſome <lb></lb>other time. </s><s>Now as for the preſent, ſince you ſay, that if <emph type="italics"></emph>Ari <lb></lb>ſtotle<emph.end type="italics"></emph.end> deny circular motion to the Earth in common with other <lb></lb>bodies Cœleſtial, it chence will follow, that the ſame which be <lb></lb>falleth the Earth, as to its being generable, alterable, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> will <lb></lb>hold alſo of Heaven, let us enquire no further if there be ſuch <lb></lb>things in nature, as generation and corruption, or not; but let <lb></lb>us return to enquire what the Globe of the Earth doth.</s></p><p type="main"><s>SIMPL. </s><s>I cannot ſuffer my ears to hear it queſtion'd, whether <lb></lb>generation and corruption be in <emph type="italics"></emph>rerum naturà,<emph.end type="italics"></emph.end> it being a thing <lb></lb>which we have continually before our eyes, and whereof <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg83"></arrow.to.target> <lb></lb>hath written two whole Books. </s><s>But if you go about to deny the <lb></lb>Principles of Sciences, and queſtion things moſt manifeſt, who <lb></lb>knows not, but that you may prove what you will, and maintain <lb></lb>any <emph type="italics"></emph>Paradox<emph.end type="italics"></emph.end>? </s><s>And if you do not dayly ſee herbs, plants, ani <lb></lb>mals to generate and corrupt, what is it that you do ſee? </s><s>Alſo, <lb></lb>do you not continually behold contrarieties contend together, <lb></lb>and the Earth change into Water, the Water turn to Air, the <lb></lb>Air into Fire, and again the Air to condenſe into Clouds, Rains, <lb></lb>Hails and Storms?</s></p><p type="margin"><s><margin.target id="marg83"></margin.target><emph type="italics"></emph>By denying Prin <lb></lb>ciples in the Scien <lb></lb>ces, any Paradox <lb></lb>may be maintain <lb></lb>ed.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. Yes, we ſee theſe things indeed, and therefore will <lb></lb>grant you the diſcourſe of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> as to this part of generation <lb></lb>and corruption made by contraries; but if I ſhall conclude by <lb></lb>virtue of the ſame propoſitions which are granted to <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> <lb></lb>that the Cœleſtial bodies themſelves are alſo generable and cor <pb xlink:href="040/01/045.jpg" pagenum="29"></pb>ruptible, aſwell as the Elementary, what will you ſay then?</s></p><p type="main"><s>SIMPL. </s><s>I will ſay you have done that which is impoſſible to <lb></lb>be done.</s></p><p type="main"><s>SAGR. </s><s>Go to; tell me, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> are not theſe affections <lb></lb>contrary to one another?</s></p><p type="main"><s>SIMPL. Which?</s></p><p type="main"><s>SAGR. </s><s>Why theſe; Alterable, unalterable; paſſible, ^{*} impaſ <lb></lb><arrow.to.target n="marg84"></arrow.to.target> <lb></lb>ſible; generable, ingenerable; corruptible, incorruptible?</s></p><p type="margin"><s><margin.target id="marg84"></margin.target>* <emph type="italics"></emph>Or,<emph.end type="italics"></emph.end> Impatible.</s></p><p type="main"><s>SIMPL. </s><s>They are moſt contrary.</s></p><p type="main"><s>SAGR. </s><s>Well then, if this be true, and it be alſo granted, <lb></lb>that Cœleſtial Bodies are ingenerable and incorruptible; I prove <lb></lb>that of neceſſity Cœleſtial Bodies muſt be generable and corru <lb></lb>ptible.</s></p><p type="main"><s>SIMPL. </s><s>This muſt needs be a <emph type="italics"></emph>Sophiſm.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Hear my Argument, and then cenſure and reſolve it. <lb></lb><arrow.to.target n="marg85"></arrow.to.target> <lb></lb>Cœleſtial Bodies, for that they are ingenerable and incorruptible, <lb></lb>have in Nature their contraries, which are thoſe Bodies that be <lb></lb>generable and corruptible; but where there is contrariety, there <lb></lb>is alſo generation and corruption; therefore Cœleſtial Bodies are <lb></lb>generable and corruptible.</s></p><p type="margin"><s><margin.target id="marg85"></margin.target><emph type="italics"></emph>Cœlestial Bodies <lb></lb>are generable and <lb></lb>corruptible, be <lb></lb>cauſe they are in <lb></lb>generable and in <lb></lb>corruptible.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>Did I not ſay it could be no other than a <emph type="italics"></emph>Sophiſm<emph.end type="italics"></emph.end>? <lb></lb></s><s>This is one of thoſe forked Arguments called <emph type="italics"></emph>Soritæ<emph.end type="italics"></emph.end>: like that <lb></lb><arrow.to.target n="marg86"></arrow.to.target> <lb></lb>of the <emph type="italics"></emph>Cretan,<emph.end type="italics"></emph.end> who ſaid that all <emph type="italics"></emph>Cretans<emph.end type="italics"></emph.end> were lyars; but he as <lb></lb>being a <emph type="italics"></emph>Cretan,<emph.end type="italics"></emph.end> had told a lye, in ſaying that the <emph type="italics"></emph>Cretans<emph.end type="italics"></emph.end> were ly <lb></lb>ars; it followed therefore, that the <emph type="italics"></emph>Cretans<emph.end type="italics"></emph.end> were no lyars, and <lb></lb>conſequently that he, as being a <emph type="italics"></emph>Cretan,<emph.end type="italics"></emph.end> had ſpoke truth: And <lb></lb>yet in ſaying the <emph type="italics"></emph>Cretans<emph.end type="italics"></emph.end> were lyars, he had ſaid true, and com <lb></lb>prehending himſelf as a <emph type="italics"></emph>Cretan,<emph.end type="italics"></emph.end> he muſt conſequently be a lyar. <lb></lb></s><s>And thus in theſe kinds of <emph type="italics"></emph>Sophiſms<emph.end type="italics"></emph.end> a man may dwell to eternity, <lb></lb>and never come to any concluſion.</s></p><p type="margin"><s><margin.target id="marg86"></margin.target><emph type="italics"></emph>The forked Syllo <lb></lb>giſm cal'd<emph.end type="italics"></emph.end> <foreign lang="grc">Ξωρίτης.</foreign></s></p><p type="main"><s>SAGR. </s><s>You have hitherto cenſured it, it remaineth now that <lb></lb>you anſwer it, ſhewing the fallacie.</s></p><p type="main"><s>SIMPL. </s><s>As to the reſolving of it, and finding out its fallacie, <lb></lb>do you not in the firſt place ſee a manifeſt contradiction in it? <lb></lb></s><s>Cœleſtial Bodies are ingenerable and incorruptible; <emph type="italics"></emph>Ergo,<emph.end type="italics"></emph.end> Cœle <lb></lb>ſtial Bodies are generable and corruptible. </s><s>And again, the con <lb></lb><arrow.to.target n="marg87"></arrow.to.target> <lb></lb>trariety is not betwixt the Cœleſtial Bodies, but betwixt the E <lb></lb>lements, which have the contrariety of the Motions, <emph type="italics"></emph>ſurſùm<emph.end type="italics"></emph.end> and <lb></lb><emph type="italics"></emph>deorſùm,<emph.end type="italics"></emph.end> and of levity and gravity; But the Heavens which move <lb></lb>circularly, to which motion no other motion is contrary, want <lb></lb>contrariety, and therefore they are incorruptible.</s></p><p type="margin"><s><margin.target id="marg87"></margin.target><emph type="italics"></emph>Amongſt Cœleſtial <lb></lb>Bodies there is no <lb></lb>contrariety.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Fair and ſoftly, <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end>; this contrariety whereby <lb></lb>you ſay ſome ſimple Bodies become corruptible, reſides it in the <lb></lb>ſame Body which is corrupted, or elſe hath it relation to ſome o <lb></lb>other? </s><s>I ſay, for example, the humidity by which a piece of Earth <pb xlink:href="040/01/046.jpg" pagenum="30"></pb>is corrupted, reſides it in the ſame Earth or in ſome other bodie, <lb></lb>which muſt either be the Air or Water? </s><s>I believe you will grant, <lb></lb>that like as the Motions upwards and downwards, and gravity <lb></lb>and levity, which you make the firſt contraries, cannot be in the <lb></lb>ſame Subject, ſo neither can moiſt and dry, hot and cold: you <lb></lb>muſt therefore conſequently acknowledg that when a bodie cor <lb></lb><arrow.to.target n="marg88"></arrow.to.target> <lb></lb>rupteth, it is occaſioned by ſome quality reſiding in another con <lb></lb>trary to its own: therefore to make the Cœleſtial Body become <lb></lb>corruptible, it ſufficeth that there are in Nature, bodies that have <lb></lb>a contrariety to that Cœleſtial body; and ſuch are the Elements, <lb></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"></emph>Contraries which <lb></lb>are the cauſes of <lb></lb>corruption, reſide <lb></lb>not in the ſame bo <lb></lb>dy that corrupteth.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>This ſufficeth not, Sir; The Elements alter and cor <lb></lb>rupt, becauſe they are intermixed, and are joyn'd to one another, <lb></lb><arrow.to.target n="marg89"></arrow.to.target> <lb></lb>and ſo may exerciſe their contrariety; but Cœleſtial bodies are <lb></lb>ſeparated from the Elements, by which they are not ſo much as <lb></lb>toucht, though indeed they have an influence upon the Elements. <lb></lb></s><s>It is requiſite, if you will prove generation and corruption in Cœ <lb></lb>leſtial bodies, that you ſhew, that there reſides contrarieties be <lb></lb>tween them.</s></p><p type="margin"><s><margin.target id="marg89"></margin.target><emph type="italics"></emph>Cœleſtial Bodies <lb></lb>touch, but are not <lb></lb>touched by the E <lb></lb>lements.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>See how I will find thoſe contrarieties between them. <lb></lb></s><s>The firſt fountain from whence you derive the contrariety of the <lb></lb>Elements, is the contrariety of their motions upwards and down <lb></lb>wards: it therefore is neceſſary that thoſe Principles be in like <lb></lb><arrow.to.target n="marg90"></arrow.to.target> <lb></lb>manner contraries to each other, upon which thoſe motions de <lb></lb>pend. </s><s>and becauſe that is moveable upwards by lightneſs, <lb></lb>and this downwards by gravitv, it is neceſſary that lightneſs and <lb></lb>gravity are contrary to each other: no leſs are we to believe thoſe <lb></lb>other Principles to be contraries, which are the cauſes that this is <lb></lb>heavy, and that light: but by your own confeſſion, levity and <lb></lb>gravity follow as conſequents of rarity and denſity; therefore <lb></lb><arrow.to.target n="marg91"></arrow.to.target> <lb></lb>rarity and denſity ſhall be contraries: the which conditions or <lb></lb>affections are ſo amply found in Cœleſtial bodies, that you e <lb></lb>ſteem the ſtars to be onely more denſe parts of their Heaven: <lb></lb>and if this be ſo, it followeth that the denſity of the ſtars exceeds <lb></lb>that of the reſt of Heaven, by almoſt infinite degrees: <lb></lb>which is manifeſt, in that Heaven is infinitely tranſparent, and <lb></lb>the ſtars extremely opacous; and for that there are there above <lb></lb>no other qualities, but more and leſs denſity and rarity, which <lb></lb>may be cauſes of the greater or leſs tranſparency. </s><s>There being <lb></lb>then ſuch contrariety between the Cœleftial bodies, it is neceſſary <lb></lb>that they alſo be generable and corruptible, in the ſame manner <lb></lb>as the Elementary bodies are; or elſe that contrariety is not the <lb></lb><arrow.to.target n="marg92"></arrow.to.target> <lb></lb>cauſe of corruptibility, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg90"></margin.target><emph type="italics"></emph>Gravity & levity, <lb></lb>varity and denſity, <lb></lb>are contrary qua <lb></lb>lities.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg91"></margin.target><emph type="italics"></emph>The ſtars infinitely <lb></lb>ſurpaſs the ſub <lb></lb>ſtance of the reſt of <lb></lb>Heaven in denſity.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg92"></margin.target><emph type="italics"></emph>Rarity & denſity <lb></lb>in Cœleſtial bodies, <lb></lb>is different from <lb></lb>the rarity & den <lb></lb>ſity of the elements.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>There is no neceſſity either of one or the other, for <lb></lb>that denſity and rarity in Cœleſtial bodies, are not contraries to <pb xlink:href="040/01/047.jpg" pagenum="31"></pb>each other, as in Elementary bodies; for that they depend not <lb></lb>on the primary qualities, cold and heat, which are contraries; but <lb></lb>on the more or leſs matter in proportion to quantity: now much <lb></lb>and little, ſpeak onely a relative oppoſition, that is, the leaſt of <lb></lb>oppoſitions, and which hath nothing to do with generation and <lb></lb>corruption.</s></p><p type="main"><s>SAGR. </s><s>Therefore affirming, that denſity and rarity, which a <lb></lb>mongſt the Elements ſhould be the cauſe of gravity and levity, <lb></lb>which may be the cauſes of contrary motions <emph type="italics"></emph>ſurſùm<emph.end type="italics"></emph.end> and <emph type="italics"></emph>deor <lb></lb>ſùm,<emph.end type="italics"></emph.end> on which, again, dependeth the contrarieties for generation <lb></lb>and corruption; it ſufficeth not that they be thoſe denſneſſes and <lb></lb>rareneſſes which under the ſame quantity, or (if you will) maſs <lb></lb>contain much or little matter, but it is neceſſary that they be denſ <lb></lb>neſſes and rareneſſes cauſed by the primary qualities, hot and <lb></lb>cold, otherwiſe they would operate nothing at all: but if this be <lb></lb>ſo, <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> hath deceived us, for that he ſhould have told it us at <lb></lb><arrow.to.target n="marg93"></arrow.to.target> <lb></lb>firſt, and ſo have left written that thoſe ſimple bodies are gene <lb></lb>rable and corruptible, that are moveable with ſimple motions <lb></lb>upwards and downwards, dependent on levity and gravity, cau <lb></lb>ſed by rarity and denſity, made by much or little matter, by <lb></lb>reaſon of heat and cold; and not to have ſtaid at the ſimple mo <lb></lb>tion <emph type="italics"></emph>ſurſùm<emph.end type="italics"></emph.end> and <emph type="italics"></emph>deorſùm<emph.end type="italics"></emph.end>: for I aſſure you that to the making <lb></lb>of bodies heavy or light, whereby they come to be moved with <lb></lb>contrary motions, any kind of denſity and rarity ſufficeth, whe <lb></lb>ther it proceed from heat and cold, or what elſe you pleaſe; for <lb></lb>heat and cold have nothing to do in this affair: and you ſhall <lb></lb>upon experiment find, that a red hot iron, which you muſt grant <lb></lb>to have heat, weigheth as much, and moves in the ſame manner <lb></lb>as when it is cold. </s><s>But to overpaſs this alſo, how know you but <lb></lb>that Cœleſtial rarity and denſity depend on heat and cold?</s></p><p type="margin"><s><margin.target id="marg93"></margin.target>Ariſtotle <emph type="italics"></emph>defective <lb></lb>in aſſigning the <lb></lb>cauſes why the ele <lb></lb>ments are genera <lb></lb>ble & corruptible.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>I know it, becauſe thoſe qualities are not amongſt <lb></lb>Cœleſtial bodies, which are neither hot nor cold.</s></p><p type="main"><s>SALV. </s><s>I ſee we are again going about to engulph our ſelves in <lb></lb>a bottomleſs ocean, where there is no getting to ſhore; for this <lb></lb>is a Navigation without Compaſs, Stars, Oars or Rudder: ſo that <lb></lb>it will follow either that we be forced to paſs from Shelf to Shelf, <lb></lb>or run on ground, or to ſail continually in danger of being loſt. <lb></lb></s><s>Therefore, if according to your advice we ſhall proceed in our <lb></lb>main deſign, we muſt of neceſſity for the preſent overpaſs this <lb></lb>general conſideration, whether direct motion be neceſſary in Na <lb></lb>ture, and agree with ſome bodies; and come to the particular <lb></lb>demonſtrations, obſervations and experiments; propounding in <lb></lb>the firſt place all thoſe that have been hitherto alledged by <emph type="italics"></emph>Ari <lb></lb>ſtotle, Ptolomey,<emph.end type="italics"></emph.end> and others, to prove the ſtability of the Earth, en <lb></lb>deavouring in the next place to anſwer them: and producing in <pb xlink:href="040/01/048.jpg" pagenum="32"></pb>the laſt place, thoſe, by which others may be perſwaded, that the <lb></lb>Earth is no leſs than the Moon, or any other Planet to be num <lb></lb>bered amongſt natural bodies that move circularly.</s></p><p type="main"><s>SAGR. </s><s>I ſhall the more willingly incline to this, in that I am <lb></lb>better ſatisfied with your Architectonical and general diſcourſe, <lb></lb>than with that of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> for yours convinceth me without the <lb></lb>leaſt ſcruple, and the other at every ſtep croſſeth my way with <lb></lb>ſome block. </s><s>And I ſee no reaſon why <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> ſhould not be <lb></lb>preſently ſatisfied with the Argument you alledg, to prove that <lb></lb>there can be no ſuch thing in nature as a motion by a right line, <lb></lb>if we do but preſuppoſe that the parts of the Univerſe are diſpo <lb></lb>ſed in an excellent conſtitution and perfect order.</s></p><p type="main"><s>SALV. </s><s>Stay a little, good <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> for juſt now a way comes <lb></lb>into my mind, how I may give <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> ſatisfaction, provided <lb></lb>that he will not be ſo ſtrictly wedded to every expreſſion of <emph type="italics"></emph>A <lb></lb>riſtotle,<emph.end type="italics"></emph.end> as to hold it hereſie to recede in any thing from him. </s><s>Nor <lb></lb>is there any queſtion to be made, but that if we grant the excel <lb></lb>lent diſpoſition and perfect order of the parts of the Univerſe, <lb></lb>as to local ſcituation, that then there is no other but the circular <lb></lb>motion, and reſt; for as to the motion by a right line, I ſee not <lb></lb>how it can be of uſe for any thing, but to reduce to their natural <lb></lb>conſtitution, ſome integral bodies, that by ſome accident were re <lb></lb>mov'd and ſeparated from their whole, as we ſaid above.</s></p><p type="main"><s>Let us now conſider the whole Terreſtrial Globe, and enquire <lb></lb>the beſt we can, whether it, and the other Mundane bodies are to <lb></lb>conſerve themſelves in their perfect and natural diſpoſition. </s><s>It <lb></lb>is neceſſary to ſay, either that it reſts and keeps perpetually im <lb></lb>moveable in its place; or elſe that continuing always in its place, <lb></lb>it revolves in its ſelf; or that it turneth about a Centre, moving <lb></lb><arrow.to.target n="marg94"></arrow.to.target> <lb></lb>by the circumference of a circle. </s><s>Of which accidents, both <emph type="italics"></emph>Ari <lb></lb>ſtotle<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ptolomey,<emph.end type="italics"></emph.end> and all their followers ſay, that it hath ever <lb></lb>obſerved, and ſhall continually keep the firſt, that is, a perpetual <lb></lb><arrow.to.target n="marg95"></arrow.to.target> <lb></lb>reſt in the ſame place. </s><s>Now, why, I pray you, ought they not <lb></lb>to have ſaid, that its natural affection is to reſt immoveable, ra <lb></lb>ther than to make natural unto it the motion ^{*} downwards, with <lb></lb>which motion it never did or ſhall move? </s><s>And as to the motion <lb></lb><arrow.to.target n="marg96"></arrow.to.target> <lb></lb>by a right line, they muſt grant us that Nature maketh uſe of it <lb></lb>to reduce the ſmall parts of the Earth, Water, Air, Fire, and every <lb></lb>other integral Mundane body to their <emph type="italics"></emph>Whole,<emph.end type="italics"></emph.end> when any of them <lb></lb>by chance are ſeparated, and ſo tranſported out of their proper <lb></lb>place; if alſo haply, ſome circular motion might not be found <lb></lb>to be more convenient to make this reſtitution. </s><s>In my judg <lb></lb>ment, this primary poſition anſwers much better, even according <lb></lb>to <emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> own method, to all the other conſequences, than <lb></lb>to attribute the ſtraight motion to be an intrinſick and natural <pb xlink:href="040/01/049.jpg" pagenum="33"></pb>principle of the Elements. </s><s>Which is manifeſt, for that if I aske <lb></lb>the <emph type="italics"></emph>Peripatetick,<emph.end type="italics"></emph.end> if, being of opinion that Cœleſtial bodies are <lb></lb>incorruptibe and eternal, he believeth that the Terreſtial Globe <lb></lb>is not ſo, but corruptible and mortal, ſo that there ſhall come a <lb></lb>time, when the Sun and Moon and other Stars, continuing their <lb></lb>beings and operations, the Earth ſhall not be found in the <lb></lb>World, but ſhall with the reſt of the Elements be deſtroyed <lb></lb>and annihilated, I am certain that he would anſwer me, no: <lb></lb><arrow.to.target n="marg97"></arrow.to.target> <lb></lb>therefore generation and corruption is in the parts and not in the <lb></lb>whole; and in the parts very ſmall and ſuperficial, which are, <lb></lb>as it were, incenſible in compariſon of the whole maſſe. </s><s>And <lb></lb>becauſe <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> deduceth generation and corruption from the <lb></lb>contrariety of ſtreight motions, let us remit ſuch motions to the <lb></lb>parts, which onely change and decay, and to the whole Globe <lb></lb>and Sphere of the Elements, let us aſcribe either the circular mo <lb></lb>tion, or a perpetual conſiſtance in its proper place: the only <lb></lb>affections apt for perpetuation, and maintaining of perfect order. <lb></lb></s><s>This which is ſpoken of the Earth, may be ſaid with the ſame <lb></lb>reaſon of Fire, and of the greateſt part of the Air; to which <lb></lb><arrow.to.target n="marg98"></arrow.to.target> <lb></lb>Elements, the <emph type="italics"></emph>Peripateticks<emph.end type="italics"></emph.end> are forced to aſcribe for intrinſical <lb></lb>and natural, a motion wherewith they were never yet moved, <lb></lb>nor never ſhall be; and to call that motion preternatural to them, <lb></lb>wherewith, if they move at all, they do and ever ſhall move. <lb></lb></s><s>This I ſay, becauſe they aſſign to the Air aud Fire the motion <lb></lb>upwards, wherewith thoſe Elements were never moved, but <lb></lb>only ſome parts of them, and thoſe were ſo moved onely in or <lb></lb>der to the recovery of their perfect conſtitution, when they were <lb></lb>out of their natural places; and on the contrary they call the <lb></lb>circular motion preternatural to them, though they are thereby <lb></lb>inceſſantly moved: forgeting, as it ſeemeth, what <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> oft in <lb></lb>culcateth, that nothing violent can be permanent.</s></p><p type="margin"><s><margin.target id="marg94"></margin.target>Ariſt. <emph type="italics"></emph>&<emph.end type="italics"></emph.end> Ptolomey <lb></lb><emph type="italics"></emph>make the Terre <lb></lb>strial Globe immo <lb></lb>veable.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg95"></margin.target><emph type="italics"></emph>It is better to ſay, <lb></lb>that the Terreſtri <lb></lb>al Globe naturally <lb></lb>resteth, than that <lb></lb>it moveth directly <lb></lb>downwards.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg96"></margin.target>*The word is, <emph type="italics"></emph>all' <lb></lb>ingiù,<emph.end type="italics"></emph.end> which the <lb></lb>Latine verſion ren <lb></lb>dreth <emph type="italics"></emph>ſurſùm,<emph.end type="italics"></emph.end> <lb></lb>which is quite con <lb></lb>trary to the Au <lb></lb>thors ſenſe.</s></p><p type="margin"><s><margin.target id="marg97"></margin.target><emph type="italics"></emph>Right Motion <lb></lb>with more reaſon <lb></lb>attributed to the <lb></lb>parts, than to the <lb></lb>whole Elements.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg98"></margin.target><emph type="italics"></emph>The Peripateticks <lb></lb>improperly aſſign <lb></lb>thoſe motious to <lb></lb>the Elements for <lb></lb>Natural, with <lb></lb>which they never <lb></lb>were moved, and <lb></lb>thoſe for Preter <lb></lb>natural with which <lb></lb>they alwayes are <lb></lb>moved.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>To all theſe we have very pertinent anſwers, which <lb></lb><arrow.to.target n="marg99"></arrow.to.target> <lb></lb>I for this time omit, that we may come to the more particular <lb></lb>reaſons, and ſenſible experiments, which ought in concluſion to <lb></lb>be oppoſed, as <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſaitn well, to whatever humane reaſon <lb></lb>can preſent us with.</s></p><p type="margin"><s><margin.target id="marg99"></margin.target><emph type="italics"></emph>Senſible experi <lb></lb>ments to be prefer <lb></lb>red to humane <lb></lb>Arguments.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>What hath been ſpoken hitherto, ſerves to clear up <lb></lb>unto us which of the two general diſcourſes carrieth with it moſt <lb></lb>of probability, I mean that of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> which would perſwade <lb></lb>us, that the ſublunary bodies are by nature generable, and corru <lb></lb>ptible, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> and therefore moſt different from the eſſence of Cœ <lb></lb>leftial bodies, which are impaſſible, ingenerable, incorruptible, <lb></lb><emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> drawn from the diverſity of ſimple motions; or elſe this of <lb></lb><emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> who ſuppoſing the integral parts of the World to be <lb></lb>diſpoſed in a perfect conſtitution, excludes by neceſſary confe <pb xlink:href="040/01/050.jpg" pagenum="34"></pb>quence the right or ſtraight motion of ſimple natural bodies, as <lb></lb>being of no uſe in nature, and eſteems the Earth it ſelf alſo to <lb></lb>be one of the Cœleſtial bodies adorn'd with all the prerogatives <lb></lb>that agree with them; which laſt diſcourſe is hitherto much <lb></lb>more likely, in my judgment, than that other. </s><s>Therefore re <lb></lb>ſolve, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> to produce all the particular reaſons, experi <lb></lb>ments and obſervations, as well Natural as Aſtronomical, that <lb></lb>may ſerve to perſwade us that the Earth differeth from the Cœ <lb></lb>leſtial bodies, is immoveable, and ſituated in the Centre of the <lb></lb>World, and what ever elſe excludes its moving like to the Planets, <lb></lb>as <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> or the <emph type="italics"></emph>Moon, &c.<emph.end type="italics"></emph.end> And <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> will be pleaſed to <lb></lb>be ſo civil as to anſwer to them one by one.</s></p><p type="main"><s>SIMPL. </s><s>See here for a beginning, two moſt convincing Argu <lb></lb>ments to demonſtrate the Earth to be moſt different from the <lb></lb>Cœleſtial bodies. </s><s>Firſt, the bodies that are generable, corru <lb></lb>ptible, alterable, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> are quite different from thoſe that are in <lb></lb>generable, incorruptible, unalterable, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> But the Earth is ge <lb></lb>nerable, corruptible, alterable, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> and the Cœleſtial bodies in <lb></lb>generable, incorruptible, unalterable, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> Therefore the Earth <lb></lb>is quite different from the Cœleſtial bodies.</s></p><p type="main"><s>SAGR. </s><s>By your firſt Argument you ſpread the Table with the <lb></lb>ſame Viands, which but juſt now with much adoe were voided.</s></p><p type="main"><s>SIMPL. </s><s>Hold a little, Sir, and take the reſt along with you, <lb></lb>and then tell me if this be not different from what you had be <lb></lb>fore. </s><s>In the former, the <emph type="italics"></emph>Minor<emph.end type="italics"></emph.end> was proved <emph type="italics"></emph>à priori,<emph.end type="italics"></emph.end> & now you ſee <lb></lb>it proved <emph type="italics"></emph>à poſteriori:<emph.end type="italics"></emph.end> Judg then if it be the ſame. </s><s>I prove the <lb></lb><emph type="italics"></emph>Minor,<emph.end type="italics"></emph.end> therefore (the <emph type="italics"></emph>Major<emph.end type="italics"></emph.end> being moſt manifeſt) by ſenſible ex <lb></lb>perience, which ſhews us that in the Earth there are made conti <lb></lb>nual generations, corruptions, alterations, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> which neither our <lb></lb>ſenſes, nor the traditions or memories of our Anceſtors, ever ſaw <lb></lb>an inſtance of in Heaven; therefore Heaven is unalterable, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg100"></arrow.to.target> <lb></lb>and the Earth alterable, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> and therefore different from Hea <lb></lb>ven. </s><s>I take my ſecond Argument from a principal and eſſential <lb></lb>accident, and it is this. </s><s>That body which is by its nature ob <lb></lb><arrow.to.target n="marg101"></arrow.to.target> <lb></lb>ſcure and deprived of light, is divers from the luminous and ſhi <lb></lb>ning bodies; but the Earth is obſcure and void of light, and the <lb></lb>Cœleſtial bodies ſplendid, and full of light; <emph type="italics"></emph>Ergo, &c.<emph.end type="italics"></emph.end> Anſwer <lb></lb>to theſe Arguments firſt, that we may not heap up too many, <lb></lb>and then I will alledge others.</s></p><p type="margin"><s><margin.target id="marg100"></margin.target><emph type="italics"></emph>Heaven immuta <lb></lb>ble, becauſe there <lb></lb>never was any mu <lb></lb>tation ſeen in it.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg101"></margin.target><emph type="italics"></emph>Bodies naturally <lb></lb>lucid, are different <lb></lb>from thoſe which <lb></lb>are by nature ob <lb></lb>ſcure.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>As to the firſt, the ſtreſſe whereof you lay upon ex <lb></lb>perience, I deſire that you would a little more diſtinctly produce <lb></lb>me the alteration which you ſee made in the Earth, and not in <lb></lb>Heaven; upon which you call the Earth alterable, and the Hea <lb></lb>vens not ſo.</s></p><p type="main"><s>SIMPL. </s><s>I ſee in the Earth, plants and animals continually ge <pb xlink:href="040/01/051.jpg" pagenum="35"></pb>nerating and decaying; winds, rains, tempeſts, ſtorms ariſing; and <lb></lb>in a word, the aſpect of the Earth to be perpetually metamorpho <lb></lb>ſing; none of which mutations are to be diſcern'd in the Cœleſtial <lb></lb>bodies; the conſtitution and figuration of which is moſt punctu <lb></lb>ally conformable to that they ever were time out of mind; without <lb></lb>the generation of any thing that is new, or corruption of any thing <lb></lb>that was old.</s></p><p type="main"><s>SALV. </s><s>But if you content your ſelf with theſe viſible, or to <lb></lb>ſay better, ſeen experiments, you muſt conſequently account <lb></lb><emph type="italics"></emph>China<emph.end type="italics"></emph.end> and <emph type="italics"></emph>America<emph.end type="italics"></emph.end> Cœleſtial bodies, for doubtleſſe you never <lb></lb>beheld in them theſe alterations which you ſee here in <emph type="italics"></emph>Italy,<emph.end type="italics"></emph.end> and <lb></lb>that therefore according to your apprehenſion they are inal <lb></lb>terable.</s></p><p type="main"><s>SIMPL. </s><s>Though I never did ſee theſe alterations ſenfibly in <lb></lb>thoſe places, the relations of them are not to be queſtioned; <lb></lb>beſides that, <emph type="italics"></emph>cum eadem ſit ratio totius, & partium,<emph.end type="italics"></emph.end> thoſe <lb></lb>Countreys being a part of the Earth, as well as ours, they <lb></lb>muſt of neceſſity be alterable as theſe are.</s></p><p type="main"><s>SALV. </s><s>And why have you not, without being put to believe <lb></lb>other mens relations, examined and obſerved thoſe alterations <lb></lb>with your own eyes?</s></p><p type="main"><s>SIMPL. </s><s>Becauſe thoſe places, beſides that they are not ex <lb></lb>poſed to our eyes, are ſo remote, that our ſight cannot reach <lb></lb>to comprehend therein ſuch like mutations.</s></p><p type="main"><s>SALV. </s><s>See now, how you have unawares diſcovered the falla <lb></lb>cy of your Argument; for, if you ſay that the alterations that <lb></lb>are ſeen on the Earth neer at hand, cannot, by reaſon of the too <lb></lb>great diſtance, be ſeen in <emph type="italics"></emph>America,<emph.end type="italics"></emph.end> much leſſe can you ſee them <lb></lb>in the Moon, which is ſo many hundred times more remote: <lb></lb>And if you believe the alterations in <emph type="italics"></emph>Mexico<emph.end type="italics"></emph.end> upon the report of <lb></lb>thoſe that come from thence, what intelligence have you from <lb></lb>the Moon, to aſſure you that there is no ſuch alterations in it? <lb></lb></s><s>Therefore, from your not ſeeing any alterations in Heaven, <lb></lb>whereas, if there were any ſuch, you could not ſee them by rea <lb></lb>ſon of their too great diſtance, and from your not having intel <lb></lb>ligence thereof, in regard that it cannot be had, you ought not <lb></lb>to argue, that there are no ſuch alterations; howbeit, from the <lb></lb>ſeeing and obſerving of them on Earth, you well argue that <lb></lb>therein ſuch there are.</s></p><p type="main"><s>SIMPL. </s><s>I will ſhew ſo great mutations that have befaln on <lb></lb>the Earth; that if any ſuch had happened in the Moon, they <lb></lb>might very well have been obſerved here below. </s><s>We find in <lb></lb><arrow.to.target n="marg102"></arrow.to.target> <lb></lb>very antient records, that heretofore at the Streights of <emph type="italics"></emph>Gibraltar,<emph.end type="italics"></emph.end> <lb></lb>the two great Mountains <emph type="italics"></emph>Abila,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Calpen,<emph.end type="italics"></emph.end> were continued to <lb></lb>gether by certain other leſſe Mountains which there gave check <pb xlink:href="040/01/052.jpg" pagenum="36"></pb>to the Ocean: but thoſe Hills, being by ſome cauſe or other ſe <lb></lb>parated, and a way being opened to the Sea to break in, it made <lb></lb>ſuch an inundation, that it gave occaſion to the calling of it ſince <lb></lb>the Mid-land Sea: the greatneſs whereof conſidered, and the di <lb></lb>vers aſpect the ſurface of the Water and Earth then made, had it <lb></lb>been beheld afar off, there is no doubt but ſo great a change <lb></lb>might have been diſcerned by one that was then in the Moon; <lb></lb>as alſo to us inhabitants of the Earth, the like alterations would <lb></lb>be perceived in the Moon; but we find not in antiquity, that e <lb></lb>ver there was ſuch a thing ſeen; therefore we have no cauſe to <lb></lb>ſay, that any of the Cœleſtial bodies are alterable, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg102"></margin.target><emph type="italics"></emph>The Mediterr ani <lb></lb>an Sea made by the <lb></lb>ſeparation of<emph.end type="italics"></emph.end> Abi <lb></lb>la <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Calpen.</s></p><p type="main"><s>SALV. </s><s>That ſo great alterations have hapned in the Moon, I <lb></lb>dare not ſay, but for all that, I am not yet certain but that ſuch <lb></lb>changes might occur; and becauſe ſuch a mutation could onely <lb></lb>repreſent unto us ſome kind of variation between the more clear, <lb></lb>and more obſcure parts of the Moon, I know not whether we <lb></lb>have had on Earth obſervant Selenographers, who have for any <lb></lb>conſiderable number of years, inſtructed us with ſo exact Seleno <lb></lb>graphy, as that we ſhould confidently conclude, that there hath <lb></lb>no ſuch change hapned in the face of the Moon; of the figura <lb></lb>tion of which I find no more particular deſcription, than the ſay <lb></lb>ing of ſome, that it repreſents an humane face; of others, that <lb></lb>it is like the muzzle of a lyon; and of others, that it is <emph type="italics"></emph>Cain<emph.end type="italics"></emph.end> with <lb></lb>a bundle of thorns on his back: therefore, to ſay Heaven is un <lb></lb>alterable, becauſe that in the Moon, or other Cœleſtial bodies, no <lb></lb>ſuch alterations are ſeen, as diſcover themſelves on Earth, is a bad <lb></lb>illation, and concludeth nothing.</s></p><p type="main"><s>SAGR. </s><s>And there is another odd kind of ſcruple in this Argu <lb></lb>ment of <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> running in my mind, which I would gladly <lb></lb>have anſwered; therefore I demand of him, whether the Earth <lb></lb>before the Mediterranian inundation was generable and corrupti <lb></lb>ble, or elſe began then ſo to be?</s></p><p type="main"><s>SIMPL. </s><s>It was doubtleſs generable and corruptible alſo be <lb></lb>fore that time; but that was ſo vaſt a mutation, that it might <lb></lb>have been obſerved as far as the Moon.</s></p><p type="main"><s>SAGR. </s><s>Go to; if the Earth was generable and corruptible <lb></lb>before that Inundation, why may not the Moon be ſo like <lb></lb>wiſe without ſuch a change? </s><s>Or why ſhould that be neceſſary <lb></lb>in the Moon, which importeth nothing on Earth?</s></p><p type="main"><s>SALV. </s><s>It is a ſhrewd queſtion: But I am doubtfull that <emph type="italics"></emph>Sim <lb></lb>plicius<emph.end type="italics"></emph.end> a little altereth the Text of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> and the other <emph type="italics"></emph>Peri <lb></lb>patelicks,<emph.end type="italics"></emph.end> who ſay, they hold the Heavens unalterable, for that <lb></lb>they ſee therein no one ſtar generate or corrupt, which is proba <lb></lb>bly a leſs part of Heaven, than a City is of the Earth, and yet <lb></lb>innumerable of theſe have been deſtroyed, ſo as that no mark of <lb></lb>them hath remain'd.</s></p> <pb xlink:href="040/01/053.jpg" pagenum="37"></pb><p type="main"><s>SAGR. </s><s>I verily believed otherwiſe, and conceited that <emph type="italics"></emph>Sim <lb></lb>plicius<emph.end type="italics"></emph.end> diſſembled this expoſition of the Text, that he might not <lb></lb>charge his Maſter and Conſectators, with a notion more abſurd <lb></lb>than the former. </s><s>And what a folly it is to ſay the Cœleſtial <lb></lb>part is unalterable, becauſe no ſtars do generate or corrupt there <lb></lb>in? </s><s>What then? </s><s>hath any ſeen a Terreſtrial Globe corrupt, and <lb></lb>another regenerate in its place? </s><s>And yet is it not on all hands <lb></lb>granted by Philoſophers, that there are very few ſtars in Heaven <lb></lb>leſs than the Earth, but very many that are much bigger? </s><s>So <lb></lb><arrow.to.target n="marg103"></arrow.to.target> <lb></lb>that for a ſtar in Heaven to corrupt, would be no leſs than if the <lb></lb>whole Terreſtrial Globe ſhould be deſtroy'd. </s><s>Therefore, if for <lb></lb>the true proof of generation and corruption in the Univerſe, it be <lb></lb>neceſſary that ſo vaſt bodies as a ſtar, muſt corrupt and regene <lb></lb>rate, you may ſatisfie your ſelf and ceaſe your opinion; for I <lb></lb>aſſure you, that you ſhall never ſee the Terreſtrial Globe or any <lb></lb>other integral body of the World, to corrupt or decay ſo, that <lb></lb>having been beheld by us for ſo many years paſt, they ſhould ſo <lb></lb>diſſolve, as not to leave any footſteps of them.</s></p><p type="margin"><s><margin.target id="marg103"></margin.target><emph type="italics"></emph>Its no leſs impoſſi <lb></lb>ble for a ſtar to <lb></lb>corrupt, than for <lb></lb>the whole Terre <lb></lb>ſtrial Globe.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>But to give <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> yet fuller ſatisfaction, and to <lb></lb>reclaim him, if poſſible, from his error; I affirm, that we have in <lb></lb><arrow.to.target n="marg104"></arrow.to.target> <lb></lb>our age new accidents and obſervations, and ſuch, that I queſtion <lb></lb>not in the leaſt, but if <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> were now alive, they would make <lb></lb>him change his opinion; which may be eaſily collected from the <lb></lb>very manner of his diſcourſing: For when he writeth that he e <lb></lb>ſteemeth the Heavens inalterable, &c. </s><s>becauſe no new thing was <lb></lb>ſeen to be begot therein, or any old to be diſſolved, he ſeems im <lb></lb>plicitely to hint unto us, that when he ſhould ſee any ſuch acci <lb></lb>dent, he would hold the contrary; and confront, as indeed it is <lb></lb>meet, ſenſible experiments to natural reaſon: for had he not <lb></lb>made any reckoning of the ſenſes, he would not then from the <lb></lb>not ſeeing of any ſenſible mutation, have argued immutability.</s></p><p type="margin"><s><margin.target id="marg104"></margin.target>Ariſtotle <emph type="italics"></emph>would <lb></lb>change his opinion, <lb></lb>did he ſee the no <lb></lb>velties of our age.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> deduceth his principal Argument <emph type="italics"></emph>à priori,<emph.end type="italics"></emph.end> <lb></lb>ſhewing the neceſſity of the inalterability of Heaven by natural, <lb></lb>manifeſt and clear principles; and then ſtabliſheth the ſame <emph type="italics"></emph>à po <lb></lb>ſteriori,<emph.end type="italics"></emph.end> by ſenſe, and the traditions of the antients.</s></p><p type="main"><s>SALV. </s><s>This you ſpeak of is the Method he hath obſerved in <lb></lb>delivering his Doctrine, but I do not bethink it yet to be that <lb></lb>wherewith he invented it; for I do believe for certain, that he <lb></lb>firſt procured by help of the ſenſes, ſuch experiments and obſer <lb></lb>vations as he could, to aſſure him as much as it was poſſible, of the <lb></lb><arrow.to.target n="marg105"></arrow.to.target> <lb></lb>concluſion, and that he afterwards ſought out the means how to <lb></lb>demonſtrate it: For this, the uſual courſe in demonſtrative Scien <lb></lb>ces, and the reaſon thereof is, becauſe when the concluſion is <lb></lb>true, by help of reſolutive Method, one may hit upon ſome pro <lb></lb>poſition before demonſtrated, or come to ſome principle known <pb xlink:href="040/01/054.jpg" pagenum="38"></pb><emph type="italics"></emph>per ſe<emph.end type="italics"></emph.end>; but if the concluſion be falſe, a man may proceed <emph type="italics"></emph>in in <lb></lb>finitum,<emph.end type="italics"></emph.end> and never meet with any truth already known; but ve <lb></lb>ry oft he ſhall meet with ſome impoſſibility or manifeſt abſurdi <lb></lb><arrow.to.target n="marg106"></arrow.to.target> <lb></lb>ty. </s><s>Nor need you queſtion but that <emph type="italics"></emph>Pythagoras<emph.end type="italics"></emph.end> along time be <lb></lb>fore he found the demonſtration for which he offered the Heca <lb></lb>tomb, had been certain, that the ſquare of the ſide ſubtending <lb></lb>the right angle in a rectangle triangle, was equal to the ſquare of <lb></lb>the other two ſides: and the certainty of the concluſion condu <lb></lb>ced not a little to the inveſtigating of the demonſtration, un <lb></lb>derſtanding me alwayes to mean in demonſtrative Sciences. </s><s>But <lb></lb>what ever was the method of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> and whether his arguing <emph type="italics"></emph>à <lb></lb>priori<emph.end type="italics"></emph.end> preceded ſenſe <emph type="italics"></emph>à poſteriori,<emph.end type="italics"></emph.end> or the contrary; it ſufficeth that <lb></lb>the ſame <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> preferreth (as hath been oft ſaid) ſenſible ex <lb></lb>periments before all diſcourſes; beſides, as to the Arugments <emph type="italics"></emph>à <lb></lb>priori<emph.end type="italics"></emph.end> their force hath been already examined. </s><s>Now returning <lb></lb>to my purpoſed matter, I ſay, that the things in our times diſ <lb></lb>covered in the Heavens, are, and have been ſuch, that they may <lb></lb>give abſolute ſatisfaction to all Philoſophers; foraſmuch as in <lb></lb>the particular bodies, and in the univerſal expanſion of Heaven, <lb></lb>there have been, and are continually, ſeen juſt ſuch accidents as <lb></lb>we call generations and corruptions, being that excellent A <lb></lb>ſtronomers have obſerved many Comets generated and diſſolved <lb></lb>in parts higher than the Lunar Orb, beſides the two new Stars, <lb></lb><arrow.to.target n="marg107"></arrow.to.target> <lb></lb><emph type="italics"></emph>Anuo<emph.end type="italics"></emph.end> 1572, and <emph type="italics"></emph>Anno<emph.end type="italics"></emph.end> 1604, without contradiction much higher <lb></lb>than all the Planets; and in the face of the Sun it ſelf, by help <lb></lb><arrow.to.target n="marg108"></arrow.to.target> <lb></lb>of the <emph type="italics"></emph>Teleſcope,<emph.end type="italics"></emph.end> certain denſe and obſcure ſubſtances, in ſem <lb></lb>blance very like to the foggs about the Earth, are ſeen to be <lb></lb>produced and diſſolved; and many of theſe are ſo vaſt, that <lb></lb>they far exceed not only the Mediterranian Streight, but all <lb></lb><arrow.to.target n="marg109"></arrow.to.target> <lb></lb><emph type="italics"></emph>Affrica<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Aſia<emph.end type="italics"></emph.end> alſo. </s><s>Now if <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> had ſeen theſe things, <lb></lb>what think you he would have ſaid, and done <emph type="italics"></emph>Simplicius?<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg105"></margin.target><emph type="italics"></emph>The certaixty of <lb></lb>the concluſion hel <lb></lb>peth by areſolutive <lb></lb>method to ſind the <lb></lb>demonstration.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg106"></margin.target>Pythagoras <emph type="italics"></emph>offered <lb></lb>an Hecatomb for <lb></lb>a Geometrical de <lb></lb>monſtration which <lb></lb>he found.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg107"></margin.target><emph type="italics"></emph>New ſtars diſco <lb></lb>vered in Heaven.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg108"></margin.target><emph type="italics"></emph>Spots generate and <lb></lb>diſſolve in the face <lb></lb>of the Sun.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg109"></margin.target><emph type="italics"></emph>Solar spots are <lb></lb>bigger than all<emph.end type="italics"></emph.end> A <lb></lb>ſia <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Affrick.</s></p><p type="main"><s>SIMPL. </s><s>I know not what <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> would have done or ſaid, <lb></lb>that was the great Maſter of all the Sciences, but yet I know in <lb></lb>part, what his Sectators do and ſay, and ought to do and ſay, <lb></lb>unleſſe they would deprive themſelves of their guide, leader, and <lb></lb>Prince in Philoſophy. </s><s>As to the Comets, are not thoſe Modern <lb></lb>Aſtronomers, who would make them Cœleſtial, convinced by <lb></lb><arrow.to.target n="marg110"></arrow.to.target> <lb></lb>the ^{*}<emph type="italics"></emph>Anti-Tycho,<emph.end type="italics"></emph.end> yea, and overcome with their own weapons, I <lb></lb>mean by way of Paralaxes and Calculations, every way tryed, <lb></lb>concluding at the laſt in favour of <emph type="italics"></emph>Aristotle,<emph.end type="italics"></emph.end> that they are all <lb></lb>Elementary? </s><s>And this being overthrown, which was as it were <lb></lb>their foundation, have theſe Novelliſts any thing more where <lb></lb>with to maintain their aſſertion?</s></p><p type="margin"><s><margin.target id="marg110"></margin.target>* <emph type="italics"></emph>Aſtronomers con <lb></lb>futed by<emph.end type="italics"></emph.end> Anti-Ty <lb></lb>cho.</s></p><p type="main"><s>SALV. </s><s>Hold a little, good <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> this modern Author, <lb></lb>what ſaith he to the new Stars, <emph type="italics"></emph>Anno<emph.end type="italics"></emph.end> 1572, and 1604, and to <pb xlink:href="040/01/055.jpg" pagenum="39"></pb>the Solar ſpots? </s><s>for as to the Comets, I for my own particular <lb></lb>little care to make them generated under or above the Moon; <lb></lb>nor did I ever put much ſtreſſe on the loquacity of <emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end>; nor <lb></lb>am I hard to believe that their matter is Elementary, and that <lb></lb>they may elevate (ſublimate) themſelves at their pleaſure, with <lb></lb>out meeting with any obſtacle from the impenetrability of the <lb></lb><emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> Heaven, which I hold to be far more thin, yielding, <lb></lb>and ſubtil than our Air; and as to the calculations of the Pa <lb></lb>rallaxes, firſt, the uncertainty whether Comets are ſubject to <lb></lb>ſuch accidents, and next, the inconſtancy of the obſervations, <lb></lb>upon which the computations are made, make me equally ſuſ <lb></lb>pect both thoſe opinions: and the rather, for that I ſee him <lb></lb><arrow.to.target n="marg111"></arrow.to.target> <lb></lb>you call <emph type="italics"></emph>Anti-Tycho,<emph.end type="italics"></emph.end> ſometimes ſtretch to his purpoſe, or elſe <lb></lb>reject thoſe obſervations which interfere with his deſign.</s></p><p type="margin"><s><margin.target id="marg111"></margin.target>Anti-Tycho <emph type="italics"></emph>wre <lb></lb>ſteth Aſtronomical <lb></lb>obſervations to his <lb></lb>own parpoſe.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>As to the new Stars, <emph type="italics"></emph>Anti-Tycho<emph.end type="italics"></emph.end> extricates himſelf <lb></lb>finely in three or four words; ſaying, That thoſe mo <lb></lb>dern new Stars are no certain parts of the Cœleſtial bodies, and <lb></lb>that the adverſaries, if they will prove alteration and genera <lb></lb>tion in thoſe ſuperior bodies, muſt ſhew ſome mutations that <lb></lb>have been made in the Stars deſcribed ſo many ages paſt, of <lb></lb>which there is no doubt but that they be Cœleſtial bodies, <lb></lb>which they can never be able to do: Next, as to thoſe mat <lb></lb>ters which ſome affirm, to generate and diſſipate in the face of <lb></lb>the Sun, he makes no mention thereof; wherefore I conclude, <lb></lb>that he believed them fictious, or the illuſions of the Tube, or <lb></lb>at moſt, ſome petty effecs cauſed by the Air, and in brief, any <lb></lb>thing rather than matters Cœleſtial.</s></p><p type="main"><s>SALV. </s><s>But you, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> what anſwer could you give to <lb></lb>the oppoſition of theſe importunate ſpots which are ſtarted up <lb></lb>to diſturb the Heavens, and more than that, the <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> <lb></lb>Philoſophy? </s><s>It cannot be but that you, who are ſo reſolute a <lb></lb>Champion of it, have found ſome reply or ſolution for the <lb></lb>ſame, of which you ought not to deprive us.</s></p><p type="main"><s>SIMPL. </s><s>I have heard ſundry opinions about this particular. <lb></lb></s><s>One ſaith: “They are Stars which in their proper Orbs, like as <lb></lb><arrow.to.target n="marg112"></arrow.to.target> <lb></lb><emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Mervury,<emph.end type="italics"></emph.end> revolve about the Sun, and in paſſing un <lb></lb>der it, repreſent themſelves to us obſcure; and for that they <lb></lb>are many, they oft happen to aggregate their parts together, <lb></lb>and afterwards ſeperate again. </s><s>Others believe them to be <lb></lb>aerial impreſſions; others, the illuſions of the chryſtals; and o <lb></lb>thers, other things: But I incline to think, yea am verily per <lb></lb>ſwaded, That they are an aggregate of many ſeveral opacous <lb></lb>bodies, as it were caſually concurrent among themſelves. </s><s>And <lb></lb>therefore we often ſee, that in one of thoſe ſpots one may <lb></lb>number ten or more ſuch ſmall bodies, which are of irregu <pb xlink:href="040/01/056.jpg" pagenum="40"></pb>lar figures, and ſeem to us like flakes of ſnow, or flocks of <lb></lb>wooll, or moaths flying: they vary ſite amongſt themſelves, <lb></lb>and one while ſever, another while meet, and moſt of all be <lb></lb>neath the Sun, about which, as about their Centre, they con <lb></lb>tinually move. </s><s>But yet, muſt we not therefore grant, that <lb></lb>they are generated or diſſolved, but that at ſometimes they are <lb></lb>hid behind the body of the Sun, and at other times, though <lb></lb>remote from it, yet are they not ſeen for the vicinity of the <lb></lb>immeaſurable light of the Sun; in regard that in the eccentrick <lb></lb>Orb of the Sun, there is conſtituted, as it were, an Onion, com <lb></lb>poſed of many folds one within another, each of which, being <lb></lb><arrow.to.target n="marg113"></arrow.to.target> <lb></lb>^{*}ſtudded with certain ſmall ſpots, doth move; and albeit their <lb></lb>motion at firſt ſeemeth inconſtant and irregular, yet neverthe <lb></lb>leſſe, it is ſaid at laſt, to be obſerved that the very ſame ſpots, <lb></lb>as before,” do within a determinate time return again. </s><s>This <lb></lb>ſeemeth to me the fitteſt anſwer that hath been found to aſſigne <lb></lb>a reaſon of that ſame appearance, and withal to maintain the <lb></lb>incorruptability and ingenerability of the Heavens; and if this <lb></lb>doth not ſuffice; there wants not more elevated wits, which will <lb></lb>give you other, more convincing.</s></p><p type="margin"><s><margin.target id="marg112"></margin.target><emph type="italics"></emph>Sundry opinions <lb></lb>touching the Solar <lb></lb>ſpots.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg113"></margin.target>* The Original <lb></lb>ſaith [<emph type="italics"></emph>tempeſtata ſi <lb></lb>muove<emph.end type="italics"></emph.end>] which the <lb></lb>Latine Tranſlati <lb></lb>on, (Miſtaking <lb></lb><emph type="italics"></emph>Tempectata,<emph.end type="italics"></emph.end> aword <lb></lb>in Heraldry, for <lb></lb><emph type="italics"></emph>Tempeſtato,<emph.end type="italics"></emph.end>) ren <lb></lb>dereth [<emph type="italics"></emph>incitata <lb></lb>movetur<emph.end type="italics"></emph.end>] which <lb></lb>ſignifieth a violent <lb></lb>tranſportmeut, as <lb></lb>in a ſtorm, that of <lb></lb>a Ship.</s></p><p type="main"><s>SALV. </s><s>If this of which we diſpute, were ſome point of Law, <lb></lb><arrow.to.target n="marg114"></arrow.to.target> <lb></lb>or other part of the Studies called <emph type="italics"></emph>Humanity,<emph.end type="italics"></emph.end> wherein there is <lb></lb>neither truth nor falſhood, if we will give ſufficient credit to <lb></lb>the acuteneſſe of the wit, readineſſe of anſwers, and the gene <lb></lb>ral practice of Writers, then he who moſt aboundeth in theſe, <lb></lb>makes his reaſon more probable and plauſible; but in Natural <lb></lb>Sciences, the concluſions of which are true and neceſſary, and <lb></lb>wherewith the judgment of men hath nothing to do, one is to <lb></lb>be more cautious how he goeth about to maintain any thing that <lb></lb>is falſe; for a man but of an ordinary wit, if it be his good for <lb></lb>tune to be of the right ſide, may lay a thouſand <emph type="italics"></emph>Demoſthenes<emph.end type="italics"></emph.end> and <lb></lb>a thouſand <emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> at his feet. </s><s>Therefore reject thoſe hopes <lb></lb>and conceits, wherewith you flatter your ſelf, that there can be <lb></lb>any men ſo much more learned, read, and verſed in Authors, <lb></lb>than we, that in deſpite of nature, they ſhould be able to <lb></lb>make that become true, which is falſe. </s><s>And ſeeing that of all <lb></lb>the opinions that have been hitherto alledged touching the eſ <lb></lb>ſence of theſe Solar ſpots, this inſtanced in by you, is in your <lb></lb>judgment the trueſt, it followeth (if this be ſo) that all the reſt <lb></lb>are falſe; and to deliver you from this alſo, which doubtleſſe is a <lb></lb>moſt falſe <emph type="italics"></emph>Chimœra,<emph.end type="italics"></emph.end> over-paſſing infinite other improbabilities <lb></lb>that are therein, I ſhall propoſe againſt it onely two experiments; <lb></lb><arrow.to.target n="marg115"></arrow.to.target> <lb></lb>one is, that many of thoſe ſpots are ſeen to ariſe in the midſt of <lb></lb>the Solar ring, and many likewiſe to diſſolve and vaniſh at a great <lb></lb>diſtance from the circumference of the Sun; a neceſſary Argu <pb xlink:href="040/01/057.jpg" pagenum="41"></pb>ment that they generate and diſſolve; for if without generating <lb></lb>or corrrupting, they ſhould appear there by onely local motion, <lb></lb>they would all be ſeen to enter, and paſs out by the extreme cir <lb></lb><arrow.to.target n="marg116"></arrow.to.target> <lb></lb>cumference. </s><s>The other obſervation to ſuch as are not ſituate in <lb></lb>the loweſt degree of ignorance in Perſpective, by the mutation <lb></lb>of the appearing figures, and by the apparent mutations of the <lb></lb>velocity of motion is neceſſarily concluding, that the ſpots are <lb></lb>contiguous to the body of the Sun, and that touching its ſuperfi <lb></lb>cies, they move either with it or upon it, and that they in no wiſe <lb></lb>move in circles remote from the ſame. </s><s>The motion proves <lb></lb><arrow.to.target n="marg117"></arrow.to.target> <lb></lb>it, which towards the circumference of the Solar Circle, <lb></lb>appeareth very ſlow, and towards the midſt, more ſwift; the fi <lb></lb>gures of the ſpots confirmeth it, which towards the circumference <lb></lb><arrow.to.target n="marg118"></arrow.to.target> <lb></lb>appear exceeding narrow in compariſon of that which they ſeem <lb></lb>to be in the parts nearer the middle; and this becauſe in the <lb></lb>midſt they are ſeen in their full luſter, and as they truly be; and <lb></lb>towards the circumference by reaſon of the convexity of the glo <lb></lb>bous ſuperficies, they ſeem more compreſſ'd: And both theſe <lb></lb>diminutions of figure and motion, to ſuch as know how to obſerve <lb></lb>and calculate them exactly, preciſely anſwer to that which ſhould <lb></lb>appear, the ſpots being contiguous to the Sun, and differ irrecon <lb></lb>cileably from a motion in circles remote, though but for ſmal <lb></lb>intervalls from the body of the Sun; as hath been diffuſely de <lb></lb><arrow.to.target n="marg119"></arrow.to.target> <lb></lb>monſtrated by our ^{*} Friend, in his Letters about the Solar ſpots, <lb></lb>to <emph type="italics"></emph>Marcus Velſerus.<emph.end type="italics"></emph.end> It may be gathered from the ſame muta <lb></lb>tion of figure, that none of them are ſtars, or other bodies of <lb></lb>ſpherical figure; for that amongſt all figures the ſphere never <lb></lb>appeareth compreſſed, nor can ever be repreſented but onely per <lb></lb>fectly round; and thus in caſe any particular ſpot were a round <lb></lb>body, as all the ſtars are held to be, the ſaid roundneſs would as <lb></lb>well appear in the midſt of the Solar ring, as when the ſpot is near <lb></lb>the extreme: whereas, its ſo great compreſſion, and ſhewing its <lb></lb>ſelf ſo ſmall towards the extreme, and contrariwiſe, ſpatious and <lb></lb>large towards the middle, aſſureth us, that theſe ſpots are flat <lb></lb><arrow.to.target n="marg120"></arrow.to.target> <lb></lb>plates of ſmall thickneſs or depth, in compariſon of their length <lb></lb>and breadth. </s><s>Laſtly, whereas you ſay that the ſpots after their <lb></lb>determinate periods are obſerved to return to their former aſpect, <lb></lb>believe it not, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> for he that told you ſo, will deceive <lb></lb>you; and that I ſpeak the truth, you may obſerve them to be hid <lb></lb>in the face of the Sun far from the circumference; nor hath your <lb></lb>Obſervator told you a word of that compreſſion, which neceſſa <lb></lb>rily argueth them to be contiguous to the Sun. </s><s>That which he <lb></lb>tells you of the return of the ſaid ſpots, is nothing elſe but what <lb></lb>is read in the forementioned Letters, namely, that ſome of them <lb></lb>may ſometimes ſo happen that are of ſo long a duration, that <pb xlink:href="040/01/058.jpg" pagenum="42"></pb>they cannot be diſſipated by one ſole converſion about the Sun, <lb></lb>which is accompliſhed in leſs than a moneth.</s></p><p type="margin"><s><margin.target id="marg114"></margin.target><emph type="italics"></emph>In natural Sci <lb></lb>ences, the art of <lb></lb>Oratory is of no <lb></lb>force.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg115"></margin.target><emph type="italics"></emph>An Argument <lb></lb>that neceſſarily <lb></lb>proveth the Solar <lb></lb>ſpots to generate <lb></lb>and diſſolwe.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg116"></margin.target><emph type="italics"></emph>A concluſive de <lb></lb>monſtration, that <lb></lb>the ſpots are conti <lb></lb>guous to the body <lb></lb>of the Sun.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg117"></margin.target><emph type="italics"></emph>The motion of the <lb></lb>spots towards the <lb></lb>circumference of <lb></lb>the Sun appears <lb></lb>ſlow.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg118"></margin.target><emph type="italics"></emph>The figure of the <lb></lb>spots appears nar <lb></lb>row towards the <lb></lb>circumference of <lb></lb>the Suns<emph.end type="italics"></emph.end> diſcus, <emph type="italics"></emph>& <lb></lb>why.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg119"></margin.target>* Under this word <lb></lb><emph type="italics"></emph>Friend,<emph.end type="italics"></emph.end> as alſo that <lb></lb>of <emph type="italics"></emph>Academick, & <lb></lb>Common Friend, <lb></lb>Galilœus<emph.end type="italics"></emph.end> modeſtly <lb></lb>conceals himſelf <lb></lb>throughout theſe <lb></lb>Dialogues.</s></p><p type="margin"><s><margin.target id="marg120"></margin.target><emph type="italics"></emph>The Solar spots <lb></lb>are not ſpherical, <lb></lb>but flat like thin <lb></lb>plates.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. I, for my part, have not made either ſo long, or ſo <lb></lb>exact obſervations, as to enable me to boaſt my ſelf Maſter of the <lb></lb><emph type="italics"></emph>Quod ect<emph.end type="italics"></emph.end> of this matter: but I will more accurately conſider the <lb></lb>ſame, and make tryal my ſelf for my own ſatisfaction, whether I <lb></lb>can reconcile that which experience ſhews us, with that which <lb></lb><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> teacheth us; for it's a certain Maxim, that two Truths <lb></lb>cannot be contrary to one another.</s></p><p type="main"><s>SALV. </s><s>If you would reconcile that which ſenſe ſheweth you, <lb></lb><arrow.to.target n="marg121"></arrow.to.target> <lb></lb>with the ſolider Doctrines of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> you will find no great dif <lb></lb>ficulty in the undertaking; and that ſo it is, doth not <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> <lb></lb>ſay, that one cannot treat confidently of the things of Heaven, <lb></lb>by reaſon of their great remoteneſs?</s></p><p type="margin"><s><margin.target id="marg121"></margin.target><emph type="italics"></emph>One cannot<emph.end type="italics"></emph.end> (<emph type="italics"></emph>ſaith<emph.end type="italics"></emph.end> <lb></lb>Ariſtotle) <emph type="italics"></emph>ſpeak <lb></lb>confidently of Hea <lb></lb>ven, by reaſon of <lb></lb>its great diſtance.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>He expreſly ſaith ſo. <lb></lb><arrow.to.target n="marg122"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg122"></margin.target>Ariſtotle <emph type="italics"></emph>prefers <lb></lb>ſenſe before ratio <lb></lb>cination.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>And doth he not likewiſe affirm, that we ought to pre <lb></lb>fer that which ſenſe demonſtrates, before all Arguments, though <lb></lb>in appearance never ſo well grounded? </s><s>and ſaith he not this <lb></lb>without the leaſt doubt or hæſitation?</s></p><p type="main"><s>SIMPL. </s><s>He doth ſo.</s></p><p type="main"><s>SALV. </s><s>Why then, the ſecond of theſe propoſitions, which are <lb></lb>both the doctrine of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> that ſaith, that ſenſe is to take </s></p><p type="main"><s><arrow.to.target n="marg123"></arrow.to.target> <lb></lb>place of Logick, is a doctrine much more ſolid and undoubted, <lb></lb>than that other which holdeth the Heavens to be unalterable; and <lb></lb>therefore you ſhall argue more <emph type="italics"></emph>Ariſtotelically,<emph.end type="italics"></emph.end> ſaying, the Hea <lb></lb>vens are alterable, for that ſo my ſenſe telleth me, than if you <lb></lb>ſhould ſay, the Heavens are u alterable, for that Logick ſo perſwa <lb></lb>ded <emph type="italics"></emph>Aristotle.<emph.end type="italics"></emph.end> Furthermore, we may diſcourſe of Cœleſtial mat <lb></lb><arrow.to.target n="marg124"></arrow.to.target> <lb></lb>ters much better than <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end>; becauſe, he confeſſing the know <lb></lb>ledg thereof to be difficult to him, by reaſon of their remoteneſs <lb></lb>from the ſenſes, he thereby acknowledgeth, that one to whom <lb></lb>the ſenſes can better repreſent the ſame, may philoſophate upon <lb></lb>them with more certainty. </s><s>Now we by help of the Teleſcope, <lb></lb>are brought thirty or forty times nearer to the Heavens, than ever <lb></lb><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> came; ſo that we may diſcover in them an hundred <lb></lb>things, which he could not ſee, and amongſt the reſt, theſe ſpots <lb></lb>in the Sun, which were to him abſolutely inviſible; therefore <lb></lb>we may diſcourſe of the Heavens and Sun, with more certainty <lb></lb>than <emph type="italics"></emph>Ariſtolte.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg123"></margin.target><emph type="italics"></emph>Its a doctrine more <lb></lb>agreeing with<emph.end type="italics"></emph.end> A <lb></lb>riſtotle, <emph type="italics"></emph>to ſay the <lb></lb>Heavens are alter <lb></lb>able, than that <lb></lb>which affirms <lb></lb>them inalterable.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg124"></margin.target><emph type="italics"></emph>We may by help of <lb></lb>the<emph.end type="italics"></emph.end> Teleſcope <emph type="italics"></emph>diſ <lb></lb>courſe better of cœ <lb></lb>leſtial matters, <lb></lb>than<emph.end type="italics"></emph.end> Ariſtot. <emph type="italics"></emph>him <lb></lb>ſelf.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I ſee into the heart of <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> and know that he is <lb></lb>much moved at the ſtrength of theſe ſo convincing Arguments; <lb></lb>but on the other ſide, when he conſidereth the great authority <lb></lb>which <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> hath won with all men, and remembreth the great <lb></lb>number of famous Interpreters, which have made it their buſineſs <lb></lb>to explain his ſenſe; and ſeeth other Sciences, ſo neceſſary and <pb xlink:href="040/01/059.jpg" pagenum="43"></pb>profitable to the publick, to build a great part of their eſteem <lb></lb>and reputation on the credit of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> he is much puzzled and <lb></lb>perplexed: and methinks I hear him ſay, To whom then ſhould <lb></lb><arrow.to.target n="marg125"></arrow.to.target> <lb></lb>we repair for the deciſion of our controverſies, if <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> were <lb></lb>removed from the chair? </s><s>What other Author ſhould we follow <lb></lb>in the Schools, Academies and Studies? </s><s>What Philoſopher hath <lb></lb>writ all the parts of Natural Philoſophy, and that ſo methodically <lb></lb>without omitting ſo much as one ſingle concluſion? </s><s>Shall we then <lb></lb>overthrow that Fabrick under which ſo many paſſengers find <lb></lb>ſhelter? </s><s>Shall we deſtroy that <emph type="italics"></emph>Aſylum,<emph.end type="italics"></emph.end> that <emph type="italics"></emph>Prytaneum,<emph.end type="italics"></emph.end> where <lb></lb>in ſo many Students meet with commodious harbour, where <lb></lb>without expoſing themſelves to the injuries of the air, with the <lb></lb>onely turning over of a few leaves, one may learn all the ſe <lb></lb>crets of Nature? </s><s>Shall we diſmantle that fort in which we are <lb></lb>ſafe from all hoſtile aſſaults? </s><s>But I pitie him no more than I do <lb></lb>that Gentleman who with great expence of time and treaſure, <lb></lb>and the help of many hundred artiſts, erects a very ſumptu <lb></lb>ous Pallace, and afterwards beholds it ready to fall, by reaſon <lb></lb>of the bad foundation; but being extremely unwilling to ſee <lb></lb>the Walls ſtript which are adorned with ſo many beautifull <lb></lb>Pictures; or to ſuffer the columns to fall, that uphold the ſtate <lb></lb>ly Galleries; or the gilded roofs, chimney-pieces, the freizes, <lb></lb>the corniſhes of marble, with ſo much coſt erected, to be rui <lb></lb>ned; goeth about with girders, props, ſhoars, butteraſſes, to pre <lb></lb>vent their ſubverſion.</s></p><p type="margin"><s><margin.target id="marg125"></margin.target><emph type="italics"></emph>The Declamation <lb></lb>of<emph.end type="italics"></emph.end> Simplicius.</s></p><p type="main"><s>SALV. </s><s>But alaſs, <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> as yet fears no ſuch fall, and <lb></lb>I would undertake to ſecure him from that miſchief at a far <lb></lb>leſs charge. </s><s>There is no danger that ſo great a multitude of <lb></lb><arrow.to.target n="marg126"></arrow.to.target> <lb></lb>ſubtle and wiſe Philoſophers, ſhould ſuffer themſelves to be <lb></lb><emph type="italics"></emph>Hector'd<emph.end type="italics"></emph.end> by one or two, who make a little bluſtering; nay, <lb></lb>they will rather, without ever turning the points of their pens <lb></lb>againſt them, by their ſilence onely render them the object of <lb></lb>univerſal ſcorn and contempt. </s><s>It is a fond conceit for any one <lb></lb>to think to introduce new Philoſophy, by reproving this or that <lb></lb>Author: it will be firſt neceſſary to new-mold the brains of <lb></lb>men, and make them apt to diſtinguiſh truth from falſhood. </s><s>A <lb></lb>thing which onely God can do. </s><s>But from one diſcourſe to another <lb></lb>whither are we ſtray'd? </s><s>your memory muſt help to guide me into <lb></lb>the way again.</s></p><p type="margin"><s><margin.target id="marg126"></margin.target><emph type="italics"></emph>Peripatetick Phi <lb></lb>loſophy unchange <lb></lb>able.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>I remember very well where we left. </s><s>We were <lb></lb>upon the anſwer of <emph type="italics"></emph>Anti-Tycho,<emph.end type="italics"></emph.end> to the objections againſt the <lb></lb>immutability of the Heavens, among which you inſerted this <lb></lb>of the Solar fpots, not ſpoke of by him; and I believe you <lb></lb>intended to examine his anſwer to the inſtance of the New <lb></lb>Stars.</s></p> <pb xlink:href="040/01/060.jpg" pagenum="44"></pb><p type="main"><s>SALV. </s><s>Now I remember the reſt, and to proceed, Methinks <lb></lb>there are ſome things in the anſwer of <emph type="italics"></emph>Anti-Tycho,<emph.end type="italics"></emph.end> worthy of <lb></lb>reprehenſion. </s><s>And firſt, if the two New Stars, which he can do <lb></lb>no leſs than place in the uppermoſt parts of the Heavens, and <lb></lb>which were of a long duration, but finally vaniſhed, give him no <lb></lb>obſtruction in maintaining the inalterability of Heaven, in that <lb></lb>they were not certain parts thereof, nor mutations made in the <lb></lb>antient Stars, why doth he ſet himſelf ſo vigorouſly and earneſtly <lb></lb>againſt the Comets, to baniſh them by all ways from the Cœle <lb></lb>ſtial Regions? </s><s>Was it not enough that he could ſay of them <lb></lb>the ſame which he ſpoke of the New ſtars? </s><s>to wit, that in re <lb></lb>gard they were no certain parts of Heaven, nor mutations made <lb></lb>in any of the Stars, they could no wiſe prejudice either Heaven, <lb></lb>or the Doctrine of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end>? </s><s>Secondly, I am not very well ſatis <lb></lb>fied of his meaning; when he ſaith that the alterations that ſhould <lb></lb>be granted to be made in the Stars, would be deſtructive to the <lb></lb>prerogative of Heaven; namely, its incorruptibility, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> and <lb></lb>this, becauſe the Stars are Cœleſtial ſubſtances, as is manifeſt <lb></lb>by the conſent of every one; and yet is nothing troubled that <lb></lb><arrow.to.target n="marg127"></arrow.to.target> <lb></lb>the ſame alterations ſhould be made ^{*} without the Stars in the reſt <lb></lb>of the Cœleſtial expanſion. </s><s>Doth he think that Heaven is no <lb></lb>Cœleſtial ſubſtance? </s><s>I, for my part, did believe that the Stars <lb></lb>were called Cœleſtial bodies, by reaſon that they were in Hea <lb></lb>ven, or for that they were made of the ſubſtance of Heaven; <lb></lb>and yet I thought that Heaven was more Cœleſtial than they; in <lb></lb>like ſort, as nothing can be ſaid to be more Terreſtrial, or more <lb></lb>fiery than the Earth or Fire themſelves. </s><s>And again, in that he ne <lb></lb>ver made any mention of the Solar ſpots, which have been evi <lb></lb>dently demonſtrated to be produced, and diſſolved, and to be <lb></lb>neer the Sun, and to turn either with, or about the ſame, I have <lb></lb>reaſon to think that this Author probably did write more for others <lb></lb>pleaſure, than for his own ſatisfaction; and this I affirm, foraſ <lb></lb>much as he having ſhewn himſelf to be skilful in the Mathema <lb></lb>ticks, it is impoſſible but that he ſhould have been convinced by <lb></lb>Demonſtrations, that thoſe ſubſtances are of neceſſity contigu <lb></lb>ous with the body of the Sun, and are ſo great generations and <lb></lb>corruptions, that none comparable to them, ever happen in the <lb></lb>Earth: And if ſuch, ſo many, and ſo frequent be made in the <lb></lb>very Globe of the Sun, which may with reaſon be held one of the <lb></lb>nobleſt parts of Heaven, what ſhould make us think that others <lb></lb>may not happen in the other Orbs? <lb></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"></emph>Generability and <lb></lb>alteration is a <lb></lb>greater perfection <lb></lb>in the Worlds bo <lb></lb>dies than the con <lb></lb>trary qualities.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I cannot without great admiration, nay more, deni <lb></lb>al of my underſtanding, hear it to be attributed to natural bodies, <lb></lb>for a great honour and perfection that they are ^{*} impaſſible, im <lb></lb>mutable, inalterable, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> 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"></pb>be eſteemed a great imperfection to be alterable, generable, mu <lb></lb>table, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> It is my opinion that the Earth is very noble and ad <lb></lb><arrow.to.target n="marg130"></arrow.to.target> <lb></lb>mirable, by reaſon of ſo many and ſo different alterations, mu <lb></lb>tations, generations, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> which are inceſſantly made therein; <lb></lb>and if without being ſubject to any alteration, it had been all <lb></lb>one vaſt heap of ſand, or a maſſe of <emph type="italics"></emph>Jaſper,<emph.end type="italics"></emph.end> or that in the time <lb></lb>of the Deluge, the waters freezing which covered it, it had <lb></lb>continued an immenſe Globe of Chriſtal, wherein nothing had <lb></lb><arrow.to.target n="marg131"></arrow.to.target> <lb></lb>ever grown, altered, or changed, I ſhould have eſteemed it a <lb></lb>lump of no benefit to the World, full of idleneſſe, and in a <lb></lb>word ſuperfluous, and as if it had never been in nature; and <lb></lb>ſhould make the ſame difference in it, as between a living and <lb></lb>dead creature: The like I ſay of the <emph type="italics"></emph>Moon, Jupiter,<emph.end type="italics"></emph.end> and all the <lb></lb>other Globes of the World. </s><s>But the more I dive into the con <lb></lb>ſideration of the vanity of popular diſcourſes, the more empty <lb></lb>and ſimple I find them. </s><s>And what greater folly can there be <lb></lb>imagined, than to call Jems, Silver and Gold pretious; and Earth <lb></lb>and dirt vile? </s><s>For do not theſe perſons conſider, that if there <lb></lb><arrow.to.target n="marg132"></arrow.to.target> <lb></lb>ſhould be as great a ſcarcity of Earth, as there is of Jewels and <lb></lb>pretious metals, there would be no Prince, but would gladly give <lb></lb>a heap of Diamonds and Rubies, and many Wedges of Gold, <lb></lb>to purchaſe onely ſo much Earth as ſhould ſuffice to plant a Geſſe <lb></lb>mine in a little pot, or to ſet therein a <emph type="italics"></emph>China Orange,<emph.end type="italics"></emph.end> that he might <lb></lb>ſee it ſprout, grow up, and bring forth ſo goodly leaves, ſo odi <lb></lb>riferous flowers, and ſo delicate fruit? </s><s>It is therefore ſcarcity and <lb></lb><arrow.to.target n="marg133"></arrow.to.target> <lb></lb>plenty that make things eſteemed and contemned by the vulgar; <lb></lb>who will ſay that ſame is a moſt beautiful Diamond, for that it <lb></lb>reſembleth a cleer water, and yet will not part with it for ten <lb></lb>Tun of water: Theſe men that ſo extol incorruptibility, inalte <lb></lb><arrow.to.target n="marg134"></arrow.to.target> <lb></lb>rability, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> ſpeak thus I believe out of the great deſire they <lb></lb>have to live long, and for fear of death; not confidering, that <lb></lb>if men had been immortal, they ſhould have had nothing to do <lb></lb>in the World. </s><s>Theſe deſerve to meet with a <emph type="italics"></emph>Meduſa<emph.end type="italics"></emph.end>'s head, <lb></lb><arrow.to.target n="marg135"></arrow.to.target> <lb></lb>that would transform them into Statues of <emph type="italics"></emph>Dimond<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Jaſper,<emph.end type="italics"></emph.end> <lb></lb>that ſo 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"></emph>The Earth very <lb></lb>noble, by reaſon of <lb></lb>the many mutati <lb></lb>ons made therein.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg131"></margin.target><emph type="italics"></emph>The carth unpro <lb></lb>ſitable and full of <lb></lb>idleneſſe, its alte <lb></lb>rations taken away<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg132"></margin.target><emph type="italics"></emph>The Earth more <lb></lb>noble than Gold <lb></lb>and Jewels.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg133"></margin.target><emph type="italics"></emph>Scarcity and plen <lb></lb>ty enhanſe and de <lb></lb>baſe the price of <lb></lb>things.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg134"></margin.target><emph type="italics"></emph>Incorruptibility e <lb></lb>ſteemed by the vul <lb></lb>gar out of their <lb></lb>fear of death.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg135"></margin.target><emph type="italics"></emph>The diſparagers of <lb></lb>corraptibility de <lb></lb>ſerve to be turned <lb></lb>into Statua's.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>And it may be ſuch a <emph type="italics"></emph>Metamorphoſis<emph.end type="italics"></emph.end> would not be al <lb></lb>together unprofitable to them; for I am of opinion that it is bet <lb></lb>ter not to diſcourſe at all, than to argue erroniouſly.</s></p><p type="main"><s>SIMPL. </s><s>There is not the leaſt queſtion to be made, but that <lb></lb>the Earth is much more perfect, being as it is alterable, mutable, <lb></lb><emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> than if it had been a maſſe of ſtone; yea although it were <lb></lb>one entire Diamond, moſt hard and impaſſile. </s><s>But look how mueh <lb></lb><arrow.to.target n="marg136"></arrow.to.target> <lb></lb>theſe qualifications enoble the Earth, they render the Heavenly <lb></lb>bodies again on the other ſide ſo much the more imperfect, in <lb></lb>which, ſuch conditions would be ſuperfluous; in regard that the <pb xlink:href="040/01/062.jpg" pagenum="46"></pb>Cœleſtial bodies, namely, the Sun, Moon, and the other Stars, <lb></lb>which are ordained for no other uſe but to ſerve the Earth, need <lb></lb>no other qualities for attaining of that end, ſave onely thoſe of <lb></lb>light and motion.</s></p><p type="margin"><s><margin.target id="marg136"></margin.target><emph type="italics"></emph>The Cœleſtial bo <lb></lb>dies deſigned to <lb></lb>ſerve the Earth, <lb></lb>need no more but <lb></lb>motion and light.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. How? </s><s>Will you affirm that nature hath produced and <lb></lb>deſigned ſo many vaſt perfect and noble Cœleſtial bodies, impaſ <lb></lb>ſible, immortal, and divine, to no other uſe but to ſerve the paſ <lb></lb>ſible, frail, and mortal Earth? </s><s>to ſerve that which you call the <lb></lb>droſſe of the World, and ſink of all uncleanneſſe? </s><s>To what <lb></lb>purpoſe were the Cœleſtial bodies made immortal, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> to ſerve a <lb></lb>frail, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> Take away this ſubſerviency to the Earth, and the in <lb></lb>numerable multitude of Cœleſtial bodies become wholly unuſe <lb></lb><arrow.to.target n="marg137"></arrow.to.target> <lb></lb>ful, and ſuperfluous, ſince they neither have nor can have any <lb></lb>mutual operation betwixt themſelves; becauſe they are all unal <lb></lb>terable, immutable, impaſſible: For if, for Example, the Moon <lb></lb>be impaſſible, what influence can the Sun or any other Star have <lb></lb>upon her? </s><s>it would doubtleſſe have far leſſe effect upon her, than <lb></lb>that of one who would with his looks or imagination, lignifie a <lb></lb>piece of Gold. </s><s>Moreover, it ſeemeth to me, that whilſt the Cœ <lb></lb>leſtial bodies concurre to the generation and alteration of the <lb></lb>Earth, they themſelves are alſo of neceſſity alterable; for other <lb></lb>wiſe I cannot underſtand how the application of the Sun or Moon <lb></lb>to the Earth, to effect production, ſhould be any other than to lay <lb></lb>a marble Statue by a Womans ſide, and from that conjunction to <lb></lb>expect children. <lb></lb><arrow.to.target n="marg138"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg137"></margin.target><emph type="italics"></emph>Celestial bodies <lb></lb>want an inter <lb></lb>changeable opera <lb></lb>tion upon each o <lb></lb>ther.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg138"></margin.target><emph type="italics"></emph>Alterability, &c. <lb></lb></s><s>are not in the whole <lb></lb>Terreſtrial Globe, <lb></lb>but in ſome of its <lb></lb>parts.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. Corruptibility, alteration, mutation, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> are not in <lb></lb>the whole Terreſtrial Globe, which as to its whole, is no leſſe eter <lb></lb>nal than the Sun or Moon, but it is generable and corruptible as to <lb></lb>its external parts; but yet it is alſo true that likewiſe in them ge <lb></lb>neration and corruption are perpetual, and as ſuch require the <lb></lb>heavenly eternal operations; and therefore it is neceſſary that <lb></lb>the Cœleſtial bodies be eternal.</s></p><p type="main"><s>SAGR. </s><s>All this is right; but if the corruptibility of the ſuper <lb></lb>ficial parts of the Earth be nowiſe prejudicial to the eternity of <lb></lb>its whole Globe, yea, if their being generable, corruptible, alter <lb></lb>able, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> gain them great ornament and perfection; why can</s></p><p type="main"><s><arrow.to.target n="marg139"></arrow.to.target> <lb></lb>not, and ought not you to admit alteration, generation, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> like <lb></lb>wiſe in the external parts of the Cœleſtial Globes, adding to <lb></lb>them ornament, without taking from them perfection, or berea <lb></lb>ving them of action; yea rather encreaſing their effects, by grant <lb></lb>ing not onely that they all operate on the Earth, but that they mu <lb></lb>tually operate upon each other, and the Earth alſo upon them <lb></lb>all?</s></p><p type="margin"><s><margin.target id="marg139"></margin.target><emph type="italics"></emph>Cœleſtial bodies <lb></lb>alterable in their <lb></lb>outward parts.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>This cannot be, becauſe the generations, mutations, <lb></lb><emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> which we ſhould ſuppoſe <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> in the Moon; would be vain <lb></lb>and uſeleſſe, <emph type="italics"></emph>& natura nihil fruſtra facit.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/063.jpg" pagenum="47"></pb><p type="main"><s>SAGR. </s><s>And why ſhould they be vain and uſeleſſe?</s></p><p type="main"><s>SIMPL. </s><s>Becauſe we cleerly ſee, and feel with our hands, that <lb></lb><arrow.to.target n="marg140"></arrow.to.target> <lb></lb>all generations, corruptions, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> made in the Earth, are all ei <lb></lb>ther mediately or immediately directed to the uſe, convenience, <lb></lb>and benefit of man; for the uſe of man are horſes brought forth, <lb></lb>for the feeding of horſes, the Earth produceth graſſe, and the <lb></lb>Clouds water it; for the uſe and nouriſhment of man, herbs, corn, <lb></lb>fruits, beaſts, birds, fiſhes, are brought forth; and in ſum, if <lb></lb>we ſhould one by one dilligently examine and reſolve all theſe <lb></lb>things, we ſhould find the end to which they are all directed, to be <lb></lb>the neceſſity, uſe, convenience, and delight of man. </s><s>Now of what <lb></lb>uſe could the generations which we ſuppoſe to be made in the <lb></lb>Moon or other Planets, ever be to mankind? </s><s>unleſſe you ſhould <lb></lb>ſay that there were alſo men in the Moon, that might enjoy the <lb></lb>benefit thereof; a conceit either fabulous or impious.</s></p><p type="margin"><s><margin.target id="marg140"></margin.target><emph type="italics"></emph>The generations & <lb></lb>mutations happen <lb></lb>ing in the Earth, <lb></lb>are all for the good <lb></lb>of Man.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>That in the Moon or other Planets, there are genera <lb></lb><arrow.to.target n="marg141"></arrow.to.target> <lb></lb>ted either herbs, or plants, or animals, like to ours, or that there <lb></lb>are rains, winds, or thunders there, as about the Earth, I nei <lb></lb>ther know, nor believe, and much leſſe, that it is inhabited by <lb></lb>men: but yet I underſtand not, becauſe there are not genera <lb></lb>ted things like to ours, that therefore it neceſſarily followeth, <lb></lb>that no alteration is wrought therein, or that there may not be <lb></lb>other things that change, generate, and diſſolve, which are not <lb></lb><arrow.to.target n="marg142"></arrow.to.target> <lb></lb>onely different from ours, but exceedingly beyond our imagina <lb></lb>tion, and in a word, not to be thought of by us. </s><s>And if, as I <lb></lb>am certain, that one born and brought up in a ſpatious Forreſt, <lb></lb>amongſt beaſts and birds, and that hath no knowledg at all of the <lb></lb>Element of Water, could never come to imagine another World <lb></lb><arrow.to.target n="marg143"></arrow.to.target> <lb></lb>to be in Nature, different from the Eatth, full of living crea <lb></lb>tures, which without legs or wings ſwiftly move, and not upon <lb></lb>the ſurface onely, as beaſts do upon the Earth, but in the very <lb></lb>bowels thereof; and not onely move, but alſo ſtay themſelves <lb></lb>and ceaſe to move at their pleaſure, which birds cannot do in the <lb></lb>air; and that moreover men live therein, and build Palaces and <lb></lb>Cities, and have ſo great convenience in travailing, that without <lb></lb>the leaſt trouble, they can go with their Family, Houſe, and <lb></lb>whole Cities, to places far remote, like as I ſay, I am certain, <lb></lb>ſuch a perſon, though of never ſo piercing an imagination, could <lb></lb>never fancy to himſelf Fiſhes, the Ocean, Ships, Fleets, <emph type="italics"></emph>Arma <lb></lb>do's<emph.end type="italics"></emph.end> at Sea; thus, and much more eaſily, may it happn, that in <lb></lb>the Moon, remote from us by ſo great a ſpace, and of a ſub <lb></lb>ſtance perchance very different from the Earth, there may be mat <lb></lb>ters, and operations, not only wide off, but altogether beyond <lb></lb>all our imaginations, as being ſuch as have no reſemblance to <lb></lb>ours, and therefore wholly inexcogitable, in regard, that what we <pb xlink:href="040/01/064.jpg" pagenum="48"></pb>imagine to our ſelves, muſt neceſſarily be either a thing already <lb></lb>ſeen, or a compoſition of things, or parts of things ſeen at ano <lb></lb>ther time; for ſuch are the <emph type="italics"></emph>Sphinxes, Sirenes, Chimœra's, Cen <lb></lb>taurs,<emph.end type="italics"></emph.end> &c.</s></p><p type="margin"><s><margin.target id="marg141"></margin.target><emph type="italics"></emph>The Moon hath <lb></lb>no generatings of <lb></lb>things, like as we <lb></lb>have, nor is it in <lb></lb>habited by men.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg142"></margin.target><emph type="italics"></emph>In the Moon may <lb></lb>be a generation of <lb></lb>things different <lb></lb>from ours.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg143"></margin.target><emph type="italics"></emph>He that had not <lb></lb>heard of the Ele <lb></lb>ment of Water, <lb></lb>could never fancy <lb></lb>to himſelf Ships <lb></lb>and Fiſhes.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>I have very often let my fancy ruminate upon theſe ſpe <lb></lb>culations, and in the end, have thought that I had found ſome <lb></lb>things that neither are nor can be in the Moon; but yet I <lb></lb>have not found therein any of thoſe which I believe are, and may <lb></lb>be there, ſave onely in a very general acceptation, namely, things <lb></lb>that adorn it by operating, moving and living; and perhaps in a way <lb></lb><arrow.to.target n="marg144"></arrow.to.target> <lb></lb>very different from ours; beholding and admiring the greatneſs and <lb></lb>beauty of the World, and of its Maker and Ruler, and with <lb></lb>continual <emph type="italics"></emph>Encomiums<emph.end type="italics"></emph.end> ſinging his prayſes; and in ſumme (which is <lb></lb>that which I intend) doing what ſacred Writers ſo frequently af <lb></lb>firm, to wit, all the creatures making it their perpetual imploy <lb></lb>ment to laud God.</s></p><p type="margin"><s><margin.target id="marg144"></margin.target><emph type="italics"></emph>There may be ſub <lb></lb>ſtances in the <lb></lb>Moon very diffe <lb></lb>rent from ours.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Theſe are the things, which ſpeaking in general terms, <lb></lb>may be there; but I would gladly hear you inſtance in ſuch as you <lb></lb>believe neither are nor can be there; which perchance may be <lb></lb>more particularly named.</s></p><p type="main"><s>SALV. </s><s>Take notice <emph type="italics"></emph>Sagredus<emph.end type="italics"></emph.end> that this will be the third time <lb></lb>that we have unawares by running from one thing to another, loſt <lb></lb>our principal ſubject; and if we continue theſe digreſſions, it <lb></lb>will be longere we come to a concluſion of our diſcourſe; there <lb></lb>fore I ſhould judg it better to remit this, as alſo ſuch other points, <lb></lb>to be decided on a particular occaſion.</s></p><p type="main"><s>SAGR. </s><s>Since we are now got into the Moon, if you pleaſe, let <lb></lb>us diſpatch ſuch things as concern her, that ſo we be not forced to <lb></lb>ſuch another tedious journey.</s></p><p type="main"><s>SALV. </s><s>It ſhall be as you would have it. </s><s>And to begin with <lb></lb>things more general, I believe that the Lunar Globe is far diffe <lb></lb>rent from the Terreſtrial, though in ſome things they agree. </s><s>I will <lb></lb>recount firſt their reſemblances, and next their differences. </s><s>The <lb></lb><arrow.to.target n="marg145"></arrow.to.target> <lb></lb>Moon is manifeſtly like to the Earth in figure, which undoubtedly <lb></lb>is ſpherical, as may be neceſſarily concluded from the aſpect of its <lb></lb>ſurface, which is perfectly Orbicular, and the manner of its re <lb></lb>ceiving the light of the Sun, from which, if its ſurface were flat, <lb></lb>it would come to be all in one and the ſame time illuminated, and <lb></lb>likewiſe again in another inſtant of time obſcured, and not thoſe <lb></lb>parts firſt, which are ſituate towards the Sun, and the reſt ſucceſ <lb></lb>ſively, ſo that in its oppoſition, and not till then, its whole <lb></lb>apparent circumference is enlightned; which would happen quite <lb></lb>contrary, if the viſible ſurface were concave; namely, the illu <lb></lb><arrow.to.target n="marg146"></arrow.to.target> <lb></lb>mination would begin from the parts oppoſite or averſe to the Sun. <lb></lb></s><s>Secondly ſhe is as the Earth, in her ſelf obſcure and opacous, by <lb></lb>which opacity it is enabled to receive, and reflect the light of the <pb xlink:href="040/01/065.jpg" pagenum="49"></pb>Sun; which were it not ſo, it could not do. </s><s>Thirdly, I hold its <lb></lb><arrow.to.target n="marg147"></arrow.to.target> <lb></lb>matter to be moſt denſe and ſolid as the Earth is, which I clearly <lb></lb>argue from the unevenneſs of its ſuperficies in moſt places, by means <lb></lb>of the many eminencies and cavities diſcovered therein by help of <lb></lb>the <emph type="italics"></emph>ſeleſcope<emph.end type="italics"></emph.end>: of which eminencies there are many all over it, di <lb></lb>rectly reſembling our moſt ſharp and craggy mountains, of which <lb></lb>you ſhall there perceive ſome extend and run in ledges of an hun <lb></lb>dred miles long; others are contracted into rounder forms; and <lb></lb>there are alſo many craggy, ſolitary, ſteep and cliffy rocks. </s><s>But <lb></lb>that of which there are frequenteſt appearances, are certain Banks <lb></lb>(I uſe this word, becauſe I cannot thing of another that better ex <lb></lb>preſſeth them) pretty high raiſed, which environ and incloſe fields <lb></lb>of ſeveral bigneſſes, and form ſundry figures, but for the moſt part <lb></lb>circular; many of which have in the midſt a mount raiſed pretty <lb></lb>high, and ſome few are repleniſhed with a matter ſomewhat ob <lb></lb>ſcure, to wit, like to the great ſpots diſcerned by the bare eye, and <lb></lb>theſe are of the greateſt magnitude; the number moreover of thoſe <lb></lb>that are leſſer and leſſer is very great, and yet almoſt all circular. <lb></lb><arrow.to.target n="marg148"></arrow.to.target> <lb></lb>Fourthly, like as the ſurface of our Globe is diſtinguiſhed into two <lb></lb>principal parts, namely, into the Terreſtrial and Aquatick: ſo in <lb></lb>the Lunar ſurface we diſcern a great diſtinction of ſome great fields <lb></lb>more reſplendant, and ſome leſs: whoſe aſpect makes me believe, <lb></lb>that that of the Earth would ſeem very like it, beheld by any one <lb></lb>from the Moon, or any other the like diſtance, to be illuminated <lb></lb><arrow.to.target n="marg149"></arrow.to.target> <lb></lb>by the Sun: and the ſurface of the ſea would appear more ob <lb></lb>ſcure, and that of the Earth more bright. </s><s>Fifthly, like as we from <lb></lb>the Earth behold the Moon, one while all illuminated, another <lb></lb><arrow.to.target n="marg150"></arrow.to.target> <lb></lb>while half; ſometimes more, ſometimes leſs; ſometimes horned, <lb></lb>ſometimes wholly inviſibly; namely, when its juſt under the Sun <lb></lb>beams; ſo that the parts which look towards the Earth are dark: <lb></lb>Thus in every reſpect, one ſtanding in the Moon would ſee the <lb></lb>illumination of the Earths ſurface by the Sun, with the ſame <lb></lb>periods to an hair, and under the ſame changes of figures. <lb></lb></s><s>Sixtly, -----</s></p><p type="margin"><s><margin.target id="marg145"></margin.target><emph type="italics"></emph>The<emph.end type="italics"></emph.end> Firſt <emph type="italics"></emph>reſem <lb></lb>blance between the <lb></lb>Moon and Earth; <lb></lb>which is that of <lb></lb>figure; is proved by <lb></lb>the manner of be <lb></lb>ing illuminated by <lb></lb>the Sun.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg146"></margin.target><emph type="italics"></emph>The<emph.end type="italics"></emph.end> Second <emph type="italics"></emph>con <lb></lb>formity is the <lb></lb>Moons being opa <lb></lb>cous as the Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg147"></margin.target><emph type="italics"></emph>Thirdly, The mat <lb></lb>ter of the Moon is <lb></lb>denſe and mo ita <lb></lb>nous as the Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg148"></margin.target><emph type="italics"></emph>Fourthly, The <lb></lb>Moon is diſtin <lb></lb>guiſhed into two <lb></lb>different parts for <lb></lb>clarity and obſcu <lb></lb>rity, as the Terre <lb></lb>strial Globe into <lb></lb>Sea and Land.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg149"></margin.target><emph type="italics"></emph>The ſurface of the <lb></lb>Sea would ſhew at <lb></lb>a diſtance more ob <lb></lb>ſoure than that of <lb></lb>the Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg150"></margin.target><emph type="italics"></emph>Fiftly, Muta <lb></lb>tion of ſigures in <lb></lb>the Earth, like to <lb></lb>thoſe of the Moon, <lb></lb>and made with the <lb></lb>ſame periods.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Stay a little, <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end>; That the illumination of <lb></lb>the Earth, as to the ſeveral figures, would repreſent it ſelf to a perſon <lb></lb>placed in the Moon, like in all things to that which we diſcover in <lb></lb>the Moon, I underſtand very well, but yet I cannot conceive how <lb></lb>it ſhall appear to be done in the ſame period; ſeeing that that <lb></lb>which the Suns illumination doth in the Lunar ſuperficies in a <lb></lb>month, it doth in the Terreſtrial in twenty four hours.</s></p><p type="main"><s>SALV. </s><s>Its true, the effect of the Sun about the illuminating <lb></lb>theſe two bodies, and repleniſhing with its ſplendor their whole <lb></lb>ſurfaces, is diſpatch'd in the Earth in a Natural day, and in the <lb></lb>Moon in a Month; but the variation of the figures in which the <pb xlink:href="040/01/066.jpg" pagenum="50"></pb>illuminated parts of the Terreſtrial ſuperficies appear beheld from <lb></lb>the Moon, depends not on this alone, but on the divers aſpects <lb></lb>which the Moon is ſtill changing with the Sun; ſo that, if for in <lb></lb>ſtance, the Moon punctually followed the motion of the Sun, and <lb></lb>ſtood, for example, always in a direct line between it and the <lb></lb>Earth, in that aſpect which we call Conjunction, it looking always <lb></lb>to the ſame Hemiſphere of the Earth which the Sun looks unto, <lb></lb>ſhe would behold the ſame all light: as on the contrary, if it ſhould <lb></lb>always ſtay in Oppoſition to the Sun, it would never behold the <lb></lb>Earth, of which the dark part would be continually turn'd towards <lb></lb>the Moon, and therefore inviſible. </s><s>But when the Moon is in <lb></lb>Quadrature of the Sun, that half of the Terreſtrial Hemiſphere ex <lb></lb>poſed to the ſight of the Moon which is towards the Sun, is lumi <lb></lb>nous; and the other towards the contrary is obſcure: and there <lb></lb>fore the illuminated part of the Earth would repreſent it ſelf to the <lb></lb>Moon in a ſemi-circular figure.</s></p><p type="main"><s>SAGR. </s><s>I clearly perceive all this, and underſtand very well, <lb></lb>that the Moon departing from its Oppoſition to the Sun, where it <lb></lb>ſaw no part of the illumination of the Terreſtrial ſuperficies, and <lb></lb>approaching day by day nearer the Sun, ſhe begins by little and <lb></lb>little to diſcover ſome part of the face of the illuminated Earth; <lb></lb>and that which appeareth of it ſhall reſemble a thin ſickle, in regard <lb></lb>the figure of the Earth is round: and the Moon thus acquiring by <lb></lb>its motion day by day greater proximity to the Sun, ſucceſſively <lb></lb>diſcovers more and more of the Terreſtrial Hemiſphere enlightned, <lb></lb>ſo that at the Quadrature there is juſt half of it viſible, inſomuch <lb></lb>that we may ſee the other part of her: continuing next to proceed <lb></lb>towards the Conjunction, it ſucceſſively diſcovers more and more <lb></lb>of its ſurface to be illuminated, and in fine, at the time of Conjun <lb></lb>ction ſeeth the whole Hemiſphere enlightned. </s><s>And in ſhort, I <lb></lb>very well conceive, that what befalls the Inhabitants of the Earth, <lb></lb>in beholding the changes of the Moon, would happen to him that <lb></lb>from the Moon ſhould obſerve the Earth; but in a contrary order, <lb></lb>namely, that when the Moon is to us at her full, and in Oppoſition <lb></lb>to the Sun, then the Earth would be in Conjunction with the Sun, <lb></lb>and wholly obſcure and inviſible; on the contrary, that poſition <lb></lb>which is to us a Conjunction of the Moon with the Sun, and for <lb></lb>that cauſe a <emph type="italics"></emph>M<emph.end type="italics"></emph.end>oon ſilent and unſeen, would be there an Oppoſition <lb></lb>of the Earth to the Sun, and, to ſo ſpeak, <emph type="italics"></emph>Full Earth,<emph.end type="italics"></emph.end> to wit, all <lb></lb>enlightned. </s><s>And laſtly, look what part of the Lunar ſurface ap <lb></lb>pears to us from time to time illuminated, ſo much of the Earth <lb></lb>in the ſame time ſhall you behold from the Moon to be obſcured: <lb></lb>and look how much of the Moon is to us deprived of light, ſo much <lb></lb>of the Earth is to the Moon illuminated. </s><s>In one thing yet theſe <lb></lb>mutual operations in my judgment ſeem to differ, and it is, that it <pb xlink:href="040/01/067.jpg" pagenum="51"></pb>being ſuppoſed, and not granted, that ſome one being placed in the <lb></lb>Moon to obſerve the Earth, he would every day ſee the whole <lb></lb>Terreſtrial ſuperficies, by means of the Moons going about the <lb></lb>Earth in twenty four or twenty five hours; but we never ſee but <lb></lb>half of the Moon, ſince it revolves not in it ſelf, as it muſt do to <lb></lb>be ſeen 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></lb>volving in her ſelf, is the cauſe that we ſee not the other half of <lb></lb>her, for ſo it would be neceſſary it ſhould be, if ſhe had the Epicy <lb></lb>cle. </s><s>But what other difference have you behind, to exchange for <lb></lb>this which you have named?</s></p><p type="main"><s>SAGR. </s><s>Let me ſee; Well for the preſent I cannot think of <lb></lb>any other.</s></p><p type="main"><s>SALV. </s><s>And what if the Earth (as you have well noted) ſeeth <lb></lb><arrow.to.target n="marg151"></arrow.to.target> <lb></lb>no more than half the Moon, whereas from the Moon one may ſee <lb></lb>all the Earth; and on the contrary, all the Earth ſeeth the Moon, and <lb></lb>but onely half of it ſeeth the Earth? </s><s>For the inhabitants, to ſo ſpeak, <lb></lb>of the ſuperior Hemiſphere of the Moon, which is to us inviſible, <lb></lb>are deprived of the ſight of the Earth: and theſe haply are the <lb></lb><emph type="italics"></emph>Anticthones.<emph.end type="italics"></emph.end> But here I remember a particular accident, newly <lb></lb>obſerved by our <emph type="italics"></emph>Academian,<emph.end type="italics"></emph.end> in the Moon, from whch are gathered <lb></lb><arrow.to.target n="marg152"></arrow.to.target> <lb></lb>two neceſſary conſequences; one is, that we ſee ſomewhat more <lb></lb>than half of the Moon; and the other is, that the motion of the <lb></lb>Moon hath exact concentricity with the Earth: and thus he finds <lb></lb>the <emph type="italics"></emph>Phœnomenon<emph.end type="italics"></emph.end> and obſervation. </s><s>When the Moon hath a cor <lb></lb>reſpondence and natural ſympathy with the Earth, towards which <lb></lb>it hath its aſpect in ſuch a determinate part, it is neceſſary that the <lb></lb>right line which conjoyns their centers, do paſſe ever by the ſame <lb></lb>point of the Moons ſuperficies; ſo that, who ſo ſhall from the cen <lb></lb>ter of the Earth behold the ſame, ſhall alwayes ſee the ſame <lb></lb><emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end> or Face of the Moon punctually determined by one and <lb></lb>the ſame circumference; But if a man be placed upon the Terre <lb></lb>ſtrial ſurface, the ray which from his eye paſſeth to the centre of the <lb></lb>Lunar Globe, will not paſs by the ſame point of its ſuperficies, by <lb></lb>which the line paſſeth that is drawn from the centre of the Earth <lb></lb>to that of the Moon, ſave onely when it is vertical to him: but <lb></lb>the Moon being placed in the Eaſt, or in the Weſt, the point of <lb></lb>incidence of the viſual ray, is higher than that of the line which <lb></lb>conjoyns the centres; and therefore the obſerver may diſcern <lb></lb>ſome part of the Lunar Hemiſphere towards the upper circumfe <lb></lb>rence, and alike part of the other is inviſible: they are diſcerna <lb></lb>ble and undiſcernable, in reſpect of the Hemiſphere beheld from <lb></lb>the true centre of the Earth: and becauſe the part of the Moons <lb></lb>circumference, which is ſuperiour in its riſing, is nethermoſt in its <lb></lb>ſetting; therefore the difference of the ſaid ſuperiour and inferi <pb xlink:href="040/01/068.jpg" pagenum="52"></pb>our parts muſt needs be very obſervable; certain ſpots and other <lb></lb>notable things in thoſe parts, being one while diſcernable, and <lb></lb>another while not. </s><s>A like variation may alſo be obſerved towards <lb></lb>the North and South extremities of the ſame <emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end> (or Surface) <lb></lb>according as the Moons poſition is in one or the other Section of <lb></lb>its Dragon; For, if it be North, ſome of its parts towards the <lb></lb>North are hid, and ſome of thoſe parts towards the South are <lb></lb>diſcovered, and ſo on the contrary. </s><s>Now that theſe conſequen <lb></lb><arrow.to.target n="marg153"></arrow.to.target> <lb></lb>ces are really true, is verified by the <emph type="italics"></emph>Teleſcope,<emph.end type="italics"></emph.end> for there be in <lb></lb>the Moon two remarkable ſpots, one of which, when the Moon <lb></lb>is in the meridian, is ſituate to the Northweſt, and the other is <lb></lb>almoſt diametrically oppoſite unto it; and the firſt of theſe is vi <lb></lb>ſible even without the <emph type="italics"></emph>Teleſcope<emph.end type="italics"></emph.end>; but the other is not. </s><s>That to <lb></lb>wards the Northweſt is a reaſonable great ſpot of oval figure, ſe <lb></lb>parated from the other great ones; the oppoſite one is leſſe, and <lb></lb>alſo ſevered from the biggeſt, and ſituate in a very cleer field; in <lb></lb>both theſe we may manifeſtly diſcern the foreſaid variations, and <lb></lb>ſee them one after another; now neer the edge or limb of the <lb></lb>Lunar <emph type="italics"></emph>Diſcus,<emph.end type="italics"></emph.end> and anon remote, with ſo great difference that <lb></lb>the diſtance betwixt the Northweſt and the circumference of the <lb></lb><emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end> is more than twice as great at one time, as at the other; <lb></lb>and as to the ſecond ſpot (becauſe it is neerer to the circumfe <lb></lb>rence) ſuch mutation importeth more, than twice ſo much in the <lb></lb>former. </s><s>Hence its manifeſt, that the Moon, as if it were drawn <lb></lb>by a magnetick vertue, conſtantly beholds the Terreſtrial Globe <lb></lb>with one and the ſame aſpect, never deviating from the ſame.</s></p><p type="margin"><s><margin.target id="marg151"></margin.target><emph type="italics"></emph>All the Earth <lb></lb>ſeeth half onely of <lb></lb>the Moon, & the <lb></lb>half onely of the <lb></lb>Moon ſeeth all the <lb></lb>Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg152"></margin.target><emph type="italics"></emph>From the Earth <lb></lb>we ſee more than <lb></lb>half the Lunar <lb></lb>Globe.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg153"></margin.target><emph type="italics"></emph>Two ſpots in the <lb></lb>Moon, by which it <lb></lb>is perceived that <lb></lb>ſhe hath respect to <lb></lb>the centre of the <lb></lb>Earth in her mo <lb></lb>tion.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. Oh! when will there be an end put to the new ob <lb></lb>ſervations aud diſcoveries of this admirable Inſtrument?</s></p><p type="main"><s>SALV. </s><s>If this ſucceed according to the progreſſe of other great <lb></lb>inventions, it is to be hoped, that in proceſſe of time, one may <lb></lb>arrive to the ſight of things, to us at preſent not to be imagined. <lb></lb><arrow.to.target n="marg154"></arrow.to.target> <lb></lb>But returning to our firſt diſcourſe, I ſay for the ſixth reſemblance <lb></lb>betwixt the Moon and Earth, that as the Moon for a great part <lb></lb>of time, ſupplies the want of the Suns light, and makes the <lb></lb>nights, by the reflection of its own, reaſonable clear; ſo the <lb></lb>Earth, in recompence, affordeth it when it ſtands in moſt need, <lb></lb>by reflecting the Solar rayes, a very cleer illumination, and ſo <lb></lb>much, in my opinion, greater than that which cometh from her to <lb></lb>us, by how much the ſuperficies of the Earth is greater than that <lb></lb>of the Moon.</s></p><p type="margin"><s><margin.target id="marg154"></margin.target><emph type="italics"></emph>Sixthly, The <lb></lb>Earth and Moon <lb></lb>interchangeably do <lb></lb>illuminate.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Hold there, <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> hold there, and permit me the <lb></lb>pleaſure of relating to you, how at this firſt hint I have penetrated <lb></lb>the cauſe of an accident, which I have a thouſand times thought <lb></lb><arrow.to.target n="marg155"></arrow.to.target> <lb></lb>upon, but could never find out. </s><s>You would ſay, that the imper <lb></lb>fect light which is ſeen in the Moon, eſpecially when it is horned, <pb xlink:href="040/01/069.jpg" pagenum="53"></pb>comes from the reflection of the light of the Sun on the Superfi <lb></lb>cies of the Earth and Sea; and that light is more clear, by how <lb></lb>much the horns are leſſe, for then the luminous part of the Earth, <lb></lb>beheld by the Moon, is greater, according to that which was <lb></lb>a little before proved; to wit, that the luminous part of the Earth, <lb></lb>expoſed to the Moon, is alway as great as the obſcure part of <lb></lb>the Moon, that is viſible to the Earth; whereupon, at ſuch time <lb></lb>as the Moon is ſharp-forked, and conſequently its tenebrous part <lb></lb>great, great alſo is the illuminated part of the Earth beheld from <lb></lb>the Moon, and its reflection of light ſo much the more potent.</s></p><p type="margin"><s><margin.target id="marg155"></margin.target><emph type="italics"></emph>Light reflected <lb></lb>from the Earth in <lb></lb>to the Moon.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>This is exactly the ſame with what I was about to ſay. <lb></lb></s><s>In a word, it is a great pleaſure to ſpeak with perſons judicious <lb></lb>and apprehenſive, and the rather to me, for that whileſt others <lb></lb>converſe and diſcourſe touching Axiomatical truths, I have ma <lb></lb>ny times creeping into my brain ſuch arduous Paradoxes, that <lb></lb>though I have a thouſand times rehearſed this which you at the ve <lb></lb>ry firſt, have of your ſelf apprehended, yet could I never beat <lb></lb>it into mens brains.</s></p><p type="main"><s>SIMPL. </s><s>If you mean by your not being able to perſwade them <lb></lb>to it, that you could not make them underſtand the ſame, I <lb></lb>much wonder thereat, and am very confident that if they did <lb></lb>not underſtand it by your demonſtration (your way of expreſſion, <lb></lb>being, in my judgment, very plain) they would very hardly have <lb></lb>apprehended it upon the explication of any other man; but if <lb></lb>you mean you have not perſwaded them, ſo as to make them be <lb></lb>lieve it, I wonder not, in the leaſt, at this; for I confeſſe my <lb></lb>ſelf to be one of thoſe who underſtand your diſcourſes, but <lb></lb>am not ſatisfied therewith; for there are in this, and ſome of <lb></lb>the other ſix congruities, or reſemblances, many difficulties, <lb></lb>which I ſhall inſtance in, when you have gone through them <lb></lb>all.</s></p><p type="main"><s>SALV. </s><s>The deſire I have to find out any truth, in the acquiſt <lb></lb>whereof the objections of intelligent perſons (ſuch as your ſelf) <lb></lb>may much aſſiſt me, will cauſe me to be very brief in diſpatching <lb></lb>that which remains. </s><s>For a ſeventh conformity, take their reci <lb></lb><arrow.to.target n="marg156"></arrow.to.target> <lb></lb>procal reſponſion as well to injuries, as favours; whereby the <lb></lb>Moon, which very often in the height of its illumination, by the <lb></lb>interpoſure of the Earth betwixt it and the Sun, is deprived of <lb></lb>light, and eclipſed, doth by way of revenge; in like manner, in <lb></lb>terpoſe it ſelf between the Earth and the Sun, and with its ſhadow <lb></lb>obſcureth the Earth; and although the revenge be not anſwer <lb></lb>able to the injury, for that the Moon often continueth, and <lb></lb>that for a reaſonable long time, wholly immerſed in the Earths <lb></lb>ſhadow, but never was the Earth wholly, nor for any long time, <lb></lb>eclipſed by the Moon; yet, nevertheleſſe, having reſpect to the <pb xlink:href="040/01/070.jpg" pagenum="54"></pb>ſmalneſſe of the body of this, in compariſon to the magnitude <lb></lb>of the other, it cannot be denied but that the <emph type="italics"></emph>will<emph.end type="italics"></emph.end> and as it <lb></lb>were <emph type="italics"></emph>valour<emph.end type="italics"></emph.end> of this, is very great. </s><s>Thus much for their con <lb></lb>gruities or reſemblances. </s><s>It ſhould next follow that we diſcourſe <lb></lb>touching their diſparity; but becauſe <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> will favour us <lb></lb>with his objections againſt the former, its neceſſary that we hear <lb></lb>and examine them, before we proceed any farther.</s></p><p type="margin"><s><margin.target id="marg156"></margin.target><emph type="italics"></emph>Seventhly, The <lb></lb>Earth and Moon <lb></lb>do mutually eclipſe.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>And the rather, becauſe it is to be ſuppoſed that <lb></lb><emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> will not any wayes oppoſe the diſparities, and incon <lb></lb>gruities betwixt the Earth and Moon, ſince that he accounts their <lb></lb>ſubſtances extremely different.</s></p><p type="main"><s>SIMPL. </s><s>Amongſt the reſemblances by you recited, in the pa <lb></lb>rallel you make betwixt the Earth and Moon, I find that I can <lb></lb>admit none confidently ſave onely the firſt, and two others; I <lb></lb>grant the firſt, namely, the ſpherical figure; howbeit, even in <lb></lb>this there is ſome kind of difference, for that I hold that of the <lb></lb>Moon to be very ſmooth and even, as a looking-glaſſe, where <lb></lb>as, we find and feel this of the Earth to be extraordinary montu <lb></lb>ous and rugged; but this belonging to the inequality of ſuperfi <lb></lb>cies, it ſhall be anon conſidered, in another of thoſe Reſemblan <lb></lb>ces by you alledged; I ſhall therefore reſerve what I have to ſay <lb></lb>thereof, till I come to the conſideration of that. </s><s>Of what you <lb></lb>affirm next, that the Moon ſeemeth, as you ſay in your ſecond <lb></lb>Reſemblance, opacous and obſcure in its ſelf, like the Earth; I <lb></lb>admit not any more than the firſt attribute of opacity, of which <lb></lb>the Eclipſes of the Sun aſſure me. </s><s>For were the Moon tranſpa <lb></lb>rent, the air in the total obſcuration of the Sun, would not be <lb></lb>come ſo duskiſh, as at ſuch a time it is, but by means of the <lb></lb>tranſparency of the body of the Moon, a refracted light would <lb></lb>paſſe through it, as we ſee it doth through the thickeſt clouds. </s><s>But <lb></lb>as to the obſcurity, I believe not that the Moon is wholly depri <lb></lb>ved of light, as the Earth; nay, that clarity which is ſeen in the <lb></lb>remainder of its <emph type="italics"></emph>Diſcus,<emph.end type="italics"></emph.end> over and above the ſmall creſcent en <lb></lb>lightened by the Sun, I repute to be its proper and natural light, <lb></lb><arrow.to.target n="marg157"></arrow.to.target> <lb></lb>and not a reflection of the Earth, which I eſteem unable, by <lb></lb>reaſon of its aſperity (craggineſſe) and obſcurity, to reflect the <lb></lb>raies of the Sun. </s><s>In the third Parallel I aſſent unto you in one <lb></lb><arrow.to.target n="marg158"></arrow.to.target> <lb></lb>part, and diſſent in another: I agree in judging the body of the <lb></lb>Moon to be moſt ſolid and hard, like the Earth, yea much more; <lb></lb><arrow.to.target n="marg159"></arrow.to.target> <lb></lb>for if from <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> we receive that the Heavens are impenetrable, <lb></lb>and the Stars the moſt denſe parts of Heaven, it muſt neceſſarily <lb></lb>follow, that they are moſt ſolid and moſt impenetrable.</s></p><p type="margin"><s><margin.target id="marg157"></margin.target><emph type="italics"></emph>The ſecond clarity <lb></lb>of the Moon e <lb></lb>ſteemed to be its <lb></lb>native light.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg158"></margin.target><emph type="italics"></emph>The Earth unable <lb></lb>to reflect the Suns <lb></lb>raies.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg159"></margin.target><emph type="italics"></emph>The ſubſtance of <lb></lb>the Heavens impe <lb></lb>netrable, accord <lb></lb>ing to<emph.end type="italics"></emph.end> Ariſtotle.</s></p><p type="main"><s>SAGR. </s><s>What excellent matter would the Heavens afford us for <lb></lb>to make Pallaces of, if we could procure a ſubſtance ſo hard and ſo <lb></lb>tranſparent?</s></p> <pb xlink:href="040/01/071.jpg" pagenum="55"></pb><p type="main"><s>SALV. </s><s>Rather how improper, for being by its tranſparence, <lb></lb>wholly inviſible, a man would not be able without ſtumbling at <lb></lb>the threſholds, and breaking his head againſt the Walls, to paſs <lb></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 ſome <lb></lb><arrow.to.target n="marg160"></arrow.to.target> <lb></lb><emph type="italics"></emph>Peripateticks<emph.end type="italics"></emph.end> ſay, that it is intangible: and if one cannot <lb></lb>touch it, much leſs can it hurt him.</s></p><p type="margin"><s><margin.target id="marg160"></margin.target><emph type="italics"></emph>The ſubstance of <lb></lb>Heaven intangi <lb></lb>ble.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>This would not ſerve the turn, for though the matter <lb></lb>of the Heavens cannot be toucht, as wanting tangible qualities: <lb></lb>yet may it eaſily touch the elementary bodies; and to offend us <lb></lb>it is as ſufficient that it ſtrike us, nay worſe, than if we ſhould <lb></lb>ſtrike it. </s><s>But let us leave theſe <emph type="italics"></emph>Pallaces,<emph.end type="italics"></emph.end> or, to ſay better, theſe <lb></lb><emph type="italics"></emph>Caſtles<emph.end type="italics"></emph.end> in the air, and not interrupt <emph type="italics"></emph>Simplicius.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>The queſtion which you have ſo caſually ſtarted, is one <lb></lb>of the moſt difficulty that is diſputed in Philoſophy; and I have <lb></lb>on that ſubject moſt excellent conceits of a very learned Doctor <lb></lb>of <emph type="italics"></emph>Padoua,<emph.end type="italics"></emph.end> but it is not now time to enter upon them. </s><s>Therefore <lb></lb>returning to our purpoſe, I ſay that the Moon, in my opinion, is <lb></lb>much more ſolid than the Earth, but do not infer the ſame, as you <lb></lb>do, from the craggineſs and montuoſity of its ſuperficies; but <lb></lb><arrow.to.target n="marg161"></arrow.to.target> <lb></lb>rather from the contrary, namely, from its aptitude to receive (as <lb></lb>we ſee it experimented in the hardeſt ſtones) a poliſh and luſtre <lb></lb>exceeding that of the ſmootheſt glaſs, for ſuch neceſſarily muſt <lb></lb>its ſuperficies be, to render it apt to make ſo lively reflection of <lb></lb>the Suns rays. </s><s>And for thoſe appearances which you mention, <lb></lb>of Mountains, Cliffs, Hills, Valleys, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> they are all illuſions: <lb></lb>and I have been preſent at certain publick diſputes, where I have <lb></lb>heard it ſtrongly maintained againſt theſe introducers of novelties, <lb></lb><arrow.to.target n="marg162"></arrow.to.target> <lb></lb>that ſuch appearances proceed from nothing elſe, but from the un <lb></lb>equal diſtribution of the opacous and perſpicuous parts, of which <lb></lb>the Moon is inwardly and outwardly compoſed: as we ſee it <lb></lb>often fall out in chryſtal, amber, and many other precious ſtones <lb></lb>of perfect luſtre; in which by reaſon of the opacity of ſome parts, <lb></lb>and the tranſparency of others, there doth appear ſeveral conca <lb></lb>vities and prominencies. </s><s>In the fourth reſemblance, I grant, that <lb></lb>the ſuperficies of Terreſtrial Globe beheld from afar, would make <lb></lb>two different appearances, namely, one more clear, the other more <lb></lb>dark; but I believe that ſuch diverſity would ſucceed quite con <lb></lb>trary to what you ſay; that is, I hold that the ſurface of the wa <lb></lb>ter would appear lucid, becauſe that it is ſmooth and tranſparent; <lb></lb>and that of the Earth would appear obſcure, by reaſon of its o <lb></lb>pacity and ſcabroſity, ill accommodated for reflecting the light of <lb></lb>the Sun. </s><s>Concernïng the fifth compariſon, I grant it wholly, and <lb></lb>am able, in caſe the Earth did ſhine as the Moon, to ſhow the <lb></lb>ſame to any one that ſhould from thence above behold it, repre <pb xlink:href="040/01/072.jpg" pagenum="56"></pb>ſented by figures anſwerable to thoſe which we ſee in the Moon: <lb></lb>I comprehend alſo, how the period of its illumination and varia <lb></lb>tion of figure, would be monthly, albeit the Sun revolves round <lb></lb>about it in twenty four hours: and laſtly, I do not ſcruple to <lb></lb>admit, that the half onely of the Moon ſeeth all the Earth, and <lb></lb>that all the Earth ſeeth but onely half of the Moon. </s><s>For what <lb></lb>remains, I repute it moſt falſe, that the Moon can receive light <lb></lb>from the Earth, which is moſt obſcure, opacous, and utterly un <lb></lb>apt to reflect the Suns light, as the Moon doth reflect it to us: and <lb></lb>as I have ſaid, I hold that that light which we ſee in the remain <lb></lb>der of the Moons face (the ſplendid creſcents ſubducted) by the <lb></lb>illumination, is the proper and natural light of the Moon, and no <lb></lb>eaſie matter would induce me to believe otherwiſe. </s><s>The ſeventh, <lb></lb>touching the mutual Eclipſes, may be alſo admitted; howbeit <lb></lb>that is wont to be called the eclipſe of the Sun, which you are <lb></lb>pleaſed to phraſe the eclipſe of the Earth. </s><s>And this is what <emph type="italics"></emph>I<emph.end type="italics"></emph.end> <lb></lb>have at this time to ſay in oppoſition to your ſeven congruities <lb></lb>or reſemblances, to which objections, if you are minded to make <lb></lb>any reply, <emph type="italics"></emph>I<emph.end type="italics"></emph.end> ſhall willingly hear you.</s></p><p type="margin"><s><margin.target id="marg161"></margin.target><emph type="italics"></emph>The ſuperficies of <lb></lb>the Moon more <lb></lb>ſleek than any <lb></lb>Looking-glaß.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg162"></margin.target><emph type="italics"></emph>The eminencies <lb></lb>and cavities in the <lb></lb>Moon are illuſions <lb></lb>of its opacous and <lb></lb>perspicuous parts.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>If I have well apprehended what you have anſwered, it <lb></lb>ſeems to me, that there ſtill remains in controverſie between us, cer <lb></lb>tain conditions, which I made common betwixt the Moon & Earth, <lb></lb>and they are theſe; You eſteem the Moon to be ſmooth and poliſht, <lb></lb>as a Looking-glaſs, and as ſuch, able to reflect the Suns light; and <lb></lb>contrarily, the Earth, by reaſon of its montuoſity, unable to make <lb></lb>ſuch reflection: You yield the Moon to be ſolid and hard, and that <lb></lb>you argue from its being ſmooth and polite, and not from its being <lb></lb>montuous; and for its appearing montuous, you aſſign as the <lb></lb>cauſe, that it conſiſts of parts more and leſs opacous and perſpi <lb></lb>cuous. </s><s>And laſtly, you eſteem that ſecondary light, to be proper <lb></lb>to the <emph type="italics"></emph>M<emph.end type="italics"></emph.end>oon, and not reflected from the Earth; howbeit you <lb></lb>ſeem not to deny the ſea, as being of a ſmooth ſurface, ſome <lb></lb>kind of reflection. </s><s>As to the convincing you of that error, that <lb></lb>the reflection of the <emph type="italics"></emph>M<emph.end type="italics"></emph.end>oon is made, as it were, like that of a <lb></lb>Looking-glaſs, <emph type="italics"></emph>I<emph.end type="italics"></emph.end> have ſmall hope, whilſt <emph type="italics"></emph>I<emph.end type="italics"></emph.end> ſee, that what hath <lb></lb><arrow.to.target n="marg163"></arrow.to.target> <lb></lb>been read in the ^{*} <emph type="italics"></emph>Saggiator<emph.end type="italics"></emph.end> and in the <emph type="italics"></emph>Solar Letters<emph.end type="italics"></emph.end> of our <emph type="italics"></emph>Com <lb></lb>mon Friend,<emph.end type="italics"></emph.end> hath profited nothing in your judgment, if haply <lb></lb>you have attentively read what he hath there written on this ſub <lb></lb>ject.</s></p><p type="margin"><s><margin.target id="marg163"></margin.target>* <emph type="italics"></emph>Il Saggiatore, & <lb></lb>Lettere Solari,<emph.end type="italics"></emph.end> <lb></lb>two Treatiſes of <lb></lb><emph type="italics"></emph>Galilæus.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. <emph type="italics"></emph>I<emph.end type="italics"></emph.end> have peruſed the ſame ſo ſuperficially, according to <lb></lb>the ſmall time of leaſure allowed me from more ſolid ſtudies; <lb></lb>therefore, if you think you can, either by repeating ſome of thoſe <lb></lb>reaſons, or by alledging others, reſolve me theſe doubts, <emph type="italics"></emph>I<emph.end type="italics"></emph.end> will <lb></lb>hearken to them attentively.</s></p><p type="main"><s>SALV. <emph type="italics"></emph>I<emph.end type="italics"></emph.end> will tell you what comes into my mind upon the <pb xlink:href="040/01/073.jpg" pagenum="57"></pb>inſtant, and its poſſible it may be a commixtion of my own con <lb></lb>ceipts; and thoſe which I have ſometime read in the fore-ſaid <lb></lb>Books, by which I well remember, that I was then perfectly <lb></lb>ſatisfied, although the concluſions, at firſt ſight ſeem'd unto me <lb></lb>ſtrange Paradoxes. </s><s>We enquire <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> whether to the ma <lb></lb>king a reflection of light, like that which we receive from the <lb></lb>Moon, it be neceſſary that the ſuperficies from whence the refle <lb></lb>ction commeth, be ſo ſmooth and polite, as the face of a Looking <lb></lb>Glaſſe, or whether a ſuperficies not ſmooth or poliſht, but rough <lb></lb>and uneven, be more apt for ſuch a purpoſe. </s><s>Now ſuppoſing <lb></lb>two reflections ſhould come unto us, one more bright, the other <lb></lb>leſſe, from two ſuperficies oppoſite unto us, I demand of you, <lb></lb>which of the two ſuperficies you think would repreſent it ſelf to <lb></lb>our ſight, to be the cleareſt, and which the obſcureſt.</s></p><p type="main"><s>SIMPL. </s><s>I am very confident, that that ſame, which moſt for <lb></lb>cibly reflected the light upon me, would ſhew its ſelf in its aſpect <lb></lb>the clearer, and the other darker.</s></p><p type="main"><s>SALV. </s><s>Be pleaſed to take that Glaſſe which hangs on yonder <lb></lb><arrow.to.target n="marg164"></arrow.to.target> <lb></lb>Wall, and let us go out into the Court-yard. </s><s>Come <emph type="italics"></emph>Sagredus.<emph.end type="italics"></emph.end> <lb></lb>Now hang the glaſſe yonder, againſt that ſame Wall, on which <lb></lb>the Sun ſhines, and now let us with-draw our ſelves into the ſhade. <lb></lb></s><s>See yonder two ſuperficies beaten by the Sun, namely, the Wall <lb></lb>and the Glaſſe. </s><s>Tell me now which appears cleareſt unto you, <lb></lb>that of the Wall or that of the Glaſſe? </s><s>Why do you not anſwer <lb></lb>me?</s></p><p type="margin"><s><margin.target id="marg164"></margin.target><emph type="italics"></emph>It is proved at <lb></lb>large that the <lb></lb>Moons ſurface is <lb></lb>ſharp.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I leave the reply to <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> who made the queſti <lb></lb>on; but I, for my own part, am perſwaded upon this ſmall be <lb></lb>ginning of the experiment, that the Moon muſt be of a very un <lb></lb>poliſht ſurface.</s></p><p type="main"><s>SALV. </s><s>What ſay you <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> if you were to depaint that <lb></lb>Wall, and that Glaſſe faſtened unto it, where would you uſe <lb></lb>your darkeſt colours, in deſigning the Wall, or elſe in painting <lb></lb>the Looking-Glaſſe.</s></p><p type="main"><s>SIMPL. </s><s>Much the darker in depainting the Glaſſe.</s></p><p type="main"><s>SALV. </s><s>Now if from the ſuperficies, which repreſents it ſelf <lb></lb>more clear, there proceedeth a more powerful reflection of light, <lb></lb>the Wall will more forcibly reflect the raies of the Sun, than the <lb></lb>Glaſſe.</s></p><p type="main"><s>SIMPL. </s><s>Very well, Sir, have you ever a better experiment <lb></lb>than this? </s><s>you have placed us where the Glaſſe doth not rever <lb></lb>berate upon us; but come along with me a little this way; how, <lb></lb>will you not ſtir?</s></p><p type="main"><s>SAGR. </s><s>You perhaps ſeek the place of the reflection, which the <lb></lb>Glaſſe makth.</s></p><p type="main"><s>SIMPL. </s><s>I do ſo.</s></p> <pb xlink:href="040/01/074.jpg" pagenum="58"></pb><p type="main"><s>SAGR. </s><s>Why look you, there it is upon the oppoſite Wall, juſt <lb></lb>as big as the Glaſſe, and little leſſe bright than if the Sun had <lb></lb>directly ſhined upon it.</s></p><p type="main"><s>SIMPL. </s><s>Come hither therefore, and ſee from hence the ſur <lb></lb>face of the Glaſſe, and tell me whether you think it more ob <lb></lb>ſcure than that of the Wall.</s></p><p type="main"><s>SAGR. </s><s>Look on it your ſelf, for I have no mind at this time, <lb></lb>to dazle my eyes; and I know very well, without ſeeing it, <lb></lb>that it there appears as ſplendid and bright as the Sun it ſelf, or <lb></lb>little leſſe.</s></p><p type="main"><s>SIMPL. </s><s>What ſay you therefore, is the reflection of a Glaſſe <lb></lb>leſſe powerful than that of a Wall? </s><s>I ſee, that in this oppoſite <lb></lb>Wall, where the reflection of the other illuminated Wall comes, <lb></lb>together with that of the Glaſſe, this of the Glaſſe is much <lb></lb>clearer; and I ſee likewiſe, that, from this place where I ſtand, <lb></lb>the glaſſe it ſelf appears with much more luſtre than the Wall.</s></p><p type="main"><s>SALV. </s><s>You have prevented me with your ſubtlety; for I ſtood <lb></lb>in need of this very obſervation to demonſtrate what remains. <lb></lb></s><s>You ſee then the difference which happens betwixt the two refle <lb></lb>ctions made by the two ſuperficies of the Wall and Glaſſe, per <lb></lb>cu'ſt in the ſelf-ſame manner, by the rayes of the Sun; and you <lb></lb>ſee, how the reflection which comes from the Wall, diffuſeth it <lb></lb>ſelf towards all the parts oppoſite to it, but that of the Glaſſe <lb></lb>goeth towards one part onely, not at all bigger than the Glaſſe <lb></lb>it ſelf: you ſee likewiſe, how the ſuperficies of the Wall, beheld <lb></lb>from what part ſoever, alwayes ſhews it ſelf of one and the ſame <lb></lb>cleerneſſe, and every way, much clearer than that of the Glaſſe, <lb></lb>excepting only in that little place, on which the Glaſſes reflection <lb></lb>reverberates, for from thence indeed the Glaſſe appears much more <lb></lb>lucid than the Wall. </s><s>By theſe ſo ſenſible, and palpable experi <lb></lb>ments, my thinks one may ſoon come to know, whether the <lb></lb>reflection which the Moon ſends upon us, proceed as from a <lb></lb>Glaſſe, or elſe, as from a Wall, that is, from a ſmooth ſuperfi <lb></lb>cies, or a rugged.</s></p><p type="main"><s>SAGR. </s><s>If I were in the Moon it ſelf, I think I could not with <lb></lb>my hands more plainly feel the unevenneſſe of its ſuperficies, than <lb></lb>I do now perceive it, by apprehending your diſcourſe. </s><s>The Moon <lb></lb>beheld in any poſture, in reſpect of the Sun and us, ſheweth us <lb></lb>its ſuperficies, touch't by the Suns rayes, alwayes equally clear; <lb></lb>an effect, which anſwers to an hair that of the Wall, which be <lb></lb>held from what place ſoever, appeareth equally bright, and dif <lb></lb>fereth from the Glaſſe, which from one place onely appeareth lu <lb></lb>cid, and from all others obſcure. </s><s>Moreover, the light which <lb></lb>cometh to me from the reflection of the Wall, is tollerable, <lb></lb>and weak, in compariſon of that of the Glaſſe, which is little <pb xlink:href="040/01/075.jpg" pagenum="59"></pb>leſſe forcible and offenſive to the ſight, than that primary and <lb></lb>direct light of the Sun. </s><s>And thus without trouble do we behold <lb></lb>the face of the Moon; which were it as a Glaſſe, it appearing to <lb></lb>us by reaſon of its vicinity, as big as the Sun it ſelf, its ſplendor <lb></lb>would be abſolutely intollerable, and would ſeem as if we beheld <lb></lb>another Sun.</s></p><p type="main"><s>SALV. </s><s>Aſcribe not, I beſeech you <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> more to my de <lb></lb>monſtration, than it produceth. </s><s>I will oppoſe you with an inſtance, <lb></lb>which I ſee not well how you can eaſily reſolve. </s><s>You inſiſt upon it <lb></lb>as a grand difference between the Moon and Glaſſe, that it emits <lb></lb>its reflection towards all parts equally, as doth the Wall; where <lb></lb>as the Glaſſe caſts it upon one onely determinate place; and from <lb></lb>hence you conclude the Moon to be like to the Wall, and not to <lb></lb>the Glaſſe: But I muſt tell you, that that ſame Glaſſe caſts its <lb></lb><arrow.to.target n="marg165"></arrow.to.target> <lb></lb>reflection on one place onely, becauſe its ſurface is flat, and the <lb></lb>reflex rayes being to depart at angles equal to thoſe of the rayes <lb></lb>of incidence, it muſt follow that from a plane or flat ſuperficies, <lb></lb>they do depart unitedly towards the ſame place; but in regard <lb></lb>that the ſuperficies of the Moon is not plain, but ſpherical, and <lb></lb>the incident rayes upon ſuch a ſuperficies, being to reflect them <lb></lb>ſelves at angles equal to thoſe of the incidence towards all parts, <lb></lb>by means of the infinity of the inclinations which compoſe the <lb></lb>ſpherical ſuperficies, therefore the Moon may ſend forth its reflecti <lb></lb>on every way; and there is no neceſſity for its repercuſſion upon one <lb></lb>place onely, as that Glaſſe which is flat.</s></p><p type="margin"><s><margin.target id="marg165"></margin.target><emph type="italics"></emph>Flat Looking <lb></lb>glaſſes caſt forth <lb></lb>the reflection to <lb></lb>wards but one <lb></lb>place, but the <lb></lb>ſpherical every <lb></lb>way.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>This is one of the very ſame objections, which I in <lb></lb>tended to have made againſt him.</s></p><p type="main"><s>SAGR. </s><s>If this be one, you had need have more of them; yet <lb></lb>I tell you, that as to this firſt, it ſeems to me to make more a <lb></lb>gainſt you, than for you.</s></p><p type="main"><s>SIMPL. </s><s>You have pronounced as a thing manifeſt, that the refle <lb></lb>ction made by that Wall, is as cleer and lucid as that which the <lb></lb>Moon ſends forth, and I eſteem it nothing in compariſon thereto. <lb></lb></s><s>“For, in this buſineſſe of the illumination, its requiſite to reſpect, <lb></lb>and to diſtinguiſh the <emph type="italics"></emph>Sphere<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Activity<emph.end type="italics"></emph.end>; and who queſtions <lb></lb><arrow.to.target n="marg166"></arrow.to.target> <lb></lb>but the Cœleſtial bodies have greater Spheres of activity, than <lb></lb>theſe our elementary, frail, and mortal ones? </s><s>and that Wall, <lb></lb>finally, what elſe is it but a little obſcure Earth, unapt to <lb></lb>ſhine?”</s></p><p type="margin"><s><margin.target id="marg166"></margin.target><emph type="italics"></emph>The ſphere of <lb></lb>Activity greater <lb></lb>in the Cœleſtial <lb></lb>bodies than in Ele <lb></lb>mentary.<emph.end type="italics"></emph.end></s></p><p type="main"><s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>AGR. </s><s>And here alſo I believe, that you very much deceive your <lb></lb>felf. </s><s>But I come to the firſt objection moved by <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end>; and <lb></lb>I conſider, that to make a body appear unto us luminous, it ſuf <lb></lb>ficeth not that the rayes of the illuminating body fall upon it, <lb></lb>but it is moreover requiſite that the reflex rayes arrive to our <lb></lb>eye; as is manifeſtly ſeen in the example of that Glaſſe, upon <pb xlink:href="040/01/076.jpg" pagenum="60"></pb>which, without queſtion, the illuminating rayes of the Sun do <lb></lb>come; yet nevertheleſſe, it appears not to us bright and ſhining, <lb></lb>unleſſe we ſet our eye in that particular place, where the refle <lb></lb>ction arriveth. </s><s>Now let us conſider what would ſucceed, were <lb></lb>the glaſſe of a ſpherical figure; for without doubt, we ſhould <lb></lb>find, that of the reflection made by the whole ſurface illumina <lb></lb>ted, that to be but a very ſmall part, which arriveth to the eye <lb></lb>of a particular beholder; by reaſon that that is but an inconſide <lb></lb>rable particle of the whole ſpherical ſuperficies, the inclination <lb></lb>of which caſts the ray to the particular place of the eye; whence <lb></lb>the part of the ſpherical ſuperficies, which ſhews it ſelf ſhining <lb></lb>to the eye, muſt needs be very ſmall; all the reſt being repre <lb></lb>ſented obſcure. </s><s>So that were the Moon ſmooth, as a Looking <lb></lb><arrow.to.target n="marg167"></arrow.to.target> <lb></lb>glaſſe, a very ſmall part would be ſeen by any particular eye to <lb></lb>be illuſtrated by the Sun, although its whole Hemiſphere were ex <lb></lb>poſed to the Suns rayes; and the reſt would appear to the eye of <lb></lb>the beholder as not illuminated, and therefore inviſible; and <lb></lb>finally, the whole Moon would be likewiſe inviſible, for ſo much <lb></lb>as that particle, whence the reflection ſhould come, by reaſon of <lb></lb>its ſmalneſſe and remoteneſſe, would be loſt. </s><s>And as it would be <lb></lb>inviſible to the eye, ſo would it not afford any light; for it is al <lb></lb>together impoſſible, that a bright body ſhould take away our <lb></lb>darkneſſe by its ſplendor, and we not to ſee it.</s></p><p type="margin"><s><margin.target id="marg167"></margin.target><emph type="italics"></emph>The Moon if it <lb></lb>were ſmooth, like a <lb></lb>ſpherical glaſſe, <lb></lb>would be inviſible.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Stay good <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> for I ſee ſome emotions in <lb></lb>the face and eyes of <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> which are to me as indices that <lb></lb>he is not either very apprehenſive of, or ſatisfied with this which <lb></lb>you, with admirable proof, and abſolute truth have ſpoken. <lb></lb></s><s>And yet I now call to mind, that I can by another experiment <lb></lb>remove all ſcruple. </s><s>I have ſeen above in a Chamber, a great <lb></lb>ſpherical Looking-glaſſe; let us ſend for it hither, and whileſt it <lb></lb>is in bringing, let <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> return to conſider, how great the <lb></lb>clarity is which cometh to the Wall here, under the penthouſe, <lb></lb>from the reflection of the flat glaſſe.</s></p><p type="main"><s>SIMPL. </s><s>I ſee it is little leſſe ſhining, than if the Sun had di <lb></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 ſmall <lb></lb>flat glaſſe, we ſhould put that great ſpherical one in the ſame <lb></lb>place, what effect (think you) would its reflection have upon the <lb></lb>ſame Wall?</s></p><p type="main"><s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>IMPL. </s><s>I believe that it would eject upon it a far greater and <lb></lb>more diffuſed light.</s></p><p type="main"><s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>ALV. </s><s>But if the illumination ſhould be nothing, or ſo <lb></lb>ſmall, that you would ſcarſe diſcern it, what would you ſay <lb></lb>then?</s></p><p type="main"><s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>IMPL. </s><s>When I have ſeen the effect, I will bethink my ſelf <lb></lb>of an anſwer.</s></p> <pb xlink:href="040/01/077.jpg" pagenum="61"></pb><p type="main"><s>SALV. </s><s>See here is the glaſſe, which I would have to be placed <lb></lb>cloſe to the other. </s><s>But firſt let us go yonder towards the reflection <lb></lb>of that flat one, and attentively obſerve its clarity; ſee how <lb></lb>bright it is here where it ſhines, and how diſtinctly one may diſcern <lb></lb>theſe ſmall unevenneſſes in the Wall.</s></p><p type="main"><s>SIMPL. </s><s>I have ſeen and very well obſerved the ſame, now place <lb></lb>the other glaſſe by the ſide of the firſt.</s></p><p type="main"><s>SALV. </s><s>See where it is. </s><s>It was placed there aſſoon as you be <lb></lb>gan to look upon the Walls ſmall unevenneſſes, and you percei <lb></lb>ved it not, ſo great was the encreaſe of the light all over the reſt of <lb></lb>the Wall. </s><s>Now take away the flat glaſſe. </s><s>Behold now all refle <lb></lb>ction removed, though the great convex glaſſe ſtill remaineth. <lb></lb></s><s>Remove this alſo, and place it there again if you pleaſe, and you <lb></lb>ſhall ſee no alteration of light in all the Wall. </s><s>See here then de <lb></lb>monſtrated to ſenſe, that the reflection of the Sun, made upon a <lb></lb>ſpherical convex glaſſe, doth not ſenſibly illuminate the places neer <lb></lb>unto it. </s><s>Now what ſay you to this experiment?</s></p><p type="main"><s>SIMPL. </s><s>I am afraid that there may be ſome <emph type="italics"></emph>Leigerdemain,<emph.end type="italics"></emph.end> <lb></lb>uſed in this affair; yet in beholding that glaſſe I ſee it dart forth <lb></lb>a great ſplendor, which dazleth my eyes; and that which im <lb></lb>ports moſt of all, I ſee it from what place ſoever I look upon it; <lb></lb>and I ſee it go changing ſituation upon the ſuperficies of the glaſſe, <lb></lb>which way ſoever I place my ſelf to look upon it; a neceſſary ar <lb></lb>gument, that the light is livelily reflected towards every ſide, and <lb></lb>conſequently, as ſtrongly upon all that Wall, as upon my eye.</s></p><p type="main"><s>SALV. </s><s>Now you ſee how cautiouſly and reſervedly you ought <lb></lb>to proceed in lending your aſſent to that, which diſcourſe alone re <lb></lb>preſenteth to you. </s><s>There is no doubt but that this which you ſay, <lb></lb>carrieth with it probability enough, yet you may ſee, how ſenſi <lb></lb>ble experience proves the contrary.</s></p><p type="main"><s>SIMPL. </s><s>How then doth this come to paſs?</s></p><p type="main"><s>SALV. </s><s>I will deliver you my thoughts thereof, but I cannot <lb></lb>tell how you may be pleaſ'd therewith. </s><s>And firſt, that lively <lb></lb>ſplendor which you ſee upon the glaſs, and which you think occu <lb></lb>pieth a good part thereof, is nothing near ſo great, nay is very ex <lb></lb>ceeding ſmall; but its livelineſs occaſioneth in your eye, (by means <lb></lb>of the reflection made on the humidity of the extream parts of the <lb></lb>eye-brows, which diſtendeth upon the pupil) an adventitious irradi <lb></lb>ation, like to that blaze which we think we ſee about the flame of <lb></lb>a candle placed at ſome diſtance; or if you will, you may <lb></lb>reſemble it to the adventitious ſplendor of a ſtar; for if you ſhould <lb></lb><arrow.to.target n="marg168"></arrow.to.target> <lb></lb>compare the ſmall body <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> of the <emph type="italics"></emph>Canicula,<emph.end type="italics"></emph.end> ſeen in the day time <lb></lb>with the <emph type="italics"></emph>Teleſcope,<emph.end type="italics"></emph.end> when it is ſeen without ſuch irradiation, with <lb></lb>the ſame ſeen by night by the eye it ſelf, you will doubtleſs com <lb></lb>prehend that being irradiated, it appeareth above a thouſand <pb xlink:href="040/01/078.jpg" pagenum="62"></pb>times bigger than the naked and real body: and a like or greater <lb></lb>augmentation doth the image of the Sun make, which you ſee in <lb></lb>that glaſs. </s><s>I ſay greater, for that it is more lively than the ſtar, <lb></lb>as is manifeſt from our being able to behold the ſtar with much <lb></lb>leſs offence, than this reflection of the glaſs. </s><s>The reverberation <lb></lb>therefore which is to diſpere it ſelf all over this wall, cometh from <lb></lb>a ſmall part of that glaſs, and that which even now came from <lb></lb>the whole flat glaſs diſperſed and reſtrain'd it ſelf to a very ſmall <lb></lb>part of the ſaid wall. </s><s>What wonder is it then, that the firſt re <lb></lb>flection very lively illuminates, and that this other is almoſt im <lb></lb>perceptible?</s></p><p type="margin"><s><margin.target id="marg168"></margin.target><emph type="italics"></emph>The ſmall body of <lb></lb>the ſtars fringed <lb></lb>round about with <lb></lb>rays, appeareth ve <lb></lb>ry much biggerthan <lb></lb>plain and naked, <lb></lb>and in its native <lb></lb>clarity.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>I find my ſelf more perplexed than ever, and there <lb></lb>preſents it ſelf unto me the other difficulty, how it can be that <lb></lb>that wall, being of a matter ſo obſcure, and of a ſuperficies ſo un <lb></lb>poliſh'd, ſhould be able to dart from it greater light, than a glaſs <lb></lb>very ſmooth and polite.</s></p><p type="main"><s>SALV. </s><s>Greater light it is not, but more univerſal; for as to <lb></lb>the degree of brightneſs, you ſee that the reflection of that ſmall <lb></lb>flat glaſs, where it beamed forth yonder under the ſhadow of the <lb></lb>penthouſe, illuminateth very much; and the reſt of the wall which <lb></lb>receiveth the reflection of the wall on which the glaſs is placed, <lb></lb>is not in any great meaſure illuminated, as was the ſmall part on <lb></lb>which the reflection of the glaſs fell. </s><s>And if you would under <lb></lb>ſtand the whole of this buſineſs, you muſt conſider that the ſuper <lb></lb><arrow.to.target n="marg169"></arrow.to.target> <lb></lb>ficies of that wall's being rough, is the ſame as if it were compo <lb></lb>ſed of innumerable ſmall ſuperficies, diſpoſed according to in <lb></lb>numerable diverſities of inclinations: amongſt which it neceſſa <lb></lb>rily happens, that there are many diſpoſed to ſend forth their <lb></lb>reflex rays from them into ſuch a place, many others into another: <lb></lb>and in ſum, there is not any place to which there comes not very <lb></lb>many rays, reflected from very many ſmall ſuperficies, diſperſed <lb></lb>throughout the whole ſuperficies of the rugged body, upon which <lb></lb>the rays of the Sun fall. </s><s>From which it neceſſarily follow <lb></lb>eth, That upon any, whatſoever, part of any ſuperficies, <lb></lb>oppoſed to that which receiveth the primary incident rays, <lb></lb>there is produced reflex rays, and conſequently illumi <lb></lb>nation. </s><s>There doth alſo follow thereupon, That the ſame <lb></lb>body upon which the illuminating rays fall, beheld from <lb></lb>whatſoever place, appeareth all illuminated and ſhining: and <lb></lb>therefore the Moon, as being of a ſuperficies rugged and <lb></lb><arrow.to.target n="marg170"></arrow.to.target> <lb></lb>not ſmooth, beameth forth the light of the Sun on every <lb></lb>ſide, and to all beholders appeareth equally lucid. </s><s>But if <lb></lb>the ſurface of it, being ſpherical, were alſo ſmooth as a glaſs, it <lb></lb>would become wholly inviſible; foraſmuch as that ſmall part, <lb></lb>from which the image of the Sun ſhould be reflected unto the eye <pb xlink:href="040/01/079.jpg" pagenum="63"></pb>of a particular perſon, by reaſon of its great diſtance would be in <lb></lb>viſible, as I have ſaid before.</s></p><p type="margin"><s><margin.target id="marg169"></margin.target><emph type="italics"></emph>The reflex light <lb></lb>of uneven bodies, is <lb></lb>more univerſal <lb></lb>than that of the <lb></lb>ſmooth, & why.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg170"></margin.target><emph type="italics"></emph>The Moon, if it <lb></lb>were ſmooth and <lb></lb>ſleek, would be in <lb></lb>viſible.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>I am very apprehenſive of your diſcourſe; yet me <lb></lb>thinks I am able to reſolve the ſame with very little trouble; and <lb></lb>eaſily to maintain, that the Moon is rotund and polite, and that it <lb></lb>reflects the Suns light unto us in manner of a glaſs; nor there <lb></lb>fore ought the image of the Sun to be ſeen in the middle of it, “for <lb></lb>aſmuch as the ſpecies of the Sun it ſelf admits not its ſmall figure <lb></lb>to be ſeen at ſo great a diſtance, but the light produced by the <lb></lb>Sun may help us to conceive that it illuminateth the whole Lu <lb></lb>nar Body: a like effect we may ſee in a plate gilded and well <lb></lb>polliſh'd, which touch't by a luminous body, appeareth to him <lb></lb>that beholds it at ſome diſtance to be all ſhining; and onely near <lb></lb>at hand one may diſcover in the middle of it the ſmall image of <lb></lb>the luminous body.”</s></p><p type="main"><s>SALV. </s><s>Ingenuouſly confeſſing my dullneſs of apprehenſion, <lb></lb>I muſt tell you, that I underſtand not any thing of this your diſ <lb></lb>courſe, ſave onely what concerns the gilt plate: and if you permit <lb></lb>me to ſpeak freely, I have a great conceit that you alſo underſtand <lb></lb>not the ſame, but have learnt by heart thoſe words written by ſome <lb></lb>one out of a deſire of contradiction, and to ſhew himſelf more intel <lb></lb>ligent than his adverſary; but it muſt be to thoſe, which to appear <lb></lb>alſo more wiſe, applaud that which they do not underſtand, and <lb></lb>entertain a greater conceit of perſons, the leſs they are by them <lb></lb>underſtood: and the writer himſelf may be one of thoſe (of which <lb></lb>there are many) who write what they do not underſtand, and <lb></lb><arrow.to.target n="marg171"></arrow.to.target> <lb></lb>conſequently underſtand not what they write. </s><s>Therefore, o <lb></lb>mitting the reſt, I reply, as to the gilt plate, that if it be flat and <lb></lb>not very big, it may appear at a diſtance very bright, whilſt a great <lb></lb>light beameth upon it, but yet it muſt be when the eye is in a de <lb></lb>terminate line, namely in that of the reflex rays: and it will ap <lb></lb>pear the more ſhining, if it were <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> of ſilver, by means of its <lb></lb>being burniſhed, and apt through the great denſity of the metal, <lb></lb>to receive a perfect poliſh. </s><s>And though its ſuperficies, being very <lb></lb>well brightned, were not exactly plain, but ſhould have various in <lb></lb>clinations, yet then alſo would its ſplendor be ſeen many ways; <lb></lb>namely, from as many places as the various reflections, made by <lb></lb>the ſeveral ſuperficies, do reach: for therefore are Diamonds <lb></lb><arrow.to.target n="marg172"></arrow.to.target> <lb></lb>ground to many ſides, that ſo their pleaſing luſtre might be beheld <lb></lb>from many places. </s><s>But if the Plate were very big, though it ſhould <lb></lb>be all plain, yet would it not at a diſtance appear all over ſhining: <lb></lb>and the better to expreſs my ſelf, Let us ſuppoſe a very large gilt <lb></lb>plate expoſed to the Sun, it will ſhew to an eye far diſtant, the <lb></lb>image of the Sun, to occupy no more but a certain part of the ſaid <lb></lb>plate; to wit, that from whence the reflection of the incident <pb xlink:href="040/01/080.jpg" pagenum="64"></pb>ſolar rays come: but it is true that by the vivacity of the light, the <lb></lb>ſaid image will appear fringed about with many rays, and ſo will <lb></lb>ſeem to occupie a far greater part of the plate, than really it doth. <lb></lb></s><s>And to ſhew that this is true, when you have noted the particular <lb></lb>place of the plate from whence the reflection cometh, and concei <lb></lb>ved likewiſe how great the ſhining place appeared to you, cover the <lb></lb>greater part of that ſame ſpace, leaving it only viſible about the <lb></lb>midſt; and all this ſhall not any whit diminiſh the apparent ſplen <lb></lb>dor to one that beholds it from afar; but you ſhall ſee it largely <lb></lb>diſpers'd upon the cloth or other matter, wherewith you covered <lb></lb>it. </s><s>If therefore any one, by ſeeing from a good diſtance a ſmall <lb></lb>gilt plate to be all over ſhining, ſhould imagine that the ſame <lb></lb>would alſo even in a plate as broad as the Moon, he is no leſs de <lb></lb>ceived, than if he ſhould believe the Moon to be no bigger than <lb></lb>the bottom of a tub. </s><s>If again the plate were turn'd into a ſphe <lb></lb>rical ſuperficies, the reflection would be ſeen ſtrong in but one ſole <lb></lb>particle of it; but yet by reaſon of its livelineſs, it will appear <lb></lb>fringed about with many glittering rays: the reſt of the Ball would <lb></lb>appear according as it was burniſhed; and this alſo onely then <lb></lb><arrow.to.target n="marg173"></arrow.to.target> <lb></lb>when it was not very much poliſhed, for ſhould it be perfectly <lb></lb>brightned, it would appear obſcure. </s><s>An example of this we <lb></lb>have dayly before our eyes in ſilver veſſels, which whilſt they are <lb></lb>only boyl'd in the <emph type="italics"></emph>Argol<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Salt,<emph.end type="italics"></emph.end> they are all as white as ſnow, and <lb></lb>do not reflect any image; but if they be in any part burniſh'd, they <lb></lb>become in that place preſently obſcure: and in them one may ſee the <lb></lb>repreſentation of any thing as in Looking-glaſſes. </s><s>And that chan <lb></lb>to obſcurity, proceeds from nothing elſe but the ſmoothing and <lb></lb>plaining of a fine grain, which made the ſuperficies of the ſilver <lb></lb>rough, and yet ſuch, as that it reflected the light into all parts, <lb></lb>whereby it ſeemed from all parts equally illuminated: which <lb></lb>ſmall unevenneſſes, when they come to be exquiſitely plained by <lb></lb>the burniſh, ſo that the reflection of the rays of incidence are all <lb></lb>directed unto one determinate place; then, from that ſame place, <lb></lb>the burniſh'd part ſhall ſhew much more bright and ſhining than <lb></lb>the reſt which is onely whitened by boyling; but from all other <lb></lb>places it looks very obſcure. </s><s>And note, that the diverſity of <lb></lb><arrow.to.target n="marg174"></arrow.to.target> <lb></lb>ſights of looking upon burniſh'd ſuperficies, occaſioneth ſuch <lb></lb>difference in appearances, that to imitate and repreſent in picture, <lb></lb><emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> a poliſh'd Cuirace, one muſt couple black plains with white, <lb></lb>one ſideways to the other, in thoſe parts of the arms where the <lb></lb>light falleth equally.</s></p><p type="margin"><s><margin.target id="marg171"></margin.target><emph type="italics"></emph>Some write what <lb></lb>they underſtand <lb></lb>not, and therefore <lb></lb>underſtand not <lb></lb>what they write.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg172"></margin.target><emph type="italics"></emph>Diamonds ground <lb></lb>to divers ſides, & <lb></lb>why.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg173"></margin.target><emph type="italics"></emph>Silver burniſhed <lb></lb>appears more ob <lb></lb>ſcuee, than the not <lb></lb>burniſhed, & why.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg174"></margin.target><emph type="italics"></emph>Burniſh'd Steel <lb></lb>beheld from one <lb></lb>place appears very <lb></lb>bright, and from <lb></lb>another, very ob <lb></lb>ſcure.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>If therefore theſe great Philoſophers would acquieſe <lb></lb>in granting, that the Moon, <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> and the other Planets, were not <lb></lb>of ſo bright and ſmooth a ſurface as a Looking-glaſs, but wanted <lb></lb>ſome ſmall matter of it, namely, were as a ſilver plate, onely boyled <pb xlink:href="040/01/081.jpg" pagenum="65"></pb>white, but not burniſhed; would this yet ſuffice to the making <lb></lb>of it viſible, and apt for darting forth the light of the Sun?</s></p><p type="main"><s>SALV. </s><s>It would ſuffice in part; but would not give a light ſo <lb></lb>ſtrong, as it doth being mountainous, and in ſum, full of <lb></lb>eminencies and great cavities. </s><s>But theſe Philoſophers will never <lb></lb>yield it to be leſſe polite than a glaſſe; but far more, if more it <lb></lb>can be imagined; for they eſteeming that to perfect bodies perfect <lb></lb>figures are moſt ſutable; it is neceſſary, that the ſphericity of thoſe <lb></lb>Cœleſtial Globes be moſt exact; beſides, that if they ſhould <lb></lb>grant me ſome inequality, though never ſo ſmall, I would not <lb></lb>ſcruple to take any other greater; for that ſuch perfection conſiſt <lb></lb>ing in indiviſibles, an hair doth as much detract from its perfection <lb></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></lb>reaſon why the greater inequality of ſuperficies maketh the ſtron <lb></lb>ger reflection of light; the other is, why theſe <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> Gen <lb></lb>tlemen are for this exact figure.</s></p><p type="main"><s>SALV. </s><s>I will anſwer to the firſt; and leave to <emph type="italics"></emph>Simplieius<emph.end type="italics"></emph.end> the <lb></lb><arrow.to.target n="marg175"></arrow.to.target> <lb></lb>care of making reply to the ſecond. </s><s>You muſt know therefore, <lb></lb>that the ſame ſuperficies happen to be by the ſame light more or leſs <lb></lb>illuminated, according as the rayes of illumination fall upon them <lb></lb><arrow.to.target n="marg176"></arrow.to.target> <lb></lb>more or leſſe obliquely; ſo that the greateſt illumination is where <lb></lb>the rayes are perpendicular. </s><s>And ſee, how I will prove it to your <lb></lb>ſenſe. </s><s>I bend this paper, ſo, that one part of it makes an angle <lb></lb>upon the other: and expoſing both theſe parts to the reflection of <lb></lb>the light of that oppoſite Wall, you ſee how this ſide which re <lb></lb>ceiveth the rayes obliquely, is leſſe ſhining than this other, where <lb></lb>the reflection fals at right angles; and obſerve, that as I by <lb></lb>degrees receive the illumination more obliquely, it groweth <lb></lb>weaker.</s></p><p type="margin"><s><margin.target id="marg175"></margin.target><emph type="italics"></emph>The more rough <lb></lb>ſuperficies make <lb></lb>greater reflection <lb></lb>of light, than the <lb></lb>leſs rough.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg176"></margin.target><emph type="italics"></emph>Perpendicular <lb></lb>rays illuminate <lb></lb>more than the ob <lb></lb>lique, and why.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I ſee the effect, but comprehend not the cauſe.</s></p><p type="main"><s>SALV. </s><s>If you thought upon it but a minute of an hour, you <lb></lb>would find it; but that I may not waſte the time, ſee a kind of <lb></lb>demonſtration thereof in <emph type="italics"></emph>Fig.<emph.end type="italics"></emph.end> 7.</s></p><p type="main"><s>SAGR. </s><s>The bare ſight of this Figure hath fully ſatisfied me, <lb></lb>therefore proceed.</s></p><p type="main"><s>SIMPL. </s><s>Pray you let me hear you out, for I am not of ſo <lb></lb>quick an apprehenſion.</s></p><p type="main"><s>SALV. </s><s>Fancie to your ſelf, that all the paralel lines, which you <lb></lb>ſee to depart from the terms A. B. are the rays which fall upon the <lb></lb><arrow.to.target n="marg177"></arrow.to.target> <lb></lb>line C. D. at right angles: then incline the ſaid C. D. till it hang <lb></lb>as D. O. now do not you ſee that a great part of thoſe rays which <lb></lb>peirce C. D. paſs by without touching D. O? </s><s>If therefore D. O. <lb></lb>be illuminated by fewer rays, it is very reaſonable, that the light <lb></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"></pb>which being of a ſpherical figure, if its ſuperficies were ſmooth, as <lb></lb>this paper, the parts of its hemiſphere illuminated by the Sun, <lb></lb>which are towards its extremity, would receive much leſs light, <lb></lb>than the middle parts; the rays falling upon them moſt obliquely, <lb></lb>and upon theſe at right angles; whereupon at the time of full <lb></lb>Moon, when we ſee almoſt its whole Hemiſphere illuminated, the <lb></lb>parts towards the midſt, would ſhew themſelves to us with more <lb></lb>ſplendor, than thoſe others towards the circumference: which is <lb></lb>not ſo in effect. </s><s>Now the face of the Moon being repreſented <lb></lb>to me full of indifferent high mountains, do not you ſee how their <lb></lb>tops and continuate ridges, being elevated above the convexity of <lb></lb>the perfect ſpherical ſuperficies, come to be expoſed to the view <lb></lb>of the Sun, and accommodated to receive its rays much leſs ob <lb></lb>liquely, and conſequently to appear as luminous as the reſt?</s></p><p type="margin"><s><margin.target id="marg177"></margin.target><emph type="italics"></emph>The more oblique <lb></lb>Rayes illuminate <lb></lb>leß, and why.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>All this I well perceive: and if there are ſuch moun <lb></lb>tains, its true, the Sun will dart upon them much more directly <lb></lb>than it would do upon the inclination of a polite ſuperficies: but <lb></lb>it is alſo true, that betwixt thoſe mountains all the valleys would <lb></lb>become obſcure, by reaſon of the vaſt ſhadows, which in that <lb></lb>time would be caſt from the mountains, whereas the parts towards <lb></lb>the middle, though full of valleys and hills, by reaſon they have <lb></lb>the Sun elevated, would appear without ſhadow, and therefore <lb></lb>more lucid by far than the extreme parts, which are no leſs diffu <lb></lb>ſed with ſhadow than light, and yet we can perceive no ſuch diffe <lb></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"></emph>Simplicius<emph.end type="italics"></emph.end> to apprehend the ob <lb></lb>jections which favour the opinions of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> than their ſoluti <lb></lb>ons? </s><s>I have a kind of ſuſpition, that he ſtrives alſo ſometimes to <lb></lb>diſſemble them; and in the preſent caſe, he being of himſelf able <lb></lb>to hit upon the doubt, which yet is very ingenious, I cannot be <lb></lb>lieve but that he alſo was adviſ'd of the anſwer; wherefore I will <lb></lb>attempt to wreſt the ſame (as they ſay) out of his mouth. </s><s>There <lb></lb>fore tell me, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> do you think there can be any ſhadow, <lb></lb>where the rays of the Sun do ſhine?</s></p><p type="main"><s>SIMPL. </s><s>I believe, nay I am certain that there cannot; for that <lb></lb>it being the grand luminary, which with its rays driveth away dark <lb></lb>neſs, it is impoſſible any tenebroſity ſhould remain where it com <lb></lb>eth; moreover, we have the definition, that <emph type="italics"></emph>Tenebræ ſunt priva <lb></lb>tio luminis.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Therefore the Sun, beholding the Earth, Moon or o <lb></lb>ther opacous body, never ſeeth any of its ſhady parts, it not ha <lb></lb>ving any other eyes to ſee with, ſave its rays, the conveyers of <lb></lb>light: and conſequently, one ſtanding in the Sun would never <lb></lb>ſee any thing of umbrage, foraſmuch as his viſive rays would ever <pb xlink:href="040/01/083.jpg" pagenum="67"></pb>go accompanied with thoſe 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 oppoſite to the Sun, what dif <lb></lb>ference is there between the tract of the rayes of your ſight, and <lb></lb>that motion which the Suns rayes make?</s></p><p type="main"><s>SIMPL. </s><s>Now I underſtand you; for you would ſay, that the <lb></lb>rayes of the ſight and thoſe of the Sun, moving by the ſame lines, <lb></lb>we cannot perceive any of the obſcure valleys of the Moon. </s><s>Be <lb></lb>pleaſed to change this your opinion, that I have either ſimulation <lb></lb>or diſſimulation in me; for I proteſt unto you, as I am a Gentle <lb></lb>man, that I did not gueſſe at this ſolution, nor ſhould I have <lb></lb>thought upon it, without your help, or without long ſtudy.</s></p><p type="main"><s>SAGR. </s><s>The reſolutions, which between you two have been <lb></lb>alledged touching this laſt doubt, hath, to ſpeak the truth, ſatisfi <lb></lb>ed me alſo. </s><s>But at the ſame time this conſideration of the vi <lb></lb>fible rayes accompanying the rayes of the Sun, hath begotten in me <lb></lb>another ſcruple, about the other part, but I know not whether I <lb></lb>can expreſſe it right, or no: for it but juſt now comming into my <lb></lb>mind, I have not yet methodized it to my mind: but let us ſee if <lb></lb>we can, all together, make it intelligible. </s><s>There is no queſtion, <lb></lb>but that the parts towards the circumference of that poliſh't, but not <lb></lb>burniſh't Hemiſphere, which is illuminated by the Sun, receiving the <lb></lb>rayes obliquely, receive much fewer thereof, than the middle <lb></lb>moſt parts, which receive them directly. </s><s>And its poſſible, that a <lb></lb>tract or ſpace of <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> twenty degrees in breadth, and which is to <lb></lb>wards the extremity of the Hemiſphere, may not receive more rays <lb></lb>than another towards the middle parts, of but four degree broad: <lb></lb>ſo that that doubtleſs will be much more obſcure than this; and <lb></lb>ſuch it will appear to whoever ſhall behold them both in the face, <lb></lb>or (as I may ſay) in their full magnitude. </s><s>But if the eye of the <lb></lb>beholder were conſtituted in ſuch a place, that the breadth of the <lb></lb>twenty degrees of the obſcure ſpace, appeared not to it longer <lb></lb>than one of four degrees, placed in the midſt of the Hemiſphere, <lb></lb>I hold it not impoſſible for it to appear to the ſaid beholder e <lb></lb>qually clear and lucid with the other; becauſe, finally, between <lb></lb>two equal angles, to wit, of four degrees apiece, there come to <lb></lb>the eye the reflections of two equal numbers of rayes: namely, <lb></lb>thoſe which are reflected from the middlemoſt ſpace, four degrees <lb></lb>in breadth, and thoſe reflected from the other of twenty degrees, <lb></lb>but ſeen by compreſſion, under the quantity of four degrees: and <lb></lb>ſuch a ſituation ſhall the eye obtain, when it is placed between the <lb></lb>ſaid Hemiſphere, and the body which illuminates it; for then the <lb></lb>ſight and rayes move in the ſame lines. </s><s>It ſeemeth not impoſſible <lb></lb>therefore, but that the Moon may be of a very equal ſuperficies; <lb></lb>and that nevertheleſſe, it may appear when it is at the full, no leſs <pb xlink:href="040/01/084.jpg" pagenum="68"></pb>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 conſideration; <lb></lb>and as it but juſt now came into your mind unawares, ſo I will <lb></lb>like wiſe anſwer with what firſt comes into my thoughts, and it may <lb></lb>happily fall out, that by thinking more upon it, I may ſtumble <lb></lb>upon a better reply. </s><s>But before, that I labyrinth my ſelf any far <lb></lb>ther, it would be neceſſary, that we aſſure our ſelves by ſome ex <lb></lb>periment, whether your objection prove in effect, what it ſeemeth <lb></lb>to conclude in appearance; and therefore taking once more the <lb></lb>ſame paper, and making it to incline, by bending a little part <lb></lb>thereof upon the remainder, let us try whether expoſing it to the <lb></lb>Sun, ſo that the rayes of light fall upon the leſſer part directly, <lb></lb>and upon the other obliquely; this which receiveth the rayes direct <lb></lb>ly appeareth more lucid; and ſee here by manifeſt experience, <lb></lb>that it is notably more clear. </s><s>Now if your objection be concluſive, <lb></lb>it will follow, that ſtooping with our eye ſo, that in beholding <lb></lb>the other greater part, leſs illuminated, in compreſſion or fore <lb></lb>ſhortning, it appear unto us no bigger than the other, more ſhining; <lb></lb>and that conſequently, it be not beheld at a greater angle than <lb></lb>that; it will neceſſarily enſue, I ſay, that its light be encreaſed, ſo <lb></lb>that it do ſeem to us as bright as the other. </s><s>See how I behold, and <lb></lb>look upon it ſo obliquely, that it appeareth to me narrower than <lb></lb>the other; but yet, notwithſtanding its obſcurity, doth not to <lb></lb>my perceiving, at all grow clearer. </s><s>Try now if the ſame ſucceed <lb></lb>to you.</s></p><p type="main"><s>SAGR. </s><s>I have look't upon it, and though I have ſtooped with <lb></lb>my eye, yet cannot I ſee the ſaid ſuperficies encreaſe in light or <lb></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></lb>jection; In the next place, as to the ſolution, I believe, that, by <lb></lb>reaſon the Superficies of this paper is little leſſe than ſmooth, the <lb></lb>rayes are very few, which be reflected towards the point of inci <lb></lb>dence, in compariſon of the multitude, which are reflected to <lb></lb>wards the oppoſite parts; and that of thoſe few more and more <lb></lb>are loſt, the nearer the viſive rayes approach to thoſe lucid rayes <lb></lb>of incidence; and becauſe it is not the incident rayes, but thoſe <lb></lb>which are reflected to the eye, that make the object appear lu <lb></lb>minous; therefore, in ſtooping the eye, there is more loſt than got, <lb></lb>as you your ſelf confeſſe to have ſeen in looking upon the obſcu <lb></lb>rer part of the paper.</s></p><p type="main"><s>SAGR. </s><s>I reſt ſatisfied with this experiment and reaſon: It re <lb></lb>mains now, that <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> anſwer to my other queſtion, and tell <lb></lb>me what moves the <emph type="italics"></emph>Peripateticks<emph.end type="italics"></emph.end> to require this ſo exact rotundity <lb></lb>in the Cœleſtial bodies.</s></p><p type="main"><s>SIMPL. </s><s>The Cœleſtial bodies being ingenerable, inalterable, im <pb xlink:href="040/01/085.jpg" pagenum="69"></pb>paſſible, immortal, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> they muſt needs be abſolutely perfect; and <lb></lb><arrow.to.target n="marg178"></arrow.to.target> <lb></lb>their being abſolute perfect, neceſſarily implies that there is in them <lb></lb>all kinds of perfection; and conſequently, that their figure be alſo <lb></lb>perfect, that is to ſay, ſpherical; and abſolutely and perfectly <lb></lb>ſpherical, and not rough and irregular.</s></p><p type="margin"><s><margin.target id="marg178"></margin.target><emph type="italics"></emph>Perfect ſphericity <lb></lb>why aſcribed to <lb></lb>Cœlestial bodies, <lb></lb>by the<emph.end type="italics"></emph.end> Peripate <lb></lb>ticks.</s></p><p type="main"><s>SALV. </s><s>And this incorruptibility, from whence do you prove <lb></lb>it?</s></p><p type="main"><s>SIMPL. </s><s>Immediately by its freedom from contraries, and me <lb></lb>diately, by its ſimple circular motion.</s></p><p type="main"><s>SALV. </s><s>So that; by what I gather from your diſcourſe, in ma <lb></lb><arrow.to.target n="marg179"></arrow.to.target> <lb></lb>king the eſſence of the Cœleſtial bodies to be incorruptible, inal <lb></lb>terable, <emph type="italics"></emph>&c,<emph.end type="italics"></emph.end> there is no need of rotundity as a cauſe, or requi <lb></lb>ſite; for if this ſhould cauſe inalterability, we might at our plea <lb></lb>ſure make wood, wax, and other Elementary matters, incorrup <lb></lb>tible, by reducing them to a ſpherical figure.</s></p><p type="margin"><s><margin.target id="marg179"></margin.target><emph type="italics"></emph>The Figure is not <lb></lb>the cauſe of incor <lb></lb>ruptibility, but of <lb></lb>longer duration.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>And is it not manifeſt that a ball of Wood will better <lb></lb>and longer be preferved, than an oblong, or other angular fi <lb></lb>gure, made of a like quantity of the ſame wood.</s></p><p type="main"><s>SALV. </s><s>This is moſt certain, but yet it doth not of corruptible <lb></lb>become incorruptible, but ſtill remains corruptible, though of a <lb></lb>much longer duration. </s><s>Therefore you muſt note, that a thing cor <lb></lb><arrow.to.target n="marg180"></arrow.to.target> <lb></lb>ruptible, is capable of being more or leſſe ſuch, and we may <lb></lb>properly ſay this is leſſe corruptible than that; as for example, the <lb></lb><emph type="italics"></emph>Jaſper,<emph.end type="italics"></emph.end> than the <emph type="italics"></emph>Pietra Sirena<emph.end type="italics"></emph.end>; but incorruptibility admits not <lb></lb>of more, or leſſe, ſo as that it may be ſaid this is more incorrupti <lb></lb>ble than that, if both be incorruptible and eternal. </s><s>The diver <lb></lb><arrow.to.target n="marg181"></arrow.to.target> <lb></lb>ſity of figure therefore cannot operate: ſave onely in matters ca <lb></lb>pable of more or leſſe duration; but in the eternal, which can <lb></lb>not be other than equally eternal, the operation of figure ceaſeth. <lb></lb></s><s>And therefore, ſince the Cœleſtial matter is not incorruptible by <lb></lb>figure, but otherwayes no man needs to be ſo ſolicitous for this <lb></lb>perfect ſphericity; for if the matter be incorruptible, let it have <lb></lb>what figure it will, it ſhall be alwayes ſuch.</s></p><p type="margin"><s><margin.target id="marg180"></margin.target><emph type="italics"></emph>Corruptibility ad <lb></lb>mits of more or <lb></lb>leſſe; ſo doth noe <lb></lb>incorruptibiliiy.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg181"></margin.target><emph type="italics"></emph>The perfection of <lb></lb>figure, operateth <lb></lb>in corruptible bo <lb></lb>dies, but not in the <lb></lb>eternal.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>But I am conſidering another thing, and ſay, that if <lb></lb><arrow.to.target n="marg182"></arrow.to.target> <lb></lb>we ſhould grant the ſpherical figure a faculty of conferring incor <lb></lb>ruptibility, all bodies of whatſoever figure, would be incorrupti <lb></lb>ble; foraſmuch as if the rotund body be incorruptible, corrupti <lb></lb>bility would then ſubſiſt in thoſe parts which alter the perfect ro <lb></lb>tundity; as for inſtance, there is in a <emph type="italics"></emph>Die<emph.end type="italics"></emph.end> a body perfectly round, <lb></lb>and, as ſuch, incorruptible; therefore it remaineth that thoſe an <lb></lb>gles be corruptible which cover and hide the rotundity; ſo that <lb></lb>the moſt that could happen, would be, that thoſe angles, and <lb></lb>(to ſo ſpeak) excreſcencies, would corrupt. </s><s>But if we proceed to a <lb></lb>more inward conſideration, that in thoſe parts alſo towards the <lb></lb>angles, there are compriſed other leſſer bals of the ſame matter; <pb xlink:href="040/01/086.jpg" pagenum="70"></pb>and therefore they alſo, as being round, muſt be alſo incorrup <lb></lb>tible; and likewife in the remainders, which environ theſe eight <lb></lb>leſſer Spheres, a man may underſtand that there are others: ſo <lb></lb>that in the end, reſolving the whole <emph type="italics"></emph>Die<emph.end type="italics"></emph.end> into innumerable balls, <lb></lb>it muſt neceſſarily be granted incorruptible. </s><s>And the ſame diſ <lb></lb>courſe and reſolution may be made in all other figures.</s></p><p type="margin"><s><margin.target id="marg182"></margin.target><emph type="italics"></emph>If the ſpherical fi <lb></lb>gure conferreth e <lb></lb>ternity, all bodies <lb></lb>would be eternal.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Your method in making the concluſion, for if <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> a <lb></lb>round Chryſtal were, by reaſon of its figure, incorruptible; namely, <lb></lb>received from thence a faculy of reſiſting all internal and external <lb></lb>alterations, we ſhould not find, that the joyning to it other Chry <lb></lb>ſtal, and reducing it <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> into a Cube, would any whit alter it <lb></lb>within, or without; ſo as that it would thereupon become leſſe <lb></lb>apt to reſiſt the new ambient, made of the ſame matter, than it <lb></lb>was to reſiſt the other, of a matter different; and eſpecially, if <lb></lb>it be true, that corruption is generated by contraries, as <emph type="italics"></emph>Ari <lb></lb>ſtotle<emph.end type="italics"></emph.end> ſaith; and with what can you encloſe that ball of Cryſtal, <lb></lb>that is leſſe contrary to it, than Cryſtal it ſelf? </s><s>But we are not a <lb></lb>ware how time flies away; and it will be too late before we come <lb></lb>to an end of our diſpute, if we ſhould make ſo long diſcourſes, <lb></lb>upon every particular; beſides our memories are ſo confounded <lb></lb>in the multiplicity of notions, that I can very hardly recal to <lb></lb>mind the Propotſiions, which I propoſed in order to <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> <lb></lb>for our conſideration.</s></p><p type="main"><s>SIMPL. </s><s>I very well remember them: And as to this particular <lb></lb>queſtion of the montuoſity of the Moon, there yet remains un <lb></lb>anſwered that which I have alledged, as the cauſe, (and which <lb></lb>may very well ſerve for a ſolution) of that <emph type="italics"></emph>Phænomenon,<emph.end type="italics"></emph.end> ſaying, <lb></lb>that it is an illuſion proceeding from the parts of the Moon, be <lb></lb>ing unequally opacous, and perſpicuous.</s></p><p type="main"><s>SAGR. </s><s>Even now, when <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> aſcribed the apparent Pro <lb></lb>tnberancies or unevenneſſes of the Moon (according to the opinion <lb></lb>of a certain <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> his friend) to the diverſly opacous, and <lb></lb><arrow.to.target n="marg183"></arrow.to.target> <lb></lb>perſpicuous parts of the ſaid Moon, conformable to which the like <lb></lb>illuſions are ſeen in Cryſtal, and Jems of divers kinds, I bethought <lb></lb>my ſelf of a matter much more commodious for the repreſenting <lb></lb>ſuch effects; which is ſuch, that I verily believe, that that Philoſo <lb></lb>pher would give any price for it; and it is the mother of Pearl, which <lb></lb>is wrought into divers figures, and though it be brought to an ex <lb></lb>treme evenneſſe, yet it ſeemeth to the eye in ſeveral parts, ſo vari <lb></lb>ouſly hollow and knotty, that we can ſcarce credit our feeling of <lb></lb>their evenneſſe.</s></p><p type="margin"><s><margin.target id="marg183"></margin.target><emph type="italics"></emph>Mother of Pearl <lb></lb>accommodated to <lb></lb>imitate the appa <lb></lb>rent unevenneſſes <lb></lb>of the Moons ſur <lb></lb>face.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>This invention is truly ingenious; and that which hath <lb></lb>not been done already, may be done in time to come; and if <lb></lb>there have been produced other Jems, and Cryſtals, which have <lb></lb>nothing to do with the illuſions of the mother of Pearl, theſe may <pb xlink:href="040/01/087.jpg" pagenum="71"></pb>be produced alſo; in the mean time, that I may not prevent any <lb></lb>one, I will ſuppreſſe the anſwer which might be given, and onely <lb></lb>for this time betake my ſelf to ſatisfie the objections brought by <lb></lb><emph type="italics"></emph>Simplicius.<emph.end type="italics"></emph.end> I ſay therefore, that this reaſon of yours is too ge <lb></lb>neral, and as you apply it not to all the appearances one by one; <lb></lb>which are ſeen in the Moon, and for which my ſelf and others <lb></lb>are induced to hold it mountainous, I believe you will not find <lb></lb>any one that will be ſatisfied with ſuch a doctrine; nor can I think, <lb></lb>that either you, or the Author himſelf, find in it any greater <lb></lb>quietude, than in any other thing wide from the purpoſe. </s><s>Of the <lb></lb><arrow.to.target n="marg184"></arrow.to.target> <lb></lb>very many ſeveral appearances which are ſeen night by night in <lb></lb>the courſe of Moon, you cannot imitate ſo much as one, by making <lb></lb>a Ball at your choice, more or leſs opacous and perſpicuous, and <lb></lb>that is of a polite ſuperficies; whereas on the contrary, one may <lb></lb><arrow.to.target n="marg185"></arrow.to.target> <lb></lb>make Balls of any ſolid matter whatſoever, that is not tranſparent, <lb></lb>which onely with eminencies and cavities, and by receiving the il <lb></lb>lumination ſeveral ways, ſhall repreſent the ſame appearances and <lb></lb>mutations to an hair, which from hour to hour are diſcovered in <lb></lb><arrow.to.target n="marg186"></arrow.to.target> <lb></lb>the Moon. </s><s>In them you ſhall ſee the ledges of Hills expoſed to <lb></lb>the Suns light, to be very ſhining, and after them the projections <lb></lb>of their ſhadows very obſcure; you ſhall ſee them greater and leſs, <lb></lb>according as the ſaid eminencies ſhall be more or leſs diſtant from <lb></lb>the confines which diſtinguiſh the parts of the Moon illuminated, <lb></lb>from the obſcure: you ſhall ſee the ſame term and confine, not <lb></lb>equally diftended, as it would be if the Ball were poliſh'd, but <lb></lb>craggie and rugged. </s><s>You ſhall ſee beyond the ſame term, in the <lb></lb>dark parts of the Moon many bright prominencies, and diſtinct <lb></lb>from the reſt of the illuminations: you ſhall ſee the ſhadows a <lb></lb>foreſaid, according as the illumination gradually riſeth, to demi <lb></lb>niſh by degrees, till they wholly diſappear; nor are there any of <lb></lb>them to be ſeen when the whole Hemiſphere is enlightned. </s><s>A <lb></lb>gain on the contrary, in the lights paſſage towards the other He <lb></lb>miſphere of the Moon, you ſhall again obſerve the ſame eminen <lb></lb>cies that were marked, and you ſhall ſee the projections of their <lb></lb>ſhadows to be made a contrary way, and to decreaſe by degrees: <lb></lb>of which things, once more I ſay, you cannot ſhew me ſo much as <lb></lb>one in yours that are opacous and perſpicuous.</s></p><p type="margin"><s><margin.target id="marg184"></margin.target><emph type="italics"></emph>The apparent un <lb></lb>evenneſſes of the <lb></lb>Moon cannot be i <lb></lb>mitated by way of <lb></lb>more and leſs opa <lb></lb>city & perſpicuity.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg185"></margin.target><emph type="italics"></emph>The various a <lb></lb>ſpects of the Moon, <lb></lb>imitable with any <lb></lb>opacous matter.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg186"></margin.target><emph type="italics"></emph>Various appear an <lb></lb>ces from which the <lb></lb>Moons montuoſity <lb></lb>is argued.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>One of them certainly he may imitate, namely, that of <lb></lb>the Full-Moon, when by reaſon of its being all illuminated, there <lb></lb>is not to be ſeen either ſhadow, or other thing, which receiveth <lb></lb>any alteration from its eminencies and cavities. </s><s>But I beſeech <lb></lb>you, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> let us ſpend no more time on this Argument, for <lb></lb>a perſon that hath had but the patience to make obſervation of but <lb></lb>one or two Lunations, and is not ſatisfied with this moſt ſenſible <lb></lb>truth, may well be adjudged void of all judgment; and upon <pb xlink:href="040/01/088.jpg" pagenum="72"></pb>ſuch why ſhould we throw away our time and breath in vain?</s></p><p type="main"><s>SIMPI. </s><s>I muſt confeſs I have not made the obſervations, for <lb></lb>that I never had ſo much curioſity, or the Inſtruments proper for <lb></lb>the buſineſs; but I will not fail to do it. </s><s>In the mean time, we <lb></lb>may leave this queſtion in ſuſpenſe, and paſs to that point which <lb></lb>follows, producing the motives inducing you to think that the <lb></lb>Earth may reflect the light of the Sun no leſs forceably than the <lb></lb>Moon, for it ſeems to me ſo obſcure and opacous, that I judg ſuch <lb></lb>an effect altogether impoſſible.</s></p><p type="main"><s>SALV. </s><s>The cauſe for which you repute the Earth unapt for <lb></lb>illumination, may rather evince the contrary: And would it not <lb></lb>be ſtrange, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> if I ſhould apprehend your diſcourſes bet <lb></lb>ter than you your ſelf?</s></p><p type="main"><s>SIMPL. </s><s>Whether I argue well or ill, it may be, that you may <lb></lb>better underſtand the ſame than I; but be it ill or well that I <lb></lb>diſcourſe, I ſhall never believe that you can penetrate what I mean <lb></lb>better than I my ſelf.</s></p><p type="main"><s>SALV. Well, I will make you believe the ſame preſently. </s><s>Tell <lb></lb>me a little, when the Moon is near the Full, ſo that it may be ſeen <lb></lb>by day, and alſo at midnight, at what do you think it more ſplen <lb></lb>did, by day or by night?</s></p><p type="main"><s>SIMPL. </s><s>By night, without all compariſon. </s><s>And methinks <lb></lb><arrow.to.target n="marg187"></arrow.to.target> <lb></lb>the Moon reſembleth that pillar of Clouds and pillar of Fire, <lb></lb>which guided the <emph type="italics"></emph>Iſraelites<emph.end type="italics"></emph.end>; which at the preſence of the Sun, <lb></lb>appeared like a Cloud, but in the night was very glorious. </s><s>Thus <lb></lb><arrow.to.target n="marg188"></arrow.to.target> <lb></lb>I have by day obſerved the Moon amidſt certain ſmall Clouds, <lb></lb>juſt as if one of them had been coloured white, but by night it <lb></lb>ſhines with much ſplendor.</s></p><p type="margin"><s><margin.target id="marg187"></margin.target><emph type="italics"></emph>The Moon ap <lb></lb>pears brighter by <lb></lb>night than by day.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg188"></margin.target><emph type="italics"></emph>The Moon be <lb></lb>held in the day <lb></lb>time, is like to a <lb></lb>little cloud.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>So that if you had never happened to ſee the Moon, <lb></lb>ſave onely in the day time, you would not have thought it more <lb></lb>ſhining than one of thoſe Clouds.</s></p><p type="main"><s>SIMPL. </s><s>I verily believe I ſhould not.</s></p><p type="main"><s>SALV. </s><s>Tell me now; do you believe that the Moon is really <lb></lb>more ſhining in the night than day, or that by ſome accident it <lb></lb>ſeemeth ſo?</s></p><p type="main"><s>SIMPL. </s><s>I am of opinion, that it reſplends in it ſelf as much in <lb></lb>the day as night, but that its light appears greater by night, be <lb></lb>cauſe we behold it in the dark mantle of Heaven; and in the day <lb></lb>time, the whole Atmoſphere being very clear, ſo that ſhe little <lb></lb>exceedeth it in luſtre, ſhe ſeems to us much leſs bright.</s></p><p type="main"><s>SALV. </s><s>Now tell me; have you ever at midnight ſeen the Ter <lb></lb>reſtrial Globe illuminated by the Sun?</s></p><p type="main"><s>SIMPL. </s><s>This ſeemeth to me a queſtion not to be ask'd, unleſs <lb></lb>in jeſt, or of ſome perſon known to be altogether void of ſenſe.</s></p><p type="main"><s>SALV. No, no; I eſteem you to be a very rational man, and <pb xlink:href="040/01/089.jpg" pagenum="73"></pb>do ask the queſtion ſeriouſly; and therefore anſwer me: and if <lb></lb>afterwards you ſhall think that I ſpeak impertinently, I will be <lb></lb>content to be the ſenſeleſs man: for he is much more a fool who <lb></lb>interrogates ſimply, than he to whom the queſtion is put.</s></p><p type="main"><s>SIMPL. </s><s>If then you do not think me altogether ſimple, take <lb></lb>it for granted that I have anſwered you already, and ſaid, that it <lb></lb>is impoſſible, that one that is upon the Earth, as we are, ſhould ſee <lb></lb>by night that part of the Earth where it is day, namely, that is il <lb></lb>luminated by the Sun.</s></p><p type="main"><s>SALV. </s><s>Therefore you have never ſeen the Earth enlightned, <lb></lb>ſave onely by day; but you ſee the Moon to ſhine alſo in the <lb></lb>dead of night. </s><s>And this is the cauſe, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> which makes <lb></lb>you believe that the Earth doth not ſhine like the Moon; but if <lb></lb>you could ſee the Earth illuminated, whilſt you were in ſome dark <lb></lb>place, like our night, you would ſee it ſhine brighter than the <lb></lb>Moon. </s><s>Now if you deſire that the compariſon may proceed <lb></lb>well, you muſt compare the light of the Earth, with that of the <lb></lb>Moon ſeen in the day time, and not with the ſame by night: for <lb></lb>it is not in our power to ſee the Earth illuminated, ſave onely in <lb></lb>the day. </s><s>Is it not ſo?</s></p><p type="main"><s>SIMPL. </s><s>So it ought to be.</s></p><p type="main"><s>SALV. </s><s>And foraſmuch as you your ſelf have already confeſſed <lb></lb>to have ſeen the Moon by day among ſome little white Clouds, <lb></lb>and very nearly, as to its aſpect, reſembling one of them; you did <lb></lb><arrow.to.target n="marg189"></arrow.to.target> <lb></lb>thereby grant, that thoſe Clouds, which yet are Elementary <lb></lb>matters, are as apt to receive illumination, as the Moon, yea <lb></lb>more, if you will but call to mind that you have ſometimes ſeen <lb></lb>ſome Clouds of vaſt greatneſs, and as perfect white as the Snow; <lb></lb>and there is no queſtion, but that if ſuch a Cloud could be con <lb></lb>tinued ſo luminous in the deep of night, it would illuminate the <lb></lb>places near about it, more than an hundred Moons. </s><s>If therefore <lb></lb>we were aſſured that the Earth is illuminated by the Sun, like one <lb></lb>of thoſe Clouds, it would be undubitable, but that it would be no <lb></lb>leſs ſhining than the Moon. </s><s>But of this there is no queſtion to <lb></lb>be made, in regard we ſee thoſe very Clouds in the abſence of <lb></lb>the Sun, to remain by night, as obſcure as the Earth: and that <lb></lb>which is more, there is not any one of us, but hath ſeen many <lb></lb>times ſome ſuch Clouds low, and far off, and queſtioned whether <lb></lb>they were Clouds or Mountains: an evident ſign that the Moun <lb></lb>tains are no leſs luminous than thoſe Clouds. <lb></lb><arrow.to.target n="marg190"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg189"></margin.target><emph type="italics"></emph>Clouds are no leſs <lb></lb>apt than the Moon <lb></lb>to be illuminated <lb></lb>by the Sun.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg190"></margin.target><emph type="italics"></emph>A wall illumina <lb></lb>ted by the Sun, <lb></lb>compared to the <lb></lb>Moon ſhineth no <lb></lb>leſs than it.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>But what needs more diſcourſe? </s><s>See yonder the Moon <lb></lb>is riſen, and more than half of it illuminated; ſee there that wall, <lb></lb>on which the Sun ſhineth; retire a little this way, ſo that you ſee <lb></lb>the Moon ſideways with the wall: look now; which of them <lb></lb>ſhews more lucid? </s><s>Do not you ſee, that if there is any advantage, <pb xlink:href="040/01/090.jpg" pagenum="74"></pb>the wall hath it? </s><s>The Sun ſhineth on that wall; from thence it </s></p><p type="main"><s><arrow.to.target n="marg191"></arrow.to.target> <lb></lb>is reverberated upon the wall of the Hall, from thence it's refle <lb></lb>cted upon that chamber, ſo that it falls on it at the third reflection: <lb></lb>and I am very certain, that there is in that place more light, than <lb></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"></emph>The third reſle <lb></lb>ction of a Wall illu <lb></lb>minates more than <lb></lb>the firſt of the <lb></lb>Moon.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>But this I cannot believe; for the illumination of the <lb></lb>Moon, eſpecially when it is at the full, is very great.</s></p><p type="main"><s>SAGR. </s><s>It ſeemeth great by reaſon of the circumjacent dark <lb></lb><arrow.to.target n="marg192"></arrow.to.target> <lb></lb>places; but abſolutely it is not much, and is leſs than that of the <lb></lb>twilight half an hour after the Sun is ſet; which is manifeſt, be <lb></lb>cauſe you ſee not the ſhadows of the bodies illuminated by the <lb></lb>Moon till then, to begin to be diſtinguiſhed on the Earth. </s><s>Whe <lb></lb>ther, again, that third reflection upon that chamber, illuminates <lb></lb>more than the firſt of the Moon, may be known by going thether, <lb></lb>and reading a Book, and afterwards ſtanding there in the night <lb></lb>by the Moons light, which will ſhew by which of them lights one <lb></lb>may read more or leſs plainly, but I believe without further tryal, <lb></lb>that one ſhould ſee leſs diſtinctly by this later.</s></p><p type="margin"><s><margin.target id="marg192"></margin.target><emph type="italics"></emph>The light of the <lb></lb>Moon weaker than <lb></lb>that of the twi <lb></lb>light.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. Now, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> (if haply you be ſatisfied) you may <lb></lb>conceive, as you your ſelf know very well, that the Earth doth <lb></lb>ſhine no leſs than the Moon; and the only remembring you of ſome <lb></lb>things, which you knew of your ſelf, and learn'd not of me, hath <lb></lb>aſſured you thereof: for I taught you not that the Moon ſhews <lb></lb>lighter by night than by day, but you underſtood it of your ſelf; <lb></lb>as alſo you could tell me that a little Cloud appeareth as lucid as <lb></lb>the Moon: you knew alſo, that the illumination of the Earth can <lb></lb>not be ſeen by night; and in a word, you knew all this, without <lb></lb>knowing that you knew it. </s><s>So that you have no reaſon to be ſcru <lb></lb>pulous of granting, that the dark part of the Earth may illuminate <lb></lb>the dark part of the Moon, with no leſs a light than that where <lb></lb>with the Moon illuminates the obſcurities of the night, yea rather <lb></lb>ſo much the greater, inaſmuch as the Earth is forty times bigger <lb></lb>than the Moon.</s></p><p type="main"><s>SIMPL. </s><s>I muſt confeſs that I did believe, that that ſecondary <lb></lb>light had been the natural light of the Moon.</s></p><p type="main"><s>SALV. </s><s>And this alſo you know of your ſelf, and perceive not <lb></lb>that you know it. </s><s>Tell me, do not you know without teaching, <lb></lb>that the Moon ſhews it ſelf more bright by night than by day, in <lb></lb><arrow.to.target n="marg193"></arrow.to.target> <lb></lb>reſpect of the obſcurity of the ſpace of the ambient? </s><s>and conſe <lb></lb>quently, do you not know <emph type="italics"></emph>in genere,<emph.end type="italics"></emph.end> that every bright body ſhews <lb></lb>the clearer, by how much the ambient is obſcurer?</s></p><p type="margin"><s><margin.target id="marg193"></margin.target><emph type="italics"></emph>Luminous bodies <lb></lb>appear the brighter <lb></lb>in an obſcurer<emph.end type="italics"></emph.end> am <lb></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 ſecondary light <lb></lb>ſeemeth to you very bright, is it not ever nigh the Sun, and con <lb></lb>ſequently, in the light of the <emph type="italics"></emph>crepuſculum,<emph.end type="italics"></emph.end> (twilight?)</s></p> <pb xlink:href="040/01/091.jpg" pagenum="75"></pb><p type="main"><s>SIMPL. </s><s>It is ſo; and I have oftentimes wiſh'd that the Air <lb></lb>would grow thicker, that I might be able to ſee that ſame light <lb></lb>more plainly; but it ever diſappeared before dark night.</s></p><p type="main"><s>SALV. </s><s>You know then very certainly, that in the depth of <lb></lb>night, that light would be more conſpicuous.</s></p><p type="main"><s>SIMPL. </s><s>I do ſo; and alſo more than that, if one could but <lb></lb>take away the great light of the creſcent illuminated by the Sun, <lb></lb>the preſence of which much obſcureth the other leſſer.</s></p><p type="main"><s>SALV. Why, doth it not ſometimes come to paſs, that one may <lb></lb>in a very dark night ſee the whole face of the Moon, without be <lb></lb>ing at all illuminated by the Sun?</s></p><p type="main"><s>SIMPL. </s><s>I know not whether this ever happeneth, ſave onely <lb></lb>in the total Ecclipſes of the Moon.</s></p><p type="main"><s>SALV. Why, at that time this its light would appear very <lb></lb>clear, being in a moſt obſcure <emph type="italics"></emph>medium,<emph.end type="italics"></emph.end> and not darkned by the <lb></lb>clarity of the luminous creſcents: but in that poſition, how light <lb></lb>did it appear to you?</s></p><p type="main"><s>SIMPL. </s><s>I have ſometimes ſeen it of the colour of braſs, and a <lb></lb>little whitiſh; but at other times it hath been ſo obſcure, that I <lb></lb>have wholly loſt the ſight of it.</s></p><p type="main"><s>SALV. </s><s>How then can that light be ſo natural, which you ſee ſo <lb></lb>cleer in the cloſe of the twilight, notwithſtanding the impediment <lb></lb>of the great and contiguous ſplendor of the creſcents; and which <lb></lb>again, in the more obſcure time of night, all other light removed, <lb></lb>appears not at all?</s></p><p type="main"><s>SIMPL. </s><s>I have heard of ſome that believed that ſame light to <lb></lb>be participated to theſe creſcents from the other Stars, and in par <lb></lb>ticular from <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> the Moons neighbour.</s></p><p type="main"><s>SALV. </s><s>And this likewiſe is a vanity; becauſe in the time of <lb></lb>its total obſcuration, it ought to appear more ſhining than ever; <lb></lb>for you cannot ſay, that the ſhadow of the Earth intercepts the <lb></lb>ſight of <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> or the other Stars. </s><s>But to ſay true, it is not at <lb></lb>that inſtant wholly deprived thereof, for that the Terreſtrial He <lb></lb>miſphere, which in that time looketh towards the Moon, is that <lb></lb>where it is night, that is, an intire privation of the light of the Sun. <lb></lb></s><s>And if you but diligently obſerve, you will very ſenſibly perceive, <lb></lb>that like as the Moon, when it is ſharp-horned, doth give very little <lb></lb>light to the Earth; and according as in her the parts illumi <lb></lb>nated by the Suns light do encreaſe: ſo likewiſe the ſplendor to <lb></lb>our ſeeming encreaſeth, which from her is reflected towards us; <lb></lb>thus the Moon, whilſt it is ſharp-forked, and that by being between <lb></lb>the Sun and the Earth, it diſcovereth a very great part of the Ter <lb></lb><arrow.to.target n="marg194"></arrow.to.target> <lb></lb>reſtrial Hemiſphere illuminated, appeareth very clear: and depart <lb></lb>ing from the Sun, and paſſing towards the ^{*}Quadrature, you <lb></lb>may ſee the ſaid light by degrees to grow dim; and after the <pb xlink:href="040/01/092.jpg" pagenum="76"></pb>Quadrature, the ſame appears very weak, becauſe it continually <lb></lb>loſeth more and more of the view of the luminous part of the <lb></lb>Earth: and yet it ſhould ſucceed quite contrary, if that light were <lb></lb>its own, or communicated to it from the Stars; for then we ſhould <lb></lb>ſee it in the depth of night, and in ſo very dark an ambient.</s></p><p type="margin"><s><margin.target id="marg194"></margin.target>*<emph type="italics"></emph>By the Moons two<emph.end type="italics"></emph.end> <lb></lb>Quadratures <emph type="italics"></emph>you <lb></lb>are to underſtand <lb></lb>its firſt and last <lb></lb>quarters, as A <lb></lb>ſtrologers call them<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>Stay a little; for I juſt now remember, that I have <lb></lb>read in a little modern tract, full of many novelties; “That this <lb></lb>ſecondary light is not derived from the Stars, nor innate in the <lb></lb>Moon, and leaſt of all communicated by the Earth, but that it is <lb></lb><arrow.to.target n="marg195"></arrow.to.target> <lb></lb>received from the ſame illumination of the Sun, which, the ſub <lb></lb>ſtance of the Lunar Globe being ſomewhat tranſparent, pene <lb></lb>trateth thorow all its body; but more livelily illuminateth the <lb></lb>ſuperficies of the Hemiſphere expoſed to the rays of the Sun: <lb></lb>and its proſundity imbuing, and (as I may ſay) ſwallowing that <lb></lb>light, after the manner of a cloud or chryſtal, tranſmits it, and <lb></lb>renders it viſibly lucid. </s><s>And this (if I remember aright) he <lb></lb>proveth by Authority, Experience and Reaſon; citing <emph type="italics"></emph>Cleomedes, <lb></lb>Vitellion, Macrobius,<emph.end type="italics"></emph.end> and a certain other modern Author: and <lb></lb>adding, That it is ſeen by experience to ſhine moſt in the days <lb></lb>neareſt the Conjunction, that is, when it is horned, and is chiefly <lb></lb>bright about its limb. </s><s>And he farther writes, That in the Solar <lb></lb>Ecclipſes, when it is under the <emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end> of the Sun, it may be ſeen <lb></lb>tranſlucid, and more eſpecially towards its utmoſt Circle. </s><s>And <lb></lb>in the next place, for Arguments, as I think, he ſaith, That it not <lb></lb>being able to derive that light either from the Earth, or from the <lb></lb>Stars, or from it ſelf, it neceſſarily follows, that it cometh from <lb></lb>the Sun. </s><s>Beſides that, if you do but grant this ſuppoſition, one <lb></lb>may eaſily give convenient reaſons for all the particulars that <lb></lb>occur. </s><s>For the reaſon why that ſecundary light ſhews more <lb></lb>lively towards the outmoſt limb, is, the ſhortneſs of the ſpace <lb></lb>that the Suns rays hath to penetrate, in regard that of the lines <lb></lb>which paſs through a circle, the greateſt is that which paſſeth <lb></lb>through the centre, and of the reſt, thoſe which are fartheſt from <lb></lb>it, are always leſs than thoſe that are nearer. </s><s>From the ſame <lb></lb>principle, he ſaith, may be ſhewn why the ſaid light doth not <lb></lb>much diminiſh. </s><s>And laſtly, by this way the cauſe is aſſigned <lb></lb>whence it comes, that that ſame more ſhining circle about the <lb></lb>utmoſt edge of the Moon, is ſeen at the time of the Solar Ec <lb></lb>clipſe, in that part which lyeth juſt under the <emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end> of the Sun, <lb></lb>but not in that which is beſide the <emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end>: which happeneth <lb></lb>becauſe the rays of the Sun paſs directly to our eye, through the <lb></lb>parts of the Moon underneath: but as for the parts which are <lb></lb>beſides it, they fall beſides the eye.”</s></p><p type="margin"><s><margin.target id="marg195"></margin.target><emph type="italics"></emph>The ſecondary <lb></lb>light of the Moon <lb></lb>cauſed by the Sun, <lb></lb>according to ſome.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>If this Philoſopher had been the firſt Author of this o <lb></lb>pinion, I would not wonder that he ſhould be ſo affectionate to it, <pb xlink:href="040/01/093.jpg" pagenum="77"></pb>as to have received it for truth; but borrowing it from others, I <lb></lb>cannot find any reaſon ſufficient to excuſe him for not perceiving <lb></lb>its fallacies; and eſpecially after he had heard the true cauſe of <lb></lb>that effect, and had it in his power to ſatisfie himſelf by a thouſand <lb></lb>experiments, and manifeſt circumſtances, that the ſame proceeded <lb></lb>from the reflection of the Earth, and from nothing elſe: and the more <lb></lb>this ſpeculation makes ſomething to be deſired, in the judgment of <lb></lb>this Author, and of all thoſe who give no credit to it: ſo much the <lb></lb>more doth their not having underſtood and remembred it, excuſe <lb></lb>thoſe more receſs Antients, who, I am very certain, did they now <lb></lb>underſtand it, would without the leaſt repugnance admit thereof. <lb></lb></s><s>And if I may freely tell you what I think, I cannot believe but <lb></lb>that this <emph type="italics"></emph>Modern<emph.end type="italics"></emph.end> doth in his heart believe it; but I rather think, <lb></lb>that the conceit he ſhould not be the firſt Author thereof, did a <lb></lb>little move him to endeavour to ſuppreſſe it, or to diſparage it at <lb></lb>leaſt amongſt the ſimple, whoſe number we know to be very <lb></lb>great; and many there are, who much more affect the nume <lb></lb>rous applauds of the people, than the approbation of a few not <lb></lb>vulgar judgments.</s></p><p type="main"><s>SAGR. </s><s>Hold good <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> for me thinks, I ſee that you <lb></lb>go not the way to hit the true mark in this your diſcourſe, for theſe <lb></lb>that ^{*} confound all propriety, know alſo how to make themſelves <lb></lb><arrow.to.target n="marg196"></arrow.to.target> <lb></lb>Authors of others inventions, provided they be not ſo ſtale, <lb></lb>and publick in the Schools and Market-places, as that they are more <lb></lb>then notorious to every one.</s></p><p type="margin"><s><margin.target id="marg196"></margin.target>* Tendono le pare <lb></lb>te al commune.</s></p><p type="main"><s>SALV. Ha! well aimed, you blame me for roving from the <lb></lb>point in hand; but what have you to do with Schools and Mar <lb></lb><arrow.to.target n="marg197"></arrow.to.target> <lb></lb>kets? </s><s>Is it not all one whether opinions and inventions be new to <lb></lb>men, or the men new to them? </s><s>If you ^{*} contend about the e <lb></lb>ſteem of the Founders of Sciences, which in all times do ſtart up, <lb></lb><arrow.to.target n="marg198"></arrow.to.target> <lb></lb>you may make your ſelf their inventor, even to the Alphabet it <lb></lb>ſelf, and ſo gain admiration amongſt that illiterate rabble; and <lb></lb>though in proceſſe of time your craft ſhould be perceived, that <lb></lb>would but little prejudice your deſigne; for that others would <lb></lb>ſucceed them in maintaining the number of your fautors; but let <lb></lb>us return to prove to <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> the invalidity of the reaſons of his <lb></lb>modern Author, in which there are ſeveral falſities, inconſequen <lb></lb><arrow.to.target n="marg199"></arrow.to.target> <lb></lb>cies, and incredible Paradoxes. </s><s>And firſt, it is falſe that this ſe <lb></lb>condary light is clearer about the utmoſt limb than in the middle <lb></lb>parts, ſo as to form, as it were, a ring or circle more bright than <lb></lb>the reſt of its ſpace or contence. </s><s>True it is, indeed, that looking <lb></lb>on the Moon at the time of twilight, at firſt ſight there is the re <lb></lb>ſemblance of ſuch a circle, but by an illuſion ariſing from the di <lb></lb>verſity of confines that bound the Moons <emph type="italics"></emph>Diſcus,<emph.end type="italics"></emph.end> which are con <lb></lb>fuſed by means of this ſecondary light; foraſmuch as on the part <pb xlink:href="040/01/094.jpg" pagenum="78"></pb>towards the Sun it is bounded by the lucid horns of the Moon, <lb></lb>and on the other part, its confining term is the obſcure tract of the <lb></lb>twilight; whoſe relation makes us think the candor of the Moons <lb></lb><emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end> to be ſo much the clearer; the which happens to be ob <lb></lb>fuſcated in the oppoſite part, by the greater clarity of the creſ <lb></lb>cents; but if this modern Author had eſſaied to make an inter <lb></lb><arrow.to.target n="marg200"></arrow.to.target> <lb></lb>poſition between the eye and the primary ſplendor, by the ridg of <lb></lb>ſome houſe, or ſome other ſcreen, ſo as to have left viſible only <lb></lb>the groſe of the Moon, the horns excluded, he might have ſeen <lb></lb>it all alike luminous.</s></p><p type="margin"><s><margin.target id="marg197"></margin.target><emph type="italics"></emph>Its all one whe <lb></lb>ther opinions be <lb></lb>new to men, or men <lb></lb>new to opinions.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg198"></margin.target>* <emph type="italics"></emph>Conteſtare<emph.end type="italics"></emph.end> falſly <lb></lb>rendered in the <lb></lb>Latine Tranſlation <lb></lb><emph type="italics"></emph>content are.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg199"></margin.target><emph type="italics"></emph>The ſecondary <lb></lb>light of the Moon <lb></lb>appears in form of <lb></lb>a Ring, that is to <lb></lb>ſay, bright in the <lb></lb>extreme circumfe <lb></lb>rence, and not in <lb></lb>the midſt, and why.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg200"></margin.target><emph type="italics"></emph>The may to ob <lb></lb>ſerve the ſeconda <lb></lb>ry light of the <lb></lb>Moon.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL, I think, now I remember, that he writes of his <lb></lb>making uſe of ſuch another Artifice, to hide from us the falſe <lb></lb><emph type="italics"></emph>Incidum.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. Oh! how is this (as I believed) inadvertency of his, <lb></lb>changed into a lie, bordering on raſhneſſe; for that every one <lb></lb>may frequently make proof of the contrary. </s><s>That in the next <lb></lb><arrow.to.target n="marg201"></arrow.to.target> <lb></lb>place, at the Suns Eclipſe, the Moons <emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end> is ſeen otherwayes <lb></lb>than by privation, I much doubt, and ſpecially when the E <lb></lb>clipſe is not total, as thoſe muſt neceſſarily have been, which <lb></lb>were obſerved by the Author; but if alſo he ſhould have diſcove <lb></lb>red ſomewhat of light, this contradicts not, rather favoureth our <lb></lb>opinion; for that at ſuch a time, the whole Terreſtrial Hemi <lb></lb>ſphere illuminated by the Sun, is oppoſite to the Moon, ſo that <lb></lb>although the Moons ſhadow doth obſcure a part thereof, yet this <lb></lb>is very ſmall in compariſon of that which remains illuminated. <lb></lb></s><s>That which he farther adds, that in this caſe, the part of the <lb></lb>limb, lying under the Sun, doth appear very lucid, but that <lb></lb>which lyeth beſides it, not ſo; and that to proceed from the co <lb></lb>ming of the ſolar rayes directly through that part to the eye, but <lb></lb>not through this, is really one of thoſe fopperies, which diſco <lb></lb>ver the other fictions, of him which relates them: For if it be <lb></lb>requiſite to the making a ſecondary light viſible in the lunar <emph type="italics"></emph>Diſ <lb></lb>cus,<emph.end type="italics"></emph.end> that the rayes of the Sun came directly through it to our <lb></lb>eyes, doth not this pitiful Philoſopher perceive, that we ſhould ne <lb></lb>ver ſee this ſame ſecondary light, ſave onely at the Eclipſe of the <lb></lb>Sun? </s><s>And if a part onely of the Moon, far leſſe than half a de <lb></lb>gree, by being remote from the Suns <emph type="italics"></emph>Diſcus,<emph.end type="italics"></emph.end> can deflect or de <lb></lb>viate the rayes of the Sun, ſo that they arrive not at our eye; <lb></lb>what ſhall it do when it is diſtant twenty or thirty degrees, as it is <lb></lb>at its firſt apparition? </s><s>and what courſe ſhall the rayes of the Sun <lb></lb>keep, which are to paſſe thorow the body of the Moon, that <lb></lb><arrow.to.target n="marg202"></arrow.to.target> <lb></lb>they may find out our eye? </s><s>This man doth go ſucceſſively conſi <lb></lb>dering what things ought to be, that they may ſerve his purpoſe, <lb></lb>but doth not gradually proceed, accommodating his conceits to <lb></lb>the things, as really they are. </s><s>As for inſtance, to make the light <pb xlink:href="040/01/095.jpg" pagenum="79"></pb>of the Sun capable to penetrate the ſubſtance of the Moon, he <lb></lb>makes her in part diaphanous, as is <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> the tranſparence of a cloud, <lb></lb>or cryſtal: but I know not what he would think of ſuch a tran <lb></lb>ſparency, in caſe the ſolar rayes were to paſſe a depth of clouds <lb></lb>of above two thouſand miles; but let it be ſuppoſed that he <lb></lb>ſhould boldly anſwer, that might well be in the Cœleſtial, which <lb></lb>are quite other things from theſe our Elementary, impure, and <lb></lb>feculent bodies; and let us convict his error by ſuch wayes, as <lb></lb>admit him no reply, or (to ſay better) ſubter-fuge. </s><s>If he will <lb></lb>maintain, that the ſubſtance of the Moon is diaphanous, he <lb></lb>muſt ſay that it is ſo, whileſt that the rayes of the Sun are to pe <lb></lb>netrate its whole profundity, that is, more than two thouſand <lb></lb>miles; but that if you oppoſe unto them onely one mile, or <lb></lb>leſſe, they ſhould no more penetrate that, than they penetrate <lb></lb>one of our mountains.</s></p><p type="margin"><s><margin.target id="marg201"></margin.target><emph type="italics"></emph>The Moons<emph.end type="italics"></emph.end> Dif <lb></lb>cus <emph type="italics"></emph>in a ſolar E <lb></lb>clipſe can be ſeen <lb></lb>onely by privation.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg202"></margin.target><emph type="italics"></emph>The Author of the <lb></lb>Book of concluſi <lb></lb>ons, accommodates <lb></lb>the things to his <lb></lb>purpoſes, and not <lb></lb>his purpoſes to the <lb></lb>things.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>You put me in mind of a man, who would have ſold <lb></lb><arrow.to.target n="marg203"></arrow.to.target> <lb></lb>me a ſecret how to correſpond, by means of a certain ſympathy of <lb></lb>magnetick needles, with one, that ſhould be two or three thou <lb></lb>ſand miles diſtant; and I telling him, that I would willingly buy <lb></lb>the ſame, but that I deſired firſt to ſee the experiment thereof, <lb></lb>and that it did ſuffice me to make it, I being in one Chamber, and <lb></lb>he in the next, he anſwered me, that in ſo ſmall a diſtance one <lb></lb>could not ſo well perceive the operation; whereupon I turn'd him <lb></lb>going, telling him, that I had no mind, at that time, to take a <lb></lb>journey unto <emph type="italics"></emph>Grand Cairo,<emph.end type="italics"></emph.end> or to <emph type="italics"></emph>Muſcovy,<emph.end type="italics"></emph.end> to make the experi <lb></lb>ment; but that, if he would go himſelf, I would perform the <lb></lb>other part, ſtaying in <emph type="italics"></emph>Venice.<emph.end type="italics"></emph.end> But let us hear whither the dedu <lb></lb>ction of our Author tendeth, and what neceſſity there is, that he <lb></lb>muſt grant the matter of the Moon to be moſt perforable by the <lb></lb>rayes of the Sun, in a depth of two thouſand miles, but more <lb></lb>opacous than one of our mountains, in a thickneſſe of one mile <lb></lb>onely.</s></p><p type="margin"><s><margin.target id="marg203"></margin.target><emph type="italics"></emph>A jeſt put upon one <lb></lb>that would ſell a <lb></lb>certain ſecret for <lb></lb>holding correſpon <lb></lb>dency with a perſon <lb></lb>a thouſand miles <lb></lb>off<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>The very mountains of the Moon themſelves are a <lb></lb>proof thereof, which percuſſed on one ſide of the Sun, do caſt <lb></lb>on the contrary ſide very dark ſhadows, terminate, and more di <lb></lb>ſtinct by much, than the ſhadows of ours; but had theſe moun <lb></lb>tains been diaphanous, we could never have come to the know <lb></lb>ledg of any unevenneſſe in the ſuperficies of the Moon, nor have <lb></lb>ſeen thoſe luminous montuoſities diſtinguiſhed by the terms which <lb></lb>ſeparate the lucid parts from the dark: much leſſe, ſhould we ſee <lb></lb>this ſame term ſo diſtinct, if it were true, that the Suns light did <lb></lb>penetrate the whole thickneſſe of the Moon; yea rather, accord <lb></lb>ing to the Authors own words, we ſhould of neceſſity diſcern the <lb></lb>paſſage, and confine, between the part of the Sun ſeen, and the <lb></lb>part not ſeen, to be very confuſed, and mixt with light and <pb xlink:href="040/01/096.jpg" pagenum="80"></pb>darkneſſe; for that that matter which admits the paſſage of the <lb></lb>Suns rayes thorow a ſpace of two thouſand miles, muſt needs be <lb></lb>ſo tranſparent, that it would very weakly reſiſt them in a hun <lb></lb>dredth, or leſſer part of that thickneſſe; nevertheleſſe, the term <lb></lb>which ſeparateth the part illuminated from the obſcure, is inci <lb></lb>dent, and as diſtinct, as white is diſtinct from black; and e <lb></lb>ſpecially where the Section paſſeth through the part of the Moon, <lb></lb>that is naturally more clear and montanous; but where the old <lb></lb>ſpots do part, which are certain plains, that by means of their <lb></lb>ſpherical inclination, receive the rayes of the Sun obliquely, <lb></lb>there the term is not ſo diſtinct, by reaſon of the more dimme il <lb></lb>lumination. </s><s>That, laſtly, which he ſaith, how that the ſecondary <lb></lb>light doth not diminiſh and languiſh, according as the Moon en <lb></lb>creaſeth, but conſerveth it ſelf continually in the ſame efficacy; <lb></lb>is moſt falſe; nay it is hardly ſeen in the quadrature, when, on <lb></lb>the contrary, it ſhould appear more ſplendid, and be viſible after <lb></lb>the <emph type="italics"></emph>crepuſculum<emph.end type="italics"></emph.end> in the dark of night. </s><s>Let us conclude therefore, <lb></lb>that the Earths reflection is very ſtrong upon the Moon; and that, <lb></lb>which you ought more to eſteem, we may deduce from thence an <lb></lb>other admirable congruity between the Moon and Earth; name <lb></lb><arrow.to.target n="marg204"></arrow.to.target> <lb></lb>ly, that if it be true, the Planets operate upon the Earth by their <lb></lb>motion and light, the Earth may probably be no leſſe potent in <lb></lb>operating reciprocally upon them with the ſame light, and perad <lb></lb>venture, motion alſo. </s><s>And though it ſhould not move, yet may <lb></lb>it retain the ſame operation; becauſe, as it hath been proved al <lb></lb>ready, the action of the light is the ſelf ſame, I mean of the light <lb></lb>of the Sun reflected; and motion doth nothing, ſave only vary <lb></lb>the aſpects, which fall out in the ſame manner, whether we make <lb></lb>the Earth move, and the Sun ſtand ſtill, or the contrary.</s></p><p type="margin"><s><margin.target id="marg204"></margin.target><emph type="italics"></emph>The Earth may re <lb></lb>ciprocally operate <lb></lb>upon Cœleſtial bo <lb></lb>dies, with its light.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>None of the Philoſophers are found to have ſaid, that <lb></lb>theſe inferiour bodies operate on the Cœleſtial, nay, <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> af <lb></lb>firmes the direct contrary.</s></p><p type="main"><s>SALV. <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> and the reſt, who knew not that the Earth and <lb></lb>Moon mutually illuminated each other, are to be excuſed; but <lb></lb>they would juſtly deſerve our cenſure, if whileſt they deſire that <lb></lb>we ſhould grant and believe with them, that the Moon operateth <lb></lb>upon the Earth with light, they ſhould deny to us, who have <lb></lb>taught them that the Earth illuminates the Moon, the operation <lb></lb>the Earth hath on the Moon.</s></p><p type="main"><s>SIMPL. </s><s>In ſhort, I find in my ſelf a great unwillingneſſe to <lb></lb>admit this commerce, which you would perſwade me to be be <lb></lb>twixt the Earth and Moon, placing it, as we ſay, amongſt the <lb></lb>number of the Stars; for if there were nothing elſe, the great <lb></lb>ſeparation and diſtance between it and the Cœleſtial bodies, doth <lb></lb>in my opinion neceſſarily conclude a vaſt diſparity between them.</s></p> <pb xlink:href="040/01/097.jpg" pagenum="81"></pb><p type="main"><s>SALV. </s><s>See <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> what an inveterate affection and radica <lb></lb>ted opinion can do, ſince it is ſo powerful, that it makes you think <lb></lb>that thoſe very things favour you, which you produce againſt <lb></lb>your ſelf. </s><s>For if ſeparation and diſtance are accidents ſufficient to <lb></lb>perſwade with you a great diverſity of natures, it mnſt follow that <lb></lb><arrow.to.target n="marg205"></arrow.to.target> <lb></lb>proximity and contiguity import ſimilitude. </s><s>Now how much more <lb></lb>neerer is the Moon to the Earth, than to any other of the Cœleſtial <lb></lb>Orbs? </s><s>You muſt acknowledg therefore, according to your own con <lb></lb>ceſſion (and you ſhall have other Philoſophers bear you company) <lb></lb>that there is a very great affinity betwixt the Earth and Moon. <lb></lb></s><s>Now let us proceed, and ſee whether any thing remains to be con <lb></lb>ſidered, touching thoſe objections which you made againſt the re <lb></lb>ſemblances that are between theſe two bodies.</s></p><p type="margin"><s><margin.target id="marg205"></margin.target><emph type="italics"></emph>Affinity between <lb></lb>he Earth & Moon <lb></lb>in reſpect of their <lb></lb>vicinity.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>It reſts, that we ſay ſomething touching the ſolidity of <lb></lb>the Moon, which I argued from its being exquiſite ſmooth and <lb></lb>polite, and you from its montuoſity. </s><s>There is another ſcruple al <lb></lb>ſo comes into my mind, from an opinion which I have, that the <lb></lb>Seas reflection ought by the equality of its ſurface, to be rendered <lb></lb>ſtronger than that of the Earth, whoſe ſuperficies is ſo rough and <lb></lb>opacous.</s></p><p type="main"><s>SALV. </s><s>As to the firſt objection; I ſay, that like as among the <lb></lb>parts of the Earth, which all by their gravity ſtrive to approach the <lb></lb><arrow.to.target n="marg206"></arrow.to.target> <lb></lb>neareſt they can poſſible to the center, ſome of them alwayes are <lb></lb>more remote from it than the reſt, as the mountains more than <lb></lb>the valleys, and that by reaſon of their ſolidity and firmneſſe <lb></lb>(for if they were of fluid, they would be even) ſo the ſeeing ſome <lb></lb>parts of the Moon to be elevated above the ſphericity of the low <lb></lb>er parts, argueth their hardneſſe; for it is probable that the mat <lb></lb>ter of the Moon is reduced into a ſpherical form by the harmoni <lb></lb>ous conſpiration of all its parts to the ſame ſentenſe. </s><s>Touching <lb></lb>the ſecond doubt, my thinks that the particulars already obſerved <lb></lb>to happen in the Looking-glaſſes, may very well aſſure us, that the <lb></lb>reflection of light comming from the Sea, is far weaker than that <lb></lb><arrow.to.target n="marg207"></arrow.to.target> <lb></lb>which cometh from Land; underſtanding it alwayes of the <lb></lb>univerſal reflection; for as to that particular, on which the wa <lb></lb>ter being calm, caſteth upon a determinate place, there is no <lb></lb>doubt, but that he who ſhall ſtand in that place, ſhall ſee a very <lb></lb>great reflection in the water, but every way elſe he ſhall ſee the <lb></lb>ſurface of the Water more obſcure than that of the Land; and to <lb></lb><arrow.to.target n="marg208"></arrow.to.target> <lb></lb>prove it to your ſenſes, let us go into yonder Hall, and power <lb></lb>forth a little water upon the Pavement. </s><s>Tell me now, doth not <lb></lb>this wet brick ſhew more dull than the other dry ones? </s><s>Doubt <lb></lb>leſſe it doth, and will ſo appear, from what place ſoever you be <lb></lb>hold it, except one onely, and this is that way which the light <lb></lb>cometh, that entereth in at yonder window; go backwards <lb></lb>therefore by a little and a little.</s></p> <pb xlink:href="040/01/098.jpg" pagenum="82"></pb><p type="margin"><s><margin.target id="marg206"></margin.target><emph type="italics"></emph>Solidity of the <lb></lb>Lunar Globe argu <lb></lb>ed from its being <lb></lb>montainous.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg207"></margin.target><emph type="italics"></emph>The Seas refle <lb></lb>ction of light much <lb></lb>weaker than that <lb></lb>of the Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg208"></margin.target><emph type="italics"></emph>An experiment <lb></lb>to prove the refle <lb></lb>ction of the Water <lb></lb>leſſe clear than <lb></lb>that of the Land.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>Here I ſee the weſt part ſhine more than all the reſt of <lb></lb>the pavement, and I ſee that it ſo hapneth, becauſe the refle <lb></lb>ction of the light which entereth in at the window, cometh to <lb></lb>wards me.</s></p><p type="main"><s>SALV. </s><s>That moiſture hath done no more but filled thoſe little <lb></lb>cavities which are in the brick with water, and reduced its ſuper <lb></lb>ficies to an exact eveneſſe; whereupon the reflex rayes iſſue <lb></lb>unitedly towards one and the ſame place; but the reſt of the <lb></lb>pavement which is dry, hath its protuberances, that is, an innu <lb></lb>merable variety of inclinations in its ſmalleſt particles; whereup <lb></lb>on the reflections of the light ſcatter towards all parts, but more <lb></lb>weakly than if they had gone all united together; and therefore, <lb></lb>the ſame ſheweth almoſt all alike, beheld ſeveral wayes, but far <lb></lb>leſſe clear than the moiſtned brick. </s><s>I conclude therefore, that the <lb></lb>ſurface of the Sea, beheld from the Moon, in like manner, as it <lb></lb>would appear moſt equal, (the Iſlands and Rocks deducted) ſo it <lb></lb>would ſhew leſſe clear than that of the Earth, which is montanous <lb></lb>and uneven. </s><s>And but that I would not ſeem, as the ſaying is, <lb></lb>to harp too much on one ſtring, I could tell you that I have ob <lb></lb>ſerved in the Moon that ſecondary light which I told you came to <lb></lb>her from the reflection of the Terreſtrial Globe, to be notably <lb></lb><arrow.to.target n="marg209"></arrow.to.target> <lb></lb>more clear two or three dayes before the conjunction, than after, <lb></lb>that is, when we ſee it before break of day in the Eaſt, than <lb></lb>when it is ſeen at night after Sun-ſet in the Weſt; of which dif <lb></lb>ference the cauſe is, that the Terreſtrial Hemiſphere, which looks <lb></lb>towards the Eaſtern Moon, hath little Sea, and much Land, to <lb></lb>wit, all <emph type="italics"></emph>Aſia,<emph.end type="italics"></emph.end> whereas, when it is in the Weſt, it beholds very <lb></lb>great Seas, that is, the whole <emph type="italics"></emph>Atlantick<emph.end type="italics"></emph.end> Ocean as far as <emph type="italics"></emph>America:<emph.end type="italics"></emph.end> <lb></lb>An Argument ſufficiently probable that the ſurface of the water <lb></lb>appears leſſe ſplendid than that of the Earth.</s></p><p type="margin"><s><margin.target id="marg209"></margin.target><emph type="italics"></emph>The ſecondary <lb></lb>light of the Moon <lb></lb>clearer before the <lb></lb>conjunction, than <lb></lb>after.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>So that perhaps you believe, thoſe great ſpots diſco <lb></lb>vered in the face of the Moon, to be Seas, and the other clearer <lb></lb>parts to be Land, or ſome ſuch thing?</s></p><p type="main"><s>SALV. </s><s>This which you ask me, is the beginning of thoſe in <lb></lb>congruities which I eſteem to be between the Moon and the <lb></lb>Earth, out of which it is time to diſ-ingage our ſelves, for we <lb></lb>have ſtayed too long in the Moon. </s><s>I ſay therefore, that if there <lb></lb>were in nature but one way onely, to make two ſuperficies illuſtra <lb></lb>ted by the Sun, to appear one more clear than the other, and <lb></lb>that this were by the being of the one Earth, and the other Wa <lb></lb>ter; it would be neceſſary to ſay that the ſurface of the Moon <lb></lb>were part earthy and part aquatick; but becauſe we know many <lb></lb>wayes to produce the ſame effect (and others there may be which <lb></lb>we know not of;) therefore I dare not affirm the Moon to con <lb></lb>ſiſt of one thing more than another: It hath been ſeen already <pb xlink:href="040/01/099.jpg" pagenum="83"></pb>that a ſilver plate boiled, being toucht with the Burniſher, be <lb></lb>cometh of white obſcure; that the moiſt part of the Earth ſhews <lb></lb>more obſcure than the dry; that in the tops of Hills, the woody <lb></lb>parts appear more gloomy than the naked and barren; which <lb></lb>hapneth becauſe there falleth very much ſhadow among the Trees, <lb></lb>but the open places are illuminated all over by the Sun. </s><s>And this <lb></lb>mixtion of ſhadow hath ſuch operation, that in tuſted velvet, the <lb></lb>ſilk which is cut, is of a far darker colour than that which is not <lb></lb>cut, by means of the ſhadows diffuſed betwixt thred and thred, <lb></lb>and a plain velvet ſhews much blacker than a Taffata, made of the <lb></lb>ſame ſilk. </s><s>So that if there were in the Moon things which ſhould <lb></lb>look like great Woods, their aſpect might repreſent unto us the <lb></lb>ſpots which we diſcover; alike difference would be occaſioned, if <lb></lb>there were Seas in her: and laſtly, nothing hindreth, but that thoſe <lb></lb>ſpots may really be of an obſcurer colour than the reſt; for thus <lb></lb>the ſnow makes the mountains ſhew brighter. </s><s>That which is plain <lb></lb><arrow.to.target n="marg210"></arrow.to.target> <lb></lb>ly obſerved in the Moon is, that its moſt obſcure parts are all <lb></lb>plains, with few riſes and bancks in them; though ſome there be; <lb></lb>the reſt which is of a brighter colour, is all full of rocks, moun <lb></lb>tains, hillocks of ſpherical and other figures; and in particular, round <lb></lb>about the ſpots are very great ledges of mountains. </s><s>That the <lb></lb><arrow.to.target n="marg211"></arrow.to.target> <lb></lb>ſpots be plain ſuperficies, we have aſſuredproof, in that we ſee, <lb></lb>how that the term which diſtinguiſheth the part illuminated from <lb></lb>the obſcure, in croſſing the ſpots makes the interſection even, but <lb></lb>in the clear parts it ſhews all craggy and ſhagged. </s><s>But I know not <lb></lb>as yet whether this evenneſſe of ſuperficies may be ſufficient of it <lb></lb>ſelf alone, to make the obſcurity appear, and I rather think not. <lb></lb></s><s>Beſides, I account the Moon exceeding different from the Earth; <lb></lb>for although I imagine to my ſelf that thoſe are not idle and dead <lb></lb>Regions, yet I affirm not, that there are in them motion and life, <lb></lb><arrow.to.target n="marg212"></arrow.to.target> <lb></lb>much leſs that there are bred plants, animals or other things like <lb></lb>to ours; but, if ſuch there be, they ſhould nevertheleſs be very <lb></lb>different, and remote from our imagination. </s><s>And I am induced ſo <lb></lb>to think, becauſe in the firſt place, I eſteem that the matter of the <lb></lb>Lunar Globe conſiſts not of Earth and Water; and this alone <lb></lb>ſufficeth to take away the generations and alterations reſembling <lb></lb>ours: but now ſuppoſing that there were in the Moon, Water and <lb></lb><arrow.to.target n="marg213"></arrow.to.target> <lb></lb>Earth, yet would they not produce plants and animals like to <lb></lb>ours; and this for two principal reaſons: The firſt is, that unto our <lb></lb><arrow.to.target n="marg214"></arrow.to.target> <lb></lb>productions there are required ſo many variable aſpects of the Sun, <lb></lb>that without them they would all miſcarry: now the habitudes of <lb></lb>the Sun towards the Earth are far different from thoſe towards <lb></lb>the Moon. </s><s>We as to the diurnal illumination, have, in the greater <lb></lb>part of the Earth, every twenty four hours part day, and part <lb></lb>night, which effect in the Moon is monethly: and that annual decli <pb xlink:href="040/01/100.jpg" pagenum="84"></pb>nation and elevation of the Sun in the Zodiack, by which it pro <lb></lb><arrow.to.target n="marg215"></arrow.to.target> <lb></lb>duceth diverſity of Seaſons, and inequality of dayes and nights, <lb></lb>are finiſhed in the Moon in a moneth; and whereas the Sun to us <lb></lb><arrow.to.target n="marg216"></arrow.to.target> <lb></lb>riſeth and declineth ſo much, that from the greateſt to the leaſt al <lb></lb>titude, there is a difference of almoſt 47 degrees, for ſo much is <lb></lb>the diſtance from one to the other Tropick; this is in the Moon <lb></lb>but ten degrees only, or little more; namely, as much as the grea <lb></lb>teſt Latitudes of the Dragon on each ſide the Ecliptick. </s><s>Now <lb></lb>conſider what effect the Sun would have in the torrid Zone, ſhould <lb></lb>it continually for fifteen dayes together beam forth its Rayes upon <lb></lb>it; which without all queſtion would deſtroy plants, herbs, <lb></lb>and living creatures: and if it ſhould chance that there were any <lb></lb>production, it would be of herbs, plants, and creatures very diffe <lb></lb><arrow.to.target n="marg217"></arrow.to.target> <lb></lb>rent from thoſe which are now there. </s><s>Secondly, I verily believe <lb></lb>that in the Moon there are no rains, for if Clouds ſhould gather <lb></lb>in any part thereof, as they do about the Earth, they would there <lb></lb>upon hide from our ſight ſome of thoſe things, which we with the <lb></lb><emph type="italics"></emph>Teleſcope<emph.end type="italics"></emph.end> behold in the Moon, and in a word, would ſome way or <lb></lb>other change its <emph type="italics"></emph>Phœnomenon,<emph.end type="italics"></emph.end> an effect which I could never by long <lb></lb>and diligent obſervations diſcover; but alwayes beheld it in a <lb></lb>even and pure ſerenity.</s></p><p type="margin"><s><margin.target id="marg210"></margin.target><emph type="italics"></emph>The obſcurer <lb></lb>parts of the Moon <lb></lb>are plains, and the <lb></lb>more bright moun <lb></lb>tainous.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg211"></margin.target><emph type="italics"></emph>Long ledges of <lb></lb>mountaixs about <lb></lb>the ſpots of the <lb></lb>Moon.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg212"></margin.target><emph type="italics"></emph>There are not <lb></lb>generated in the <lb></lb>Moon things like <lb></lb>to ours, but if <lb></lb>there be any pro <lb></lb>ductions, they are <lb></lb>very different.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg213"></margin.target><emph type="italics"></emph>The Moon not <lb></lb>compoſed of Water <lb></lb>and Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg214"></margin.target><emph type="italics"></emph>Thoſe aſpects of <lb></lb>the Sun neceſſary <lb></lb>for our generati <lb></lb>ons, are not ſo in <lb></lb>the Moon.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg215"></margin.target><emph type="italics"></emph>Natural dayas <lb></lb>in the Moon are of <lb></lb>a Moneth long.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg216"></margin.target><emph type="italics"></emph>To the Moon <lb></lb>the Sun aſeondeth <lb></lb>and declineth with <lb></lb>a difference of ten <lb></lb>degrees, and to the <lb></lb>Earth of forty ſe <lb></lb>ven degrees.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg217"></margin.target><emph type="italics"></emph>There are no <lb></lb>rains in the Moon.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>To this may be anſwered, either that there might be <lb></lb>great miſts, or that it might rain in the time of their night, that is, <lb></lb>when the Sun doth not illuminate it.</s></p><p type="main"><s>SALV. </s><s>If other paſſages did but aſſure us, that there were ge <lb></lb>nerations in it like to ours, and that there was onely wanting the <lb></lb>concourſe of rains, we might find out this, or ſome other tempe <lb></lb>rament to ſerve inſtead thereof, as it happens in <emph type="italics"></emph>Egypt<emph.end type="italics"></emph.end> by the in <lb></lb>undation of <emph type="italics"></emph>Nile:<emph.end type="italics"></emph.end> but not meeting with any accident, which cor <lb></lb>reſponds with ours, of many that have been ſought out for the pro <lb></lb>duction of the like effects, we need not trouble our ſelves to intro <lb></lb>duce one alone; and that alſo, not becauſe we have certain obſer <lb></lb>vation of it, but for a bare non-repugnance that we find therein. <lb></lb></s><s>Moreover, if I was demanded what my firſt apprehenſion, and pure <lb></lb>natural reaſon dictated to me concerning the production of things <lb></lb>like or unlike there above, I would alwayes reply, that they are <lb></lb>moſt different, and to us altogether unimaginable, for ſo me thinks <lb></lb>the riches of Nature, and the omnipotence of our Creator and <lb></lb>Governour, do require.</s></p><p type="main"><s>SAGR. </s><s>I ever accounted extraordinary madneſſe that of thoſe, <lb></lb>who would make humane comprehenſion the meaſure of what na <lb></lb>ture hath a power or knowledge to effect; whereas on the con <lb></lb><arrow.to.target n="marg218"></arrow.to.target> <lb></lb>trary there is not any the leaſt effect in Nature, which can be fully <lb></lb>underſtood by the moſt ſpeculative wits in the world. </s><s>This their <lb></lb>ſo vain preſumption of knowing all, can take beginning from no <pb xlink:href="040/01/101.jpg" pagenum="85"></pb>thing, unleſſe from their never having known any thing; for if <lb></lb>one hath but once onely experienced the perfect knowledg of one <lb></lb>onely thing, and but truly taſted what it is to know, he ſhall per <lb></lb>ceive that of infinite other concluſions, he underſtands not ſo much <lb></lb>as one.</s></p><p type="margin"><s><margin.target id="marg218"></margin.target><emph type="italics"></emph>The having a <lb></lb>perfect knowledg <lb></lb>of nothing, maketh <lb></lb>ſome believe they <lb></lb>underſtand all <lb></lb>things.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Your diſcourſe is very concluding; in confirmation of <lb></lb>which we have the example of thoſe who underſtand, or have <lb></lb>known ſome thing, which the more knowing they are, the more <lb></lb>they know, and freely confeſſe that they know little; nay, the <lb></lb>wiſeſt man in all <emph type="italics"></emph>Greece,<emph.end type="italics"></emph.end> and for ſuch pronounced by the Oracle, <lb></lb>openly profeſſed to know that he knew nothing.</s></p><p type="main"><s>SIMPL. </s><s>It muſt be granted therefore, either that <emph type="italics"></emph>Socrates<emph.end type="italics"></emph.end> or <lb></lb>that the <emph type="italics"></emph>Oracle<emph.end type="italics"></emph.end> it ſelf was a lyar, <emph type="italics"></emph>that declaring him to be moſt <lb></lb>wiſe, and he confeſſing that he knew himſelf to be moſt ig <lb></lb>norant.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Neither one nor the other doth follow, for that both <lb></lb><arrow.to.target n="marg219"></arrow.to.target> <lb></lb>the aſſertions may be true. </s><s>The <emph type="italics"></emph>Oracle<emph.end type="italics"></emph.end> adjudged <emph type="italics"></emph>Socrates<emph.end type="italics"></emph.end> the wi <lb></lb>ſeſt of all men, whoſe knowledg is limited; <emph type="italics"></emph>Socrates<emph.end type="italics"></emph.end> acknow <lb></lb>ledgeth that he knew nothing in relation to abſolute wiſdome, <lb></lb>which is infinite; and becauſe of infinite, much is the ſame part, <lb></lb>as is little, and as is nothing (for to arrive <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> to the infinite <lb></lb>number, it is all one to accumulate thouſands, tens, or ciphers,) <lb></lb>therefore <emph type="italics"></emph>Socrates<emph.end type="italics"></emph.end> well perceived his wiſdom to be nothing, in <lb></lb>compariſon of the infinite knowledg which he wanted. </s><s>But yet, <lb></lb>becauſe there is ſome knowledg found amongſt men, and this <lb></lb>not equally ſhared to all, <emph type="italics"></emph>Socrates<emph.end type="italics"></emph.end> might have a greater ſhare <lb></lb>thereof than others, and therefore verified the anſwer of the <lb></lb><emph type="italics"></emph>Oracle.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg219"></margin.target><emph type="italics"></emph>The anſwer of <lb></lb>the Oracle true in <lb></lb>judging<emph.end type="italics"></emph.end> Socrates <lb></lb><emph type="italics"></emph>the wiſeft of his <lb></lb>time.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I think I very well underſtand this particular amongſt <lb></lb>men, <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> there is a power of operating, but not equally <lb></lb>diſpenſed to all; and it is without queſtion, that the power of an <lb></lb>Emperor is far greater than that of a private perſon; but, both <lb></lb>this and that are nothing in compariſon of the Divine Omnipo <lb></lb>tence. </s><s>Amongſt men, there are ſome that better underſtand <lb></lb>Agriculture than many others; but the knowledg of planting a <lb></lb>Vine in a trench, what hath it to do with the knowledg of ma <lb></lb>king it to ſprout forth, to attract nouriſhment, to ſelect this good <lb></lb>part from that other, for to make thereof leaves, another to make <lb></lb>ſprouts, another to make grapes, another to make raiſins, ano <lb></lb>ther to make the huskes of them, which are the works of moſt <lb></lb>wiſe Nature? </s><s>This is one only particular act of the innumerable, <lb></lb>which Nature doth, and in it alone is diſcovered an infinite wiſ <lb></lb><arrow.to.target n="marg220"></arrow.to.target> <lb></lb>dom, ſo that Divine Wiſdom may be concluded to be infinitely <lb></lb>infinite.</s></p><p type="margin"><s><margin.target id="marg220"></margin.target><emph type="italics"></emph>Divine Wiſdom <lb></lb>infinitely infinise.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Take hereof another example. </s><s>Do we not ſay that the <pb xlink:href="040/01/102.jpg" pagenum="86"></pb>judicious diſcovering of a moſt lovely <emph type="italics"></emph>Statua<emph.end type="italics"></emph.end> in a piece of Marble, <lb></lb><arrow.to.target n="marg221"></arrow.to.target> <lb></lb>hath ſublimated the wit of <emph type="italics"></emph>Buonarruotti<emph.end type="italics"></emph.end> far above the vulgar wits <lb></lb>of other men? </s><s>And yet this work is onely the imitation of a <lb></lb>meer aptitude and diſpoſition of exteriour and ſuperficial mem <lb></lb>bers of an immoveable man; but what is it in compariſon of a <lb></lb>man made by nature, compoſed of as many exteriour and inte <lb></lb>riour members, of ſo many muſcles, tendons, nerves, bones, <lb></lb>which ſerve to ſo many and ſundry motions? </s><s>but what ſhall we <lb></lb>ſay of the ſenſes, and of the powers of the ſoul, and laſtly, of <lb></lb>the underſtanding? </s><s>May we not ſay, and that with reaſon, that <lb></lb>the ſtructure of a Statue fals far ſhort of the formation of a living <lb></lb>man, yea more of a contemptible worm?</s></p><p type="margin"><s><margin.target id="marg221"></margin.target>Buonarruotti, <emph type="italics"></emph>a <lb></lb>ſtatuary of admi <lb></lb>rable ingenuity.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>And what difference think you, was there betwixt the <lb></lb>Dove of <emph type="italics"></emph>Architas,<emph.end type="italics"></emph.end> and one made by Nature?</s></p><p type="main"><s>SIMPL. </s><s>Either I am none of theſe knowing men, or elſe <lb></lb>there is a manifeſt contradiction in this your diſcourſe. </s><s>You ac <lb></lb>count underſtanding amongſt the greateſt (if you make it not the <lb></lb>chief of the) <emph type="italics"></emph>Encomiums<emph.end type="italics"></emph.end> aſcribed to man made by Nature, and <lb></lb>a little before you ſaid with <emph type="italics"></emph>Socrates,<emph.end type="italics"></emph.end> that he had no knowledg at <lb></lb>all; therefore you muſt ſay, that neither did Nature underſtand <lb></lb>how to make an underſtanding that underſtandeth.</s></p><p type="main"><s>SALV. </s><s>You argue very cunningly, but to reply to your obje <lb></lb>ction I muſt have recourſe to a Philoſophical diſtinction, and ſay <lb></lb>that the underſtanding is to be taken too ways, that is <emph type="italics"></emph>intenſivè,<emph.end type="italics"></emph.end> or <lb></lb><arrow.to.target n="marg222"></arrow.to.target> <lb></lb><emph type="italics"></emph>extenſivè<emph.end type="italics"></emph.end>; and that <emph type="italics"></emph>extenſive,<emph.end type="italics"></emph.end> that is, as to the multitude of intel <lb></lb>ligibles, which are infinite, the underſtanding of man is as no <lb></lb>thing, though he ſhould underſtand a thouſand propoſitions; for <lb></lb>that a thouſand, in reſpect of infinity is but as a cypher: but taking <lb></lb>the underſtanding <emph type="italics"></emph>intenſive,<emph.end type="italics"></emph.end> (in as much as that term imports) in <lb></lb>tenſively, that is, perfectly ſome propoſitions, I ſay, that humane wiſ <lb></lb>dom underſtandeth ſome propoſitions ſo perfectly, and is as abſo <lb></lb>lutely certain thereof, as Nature her ſelf; and ſuch are the pure <lb></lb>Mathematical ſciences, to wit, Geometry and Arithmetick: in which <lb></lb>Divine Wiſdom knows infinite more propoſitions, becauſe it knows <lb></lb>them all; but I believe that the knowledge of thoſe few compre <lb></lb>hended by humane underſtanding, equalleth the divine, as to the <lb></lb>certainty <emph type="italics"></emph>objectivè,<emph.end type="italics"></emph.end> for that it arriveth to comprehend the neceſ <lb></lb>ſity thereof, than which there can be no greater certainty.</s></p><p type="margin"><s><margin.target id="marg222"></margin.target><emph type="italics"></emph>Man underſtand <lb></lb>eth very well<emph.end type="italics"></emph.end> in <lb></lb>tenſivè, <emph type="italics"></emph>but little<emph.end type="italics"></emph.end> <lb></lb>extenſivè.</s></p><p type="main"><s>SIMPL. </s><s>This ſeemeth to me a very bold and raſh expreſſion.</s></p><p type="main"><s>SALV. </s><s>Theſe are common notions, and far from all umbrage <lb></lb>of temerity, or boldneſs, and detract not in the leaſt from the Ma <lb></lb>jeſty of divine wiſdom; as it nothing diminiſheth the omnipotence <lb></lb>thereof to ſay, that God cannot make what is once done, to be un <lb></lb>done: but I doubt, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that your ſcruple ariſeth from an o <lb></lb>pinion you have, that my words are ſomewhat equivocal; there <pb xlink:href="040/01/103.jpg" pagenum="87"></pb>fore the better to expreſs my ſelf I ſay, that as to the truth, of <lb></lb>which Mathematical demonſtrations give us the knowledge, it is <lb></lb>the ſame, which the divine wiſdom knoweth; but this I muſt grant <lb></lb>you, that the manner whereby God knoweth the infinite propo <lb></lb><arrow.to.target n="marg223"></arrow.to.target> <lb></lb>ſitions, of which we underſtand ſome few, is highly more excellent <lb></lb>than ours, which proceedeth by ratiocination, and paſſeth from con <lb></lb><arrow.to.target n="marg224"></arrow.to.target> <lb></lb>cluſion to concluſion, whereas his is done at one ſingle thought or <lb></lb>intuition; and whereas we, for example, to attain the knowledg <lb></lb>of ſome paſſion of the Circle, which hath infinite, beginning <lb></lb>from one of the moſt ſimple, and taking that for its definition, <lb></lb>do proceed with argumentation to another, and from that to a <lb></lb>third, and then to a fourth, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> the Divine Wiſdom, by the <lb></lb>apprehenſion of its eſſence comprehends, without temporary raci <lb></lb>ocination, all theſe infinite paſſions; which notwithſtanding, are <lb></lb>in effect virtually compriſed in the definitions of all things; and, to <lb></lb><arrow.to.target n="marg225"></arrow.to.target> <lb></lb>conclude, as being infinite, perhaps are but one alone in their nature, <lb></lb>and in the Divine Mind; the which neither is wholly unknown to <lb></lb>humane underſtanding, but onely be-clouded with thick and <lb></lb><arrow.to.target n="marg226"></arrow.to.target> <lb></lb>groſſe miſts; which come in part to be diſſipated and clarified, <lb></lb>when we are made Maſters of any concluſions, firmly demon <lb></lb>ſtrated, and ſo perfectly made ours, as that we can ſpeedily run <lb></lb>through them; for in ſum, what other, is that propoſition, that <lb></lb>the ſquare of the ſide ſubtending the right angle in any triangle, <lb></lb>is equal to the ſquares of the other two, which include it, but <lb></lb>onely the Paralellograms being upon common baſes, and between <lb></lb>parallels equal amongſt themſelves? </s><s>and this, laſtly, is it not the <lb></lb>ſame, as to ſay that thoſe two ſuperficies are equal, of which <lb></lb>equal parts applyed to equal parts, poſſeſſe equal place? </s><s>Now <lb></lb><arrow.to.target n="marg227"></arrow.to.target> <lb></lb>theſe inferences, which our intellect apprehendeth with time and a <lb></lb>gradual motion, the Divine Wiſdom, like light, penetrateth in <lb></lb>an inſtant, which is the ſame as to ſay, hath them alwayes pre <lb></lb>ſent: I conclude therefore, that our underſtanding, both as to <lb></lb>the manner and the multitude of the things comprehended by us, <lb></lb>is infinitely ſurpaſt by the Divine Wiſdom; but yet I do not ſo <lb></lb>vilifie it, as to repute it abſolutely nothing; yea rather, when I <lb></lb>conſider how many and how great miſteries men have underſtood, <lb></lb>diſcovered, and contrived, I very plainly know and underſtand <lb></lb>the mind of man to be one of the works, yea one of the moſt ex <lb></lb>cellent works of God.</s></p><p type="margin"><s><margin.target id="marg223"></margin.target><emph type="italics"></emph>Gods manner of <lb></lb>knowing different <lb></lb>from that of men.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg224"></margin.target><emph type="italics"></emph>Humane under <lb></lb>ſtanding done by <lb></lb>raciocination.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg225"></margin.target><emph type="italics"></emph>Definitions con <lb></lb>tein virtually all <lb></lb>the paſſions of the <lb></lb>things defined.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg226"></margin.target><emph type="italics"></emph>Infinite Paſſions <lb></lb>are perhaps but <lb></lb>one onely.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg227"></margin.target><emph type="italics"></emph>The diſcourſes <lb></lb>which humane <lb></lb>reaſon makes in a <lb></lb>certain time, the <lb></lb>Divine Wiſdom re <lb></lb>ſolveth in a mo <lb></lb>ment; that is, hath <lb></lb>them alwayes pre <lb></lb>ſent.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I have oft times conſidered with my ſelf, in purſuance <lb></lb><arrow.to.target n="marg228"></arrow.to.target> <lb></lb>of that which you ſpeak of, how great the wit of man is; and <lb></lb>whil'ſt I run thorow ſuch and ſo many admirable inventions found <lb></lb>out by him, as well in the Arts, as Sciences; and again reflecting <lb></lb>upon my own wit, ſo far from promiſing me the diſcovery of any <lb></lb>thing new, that I deſpair of comprehending what is already diſ <pb xlink:href="040/01/104.jpg" pagenum="88"></pb>covered, confounded with wonder, and ſurpriſed with deſpera <lb></lb>tion, I account my ſelf little leſſe than miſerable. </s><s>If I behold a <lb></lb>Statue of ſome excellent Maſter, I ſay with my ſelf; When wilt <lb></lb>thou know how to chizzle away the refuſe of a piece of Marble, <lb></lb>and diſcover ſo lovely a figure, as lyeth hid therein? </s><s>When wilt <lb></lb>thou mix and ſpread ſo many different colours upon a Cloth, or <lb></lb>Wall, and repreſent therewith all viſible objects, like a <emph type="italics"></emph>Michael <lb></lb>Angelo,<emph.end type="italics"></emph.end> a <emph type="italics"></emph>Raphaello,<emph.end type="italics"></emph.end> or a <emph type="italics"></emph>Tizvano<emph.end type="italics"></emph.end>? </s><s>If I behold what inventions <lb></lb>men have in comparting Muſical intervals, in eſtabliſhing Pre <lb></lb>cepts and Rules for the management thereof with admirable de <lb></lb>light to the ear: When ſhall I ceaſe my aſtoniſhment? </s><s>What <lb></lb>ſhall I ſay of ſuch and ſo various Inſtruments of that Art? </s><s>The <lb></lb>reading of excellent Poets, with what admiration doth it ſwell <lb></lb>any one that attentively conſidereth the invention of conceits, <lb></lb>and their explanation? </s><s>What ſhall we ſay of Architecture? <lb></lb><arrow.to.target n="marg229"></arrow.to.target> <lb></lb>What of Navigation? </s><s>But, above all other ſtupendious inventi <lb></lb>ons, what ſublimity of mind was that in him, that imagined to <lb></lb>himſelf to find out a way to communicate his moſt ſecret thoughts <lb></lb>to any other perſon, though very far diſtant from him either in <lb></lb>time, or place, ſpeaking with thoſe that are in the <emph type="italics"></emph>India's<emph.end type="italics"></emph.end>; ſpeak <lb></lb>ing to thoſe that are not yet born, nor ſhall be this thouſand, or <lb></lb>ten thouſand years? </s><s>and with how much facility? </s><s>but by the va <lb></lb><arrow.to.target n="marg230"></arrow.to.target> <lb></lb>rious collocation of ^{*} twenty little letters upon a paper? </s><s>Let this <lb></lb>be the Seal of all the admirable inventions of man, and the cloſe <lb></lb>of our Diſcourſe for this day: For the warmer hours being paſt, <lb></lb>I ſuppoſe that <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> hath a deſire to go and take the air in his <lb></lb>Gondelo; but too morrow we will both wait upon you, to con <lb></lb>tinue the Diſcourſes we have begun, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg228"></margin.target><emph type="italics"></emph>The wit of man <lb></lb>admirably acute.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg229"></margin.target><emph type="italics"></emph>The invention of <lb></lb>writing ſtupendious <lb></lb>above all others.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg230"></margin.target>* For of ſo many <lb></lb>only the Italian <lb></lb>Alphabet conſiſts.</s></p><pb xlink:href="040/01/105.jpg"></pb><figure id="id.040.01.105.1.jpg" xlink:href="040/01/105/1.jpg"></figure><figure id="id.040.01.105.2.jpg" xlink:href="040/01/105/2.jpg"></figure><figure id="id.040.01.105.3.jpg" xlink:href="040/01/105/3.jpg"></figure><figure id="id.040.01.105.4.jpg" xlink:href="040/01/105/4.jpg"></figure><figure id="id.040.01.105.5.jpg" xlink:href="040/01/105/5.jpg"></figure><figure id="id.040.01.105.6.jpg" xlink:href="040/01/105/6.jpg"></figure><figure id="id.040.01.105.7.jpg" xlink:href="040/01/105/7.jpg"></figure><p type="caption"><s><emph type="italics"></emph>Place this Plate <lb></lb>at the end of <lb></lb>the first<emph.end type="italics"></emph.end><lb></lb>Dialogue</s></p><pb xlink:href="040/01/106.jpg"></pb></chap><chap> <pb xlink:href="040/01/107.jpg" pagenum="89"></pb><p type="head"><s>GALILÆUS <lb></lb>Galilæus Lyncæus, <lb></lb>HIS <lb></lb>SYSTEME <lb></lb>OF THE <lb></lb>WORLD.</s></p><p type="head"><s>The Second Dialogue.</s></p><p type="head"><s><emph type="italics"></emph>INTERLOCVTORS.<emph.end type="italics"></emph.end></s></p><p type="head"><s>SALVIATUS, SAGREDUS, and SIMPLICIUS.</s></p><p type="main"><s>SALV. </s><s>The yeſter-dayes diverſions which led us <lb></lb>out of the path of our principal diſcourſe, <lb></lb>were ſuch and ſo many, that I know not <lb></lb>how I can without your aſſiſtance reco <lb></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></lb>have your fancy charged and laden with <lb></lb>both what hath been, and is to be ſpo <lb></lb>ken, do find your ſelf in ſome confuſi <lb></lb>on; but I, who as being onely an Auditor, have nothing to bur <lb></lb>then my memory withal, but ſuch things as I have heard, may <lb></lb>happily by a ſuccinct rehearſal of them, recover the firſt thred <lb></lb>of our Diſcourſe. </s><s>As far therefore as my memory ſerves me, the <lb></lb>ſum of yeſterdayes conferences were an examination of the Prin <pb xlink:href="040/01/108.jpg" pagenum="90"></pb>ciples of <emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> and which of their opinions is <lb></lb>the more probable and rational; that, which affirmeth the ſub <lb></lb>ſtance of the Cœleſtial bodies to be ingenerable, incorruptible, un <lb></lb>alterable, impaſſible, and in a word, exempt from all kind of change, <lb></lb>ſave that of local, and therefore to be a <emph type="italics"></emph>fifth eſſence,<emph.end type="italics"></emph.end> quite different <lb></lb>from this of our Elementary bodies, which are generable, corrup <lb></lb>tible, alterable, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> or elſe the other, which taking away ſuch <lb></lb>deformity from the parts of the World, holdeth the Earth to en <lb></lb>joy the ſame perfections as the other integral bodies of the uni <lb></lb>verſe; and eſteemeth it a moveable and erratick Globe, no leſſe <lb></lb>than the Moon, <emph type="italics"></emph>Jupiter, Venus,<emph.end type="italics"></emph.end> or any other Planet: And laſtly, <lb></lb>maketh many particular parallels betwixt the Earth and Moon; <lb></lb>and more with the Moon, than with any other Planet; hap <lb></lb>ly by reaſon we have greater and more certain notice of it, as <lb></lb>being leſſe diſtant from us. </s><s>And having, laſtly, concluded this <lb></lb>ſecond opinion to have more of probability with it than the firſt, <lb></lb>I ſhould think it beſt in the ſubſequent diſcourſes to begin to exa <lb></lb>mine whether the Earth be eſteemed immoveable, as it hath <lb></lb>been till now believed by moſt men, or elſe moveable, as ſome <lb></lb>ancient <emph type="italics"></emph>Philoſophers<emph.end type="italics"></emph.end> held, and others of not very receſſe times, <lb></lb>were of opinion; and if it be moveable, to enquire of what <lb></lb>kind its motion may be?</s></p><p type="main"><s>SALV. </s><s>I ſee already what way I am to take; but before we <lb></lb>offer to proceed any farther, I am to ſay ſomething to you touch <lb></lb>ing thoſe laſt words which you ſpake, how that the opinion which <lb></lb>holds the Earth to be endued with the ſame conditions that the <lb></lb>Cœleſtial bodies enjoy, ſeems to be more true than the contra <lb></lb>ry; for that I affirmed no ſuch thing, nor would I have any of the <lb></lb>Propoſitions in controverſie, be made to ſpeak to any definitive <lb></lb>ſenſe: but I onely intended to produce on either part, thoſe rea <lb></lb>ſons and anſwers, arguments and ſolutions, which have been hi <lb></lb>therto thought upon by others, together with certain others, <lb></lb>which I have ſtumbled upon in my long ſearching thereinto, al <lb></lb>wayes remitting the deciſion thereof to the judgment of others.</s></p><p type="main"><s>SAGR. </s><s>I was unawares tranſported by my own ſenſe of the <lb></lb>thing; and believing that others ought to judg as I did, I made <lb></lb>that concluſion univerſal, which ſhould have been particular; and <lb></lb>therefore confeſſe I have erred, and the rather, in that I know <lb></lb>not what <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> his judgment is in this particular.</s></p><p type="main"><s>SIMPL. </s><s>I muſt confeſſe, that I have been ruminating all this <lb></lb>night of what paſt yeſterday, and to ſay the truth, I meet there <lb></lb>in with many acute, new, aud plauſible notions; yet nevertheleſs, <lb></lb>I find my ſelf over-perſwaded by the authority of ſo many great <lb></lb><emph type="italics"></emph>Writers,<emph.end type="italics"></emph.end> and in particular -------<emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> I ſee you ſhake your <lb></lb>head <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> and ſmile to your ſelf, as if I had uttered ſome <lb></lb>great abſurdity.</s></p> <pb xlink:href="040/01/109.jpg" pagenum="91"></pb><p type="main"><s>SAGR. </s><s>I not onely ſmile, but to tell you true, am ready to <lb></lb>burſt with holding in my ſelf from laughing outright, for you <lb></lb>have put me in mind of a very pretty paſſage, that I was a wit <lb></lb>neſſe of, not many years ſince, together with ſome others of <lb></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 ſo <lb></lb><emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> may not ſtill think that he gave you the occaſion of <lb></lb>laughter.</s></p><p type="main"><s>SAGR. </s><s>I am content. </s><s>I found one day, at home in his houſe, at <lb></lb><emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> a famous Phiſician, to whom ſome flockt for their ſtudies, <lb></lb>and others out of curioſity, ſometimes came thither to ſee certain A <lb></lb>natomies diſſected by the hand of a no leſſe learned, than careful <lb></lb>and experienced Anatomiſt. </s><s>It chanced upon that day, when I was <lb></lb><arrow.to.target n="marg231"></arrow.to.target> <lb></lb>there, that he was in ſearch of the original and riſe of the Nerves, <lb></lb>about which there is a famous controverſie between the <emph type="italics"></emph>Galeniſts<emph.end type="italics"></emph.end> <lb></lb>and <emph type="italics"></emph>Peripateticks<emph.end type="italics"></emph.end>; and the Anatomiſt ſhewing, how that the great <lb></lb>number of Nerves departing from the Brain, as their root, and <lb></lb>paſſing by the nape of the Neck, diſtend themſelves afterwards <lb></lb>along by the Back-bone, and branch themſelves thorow all the <lb></lb>Body; and that a very ſmall filament, as fine as a thred went to <lb></lb>the Heart; he turned to a Gentleman whom he knew to be a <emph type="italics"></emph>Pe <lb></lb>ripatetick<emph.end type="italics"></emph.end> Philoſopher, and for whoſe ſake he had with extraor <lb></lb>dinary exactneſſe, diſcovered and proved every thing, and demand <lb></lb>ed of him, if he was at length ſatisfied and perſwaded that the origi <lb></lb>nal of the Nerves proceeded from the Brain, and not from the <lb></lb>Heart? </s><s>To which the Philoſopher, after he had ſtood muſing a <lb></lb><arrow.to.target n="marg232"></arrow.to.target> <lb></lb>while, anſwered; you have made me to ſee this buſineſſe ſo <lb></lb>plainly and ſenſibly, that did not the <emph type="italics"></emph>Text<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> aſſert the <lb></lb>contrary, which poſitively affirmeth the Nerves to proceed from <lb></lb>the Heart, I ſhould be conſtrained to confeſſe your opinion to be <lb></lb>true.</s></p><p type="margin"><s><margin.target id="marg231"></margin.target><emph type="italics"></emph>The original of <lb></lb>the Nerv s. </s><s>ac <lb></lb>cording to<emph.end type="italics"></emph.end> Ariſto <lb></lb>tle, <emph type="italics"></emph>and according <lb></lb>to Phiſicians.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg232"></margin.target><emph type="italics"></emph>The ridiculus <lb></lb>anſwer of a Philo <lb></lb>ſopher, determi <lb></lb>ning the original of <lb></lb>the Nerves.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>I would have you know my Maſters, that this contro <lb></lb>verſie about the original of the Nerves is not yet ſo proved and <lb></lb>decided, as ſome may perhaps perſwade themſelves.</s></p><p type="main"><s>SAGR. </s><s>Nor queſtionleſſe ever ſhall it be, if it find ſuch like <lb></lb>contradictors; but that which you ſay, doth not at all leſſen the <lb></lb>extravagance of the anſwer of that <emph type="italics"></emph>Peripatetick,<emph.end type="italics"></emph.end> who againſt <lb></lb>ſuch ſenſible experience produced not other experiments, or rea <lb></lb>ſons of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> but his bare authority and pure <emph type="italics"></emph>ipſe dixit.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> had not gained ſo great authority, but for <lb></lb>the force of his Demonſtrations, and the profoundneſſe of his <lb></lb>arguments; but it is requiſite that we underſtand him, and not <lb></lb>onely underſtand him, but have ſo great familiarity with his <lb></lb>Books, that we form a perfect <emph type="italics"></emph>Idea<emph.end type="italics"></emph.end> thereof in our minds, ſo as <lb></lb>that every ſaying of his may be alwayes as it were, preſent in our <pb xlink:href="040/01/110.jpg" pagenum="92"></pb>memory for he did not write to the vulgar, nor is he obliged to <lb></lb>ſpin out his Sillogiſmes with the trivial method of diſputes; nay <lb></lb>rather, uſing a freedome, he hath ſometimes placed the proof <lb></lb>of one Propoſition amongſt Texts, which ſeem to treat of quite <lb></lb><arrow.to.target n="marg233"></arrow.to.target> <lb></lb>another point; and therefore it is requiſite to be maſter of all <lb></lb>that vaſt <emph type="italics"></emph>Idea,<emph.end type="italics"></emph.end> and to learn how to connect this paſſage with that, <lb></lb>and to combine this Text with another far remote from it; for it <lb></lb>is not to be queſtioned but that he who hath thus ſtudied him, <lb></lb>knows how to gather from his Books the demonſtrations of every <lb></lb>knowable deduction, for that they contein all things.</s></p><p type="margin"><s><margin.target id="marg233"></margin.target><emph type="italics"></emph>Requiſites to fit <lb></lb>a man to philoſo <lb></lb>phate well after <lb></lb>the manner of<emph.end type="italics"></emph.end> A <lb></lb>riſtotle.</s></p><p type="main"><s>SAGR. </s><s>But good <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> like as the things ſcattered here <lb></lb>and there in <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> give you no trouble in collecting them, <lb></lb>but that you perſwade your ſelf to be able by comparing and <lb></lb><arrow.to.target n="marg234"></arrow.to.target> <lb></lb>connecting ſeveral ſmall ſentences to extract thence the juice of <lb></lb>ſome deſired concluſion, ſo this, which you and other egregi <lb></lb>ous Philoſophers do with the Text of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> I could do by the <lb></lb><arrow.to.target n="marg235"></arrow.to.target> <lb></lb>verſes of <emph type="italics"></emph>Virgil,<emph.end type="italics"></emph.end> or of <emph type="italics"></emph>Ovid,<emph.end type="italics"></emph.end> compoſing thereof ^{*} <emph type="italics"></emph>Centones,<emph.end type="italics"></emph.end> and <lb></lb>therewith explaining all the affairs of men, and ſecrets of Na <lb></lb>ture. </s><s>But what talk I of <emph type="italics"></emph>Virgil,<emph.end type="italics"></emph.end> or any other Poet? </s><s>I have a lit <lb></lb>tle Book much ſhorter than <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ovid,<emph.end type="italics"></emph.end> in which are con <lb></lb>teined all the Sciences, and with very little ſtudy, one may gather <lb></lb>out of it a moſt perfect <emph type="italics"></emph>Idea,<emph.end type="italics"></emph.end> and this is the <emph type="italics"></emph>Alphabet<emph.end type="italics"></emph.end>; and there <lb></lb>is no doubt but that he who knows how to couple and diſpoſe <lb></lb>aright this and that vowel, with thoſe, or thoſe other conſonants, <lb></lb>may gather thence the infallible anſwers to all doubts, and de <lb></lb>duce from them the principles of all Sciences and Arts, juſt in the <lb></lb>ſame manner as the Painter from divers ſimple colours, laid ſeve <lb></lb>rally upon his <emph type="italics"></emph>Pallate,<emph.end type="italics"></emph.end> proceedeth by mixing a little of this and <lb></lb>a little of that, with a little of a third, to repreſent to the life <lb></lb>men, plants, buildings, birds, fiſhes, and in a word, counterfeit <lb></lb>ing what ever object is viſible, though there be not on the <emph type="italics"></emph>Pallate<emph.end type="italics"></emph.end> <lb></lb>all the while, either eyes, or feathers, or fins, or leaves, or ſtones. <lb></lb></s><s>Nay, farther, it is neceſſary, that none of the things to be imita <lb></lb>ted, or any part of them, be actually among colours, if you <lb></lb>would be able therewith to repreſent all things; for ſhould there <lb></lb>be amongſt them <emph type="italics"></emph>v. </s><s>gr.<emph.end type="italics"></emph.end> feathers, theſe would ſerve to repreſent <lb></lb>nothing ſave birds, and plumed creatures.</s></p><p type="margin"><s><margin.target id="marg234"></margin.target><emph type="italics"></emph>A cunning way <lb></lb>to gather Philoſo <lb></lb>phy out of any book <lb></lb>whatſoever.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg235"></margin.target>* A word ſignify <lb></lb>ing works compo <lb></lb>ſed of many frag <lb></lb>ments of verſes <lb></lb>collected out of the <lb></lb>Poets.</s></p><p type="main"><s>SALV. </s><s>And there are certain Gentlemen yet living, and in health, <lb></lb>who were preſent, when a Doctor, that was Profeſſor in a fa <lb></lb><arrow.to.target n="marg236"></arrow.to.target> <lb></lb>mous Academy, hearing the deſcription of the <emph type="italics"></emph>Teleſcope,<emph.end type="italics"></emph.end> by him <lb></lb>not ſeen as then, ſaid, that the invention was taken from <emph type="italics"></emph>Ari <lb></lb>ſtotle,<emph.end type="italics"></emph.end> and cauſing his works to be fetch't, he turned to a place <lb></lb>where the Philoſopher gives the reaſon, whence it commeth, that <lb></lb>from the bottom of a very deep Well, one may ſee the ſtars in <lb></lb>Heaven, at noon day; and, addreſſing himſelf to the company, <pb xlink:href="040/01/111.jpg" pagenum="93"></pb>ſee here, ſaith he, the Well, which repreſenteth the Tube, ſee <lb></lb>here the groſs vapours, from whence is taken the invention of <lb></lb>the Cryſtals, and ſee here laſtly the ſight fortified by the paſſage <lb></lb>of the rays through a diaphanous, but more denſe and obſcure <lb></lb><emph type="italics"></emph>medium.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg236"></margin.target><emph type="italics"></emph>Invention of the<emph.end type="italics"></emph.end> <lb></lb>Teleſcope <emph type="italics"></emph>taken <lb></lb>from<emph.end type="italics"></emph.end> Ariſtotle.</s></p><p type="main"><s>SAGR. </s><s>This is a way to comprehend all things knowable, much <lb></lb>like to that wherewith a piece of marble conteineth in it one, yea, <lb></lb>a thouſand very beautiful Statua's, but the difficulty lieth in be <lb></lb>ing able to diſcover them; or we may ſay, that it is like to the <lb></lb>propheſies of Abbot <emph type="italics"></emph>Joachim,<emph.end type="italics"></emph.end> or the anſwers of the Heathen <lb></lb><emph type="italics"></emph>Oracles,<emph.end type="italics"></emph.end> which are not to be underſtood, till after the things <lb></lb>fore-told are come to paſſe.</s></p><p type="main"><s>SALV. </s><s>And why do you not adde the predictions of the <emph type="italics"></emph>Ge <lb></lb>nethliacks,<emph.end type="italics"></emph.end> which are with like cleerneſſe ſeen after the event, in <lb></lb>their Horoſcopes, or, if you will, Configurations of the Heavens.</s></p><p type="main"><s>SAGR. </s><s>In this manner the Chymiſts find, being led by their <lb></lb><arrow.to.target n="marg237"></arrow.to.target> <lb></lb>melancholly humour, that all the ſublimeſt wits of the World <lb></lb>have writ of nothing elſe in reality, than of the way to make <lb></lb>Gold; but, that they might tranſmit the ſecret to poſterity with <lb></lb>out diſcovering it to the vulgar, they contrived ſome one way, and <lb></lb>ſome another how to conceal the ſame under ſeveral maskes; and <lb></lb>it would make one merry to hear their comments upon the ancient <lb></lb><emph type="italics"></emph>Poets,<emph.end type="italics"></emph.end> finding out the important miſteries, which lie hid under <lb></lb>their Fables; and the ſignification of the Loves of the <emph type="italics"></emph>Moon,<emph.end type="italics"></emph.end> <lb></lb>and her deſcending to the Earth for <emph type="italics"></emph>Endimion<emph.end type="italics"></emph.end>; her diſpleaſure <lb></lb>againſt <emph type="italics"></emph>Acteon,<emph.end type="italics"></emph.end> and what was meant by <emph type="italics"></emph>Jupiters<emph.end type="italics"></emph.end> turning himſelf <lb></lb>into a ſhowre of <emph type="italics"></emph>Gold<emph.end type="italics"></emph.end>; and into flames of fire; and what great <lb></lb>ſecrets of Art are conteined in that <emph type="italics"></emph>Mercury<emph.end type="italics"></emph.end> the <emph type="italics"></emph>Interpreter<emph.end type="italics"></emph.end>; in <lb></lb>thoſe thefts of <emph type="italics"></emph>Pluto<emph.end type="italics"></emph.end>; and in thoſe <emph type="italics"></emph>Branches<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Gold.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg237"></margin.target><emph type="italics"></emph>Chymiſts inter <lb></lb>pret the Eables of <lb></lb>the Poets to be ſe <lb></lb>crets for making of <lb></lb>Gold.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>I believe, and in part know, that there want not in the <lb></lb>World very extravagant heads, the vanities of whom ought not to <lb></lb>redound to the prejudice of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> of whom my thinks you <lb></lb>ſpeak ſometimes with too little reſpect, and the onely antiquity <lb></lb>and bare name that he hath acquired in the opinions of ſo many <lb></lb>famous men, ſhould ſuffice to render him honourable with all <lb></lb>that profeſſe themſelves learned.</s></p><p type="main"><s>SALV. </s><s>You ſtate not the matter rightly, <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end>; There <lb></lb>are ſome of his followers that fear before they are in danger, <lb></lb>who give us occaſion, or, to ſay better, would give us cauſe to <lb></lb>eſteem him leſſe, ſhould we conſent to applaud their <emph type="italics"></emph>Capricio's.<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg238"></arrow.to.target> <lb></lb>And you, pray you tell me, are you for your part ſo ſimple, as <lb></lb>not to know that had <emph type="italics"></emph>Arictotle<emph.end type="italics"></emph.end> been preſent, to have heard the <lb></lb>Doctor that would have made him Author of the <emph type="italics"></emph>Teleſcope,<emph.end type="italics"></emph.end> he <lb></lb>would have been much more diſpleaſed with him, than with thoſe, <lb></lb>who laught at the Doctor and his Comments? </s><s>Do you queſtion <pb xlink:href="040/01/112.jpg" pagenum="94"></pb>whether <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> had he but ſeen the novelties diſcovered in Hea <lb></lb>ven, would not have changed his opinion, amended his Books, <lb></lb>and embraced the more ſenſible Doctrine; rejecting thoſe ſilly <lb></lb>Gulls, which too ſcrupulouſly, go about to defend what ever he <lb></lb>hath ſaid; not conſidering, that if <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> were ſuch a one as <lb></lb>they fancy him to themſelves, he would be a man of an untracta <lb></lb>ble wit, an obſtinate mind, a barbarous ſoul, a ſtubborn will, <lb></lb>that accounting all men elſe but as ſilly ſheep, would have his <lb></lb>Oracles preferred before the Senſes, Experience, and Nature her <lb></lb>ſelf? </s><s>They are the Sectators of <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> that have given him this <lb></lb>Authority, and not he that hath uſurped or taken it upon him; <lb></lb>and becauſe it is more eaſie for a man to ſculk under anothers <lb></lb>ſhield than to ſhew himſelf openly, they tremble, and are affraid <lb></lb>to ſtir one ſtep from him; and rather than they will admit ſome <lb></lb>alterations in the Heaven of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> they will impertinently de <lb></lb>ny thoſe they behold in the Heaven of <emph type="italics"></emph>Nature.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg238"></margin.target><emph type="italics"></emph>Some of<emph.end type="italics"></emph.end> Ariſto <lb></lb>tles <emph type="italics"></emph>Sectators im <lb></lb>pare the reputation <lb></lb>of their Maſter, in <lb></lb>going about to en <lb></lb>hanſe it.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Theſe kind of Drolleries put me in mind of that Statu <lb></lb><arrow.to.target n="marg239"></arrow.to.target> <lb></lb>ary which having reduced a great piece of Marble to the Image of <lb></lb>an <emph type="italics"></emph>Hercules,<emph.end type="italics"></emph.end> or a thundring <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> I know not whether, and <lb></lb>given it with admirable Art ſuch a vivacity and threatning fury, <lb></lb>that it moved terror in as many as beheld it; he himſelf began <lb></lb>alſo to be affraid thereof, though all its ſprightfulneſſe, and life <lb></lb>was his own workmanſhip; and his affrightment was ſuch, that <lb></lb>he had no longer the courage to affront it with his Chizzels and <lb></lb>Mallet.</s></p><p type="margin"><s><margin.target id="marg239"></margin.target><emph type="italics"></emph>A ridiculous <lb></lb>paſſage of a certain <lb></lb>Statuary.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>I have many times wondered how theſe nice maintain <lb></lb>ers of what ever fell from <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> are not aware how great a pre <lb></lb>judice they are to his reputation and credit; and how that the <lb></lb>more they go about to encreaſe his Authority, the more they <lb></lb>diminiſh it; for whileſt I ſee them obſtinate in their attempts <lb></lb>to maintain thoſe Propoſitions which I palpably diſcover to <lb></lb>be manifeſtly falſe; and in their deſires to perſwade me that <lb></lb>ſo to do, is the part of a Philoſopher; and that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> himſelf <lb></lb>would do the ſame, it much abates in me of the opinion that he <lb></lb>hath rightly philoſophated about other concluſions, to me more <lb></lb>abſtruſe: for if I could ſee them concede and change opinion in <lb></lb>a manifeſt truth, I would believe, that in thoſe in which they <lb></lb>ſhould perſiſt, they may have ſome ſolid demonſtrations to me un <lb></lb>known, and unheard of.</s></p><p type="main"><s>SAGR. </s><s>Or when they ſhould be made to ſee that they have ha <lb></lb>zarded too much of their own and <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end>'s repuatation in con <lb></lb>feſſing, that they had not underſtood this or that concluſion found <lb></lb>out by ſome other man; would it not be a leſs evil for them to <lb></lb>ſeek for it amongſt his Texts, by laying many of them together, <lb></lb>according to the art intimated to us by <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end>? </s><s>for if his <pb xlink:href="040/01/113.jpg" pagenum="95"></pb>works contain all things knowable, it muſt follow alſo that they <lb></lb>may be therein diſcovered.</s></p><p type="main"><s>SALV. </s><s>Good <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> make no jeſt of this advice, which me <lb></lb>thinks you rehearſe in too Ironical a way; for it is not long ſince <lb></lb>that a very eminent Philoſopher having compoſed a Book <emph type="italics"></emph>de animà,<emph.end type="italics"></emph.end> <lb></lb>wherein, citing the opinion of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> about its being or not be <lb></lb>ing immortal, he alledged many Texts, (not any of thoſe hereto <lb></lb>fore quoted by <emph type="italics"></emph>Alexander ab Alexandro<emph.end type="italics"></emph.end>: for in thoſe he ſaid, that <lb></lb><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> had not ſo much as treated of that matter, much leſs de <lb></lb>termined any thing pertaining to the ſame, but others) by himſelf <lb></lb>found out in other more abſtruſe places, which tended to an er <lb></lb>roneous ſenſe: and being adviſed, that he would find it an hard <lb></lb>matter to get a Licence from the Inquiſitors, he writ back unto <lb></lb><arrow.to.target n="marg240"></arrow.to.target> <lb></lb>his friend, that he would notwithſtanding, with all expedition <lb></lb>procure the ſame, for that if no other obſtacle ſhould interpoſe, <lb></lb>he would not much ſcruple to change the Doctrine of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> <lb></lb>and with other expoſitions, and other Texts to maintain the con <lb></lb>trary opinion, which yet ſhould be alſo agreeable to the ſenſe of <lb></lb><emph type="italics"></emph>Ariſtotle.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg240"></margin.target><emph type="italics"></emph>A brave reſolu <lb></lb>tion of a certain<emph.end type="italics"></emph.end> <lb></lb>Peripatetick <emph type="italics"></emph>Phi <lb></lb>loſopher.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Oh moſt profound Doctor, this! that can command <lb></lb>me that I ſtir not a ſtep from <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> but will himſelf lead <lb></lb>him by the noſe, and make him ſpeak as he pleaſeth. </s><s>See how <lb></lb>much it importeth to learn to take <emph type="italics"></emph>Time<emph.end type="italics"></emph.end> by the <emph type="italics"></emph>Fore-top.<emph.end type="italics"></emph.end> Nor <lb></lb>is it ſeaſonable to have to do with <emph type="italics"></emph>Hercules,<emph.end type="italics"></emph.end> whil'ſt he is en <lb></lb>raged, and amongſt the Furies, but when he is telling merry tales <lb></lb>amongſt the <emph type="italics"></emph>Meonion Damoſels.<emph.end type="italics"></emph.end> Ah, unheard of ſordidneſſe of <lb></lb><arrow.to.target n="marg241"></arrow.to.target> <lb></lb>ſervile ſouls! to make themſelves willing ſlaves to other mens opi <lb></lb>nions; to receive them for inviolable Decrees, to engage them <lb></lb>ſelves to ſeem ſatisfied and convinced by arguments, of ſuch effi <lb></lb>cacy, and ſo manifeſtly concludent, that they themſelves can <lb></lb>not certainly reſolve whether they were really writ to that pur <lb></lb>poſe, or ſerve to prove that aſſumption in hand, or the contrary. <lb></lb></s><s>But, which is a greater madneſſe, they are at variance amongſt <lb></lb>themſelves, whether the Author himſelf hath held the affirmative <lb></lb>part, or the negative. </s><s>What is this, but to make an Oracle of a <lb></lb>Log, and to run to that for anſwers, to fear that, to reverence <lb></lb>and adore that?</s></p><p type="margin"><s><margin.target id="marg241"></margin.target><emph type="italics"></emph>The ſervile ſpi <lb></lb>rit of ſome of<emph.end type="italics"></emph.end> Ari <lb></lb>ſtotles <emph type="italics"></emph>followers.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>But in caſe we ſhould recede from <emph type="italics"></emph>Aristotle,<emph.end type="italics"></emph.end> who have <lb></lb>we to be our Guid in Philoſophy? </s><s>Name you ſome Author.</s></p><p type="main"><s>SALV. </s><s>We need a Guid in unknown and uncouth wayes, but <lb></lb>in champion places, and open plains, the blind only ſtand in need <lb></lb>of a Leader; and for ſuch, it is better that they ſtay at home. <lb></lb></s><s>But he that hath eyes in his head, and in his mind, him ſhould <lb></lb>a man chooſe for his Guid. </s><s>Yet miſtake me not, thinking that I <lb></lb><arrow.to.target n="marg242"></arrow.to.target> <lb></lb>ſpeak this, for that I am againſt hearing of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end>; for on the <pb xlink:href="040/01/114.jpg" pagenum="96"></pb>contrary, I commend the reading, and diligently ſtudying of him; <lb></lb>and onely blame the ſervile giving ones ſelf up a ſlave unto him, <lb></lb>ſo, as blindly to ſubſcribe to what ever he delivers, and without <lb></lb>ſearch of any farther reaſon thereof, to receive the ſame for an in <lb></lb>violable decree. </s><s>Which is an abuſe, that carrieth with it ano <lb></lb>ther great inconvenience, to wit, that others will no longer take <lb></lb>pains to underſtand the validity of his Demonſtrations. </s><s>And <lb></lb>what is more ſhameful, than in the middeſt of publique diſputes, <lb></lb>whileſt one perſon is treating of demonſtrable concluſions, to <lb></lb>hear aother interpoſe with a paſſage of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> and not ſel <lb></lb>dome writ to quite another purpoſe, and with that to ſtop the <lb></lb>mouth of his opponent? </s><s>But if you will continue to ſtudy in this <lb></lb>manner, I would have you lay aſide the name of Philoſophers; <lb></lb><arrow.to.target n="marg243"></arrow.to.target> <lb></lb>and call your ſelves either Hiſtorians or Doctors of Memory, for <lb></lb>it is not ſit, that thoſe who never philoſophate, ſhould uſurp <lb></lb>the honourable title of Philoſophers. </s><s>But it is beſt for us to re <lb></lb>turn to ſhore, and not lanch farther into a boundleſſe Gulph, out <lb></lb>of which we ſhall not be able to get before night. </s><s>Therefore <lb></lb><emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> come either with arguments and demonſtrations of <lb></lb>your own, or of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> and bring us no more Texts and na <lb></lb><arrow.to.target n="marg244"></arrow.to.target> <lb></lb>ked authorities, for our diſputes are about the Senſible World, <lb></lb>and not one of Paper. </s><s>And foraſmuch as in our diſcourſes yeſter <lb></lb>day, we retrein'd the Earth from darkneſſe, and expoſed it to the <lb></lb>open skie, ſhewing, that the attempt to enumerate it amongſt <lb></lb>thoſe which we call Cœleſtial bodies, was not a poſition ſo foil'd, <lb></lb>and vanquiſh't, as that it had no life left in it; it followeth next, <lb></lb>that we proceed to examine what probability there is for holding <lb></lb>of it fixt, and wholly immoveable, <emph type="italics"></emph>ſcilicet<emph.end type="italics"></emph.end> as to its entire Globe, <lb></lb>what likelyhood there is for making it moveable with ſome motion, <lb></lb>and of what kind that may be. </s><s>And foraſmuch as in this ſame <lb></lb>queſtion I am ambiguous, and <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> is reſolute, as likewiſe <lb></lb><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> for the opinion of its immobility, he ſhall one by one <lb></lb>produce the arguments in favour of their opinion, and I will al <lb></lb>ledge the anſwers and reaſons on the contrary part; and next <emph type="italics"></emph>Sa <lb></lb>gredus<emph.end type="italics"></emph.end> ſhall tell us his thoughts, and to which ſide he finds him <lb></lb>ſelf inclined.</s></p><p type="margin"><s><margin.target id="marg242"></margin.target><emph type="italics"></emph>Too cloſe adhe <lb></lb>ring to<emph.end type="italics"></emph.end> Ariſtotle <emph type="italics"></emph>is <lb></lb>blameable.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg243"></margin.target><emph type="italics"></emph>It is not juſt, that <lb></lb>thoſe who never <lb></lb>philoſophate, ſhould <lb></lb>uſurp the title of <lb></lb>Philoſophers.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg244"></margin.target><emph type="italics"></emph>The Senſible <lb></lb>World.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. Content; provided alwayes that I may reſerve the li <lb></lb>berty to my ſelf of alledging what pure natural reaſon ſhall ſome <lb></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></lb>for, amongſt the more eaſie, and, to ſo ſpeak, material conſidera <lb></lb>tions, I believe there are but few of them that have been omit <lb></lb>ted by Writers, ſo that onely ſome of the more ſubtle, and re <lb></lb>mote can be deſired, or wanting; and to inveſtigate theſe, what <lb></lb>other ingenuity can be more ſit than that of the moſt acute and <lb></lb>piercing wit of <emph type="italics"></emph>Sagredus<emph.end type="italics"></emph.end>?</s></p> <pb xlink:href="040/01/115.jpg" pagenum="97"></pb><p type="main"><s>SAGR. </s><s>I am what ever pleaſeth <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> but I pray you, <lb></lb>let us not ſally out into another kind of digreſſion complemental; <lb></lb>for at this time I am a Philoſopher, and in the Schools, not in the <lb></lb>Court.</s></p><p type="main"><s>SALV. </s><s>Let our contemplation begin therefore with this conſi <lb></lb>deration, that whatſoever motion may be aſcribed to the Earth, <lb></lb>it is neceſſary that it be to us, (as inhabitants upon it, and conſe <lb></lb>quently partakers of the ſame) altogether imperceptible, and as if <lb></lb>it were not at all, ſo long as we have regard onely to terreſtrial <lb></lb>things; but yet it is on the contrary, as neceſſary that the ſame <lb></lb><arrow.to.target n="marg245"></arrow.to.target> <lb></lb>motion do ſeem common to all other bodies, and viſible ob <lb></lb>jects, that being ſeparated from the Earth, participate not of the <lb></lb>ſame. </s><s>So that the true method to find whether any kind of motion <lb></lb>may be aſcribed to the Earth, and that found, to know what it <lb></lb>is, is to conſider and obſerve if in bodies ſeparated from the <lb></lb>Earth, one may diſcover any appearance of motion, which e <lb></lb><arrow.to.target n="marg246"></arrow.to.target> <lb></lb>qually ſuiteth to all the reſt; for a motion that is onely ſeen, <emph type="italics"></emph>v. </s><s>gr.<emph.end type="italics"></emph.end> <lb></lb>in the <emph type="italics"></emph>Moon,<emph.end type="italics"></emph.end> and that hath nothing to do with <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> or <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> <lb></lb>or any other Stars, cannot any way belong to the Earth, or to <lb></lb>any other ſave the Moon alone. </s><s>Now there is a moſt general and <lb></lb>grand motion above all others, and it is that by which the Sun, <lb></lb><arrow.to.target n="marg247"></arrow.to.target> <lb></lb>the Moon, the other Planets, and the Fixed Stars, and in a word, <lb></lb>the whole Univerſe, the Earth onely excepted, appeareth in our <lb></lb>thinking to move from the Eaſt towards the Weſt, in the ſpace of <lb></lb>twenty four hours; and this, as to this firſt appearance, hath no <lb></lb>obſtacle to hinder it, that it may not belong to the Earth alone, <lb></lb>as well as to all the World beſides, the Earth excepted; for the <lb></lb>ſame aſpects will appear in the one poſition, as in the other. <lb></lb></s><s>Hence it is that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ptolomy,<emph.end type="italics"></emph.end> as having hit upon this con <lb></lb><arrow.to.target n="marg248"></arrow.to.target> <lb></lb>ſideration, in going about to prove the Earth to be immoveable, <lb></lb>argue not againſt any other than this <emph type="italics"></emph>Diurnal<emph.end type="italics"></emph.end> Motion; ſave onely <lb></lb>that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> hinteth ſomething in obſcure terms againſt another <lb></lb>Motion aſcribed to it by an <emph type="italics"></emph>Ancient,<emph.end type="italics"></emph.end> of which we ſhall ſpeak in <lb></lb>its place.</s></p><p type="margin"><s><margin.target id="marg245"></margin.target><emph type="italics"></emph>The motions of <lb></lb>the Earth are im <lb></lb>perceptible to its <lb></lb>inhabitants.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg246"></margin.target><emph type="italics"></emph>The Earth can <lb></lb>have no other mo <lb></lb>tions, than thoſe <lb></lb>which to us appear <lb></lb>commune to all the <lb></lb>rest of the Vni <lb></lb>verſe, the Earth <lb></lb>excepted.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg247"></margin.target><emph type="italics"></emph>The Diurnal Mo <lb></lb>tion, ſeemeth com <lb></lb>mune to all the V <lb></lb>niverſe, ſave onely <lb></lb>the Earth excepted.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg248"></margin.target>Ariſtotle <emph type="italics"></emph>and<emph.end type="italics"></emph.end> <lb></lb>Ptolomy <emph type="italics"></emph>argue a <lb></lb>gainſt the Diur <lb></lb>nal Motion attri <lb></lb>buted to the Earth.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I very well perceive the neceſſity of your illation: but <lb></lb>I meet with a doubt which I know not how to free my ſelf from, <lb></lb>and this it is, That <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> aſſigning to the Earth another mo <lb></lb>tion beſide the Diurnal, which, according to the rule even now laid <lb></lb>down, ought to be to us, as to appearance, imperceptible in the <lb></lb>Earth, but viſible in all the reſt of the World; me thinks I may <lb></lb>neceſſarily infer, either that he hath manifeſtly erred in aſſigning <lb></lb>the Earth a motion, to which there appears not a general corre <lb></lb>ſpondence in Heaven; or elſe that if there be ſuch a congruity <lb></lb>therein, <emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> on the other hand hath been deficient in not con <lb></lb>futing this, as he hath done the other.</s></p> <pb xlink:href="040/01/116.jpg" pagenum="98"></pb><p type="main"><s>SALV. </s><s>You have good cauſe for your doubt: and when we <lb></lb>come to treat of the other Motion, you ſhall ſee how far <emph type="italics"></emph>Coper <lb></lb>nicus<emph.end type="italics"></emph.end> excelled <emph type="italics"></emph>Ptolomey<emph.end type="italics"></emph.end> in clearneſs and ſublimity of wit, in that <lb></lb>he ſaw what the other did not, I mean the admirable harmony <lb></lb>wherein that Motion agreed with all the other Cœleſtial Bodies. <lb></lb></s><s>But for the preſent we will ſuſpend this particular, and return to <lb></lb>our firſt conſideration; touching which I will proceed to propoſe <lb></lb>(begining with things more general) thoſe reaſons which ſeem to <lb></lb>favour the mobility of the Earth, and then wait the anſwers which <lb></lb><arrow.to.target n="marg249"></arrow.to.target> <lb></lb><emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> ſhall make thereto. </s><s>And firſt, if we conſider onely <lb></lb>the immenſe magnitude of the Starry Sphere, compared to the <lb></lb>ſmalneſs of the Terreſtrial Globe, contained therein ſo many mil <lb></lb>lions of times; and moreover weigh the velocity of the motion <lb></lb>which muſt in a day and night make an entire revolution thereof, <lb></lb>I cannot perſwade my ſelf, that there is any man who believes it <lb></lb>more reaſonable and credible, that the Cœleſtial Sphere turneth <lb></lb>round, and the Terreſtrial Globe ſtands ſtill.</s></p><p type="margin"><s><margin.target id="marg249"></margin.target><emph type="italics"></emph>Why the diurnal <lb></lb>motion more pro <lb></lb>bably ſhould belong <lb></lb>to the Earth, than <lb></lb>to the reſt of the <lb></lb>Vniverſe.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>If from the univerſality of effects, which may in nature <lb></lb>have dependence upon ſuch like motions, there ſhould indifferent <lb></lb>ly follow all the ſame conſequences to an hair, aſwell in one <emph type="italics"></emph>Hypo <lb></lb>theſis<emph.end type="italics"></emph.end> as in the other; yet I for my part, as to my firſt and general <lb></lb>apprehenſion, would eſteem, that he which ſhould hold it more ra <lb></lb>tional to make the whole Univerſe move, and thereby to ſalve the <lb></lb>Earths mobility, is more unreaſonable than he that being got to <lb></lb>the top of your Turret, ſhould deſire, to the end onely that he <lb></lb>might behold the City, and the Fields about it, that the whole <lb></lb>Country might turn round, that ſo he might not be put to the <lb></lb>trouble to ſtir his head. </s><s>And yet doubtleſs the advantages would <lb></lb>be many and great which the <emph type="italics"></emph>Copernican Hypotheſis<emph.end type="italics"></emph.end> is attended <lb></lb>with, above thoſe of the <emph type="italics"></emph>Ptolomaique,<emph.end type="italics"></emph.end> which in my opinion re <lb></lb>ſembleth, nay ſurpaſſeth that other folly; ſo that all this makes <lb></lb>me think that far more probable than this. </s><s>But haply <emph type="italics"></emph>Ariſtotle, <lb></lb>Ptolomey,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> may find the advantages of their Sy <lb></lb>ſteme, which they would do well to communicate to us alſo, if <lb></lb>any ſuch there be; or elſe declare to me, that there neither are or <lb></lb>can be any ſuch 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></lb>thought upon it, to find any diverſity therein; ſo I think I have <lb></lb>found, that no ſuch diverſity can be in them: in ſo much that I <lb></lb><arrow.to.target n="marg250"></arrow.to.target> <lb></lb>eſteem it to no purpoſe to ſeek farther after it. </s><s>Therefore ob <lb></lb>ſerve: Motion is ſo far Motion, and as Motion operateth, by how <lb></lb>far it hath relation to things which want Motion: but in thoſe <lb></lb>things which all equally partake thereof it hath nothing to do, and <lb></lb>is as if it never were. </s><s>And thus the Merchandiſes with which a <lb></lb>ſhip is laden, ſo far move, by how far leaving <emph type="italics"></emph>London,<emph.end type="italics"></emph.end> they paſs <pb xlink:href="040/01/117.jpg" pagenum="99"></pb>by <emph type="italics"></emph>France, Spain, Italy,<emph.end type="italics"></emph.end> and ſail to <emph type="italics"></emph>Aleppo,<emph.end type="italics"></emph.end> which <emph type="italics"></emph>London, France, <lb></lb>Spain &c.<emph.end type="italics"></emph.end> ſtand ſtill, not moving with the ſhip: but as to the <lb></lb>Cheſts, Bales and other Parcels, wherewith the ſhip is ſtow'd and <lb></lb>and laden, and in reſpect of the ſhip it ſelf, the Motion from <emph type="italics"></emph>Lon <lb></lb>don<emph.end type="italics"></emph.end> to <emph type="italics"></emph>Syria<emph.end type="italics"></emph.end> is as much as nothing; and nothing-altereth the re <lb></lb>lation which is between them: and this, becauſe it is common to <lb></lb>all, and is participated by all alike: and of the Cargo which is in <lb></lb>the ſhip, if a Bale were romag'd from a Cheſt but one inch onely, <lb></lb>this alone would be in that Cargo, a greater Motion in reſpect of <lb></lb>the Cheſt, than the whole Voyage of above three thouſand miles, <lb></lb>made by them as they were ſtived together.</s></p><p type="margin"><s><margin.target id="marg250"></margin.target><emph type="italics"></emph>Motion, as to the <lb></lb>things that equally <lb></lb>move thereby, is as <lb></lb>of it never were, & <lb></lb>ſo far operates as it <lb></lb>hath relation to <lb></lb>things deprived of <lb></lb>motion.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>This Doctrine is good, ſound, and altogether <emph type="italics"></emph>Peri <lb></lb>patetick.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>I hold it to be much more antient: and ſuſpect that <emph type="italics"></emph>A-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg251"></arrow.to.target> <lb></lb><emph type="italics"></emph>riſtotle<emph.end type="italics"></emph.end> in receiving it from ſome good School, did not fully under <lb></lb>ſtand it, and that therefore, having delivered it with ſome altera <lb></lb>tion, it hath been an occaſion of confuſion amongſt thoſe, who <lb></lb>would defend whatever he ſaith. </s><s>And when he writ, that what <lb></lb>ſoever moveth, doth move upon ſomething immoveable, I ſuppoſe <lb></lb>that he equivocated, and meant, that whatever moveth, moveth <lb></lb>in reſpect to ſomething immoveable; which propoſition admitteth <lb></lb>no doubt, and the other many.</s></p><p type="margin"><s><margin.target id="marg251"></margin.target><emph type="italics"></emph>A propoſition ta <lb></lb>ken by<emph.end type="italics"></emph.end> Ariſtotle <lb></lb><emph type="italics"></emph>from the Antients, <lb></lb>but ſomewhat al <lb></lb>tered by him.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Pray you make no digreſſion, but proceed in the diſ <lb></lb>ſertation you began.</s></p><p type="main"><s>SALV. </s><s>It being therefore manifeſt, that the motion which is <lb></lb><arrow.to.target n="marg252"></arrow.to.target> <lb></lb>common to many moveables, is idle, and as it were, null as to the <lb></lb>relation of thoſe moveables between themſelves, becauſe that a <lb></lb>mong themſelves they have made no change: and that it is ope <lb></lb>rative onely in the relation that thoſe moveables have to other <lb></lb>things, which want that motion, among which the habitude is <lb></lb>changed: and we having divided the Univerſe into two parts, one <lb></lb>of which is neceſſarily moveable, and the other immoveable; for <lb></lb>the obtaining of whatſoever may depend upon, or be required <lb></lb>from ſuch a motion, it may as well be done by making the Earth <lb></lb>alone, as by making all the reſt of the World to move: for that <lb></lb>the operation of ſuch a motion conſiſts in nothing elſe, ſave in <lb></lb>the relation or habitude which is between the Cœleſtial Bodies, <lb></lb>and the Earth, the which relation is all that is changed. </s><s>Now if <lb></lb>for the obtaining of the ſame effect <emph type="italics"></emph>ad unguem,<emph.end type="italics"></emph.end> it be all one whe <lb></lb>ther the Earth alone moveth, the reſt of the Univerſe ſtanding <lb></lb>ſtill; or that, the Earth onely ſtanding ſtill, the whole Univerſe <lb></lb><arrow.to.target n="marg253"></arrow.to.target> <lb></lb>moveth with one and the ſame motion; who would believe, that <lb></lb>Nature (which by common conſent, doth not that by many things, <lb></lb>which may be done by few) hath choſen to make an innumerable <lb></lb>number of moſt vaſt bodies move, and that with an unconceivable <pb xlink:href="040/01/118.jpg" pagenum="100"></pb>velocity, to perform that, which might be done by the moderate <lb></lb>motion of one alone about its own Centre?</s></p><p type="margin"><s><margin.target id="marg252"></margin.target><emph type="italics"></emph>The firſt diſcourſe <lb></lb>to prove that the <lb></lb>diurnal motion be <lb></lb>longs to the Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg253"></margin.target><emph type="italics"></emph>Nature never <lb></lb>doth that by many <lb></lb>things, which may <lb></lb>be done by a few.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>I do not well underſtand, how this grand motion ſig <lb></lb>niſieth nothing as to the Sun, as to the Moon, as to the other Pla <lb></lb>nets, and as to the innumerable multitude of fixed ſtars: or why <lb></lb>you ſhould ſay that it is to no purpoſe for the Sun to paſs from one <lb></lb>Meridian to another; to riſe above this Horizon, to ſet beneath <lb></lb>that other; to make it one while day, another while night: the <lb></lb>like variations are made by the Moon, the other Planets, and the <lb></lb>fixed ſtars themſelves.</s></p><p type="main"><s>SALV. </s><s>All theſe alterations inſtanced by you, are nothing, ſave <lb></lb>onely in relation to the Earth: and that this is true, do but i <lb></lb><arrow.to.target n="marg254"></arrow.to.target> <lb></lb>magine the Earth to move, and there will be no ſuch thing in the <lb></lb>World as the riſing or ſetting of the Sun or Moon, nor Horizons, <lb></lb>nor Meridians, nor days, nor nights; nor, in a word, will ſuch a <lb></lb>motion cauſe any mutation between the Moon and Sun, or any <lb></lb>other ſtar whatſoever, whether fixed or erratick; but all theſe <lb></lb>changes have relation to the Earth: which all do yet in ſum <lb></lb>import no other than as if the Sun ſhould ſhew it ſelf now to <lb></lb><emph type="italics"></emph>China,<emph.end type="italics"></emph.end> anon to <emph type="italics"></emph>Perſia,<emph.end type="italics"></emph.end> then to <emph type="italics"></emph>Egypt, Greece, France, Spain, A <lb></lb>merica, &c.<emph.end type="italics"></emph.end> and the like holdeth in the Moon, and the reſt of the <lb></lb>Cœleſtial Bodies: which ſelf ſame effect falls out exactly in the <lb></lb>ſame manner, if, without troubling ſo great a part of the Univerſe, <lb></lb><arrow.to.target n="marg255"></arrow.to.target> <lb></lb>the Terreſtrial Globe be made to revolve in it ſelf. </s><s>But we will <lb></lb>augment the difficulty by the addition of this other, which is a <lb></lb>very great one, namely, that if you will aſcribe this <emph type="italics"></emph>Great<emph.end type="italics"></emph.end> Motion to <lb></lb>Heaven, you muſt of neceſſity make it contrary to the particular <lb></lb>motion of all the Orbs of the Planets, each of which without <lb></lb>controverſie hath its peculiar motion from the Weſt towards the <lb></lb>Eaſt, and this but very eaſie and moderate: and then you make <lb></lb>them to be hurried to the contrary part, <emph type="italics"></emph>i. </s><s>e.<emph.end type="italics"></emph.end> from Eaſt to Weſt, <lb></lb>by this moſt furious diurnal motion: whereas, on the contrary, <lb></lb>making the Earth to move in it ſelf, the contrariety of motions is <lb></lb>taken away, and the onely motion from Weſt to Eaſt is accom <lb></lb>modated to all appearances, and exactly ſatisfieth every <emph type="italics"></emph>Phœno <lb></lb>menon.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg254"></margin.target><emph type="italics"></emph>The diurnal mo <lb></lb>tion cauſeth no <lb></lb>mutation amongſt <lb></lb>the Cœleſtial Bo <lb></lb>dies, but all chan <lb></lb>ges have relation <lb></lb>to the Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg255"></margin.target><emph type="italics"></emph>A ſccond con <lb></lb>firmation that the <lb></lb>diurnal motion be <lb></lb>longs to the Earth.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>As to the contrariety of Motions it would import lit <lb></lb><arrow.to.target n="marg256"></arrow.to.target> <lb></lb>tle, for <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> demonſtrateth, that circular motions, are not con <lb></lb>trary to one another; and that theirs cannot be truly called con <lb></lb>trariety.</s></p><p type="margin"><s><margin.target id="marg256"></margin.target><emph type="italics"></emph>Circular moti <lb></lb>ons are not contra <lb></lb>ry, according to<emph.end type="italics"></emph.end> <lb></lb>Ariſtotle.</s></p><p type="main"><s>SALV. </s><s>Doth <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> demonſtrate this, or doth he not rather <lb></lb>barely affirm it, as ſerving to ſome certain deſign of his? </s><s>If con <lb></lb>traries be thoſe things, that deſtroy one another, as he himſelf <lb></lb>affirmeth, I do not ſee how two moveables that encounter each <lb></lb>other in a circular line, ſhould leſſe prejudice one another, than if <lb></lb>they interfered in a right line.</s></p> <pb xlink:href="040/01/119.jpg" pagenum="101"></pb><p type="main"><s>SAGR. </s><s>Hold a little, I pray you. </s><s>Tell me <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> when <lb></lb>two Knights encounter each other, tilting in open field, or when <lb></lb>two whole Squadrons, or two Fleets at Sea, make up to grapple, <lb></lb>and are broken and ſunk, do you call theſe encounters contrary to <lb></lb>one another?</s></p><p type="main"><s>SIMPL. Yes, we ſay they are contrary.</s></p><p type="main"><s>SAGR. </s><s>How then, is there no contrariety in circular motions. <lb></lb></s><s>Theſe motions, being made upon the ſuperſicies of the Earth or <lb></lb>Water, which are, as you know, ſpherical, come to be circular. <lb></lb></s><s>Can you tell, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> which thoſe circular motions be, that <lb></lb>are not contrary to each other? </s><s>They are (if I miſtake not) thoſe <lb></lb>of two circles, which touching one another without, one thereof <lb></lb>being turn'd round, naturally maketh the other move the contra <lb></lb>ry ^{*} way; but if one of them ſhall be within the other, it is im <lb></lb><arrow.to.target n="marg257"></arrow.to.target> <lb></lb>poſſible that their motion being made towards different points, <lb></lb>they ſhould not juſtle one another.</s></p><p type="margin"><s><margin.target id="marg257"></margin.target>As you ſee in a <lb></lb>Mill, wherein the <lb></lb>implicated cogs ſet <lb></lb>the wheels on mo <lb></lb>ving.</s></p><p type="main"><s>SALV. </s><s>But be they contrary, or not contrary, theſe are but <lb></lb>alterations of words; and I know, that upon the matter, it would <lb></lb>be far more proper and agreeable with Nature, if we could ſalve <lb></lb>all with one motion onely, than to introduce two that are (if you <lb></lb>will not call them contrary) oppoſite; yet do I not cenſure this <lb></lb>introduction (of contrary motions) as impoſſible; nor pretend I <lb></lb>from the denial thereof, to inferre a neceſſary Demonſtration, <lb></lb>but onely a greater probability, of the other. </s><s>A third reaſon <lb></lb><arrow.to.target n="marg258"></arrow.to.target> <lb></lb>which maketh the <emph type="italics"></emph>Ptolomaique Hypotheſis<emph.end type="italics"></emph.end> leſſe probable is, that it <lb></lb>moſt unreaſonably confoundeth the order, which we aſſuredly <lb></lb>ſee to be amongſt thoſe Cœleſtial Bodies, the circumgyration of <lb></lb>which is not queſtionable, but moſt certain. </s><s>And that Order is, <lb></lb><arrow.to.target n="marg259"></arrow.to.target> <lb></lb>that according as an Orb is greater, it finiſheth its revolution in a <lb></lb>longer time, and the leſſer, in ſhorter. </s><s>And thus <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> deſcri <lb></lb>bing a greater Circle than all the other Planets, compleateth the <lb></lb>ſame in thirty yeares: <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> finiſheth his; that is leſſe, in <lb></lb>twelve years: <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> in two: The Moon runneth thorow hers, ſo <lb></lb>much leſſe than the reſt, in a Moneth onely. </s><s>Nor do we leſſe <lb></lb>ſenſibly ſee that of the <emph type="italics"></emph>Medicean Stars,<emph.end type="italics"></emph.end> which is neareſt to <emph type="italics"></emph>Ju-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg260"></arrow.to.target> <lb></lb><emph type="italics"></emph>piter,<emph.end type="italics"></emph.end> to make its revolution in a very ſhort time, that is, in four <lb></lb>and forty hours, or thereabouts, the next to that in three dayes and <lb></lb>an half, the third in ſeven dayes, and the moſt remote in ſixteen. <lb></lb></s><s>And this rate holdeth well enough, nor will it at all alter, whileſt <lb></lb>we aſſign the motion of 24 hours to the Terreſtrial Globe, for it <lb></lb>to move round its own center in that time; but if you would have <lb></lb>the Earth immoveable, it is neceſſary, that when you have paſt <lb></lb>from the ſhort period of the Moon, to the others ſucceſſively <lb></lb>bigger, until you come to that of <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> in two years, and from <lb></lb>thence to that of the bigger Sphere of <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> in twelve years, and <pb xlink:href="040/01/120.jpg" pagenum="102"></pb>from this to the other yet bigger of <emph type="italics"></emph>Saturn,<emph.end type="italics"></emph.end> whoſe period is of <lb></lb>thirty years, it is neceſſary, I ſay, that you paſſe to another <lb></lb>Sphere incomparably greater ſtill than that, and make this to ac <lb></lb><arrow.to.target n="marg261"></arrow.to.target> <lb></lb>compliſh an entire revolution in twenty four hours. </s><s>And this yet is <lb></lb>the leaſt diſorder that can follow. </s><s>For if any one ſhould paſſe <lb></lb>from the Sphere of <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> to the Starry Orb, and make it ſo <lb></lb>much bigger than that of <emph type="italics"></emph>Saturn,<emph.end type="italics"></emph.end> as proportion would require, in <lb></lb>reſpect of its very ſlow motion, of many thouſands of years, then <lb></lb>it muſt needs be a <emph type="italics"></emph>Salt<emph.end type="italics"></emph.end> much more abſurd, to skip from this to <lb></lb>another bigger, and to make it convertible in twenty four hours. <lb></lb></s><s>But the motion of the Earth being granted, the order of the pe <lb></lb>riods will be exactly obſerved, and from the very ſlow Sphere of <lb></lb><emph type="italics"></emph>Saturn,<emph.end type="italics"></emph.end> we come to the fixed Stars, which are wholly immovea <lb></lb><arrow.to.target n="marg262"></arrow.to.target> <lb></lb>ble, and ſo avoid a fourth difficulty, which we muſt of neceſſity ad <lb></lb>mit, if the Starry Sphere be ſuppoſed moveable, and that is the <lb></lb><arrow.to.target n="marg263"></arrow.to.target> <lb></lb>immenſe diſparity between the motions of thoſe ſtars themſelves; <lb></lb>of which ſome would come to move moſt ſwiftly in moſt vaſt cir <lb></lb>cles, others moſt ſlowly in circles very ſmall, according as thoſe <lb></lb>or theſe ſhould be found nearer, or more remote from the Poles; <lb></lb>which ſtill is accompanied with an inconvenience, as well becauſe <lb></lb>we ſee thoſe, of whoſe motion there is no queſtion to be made, <lb></lb>to move all in very immenſe circles; as alſo, becauſe it ſeems to <lb></lb>be an act done with no good conſideration, to conſtitute bodies, <lb></lb>that are deſigned to move circularly, at immenſe diſtances from <lb></lb>the centre, and afterwards to make them move in very ſmall cir <lb></lb>cles. </s><s>And not onely the magnitudes of the circles, and conſe <lb></lb>quently the velocity of the motions of theſe Stars, ſhall be moſt <lb></lb><arrow.to.target n="marg264"></arrow.to.target> <lb></lb>different from the circles and motions of thoſe others, but <lb></lb>(which ſhall be the fifth inconvenience) the ſelf-ſame Stars <lb></lb>ſhall ſucceſſively vary its circles and velocities: For that <lb></lb><arrow.to.target n="marg265"></arrow.to.target> <lb></lb>thoſe, which two thouſand years ſince were in the Equinoctial, <lb></lb>and conſequently did with their motion deſcribe very vaſt cir <lb></lb>cles, being in our dayes many degrees diſtant from thence, muſt <lb></lb>of neceſſity become more ſlow of motion, and be reduced to <lb></lb>move in leſſer circles, and it is not altogether impoſſible but that <lb></lb>a time may come, in which ſome of them which in aforetime had <lb></lb>continually moved, ſhall be reduced by uniting with the Pole, to <lb></lb>a ſtate of reſt, and then after ſome time of ceſſation, ſhall return <lb></lb>to their motion again; whereas the other Stars, touching whoſe <lb></lb>motion none ſtand in doubt, do all deſcribe, as hath been ſaid, <lb></lb>the great circle of their Orb, and in that maintain themſelves <lb></lb>without any variation. </s><s>The abſurdity is farther enlarged (which <lb></lb><arrow.to.target n="marg266"></arrow.to.target> <lb></lb>let be the ſixth inconvenience) to him that more ſeriouſly exami <lb></lb>neth the thing, in that no thought can comprehend what ought to <lb></lb>be the ſolidity of that immenſe Sphere, whoſe depth ſo ſtedfaſtly <pb xlink:href="040/01/121.jpg" pagenum="103"></pb>holdeth faſt ſuch a multitude of Stars, which without ever chang <lb></lb>ing fite among themſelves, are with ſo much concord carried a <lb></lb>bout, with ſo great diſparity of motions. </s><s>Or elſe, ſuppoſing the <lb></lb>Heavens to be fluid, as we are with more reaſon to believe, ſo <lb></lb>as that every Star wandereth to and fro in it, by wayes of its <lb></lb>own, what rules ſhall regulate their motions, and to what pur <lb></lb>poſe, ſo, as that being beheld from the Earth, they appear as if <lb></lb>they were made by one onely Sphere? </s><s>It is my opinion, that they <lb></lb>might ſo much more eaſily do that, and in a more commodious <lb></lb>manner, by being conſtituted immoveable, than by being made <lb></lb>errant, by how much more facile it is to number the quarries in the <lb></lb>Pavement of a <emph type="italics"></emph>Piazza,<emph.end type="italics"></emph.end> than the rout of boyes which run up and <lb></lb>down upon them. </s><s>And laſtly, which is the ſeventh inſtance, if <lb></lb><arrow.to.target n="marg267"></arrow.to.target> <lb></lb>we atribute the Diurnal Motion to the higheſt Heaven, it muſt be <lb></lb>conſtituted of ſuch a force and efficacy, as to carry along with <lb></lb>it the innumerable multitude of fixed Stars, Bodies all of vaſt <lb></lb>magnitude, and far bigger than the Earth; and moreover all the <lb></lb>Spheres of the Planets; notwithſtanding that both theſe and thoſe <lb></lb>of their own nature move the contrary way. </s><s>And beſides all this, <lb></lb>it muſt be granted, that alſo the Element of Fire, and the great <lb></lb>er part of the Air, are likewiſe forcibly hurried along with the <lb></lb>reſt, and that the ſole little Globe of the Earth pertinaciouſly <lb></lb>ſtands ſtill, and unmoved againſt ſuch an impulſe; a thing, which <lb></lb>in my thinking, is very difficult; nor can I ſee how the Earth, a <lb></lb>pendent body, and equilibrated upon its centre, expoſed indif <lb></lb><arrow.to.target n="marg268"></arrow.to.target> <lb></lb>ferently to either motion or reſt, and environed with a liquid <emph type="italics"></emph>am <lb></lb>bient,<emph.end type="italics"></emph.end> ſhould not yield alſo as the reſt, and be carried about. <lb></lb></s><s>But we find none of theſe obſtacles in making the Earth to move; <lb></lb>a ſmall body, and inſenſible, compared to the Univerſe, and <lb></lb>therefore unable to offer it any violence.</s></p><p type="margin"><s><margin.target id="marg258"></margin.target><emph type="italics"></emph>A third confir <lb></lb>mation of the ſame <lb></lb>Doctrine.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg259"></margin.target><emph type="italics"></emph>The greater Orbs <lb></lb>make their conver <lb></lb>ſions in greater <lb></lb>times.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg260"></margin.target><emph type="italics"></emph>The times of the<emph.end type="italics"></emph.end> <lb></lb>Medicean <emph type="italics"></emph>Planets <lb></lb>converſions.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg261"></margin.target><emph type="italics"></emph>The motion of<emph.end type="italics"></emph.end> <lb></lb>24 <emph type="italics"></emph>hours aſcribed <lb></lb>to the higheſt <lb></lb>Sphere diſorders <lb></lb>the period of the <lb></lb>inferiour.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg262"></margin.target><emph type="italics"></emph>The fourth Con <lb></lb>firmation.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg263"></margin.target><emph type="italics"></emph>Great diſparity <lb></lb>amongſt the moti <lb></lb>ons of the particu <lb></lb>lar fixed ſtars, if <lb></lb>their Sphere be <lb></lb>moveable.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg264"></margin.target><emph type="italics"></emph>The fifth Con <lb></lb>firmation.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg265"></margin.target><emph type="italics"></emph>The motions of <lb></lb>the fixed ſtars <lb></lb>would accelerate <lb></lb>and grow ſlow in <lb></lb>divers times, if the <lb></lb>ſtarry Sphere were <lb></lb>moueable.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg266"></margin.target><emph type="italics"></emph>The ſixth Con <lb></lb>firmatiox.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg267"></margin.target><emph type="italics"></emph>The Seventh Con <lb></lb>firmation.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg268"></margin.target><emph type="italics"></emph>The Earth a <lb></lb>pendent Body, and <lb></lb>equilibrated in a <lb></lb>fluid<emph.end type="italics"></emph.end> Medium <lb></lb><emph type="italics"></emph>ſeems unable to <lb></lb>reſiſt the rapture <lb></lb>of the Diurnal <lb></lb>Motion.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I find my fancy diſturbed with certain conjectures ſo con <lb></lb>fuſedly ſprung from your later diſcourſes; that, if I would be ena <lb></lb>bled to apply my ſelf with atention to what followeth, I muſt of ne <lb></lb>ceſſity attempt whether I can better methodize them, and gather <lb></lb>thence their true conſtruction, if haply any can be made of them; <lb></lb>and peradventure, the proceeding by interrogations may help me <lb></lb>the more eaſily to expreſſe my ſelf. </s><s>Therefore I demand firſt of <emph type="italics"></emph>Sim <lb></lb>plicius,<emph.end type="italics"></emph.end> whether he believeth, that divers motions may natural <lb></lb>ly agree to one and the ſame moveable body, or elſe that it be <lb></lb>requiſite its natural and proper motion be onely one.</s></p><p type="main"><s>SIMPL. </s><s>To one ſingle moveable, there can naturally agree <lb></lb><arrow.to.target n="marg269"></arrow.to.target> <lb></lb>but one ſole motion, and no more; the reſt all happen acciden <lb></lb>tally and by participation; like as to him that walketh upon the <lb></lb>Deck of a Ship, his proper motion is that of his walk, his motion <lb></lb>by participation that which carrieth him to his Port, whither he <pb xlink:href="040/01/122.jpg" pagenum="104"></pb>would never with his walking have arrived, if the Ship with its <lb></lb>motion had not wafted him thither.</s></p><p type="margin"><s><margin.target id="marg269"></margin.target><emph type="italics"></emph>A ſingle move <lb></lb>able hath but onely <lb></lb>one natural moti <lb></lb>on, and all the <lb></lb>reſt are by partici <lb></lb>pation.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Tell me ſecondly. </s><s>That motion, which is communi <lb></lb>cated to any moveable by participation, whileſt it moveth by it <lb></lb>ſelf, with another motion different from the participated, is it <lb></lb>neceſſary, that it do reſide in ſome certain ſubject by it ſelf, or <lb></lb>elſe can it ſubſiſt in nature alone, without other ſupport.</s></p><p type="main"><s>SIMPL. <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> giveth you an anſwer to all theſe queſtions, <lb></lb><arrow.to.target n="marg270"></arrow.to.target> <lb></lb>and tels you, that as of one ſole moveable the motion is but one; <lb></lb>ſo of one ſole motion the moveable is but one; and conſequent <lb></lb>ly, that without the inherence in its ſubject, no motion can ei <lb></lb>ther ſubſiſt, or be imagined.</s></p><p type="margin"><s><margin.target id="marg270"></margin.target><emph type="italics"></emph>Motion cannot <lb></lb>be made without <lb></lb>its moveable ſub <lb></lb>ject.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I would have you tell me in the third place, whether <lb></lb>you beblieve that the Moon and the other Planets and Cœleſtial <lb></lb>bodies, have their proper motions, and what they are.</s></p><p type="main"><s>SIMPL. </s><s>They have ſo, and they be thoſe according to which <lb></lb>they run through the Zodiack, the Moon in a Moneth, the Sun <lb></lb>in a Year, <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> in two, the Starry Sphere in thoſe ſo many thou <lb></lb>ſand. </s><s>And theſe are their proper, or natural motions.</s></p><p type="main"><s>SAGR. </s><s>But that motion wherewith I ſee the fixed Stars, and <lb></lb>with them all the Planets go unitedly from Eaſt to Weſt, and re <lb></lb>turn round to the Eaſt again in twenty four hours, how doth it <lb></lb>agree with them?</s></p><p type="main"><s>SIMPL. </s><s>It ſuiteth with them by participation.</s></p><p type="main"><s>SAGR. </s><s>This then reſides not in them, and not reſiding in <lb></lb>them, nor being able to ſubſiſt without ſome ſubject in which it <lb></lb>is reſident, it muſt of force be the proper and natural motion of <lb></lb>ſome other Sphere.</s></p><p type="main"><s>SIMPL. </s><s>For this purpoſe Aſtronomers, and Philoſophers have <lb></lb>found another high Sphere, above all the reſt, without Stars, to <lb></lb>which Natural agreeth the Diurnal Motion; and this they call <lb></lb>the <emph type="italics"></emph>Primum mobile<emph.end type="italics"></emph.end>; the which carrieth along with it all the in <lb></lb>feriour Spheres, contributing and imparting its motion to <lb></lb>them.</s></p><p type="main"><s>SAGR. </s><s>But when, without introducing other Spheres unknown <lb></lb>and hugely vaſt, without other motions or communicated raptures, <lb></lb>with leaving to each Sphere its ſole and ſimple motion, without <lb></lb>intermixing contrary motions, but making all turn one way, as <lb></lb>it is neceſſary that they do, depending all upon one ſole principle, <lb></lb>all things proceed orderly, and correſpond with moſt perfect har <lb></lb>mony, why do we reject this <emph type="italics"></emph>Phœnomenon,<emph.end type="italics"></emph.end> and give our aſſent to <lb></lb>thoſe prodigious and laborious conditions?</s></p><p type="main"><s>SIMPL. </s><s>The difficulty lyeth in finding out this ſo natural and <lb></lb>expeditious way.</s></p> <pb xlink:href="040/01/123.jpg" pagenum="105"></pb><p type="main"><s>SAGR. </s><s>In my judgment this is found. </s><s>Make the Earth the <lb></lb><emph type="italics"></emph>Primum mobile,<emph.end type="italics"></emph.end> that is, make it turn round its own <emph type="italics"></emph>axis<emph.end type="italics"></emph.end> in twenty <lb></lb>four hours, and towards the ſame point with all the other Spheres; <lb></lb>and without participating this ſame motion to any other Planet or <lb></lb>Star, all ſhall have their riſings, ſettings, and in a word, all their <lb></lb>other appearances.</s></p><p type="main"><s>SIMPL. </s><s>The buſineſs is, to be able to make the Earth move <lb></lb>without athouſand inconveniences.</s></p><p type="main"><s>SALV. </s><s>All the inconveniences ſhall be removed as faſt as you <lb></lb>propound them: and the things ſpoken hitherto are onely the <lb></lb>primary and more general inducements which give us to believe <lb></lb>that the diurnal converſion may not altogether without probabi <lb></lb>lity be applyed to the Earth, rather than to all the reſt of the U <lb></lb>niverſe: the which inducements I impoſe not upon you as invio <lb></lb>lable Axioms, but as hints, which carry with them ſomewhat of <lb></lb>likelihood. </s><s>And in regard I know very well, that one ſole ex <lb></lb><arrow.to.target n="marg271"></arrow.to.target> <lb></lb>periment, or concludent demonſtration, produced on the contrary <lb></lb>part, ſufficeth to batter to the ground theſe and a thouſand other <lb></lb>probable Arguments; therefore it is not fit to ſtay here, but proceed <lb></lb>forwards and hear what <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> anſwereth, and what greater <lb></lb>probabilities, or ſtronger arguments he alledgeth on the contrary.</s></p><p type="margin"><s><margin.target id="marg271"></margin.target><emph type="italics"></emph>One ſingle ex <lb></lb>periment, or ſound <lb></lb>demonſtration bat <lb></lb>tereth down all ar <lb></lb>guments meerly <lb></lb>probable.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>I will firſt ſay ſomething in general upon all theſe con <lb></lb>ſiderations together, and then I will deſcend to ſome particulars. <lb></lb></s><s>It ſeems that you univerſally bottom all you ſay upon the greater <lb></lb>ſimplicity and facility of producing the ſame effects, whilſt you <lb></lb>hold, that as to the cauſing of them, the motion of the Earth a <lb></lb>lone, ſerveth <emph type="italics"></emph>as well<emph.end type="italics"></emph.end> as that of all the reſt of the World, the Earth <lb></lb>deducted: but as to the operations, you eſteem that much eaſier <lb></lb>than this. </s><s>To which I reply, that I am alſo of the ſame opinion, <lb></lb>ſo long as I regard my own not onely finite, but feeble power; <lb></lb>but having a reſpect to the ſtrength of the <emph type="italics"></emph>Mover,<emph.end type="italics"></emph.end> which is in <lb></lb>finite, its no leſſe eaſie to move the Univerſe, than the Earth, <lb></lb>yea than a ſtraw. </s><s>And if his power be infinite, why ſhould he not <lb></lb><arrow.to.target n="marg272"></arrow.to.target> <lb></lb>rather exerciſe a greater part thereof than a leſſe? </s><s>Therefore, <lb></lb>I hold that your diſcourſe in general is not convincing.</s></p><p type="margin"><s><margin.target id="marg272"></margin.target><emph type="italics"></emph>Of an infinite <lb></lb>power one would <lb></lb>think a greater <lb></lb>part ſhould rather <lb></lb>be imploy'd than a <lb></lb>leſſe.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>If I had at any time ſaid, that the Univerſe moved not <lb></lb>for want of power in the <emph type="italics"></emph>Mover,<emph.end type="italics"></emph.end> I ſhould have erred, and your <lb></lb>reproof would have been ſeaſonable; and I grant you, that to <lb></lb>an infinite power, it is as eaſie to move an hundred thouſand, as <lb></lb>one. </s><s>But that which I did ſay, concerns not the Mover, but one <lb></lb>ly hath reſpect to the Moveables; and in them, not onely to <lb></lb>their reſiſtance, which doubtleſſe is leſſer in the Earth, than in <lb></lb>the Univerſe; but to the many other particulars, but even now <lb></lb>conſidered. </s><s>As to what you ſay in the next place, that of an in <lb></lb>finite power it is better to exerciſe a great part than a ſmall: I an <pb xlink:href="040/01/124.jpg" pagenum="106"></pb>ſwer, that of infinite one part is not greater than another, ſince <lb></lb><arrow.to.target n="marg273"></arrow.to.target> <lb></lb>both are infinite; nor can it be ſaid, that of the infinite number, <lb></lb>an hundred thouſand is a greater part than two, though that be <lb></lb>fifty thouſand times greater than this; and if to the moving of <lb></lb>the Univerſe there be required a finite power, though very great <lb></lb>in compariſon of that which ſufficeth to move the Earth onely; <lb></lb>yet is there not implied therein a greater part of the infinite power, <lb></lb>nor is that part leſſe infinite which remaineth unimploy'd. </s><s>So that <lb></lb>to apply unto a particular effect, a little more, or a little leſſe <lb></lb>power, importeth nothing; beſides that the operation of ſuch <lb></lb>vertue, hath not for its bound or end the Diurnal Motion onely; <lb></lb>but there are ſeveral other motions in the World, which we <lb></lb>know of, and many others there may be, that are to us unknown. <lb></lb></s><s>Therefore if we reſpect the Moveables, and granting it as out of <lb></lb>queſtion, that it is a ſhorter and eaſier way to move the Earth, <lb></lb>than the Univerſe; and moreover, having an eye to the ſo many <lb></lb>other abreviations, and facilities that onely this way are to be ob <lb></lb>tained, an infallible Maxime of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> which he teacheth us, <lb></lb>that, <emph type="italics"></emph>fruſtra fit per plura, quod poteſt fieri per pauciora,<emph.end type="italics"></emph.end> ren <lb></lb>dereth it more probable that the Diurnal Motion belongs to the <lb></lb>Earth alone, than to the Univerſe, the Earth ſubducted.</s></p><p type="margin"><s><margin.target id="marg273"></margin.target><emph type="italics"></emph>Of infinity one <lb></lb>part is no bigger <lb></lb>than auother, al <lb></lb>though they are <lb></lb>comparatively un <lb></lb>equal.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>In reciting that Axiom, you have omitted a ſmall <lb></lb>clauſe, which importeth as much as all the reſt, eſpecially in our <lb></lb>caſe, that is to ſay, the words <emph type="italics"></emph>æquè bene.<emph.end type="italics"></emph.end> It is requiſite therefore <lb></lb>to examine whether this <emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> doth <emph type="italics"></emph>equally well<emph.end type="italics"></emph.end> ſatisfie in all <lb></lb>particulars, as the other.</s></p><p type="main"><s>SALV. </s><s>The knowledg whether both theſe poſitions do <emph type="italics"></emph>æquè <lb></lb>bene,<emph.end type="italics"></emph.end> ſatisfie, may be comprehended from the particular exami <lb></lb>nation of the appearances which they are to ſatisfie; for hitherto <lb></lb>we have diſcourſed, and will continue to argue <emph type="italics"></emph>ex hypotheſi,<emph.end type="italics"></emph.end> <lb></lb>namely, ſuppoſing, that as to the ſatisfaction of the appearances, <lb></lb><arrow.to.target n="marg274"></arrow.to.target> <lb></lb>both the aſſumptions are equally accomodated. </s><s>As to the clauſe <lb></lb>which you ſay was omitted by me, I have more reaſon to ſuſpect <lb></lb>that it was ſuperfluouſly inſerted by you. </s><s>For the expreſſion <emph type="italics"></emph>æquè <lb></lb>bene,<emph.end type="italics"></emph.end> is a relative that neceſſarily requireth two terms at leaſt, <lb></lb>for a thing cannot have relation to its ſelf, nor do we ſay, <emph type="italics"></emph>v. </s><s>gr.<emph.end type="italics"></emph.end> <lb></lb>reſt to be <emph type="italics"></emph>equally good,<emph.end type="italics"></emph.end> as reſt. </s><s>And becauſe, when we ſay, <emph type="italics"></emph>that <lb></lb>is done in vain by many means, which may be done with fewer,<emph.end type="italics"></emph.end> <lb></lb>we mean, that that which is to be done, ought to be the ſame <lb></lb>thing, not two different ones; and becauſe the ſame thing can <lb></lb>not be ſaid to be done as well as its ſelf; therefore, the addition <lb></lb>of the Phraſe <emph type="italics"></emph>æquè bene<emph.end type="italics"></emph.end> is ſuperfluous, and a relation, that hath <lb></lb>but one term onely.</s></p><p type="margin"><s><margin.target id="marg274"></margin.target><emph type="italics"></emph>In the Axiome<emph.end type="italics"></emph.end> <lb></lb>Fruſtra fit per plu <lb></lb>ra, &c. <emph type="italics"></emph>the addi <lb></lb>tion of<emph.end type="italics"></emph.end> æque benè, <lb></lb><emph type="italics"></emph>is ſuperfluous.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Unleſſe you will have the ſame befal us, as did yeſter <lb></lb>day, let us return to our matter in hand; and let <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> be <pb xlink:href="040/01/125.jpg" pagenum="107"></pb>gin to produce thoſe difficulties that ſeem in his opinion, to thwart <lb></lb>this new diſpoſition of the World.</s></p><p type="main"><s>SIMPL. </s><s>That diſpoſition is not new, but very old, and that <lb></lb>you may ſee it is ſo, <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> confuteth it; and his confutations <lb></lb>are theſe: “Firſt if the Earth moveth either in it felf about its <lb></lb><arrow.to.target n="marg275"></arrow.to.target> <lb></lb>own Centre, or in an Excentrick Circle, it is neceſſary that that <lb></lb>ſame motion be violent; for it is not its natural motion, for <lb></lb>if it were, each of its parts would partake thereof; but each <lb></lb>of them moveth in a right line towards its Centre. </s><s>It being <lb></lb>therefore violent and pteternatural, it could never be perpetu <lb></lb>al: But the order of the World is perpetual. </s><s>Therefore, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> <lb></lb>Secondly, all the other moveables that move circularly, ſeem <lb></lb>to ^{*} ſtay behind, and to move with more than one motion, the <lb></lb><arrow.to.target n="marg276"></arrow.to.target> <lb></lb><emph type="italics"></emph>Primum Mobile<emph.end type="italics"></emph.end> excepted: Whence it would be neceſſary that <lb></lb>the Earth alſo do move with two motions; and if that ſhould <lb></lb>be ſo, it would inevitably follow, that mutations ſhould be <lb></lb>made in the Fixed Stars, the which none do perceive; nay <lb></lb>without any variation, the ſame Stars alwayes riſe from towards <lb></lb>the ſame places, and in the ſame places do ſet. </s><s>Thirdly, the mo <lb></lb>tion of the parts is the ſame with that of the whole, and natural <lb></lb>ly tendeth towards the Centre of the Univerſe; and for the ſame <lb></lb>cauſe reſt, being arrived thither. </s><s>He thereupon moves the que <lb></lb>ſtion whether the motion of the parts hath a tendency to the <lb></lb>centre of the Univerſe, or to the centre of the Earth; and conclu <lb></lb>deth that it goeth by proper inſtinct to the centre of the Univerſe, <lb></lb>and <emph type="italics"></emph>per accidence<emph.end type="italics"></emph.end> to that of the Earth; of which point we largely <lb></lb>diſcourſed yeſterday. </s><s>He laſtly confirmeth the ſame with a fourth <lb></lb>argument taken from the experiment of grave bodies, which fal <lb></lb>ing from on high, deſcend perpendicularly unto the Earthsſurface; <lb></lb>and in the ſame manner <emph type="italics"></emph>Projections<emph.end type="italics"></emph.end> ſhot perpendicularly upwards, <lb></lb>do by the ſame lines return perpendicularly down again, though <lb></lb>they were ſhot to a very great height. </s><s>All which arguments neceſ <lb></lb>ſarily prove their motion to be towards the Centre of the Earth, <lb></lb>which without moving at all waits for, and receiveth them. </s><s>He <lb></lb>intimateth in the laſt place that the Aſtronomers alledg other <lb></lb>reaſons in confirmation of the ſame concluſions, I mean of the <lb></lb>Earths being in the Centre of the Univerſe, and immoveable; <lb></lb>and inſtanceth onely in one of them, to wit, that all the <emph type="italics"></emph>Phæ <lb></lb>nomena<emph.end type="italics"></emph.end> or appearances that are ſeen in the motions of the Stars, <lb></lb>perfectly agree with the poſition of the Earth in the Centre; <lb></lb>which would not be ſo, were the Earth ſeated otherwiſe. <lb></lb></s><s>The reſt produced by <emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> and the other Aſtronomers, I can <lb></lb>give you now if you pleaſe, or after you have ſpoken what you <lb></lb>have to ſay in anſwer to theſe of <emph type="italics"></emph>Ariſtotle.”<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg275"></margin.target>Ariſtotles <emph type="italics"></emph>Ar <lb></lb>guments for the <lb></lb>Earths quieſſence.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg276"></margin.target>* <emph type="italics"></emph>Reſtino indietzo,<emph.end type="italics"></emph.end> <lb></lb>which is meant <lb></lb>here of that moti <lb></lb>on which a bowl <lb></lb>makes when its <lb></lb>born by its by as to <lb></lb>one ſide or other, <lb></lb>and ſo hindered in <lb></lb>its direct motion.</s></p><p type="main"><s>SALV. </s><s>The arguments which are brought upon this occaſion <pb xlink:href="040/01/126.jpg" pagenum="108"></pb>are of two kinds: ſome have reſpect to the accidents Terreſtrial, <lb></lb><arrow.to.target n="marg277"></arrow.to.target> <lb></lb>without any relation to the Stars, and others are taken from the <lb></lb><emph type="italics"></emph>Phænomena<emph.end type="italics"></emph.end> and obſervations of things Cœleſtial. </s><s>The arguments <lb></lb>of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> are for the moſt part taken from things neer at hand, <lb></lb>and he leaveth the others to <emph type="italics"></emph>Aſtronomers<emph.end type="italics"></emph.end>; and therefore it is the <lb></lb>beſt way, if you like of it, to examine theſe taken from experi <lb></lb>ments touching the Earth, and then proceed to thoſe of the other <lb></lb>kind. </s><s>And becauſe <emph type="italics"></emph>Ptolomy, Tycho,<emph.end type="italics"></emph.end> and the other <emph type="italics"></emph>Aſtronomers<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg278"></arrow.to.target> <lb></lb>and <emph type="italics"></emph>Philoſophers,<emph.end type="italics"></emph.end> beſides the arguments of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> by them aſſu <lb></lb>med, confirmed, and made good, do produce certain others; we <lb></lb>will put them all together, that ſo we may not anſwer twice to <lb></lb>the ſame, or the like objections. </s><s>Therefore <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> chooſe <lb></lb>whether you will recite them your ſelf, or cauſe me to eaſe you of <lb></lb>this task, for I am ready to ſerve you.</s></p><p type="margin"><s><margin.target id="marg277"></margin.target><emph type="italics"></emph>Two kindes of <lb></lb>Arguments tou <lb></lb>ching the Earths <lb></lb>motion or rest.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg278"></margin.target><emph type="italics"></emph>Arguments of<emph.end type="italics"></emph.end> <lb></lb>Ptolomy <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Ty <lb></lb>cho, <emph type="italics"></emph>and other per <lb></lb>ſons, over and a <lb></lb>bove thoſe of<emph.end type="italics"></emph.end> Ari <lb></lb>ſtotle.</s></p><p type="main"><s>SIMPL. </s><s>It is better that you quote them, becauſe, as having <lb></lb>taken more pains in the ſtudy of them, you can produce them with <lb></lb>more readineſſe, and in greater number. <lb></lb><arrow.to.target n="marg279"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg279"></margin.target><emph type="italics"></emph>The firſt argu <lb></lb>ment taken from <lb></lb>grave bodies fal <lb></lb>ling from on high <lb></lb>to the ground.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. All, for the ſtrongeſt reaſon, alledge that of grave bo <lb></lb>dies, which falling downwards from on high, move by a right line, <lb></lb>that is perpendicular to the ſurface of the Earth, an argument <lb></lb>which is held undeniably to prove that the Earth is immoveable: <lb></lb>for in caſe it ſhould have the diurnal motion, a Tower, from the <lb></lb>top of which a ſtone is let fall, being carried along by the conver <lb></lb>ſion of the Earth, in the time that the ſtone ſpends in falling, would <lb></lb>be tranſported many hundred yards Eaſtward, and ſo far diſtant <lb></lb>from the Towers foot would the ſtone come to ground. </s><s>The <lb></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></lb>ting a bullet of lead fall from the round top of a Ship, that lieth at <lb></lb>anchor, and obſerving the mark it makes where it lights, which they <lb></lb>find to be neer the ^{*} partners of the Maſt; but if the ſame bullet <lb></lb><arrow.to.target n="marg281"></arrow.to.target> <lb></lb>be let fall from the ſame place when the ſhip is under ſail, it ſhall <lb></lb>light as far from the former place, as the ſhip hath run in the time <lb></lb>of the leads deſcent; and this for no other reaſon, than becauſe <lb></lb>the natural motion of the ball being at liberty is by a right line to <lb></lb><arrow.to.target n="marg282"></arrow.to.target> <lb></lb>wards the centre of the Earth. </s><s>They fortiſie this argument with <lb></lb>the experiment of a projection ſhot on high at a very great di <lb></lb>ſtance; as for example, a ball ſent out of a Cannon, erected per <lb></lb>pendicular to the horizon, the which ſpendeth ſo much time in aſ <lb></lb>cending and falling, that in our parallel the Cannon and we both <lb></lb>ſhould be carried by the Earth many miles towards the Eaſt, ſo <lb></lb>that the ball in its return could never come neer the Peece, but <lb></lb><arrow.to.target n="marg283"></arrow.to.target> <lb></lb>would fall as far Weſt, as the Earth had run Eaſt. </s><s>They againe <lb></lb>adde a third, and very evident experiment, <emph type="italics"></emph>ſcilicet,<emph.end type="italics"></emph.end> that ſhooting a <lb></lb>bullet point blank (or as Gunners ſay, neither above nor under me <lb></lb>tal) out of a Culverin towards the Eaſt, and afterwards another, <pb xlink:href="040/01/127.jpg" pagenum="109"></pb>with the ſame charge, and at the ſame elevation or diſport towards <lb></lb>the Weſt, the range towards the Weſt ſhould be very much grea <lb></lb>ter then the other towards the Eaſt: for that whil'ſt the ball goeth <lb></lb>Weſtward, and the Peece is carried along by the Earth Eaſtward, <lb></lb>the ball will fall from the Peece as far diſtant as is the aggregate of <lb></lb>the two motions, one made by it ſelf towards the Weſt, and the <lb></lb>other by the Peece carried about by the Earth towards the Eaſt; <lb></lb>and on the contrary, from the range of the ball ſhot Eaſtward you <lb></lb>are to ſubſtract the ſpace the Peece moved, being carried after it. <lb></lb></s><s>Now ſuppoſe, for example, that the range of the ball ſhot Weſt <lb></lb>were five miles, and that the Earth in the ſame parallel and in the <lb></lb>time of the Bals ranging ſhould remove three miles, the Ball in this <lb></lb>caſe would fall eight miles diſtant from the Culverin, namely, its <lb></lb>own five Weſtward, and the Culverins three miles Eaſtward: but <lb></lb>the range of the ſhot towards the Eaſt would be but two miles <lb></lb>long, for ſo much is the remainder, after you have ſubſtracted <lb></lb>from the five miles of the range, the three miles which the Peece <lb></lb>had moved towards the ſame part. </s><s>But experience ſheweth the <lb></lb>Ranges to be equal, therefore the Culverin, and conſequently the <lb></lb>Earth are immoveable. </s><s>And the ſtability of the Earth is no leſfe <lb></lb><arrow.to.target n="marg284"></arrow.to.target> <lb></lb>confirmed by two other ſhots made North and South; for they <lb></lb>would never hit the mark, but the Ranges would be alwayes wide, <lb></lb>or towards the Weſt, by meanes of the remove the mark would <lb></lb>make, being carried along with the Earth towards the Eaſt, whil'ſt <lb></lb>the ball is flying. </s><s>And not onely ſhots made by the Meridians, <lb></lb><arrow.to.target n="marg285"></arrow.to.target> <lb></lb>but alſo thoſe aimed Eaſt or Weſt would prove uncertain; for <lb></lb>thoſe aim'd Eaſt would be too high, and thoſe directed Weſt too <lb></lb>low, although they were ſhot point blank, as I ſaid. </s><s>For the <lb></lb>Range of the Ball in both the ſhots being made by the Tangent, <lb></lb>that is, by a line parallel to the Horizon, and being that in the di <lb></lb>urnal motion, if it be of the Earth, the Horizon goeth continually <lb></lb>deſcending towards the Eaſt, and riſing from the Weſt (therefore <lb></lb>the Oriental Stars ſeem to riſe, and the Occidental to decline) ſo <lb></lb>that the Oriental mark would deſcend below the aime, and there <lb></lb>upon the ſhot would fly too high, and the aſcending of the Weſt <lb></lb>ern mark would make the ſhot aimed that way range too low; ſo <lb></lb>that the Peece would never carry true towards any point; and for <lb></lb>that experience telleth us the contrary, it is requiſite to ſay, that <lb></lb>the Earth is immoveable.</s></p><p type="margin"><s><margin.target id="marg280"></margin.target><emph type="italics"></emph>Which is confir <lb></lb>med by the experi <lb></lb>ment of a body let <lb></lb>fall from the round <lb></lb>top of a Ship.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg281"></margin.target>* That is, at the <lb></lb>foot of the Maſt, <lb></lb>upon the upper <lb></lb>deck.</s></p><p type="margin"><s><margin.target id="marg282"></margin.target><emph type="italics"></emph>The ſecond ar <lb></lb>gument taken from <lb></lb>a Projection ſhot <lb></lb>very high.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg283"></margin.target><emph type="italics"></emph>The third argu <lb></lb>ment taken from <lb></lb>the ſhots of a Can <lb></lb>non, towards the <lb></lb>Eaſt, and towards <lb></lb>the West.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg284"></margin.target><emph type="italics"></emph>This argument <lb></lb>is confirmed by two <lb></lb>ſhots towards the <lb></lb>South and towards <lb></lb>the North.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg285"></margin.target><emph type="italics"></emph>And it is like <lb></lb>wiſe confirmed by <lb></lb>two ſhots towards <lb></lb>the Eaſt, and to <lb></lb>wards the Weſt.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>Theſe are ſolid reaſons, and ſuch as I believe no man <lb></lb>can anſwer.</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 ſee with how many ad <lb></lb>mirable experiments Nature is pleaſed to favour us, wherewith to <lb></lb>aſſiſt us in the knowledge of the Truth. </s><s>Oh! how exactly one <pb xlink:href="040/01/128.jpg" pagenum="110"></pb>truth agreeth with another, and all conſpire to render each other <lb></lb>inexpugnable!</s></p><p type="main"><s>SAGR. </s><s>What pity it is that Guns were not uſed in <emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> <lb></lb>age, he would with help of them have eaſily battered down ig <lb></lb>norance, and ſpoke without hæſitation of theſe mundane points.</s></p><p type="main"><s>SALV. </s><s>I am very glad that theſe reaſons are new unto you, that <lb></lb>ſo you may not reſt in the opinion of the <emph type="italics"></emph>major<emph.end type="italics"></emph.end> part of <emph type="italics"></emph>Peripate <lb></lb>ticks,<emph.end type="italics"></emph.end> who believe, that if any one forſakes the Doctrine of <emph type="italics"></emph>Ari <lb></lb>ſtotle,<emph.end type="italics"></emph.end> it is becauſe they did not underſtand or rightly apprehend <lb></lb>his demonſtrations. </s><s>But you may expect to hear of other Novel <lb></lb><arrow.to.target n="marg286"></arrow.to.target> <lb></lb>ties, and you ſhall ſee the followers of this new Syſteme produce a <lb></lb>gainſt themſelves obſervations, experiences, and reaſons of farre <lb></lb>greater force than thoſe alledged by <emph type="italics"></emph>Aristotle, Ptolomy,<emph.end type="italics"></emph.end> and other <lb></lb>oppoſers of the ſame concluſions, and by this means you ſhall come <lb></lb>to aſcertain your ſelf that they were not induced through want of <lb></lb>knowledge or experience to follow that opinion.</s></p><p type="margin"><s><margin.target id="marg286"></margin.target>Copernicus <emph type="italics"></emph>his <lb></lb>followers are not <lb></lb>moved through ig <lb></lb>nor ance of the ar <lb></lb>guments on the o <lb></lb>ther part.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>It is requiſite that upon this occaſion I relate unto you <lb></lb>ſome accidents that befell me, ſo ſoon as I firſt began to hear ſpeak <lb></lb>of this new doctrine. </s><s>Being very young, and having ſcarcely fi <lb></lb>niſhed my courſe of Philoſophy, which I left off, as being ſet upon <lb></lb>other employments, there chanced to come into theſe parts a cer <lb></lb>tain Foreigner of <emph type="italics"></emph>Roſtock,<emph.end type="italics"></emph.end> whoſe name, as I remember, was <emph type="italics"></emph>Chri-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg287"></arrow.to.target> <lb></lb><emph type="italics"></emph>ſtianus Vurſtitius,<emph.end type="italics"></emph.end> a follower of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> who in an <emph type="italics"></emph>Academy<emph.end type="italics"></emph.end> <lb></lb>made two or three Lectures upon this point, to whom many flock't <lb></lb>as Auditors; but I thinking they went more for the novelty of the <lb></lb>ſubject than otherwiſe, did not go to hear him: for I had conclu <lb></lb>ded with my ſelf that that opinion could be no other than a ſolemn <lb></lb>madneſſe. </s><s>And queſtioning ſome of thoſe who had been there, I <lb></lb>perceived they all made a jeſt thereof, execpt one, who told me <lb></lb>that the buſineſſe was not altogether to be laugh't at, and becauſe <lb></lb>this man was reputed by me to be very intelligent and wary, I re <lb></lb>pented that I was not there, and began from that time forward as <lb></lb>oft as I met with any one of the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> perſwaſion, to demand <lb></lb>of them, if they had been alwayes of the ſame judgment; and of as <lb></lb>many as I examined, I found not ſo much as one, who told me not <lb></lb>that he had been a long time of the contrary opinion, but to have <lb></lb>changed it for this, as convinced by the ſtrength of the reaſons pro <lb></lb>ving the ſame: and afterwards queſtioning them, one by one; to <lb></lb>ſee whether they were well poſſeſt of the reaſons of the other ſide; <lb></lb><arrow.to.target n="marg288"></arrow.to.target> <lb></lb>I found them all to be very ready and perfect in them; ſo that I <lb></lb>could not truly ſay, that they had took up this opinion out of ig <lb></lb>norance, vanity, or to ſhew the acuteneſſe of their wits. </s><s>On the <lb></lb>contrary, of as many of the <emph type="italics"></emph>Peripateticks<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ptolomeans<emph.end type="italics"></emph.end> as I <lb></lb>have asked (and out of curioſity I have talked with many) what <lb></lb>pains they had taken in the Book of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> I found very <pb xlink:href="040/01/129.jpg" pagenum="111"></pb>few that had ſo much as ſuperficially peruſed it; but of thoſe <lb></lb>whom, I thought, had underſtood the ſame, not one; and more <lb></lb>over, I have enquired amongſt the followers of the <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> <lb></lb>Doctrine, if ever any of them had held the contrary opinion, and <lb></lb>likewiſe found none that had. </s><s>Whereupon conſidering that there <lb></lb>was no man who followed the opinion of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> that had <lb></lb>not been firſt on the contrary ſide, and that was not very well ac <lb></lb>quainted with the reaſons of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end>; and, on the <lb></lb>contrary, that there is not one of the followers of <emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> that <lb></lb>had ever been of the judgment of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> and had left that, <lb></lb>to imbrace this of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> conſidering, I ſay, theſe things, I <lb></lb>began to think, that one, who leaveth an opinion imbued with <lb></lb>his milk, and followed by very many, to take up another owned <lb></lb>by very few, and denied by all the Schools, and that really <lb></lb>ſeems a very great Paradox, muſt needs have been moved, not <lb></lb>to ſay forced, by more powerful reaſons. </s><s>For this cauſe, I am <lb></lb>become very curious to dive, as they ſay, into the bottom of this <lb></lb>buſineſſe, and account it my great good fortune that I have met <lb></lb>you two, from whom I may without any trouble, hear all that <lb></lb>hath been, and, haply, can be ſaid on this argument, aſſuring <lb></lb>my ſelf that the ſtrength of your reaſons will reſolve all ſcruples, <lb></lb>and bring me to a certainty in this ſubject.</s></p><p type="margin"><s><margin.target id="marg287"></margin.target>Chriſtianus Vur <lb></lb>ſtitius <emph type="italics"></emph>read certain <lb></lb>Lectures touching <lb></lb>the opinion of<emph.end type="italics"></emph.end> Co <lb></lb>pernicus, <emph type="italics"></emph>& what <lb></lb>enſued thereupon.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg288"></margin.target><emph type="italics"></emph>The followers of<emph.end type="italics"></emph.end> <lb></lb>Copernicus <emph type="italics"></emph>were <lb></lb>all firſt againſt <lb></lb>that opinion, but <lb></lb>the Sectators of<emph.end type="italics"></emph.end> <lb></lb>Ariſtotle <emph type="italics"></emph>&<emph.end type="italics"></emph.end> Pto <lb></lb>lomy, <emph type="italics"></emph>were never <lb></lb>of the other ſide.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>But its poſſible your opinion and hopes may be diſap <lb></lb>pointed, and that you may find your ſelves more at a loſſe in the <lb></lb>end than you was at firſt.</s></p><p type="main"><s>SAGR. </s><s>I am very confident that this can in no wiſe befal <lb></lb>me.</s></p><p type="main"><s>SIMPL. </s><s>And why not? </s><s>I have a manifeſt example in my ſelf, <lb></lb>that the farther I go, the more I am confounded.</s></p><p type="main"><s>SAGR. </s><s>This is a ſign that thoſe reaſons that hitherto ſeemed <lb></lb>concluding unto you, and aſſured you in the truth of your opi <lb></lb>nion, begin to change countenance in your mind, and to let you <lb></lb>by degrees, if not imbrace, at leaſt look towards the contrary te <lb></lb>nent; but I, that have been hitherto indifferent, do greatly hope <lb></lb>to acquire reſt and ſatisfaction by our future diſcourſes, and you <lb></lb>will not deny but I may, if you pleaſe but to hear what perſwa <lb></lb>deth me to this expectation.</s></p><p type="main"><s>SIMPL. </s><s>I will gladly hearken to the ſame, and ſhould be no <lb></lb>leſſe glad that the like effect might be wrought in me.</s></p><p type="main"><s>SAGR. </s><s>Favour me therefore with anſwering to what I ſhall ask <lb></lb>you. </s><s>And firſt, tell me, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> is not the concluſion, which <lb></lb>we ſeek the truth of, Whether we ought to hold with <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> <lb></lb>and <emph type="italics"></emph>Ptolomy,<emph.end type="italics"></emph.end> that the Earth onely abiding without motion in the <lb></lb>Centre of the Univerſe, the Cœleſtial bodies all move, or elſe, <lb></lb>Whether the Starry Sphere and the Sun ſtanding ſtill in the Centre, <pb xlink:href="040/01/130.jpg" pagenum="112"></pb>the Earth is without the ſame, and owner of all thoſe motions that <lb></lb>in our ſeeming belong to the Sun and fixed Stars?</s></p><p type="main"><s>SIMPL. </s><s>Theſe are the concluſions which are in diſpute.</s></p><p type="main"><s>SAGR. </s><s>And theſe two concluſions, are they not of ſuch a na <lb></lb>ture, that one of them muſt neceſſarily be true, and the other <lb></lb>falſe?</s></p><p type="main"><s>SIMPL. </s><s>They are ſo. </s><s>We are in a <emph type="italics"></emph>Dilemma,<emph.end type="italics"></emph.end> one part of which <lb></lb>muſt of neceſſity be true, and the other untrue; for between Mo <lb></lb>tion and Reſt, which are contradictories, there cannot be inſtanced <lb></lb>a third, ſo as that one cannot ſay the Earth moves not, nor ſtands <lb></lb>ſtill; the Sun and Stars do not move, and yet ſtand not ſtill.</s></p><p type="main"><s>SAGR. </s><s>The Earth, the Sun, and Stars, what things are they in <lb></lb>nature? </s><s>are they petite things not worth our notice, or grand and <lb></lb>worthy of conſideration?</s></p><p type="main"><s>SIMPL They are principal, noble, integral bodies of the Uni <lb></lb>verſe, moſt vaſt and conſiderable.</s></p><p type="main"><s>SAGR. </s><s>And Motion, and Reſt, what accidents are they in <lb></lb>Nature? <lb></lb><arrow.to.target n="marg289"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg289"></margin.target><emph type="italics"></emph>Motion and reſt <lb></lb>principal accidents <lb></lb>in nature.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>So great and principal, that Nature her ſelf is defined <lb></lb>by them.</s></p><p type="main"><s>SAGR. </s><s>So that moving eternally, and the being wholly immo <lb></lb>veable are two conditions very conſiderable in Nature, and indi <lb></lb>cate very great diverſity; and eſpecially when aſcribed to the <lb></lb>principal bodies of the Univerſe, from which can enſue none but <lb></lb>very different events.</s></p><p type="main"><s>SIMPL. </s><s>Yea doubtleſſe.</s></p><p type="main"><s>SAGR. </s><s>Now anſwer me to another point. </s><s>Do you believe that <lb></lb>in <emph type="italics"></emph>Logick, Rhethorick,<emph.end type="italics"></emph.end> the <emph type="italics"></emph>Phyſicks, Metaphyſicks, Mathematicks,<emph.end type="italics"></emph.end> <lb></lb>and finally, in the univerſality of Diſputations there are arguments <lb></lb>ſufficient to perſwade and demonſtrate to a perſon the fallacious, <lb></lb>no leſſe then the true concluſions?</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"></emph>Vntruths cannot <lb></lb>be demonstrated, <lb></lb>as Truths are.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>No Sir; rather I am very confident and certain, that <lb></lb>for the proving of a true and neceſſary concluſion, there are in </s></p><p type="main"><s><arrow.to.target n="marg291"></arrow.to.target> <lb></lb>nature not onely one, but many very powerfull demonſtrations: <lb></lb>and that one may diſcuſſe and handle the ſame divers and ſundry <lb></lb>wayes, without ever falling into any abſurdity; and that the more <lb></lb>any Sophiſt would diſturb and muddy it, the more clear would its <lb></lb>certainty appear: And that on the contrary to make a falſe poſi <lb></lb>tion paſſe for true, and to perſwade the belief thereof, there can <lb></lb>not be any thing produced but fallacies, Sophiſms, Paralogiſmes, <lb></lb>Equivocations, and Diſcourſes vain, inconſiſtant, and full of re <lb></lb>pugnances and contradictions.</s></p><p type="margin"><s><margin.target id="marg291"></margin.target><emph type="italics"></emph>For proof of true <lb></lb>concluſions, many <lb></lb>ſolid arguments <lb></lb>may be produced, <lb></lb>but to prove a fal <lb></lb>ſity, none.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Now if eternal motion, and eternal reſt be ſo princi <lb></lb>pal accidents of Nature, and ſo different, that there can depend <lb></lb>on them only moſt different conſequences, and eſpecially when <pb xlink:href="040/01/131.jpg" pagenum="113"></pb>applyed to the Sun, and to the Earth, ſo vaſt and famous bodies <lb></lb>of the Univerſe; and it being, moreover, impoſſible, that one of <lb></lb>two contradictory Propoſitions, ſhould not be true, and the other <lb></lb>falſe; and that for proof of the falſe one, any thing can be pro <lb></lb>duced but fallacies; but the true one being perſwadeable by all <lb></lb>kind of concluding and demonſtrative arguments, why ſhould <lb></lb>you think that he, of you two, who ſhall be ſo fortunate as to <lb></lb>maintain the true Propoſition ought not to perſwade me? </s><s>You <lb></lb>muſt ſuppoſe me to be of a ſtupid wit, perverſe judgment, dull <lb></lb>mind and intellect, and of a blind reaſon, that I ſhould not be <lb></lb>able to diſtinguiſh light from darkneſſe, jewels from coals, or <lb></lb>truth from falſhood.</s></p><p type="main"><s>SIMPL. </s><s>I tell you now, and have told you upon other <lb></lb>occaſions, that the beſt Maſter to teach us how to diſcern So <lb></lb>phiſmes, Paralogiſmes, and other fallacies, was <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> who <lb></lb>in this particular can never be deceived.</s></p><p type="main"><s>SAGR. </s><s>You inſiſt upon <emph type="italics"></emph>Aristotle,<emph.end type="italics"></emph.end> who cannot ſpeak. </s><s>Yet I <lb></lb>tell you, that if <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> were here, he would either yield him <lb></lb><arrow.to.target n="marg292"></arrow.to.target> <lb></lb>ſelf to be perſwaded by us, or refuting our arguments, convince <lb></lb>us by better of his own. </s><s>And you your ſelf, when you heard the <lb></lb>experiments of the Suns related, did you not acknowledg and <lb></lb>admire them, and confeſſe them more concludent than thoſe of <lb></lb><emph type="italics"></emph>Ariſtotle?<emph.end type="italics"></emph.end> Yet nevertheleſſe I cannot perceive that <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> <lb></lb>who hath produced them, examined them, and with exquiſite <lb></lb>care ſcan'd them, doth confeſſe himſelf perſwaded by them; no <lb></lb>nor by others of greater force, which he intimated that he was <lb></lb>about to give us an account of. </s><s>And I know not on what grounds <lb></lb>you ſhould cenſure Nature, as one that for many Ages hath <lb></lb>been lazie, and forgetful to produce ſpeculative <emph type="italics"></emph>wits<emph.end type="italics"></emph.end>; and <lb></lb>that knoweth not how to make more ſuch, unleſſe they be ſuch <lb></lb>kind of men as ſlaviſhly giving up their judgments to <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> do <lb></lb>underſtand with his brain, and reſent with his ſenſes. </s><s>But let us <lb></lb>hear the reſidue of thoſe reaſons which favour his opinion, that <lb></lb>we may thereupon proceed to ſpeak to them; comparing and <lb></lb>weighing them in the ballance of impartiality.</s></p><p type="margin"><s><margin.target id="marg292"></margin.target>Ariſtotle <emph type="italics"></emph>would <lb></lb>either refute his <lb></lb>adverſaries argu <lb></lb>ments, or would <lb></lb>alter his opinion.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Before I proceed any farther, I muſt tell <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> that <lb></lb>in theſe our Diſputations, I perſonate the <emph type="italics"></emph>Copernican,<emph.end type="italics"></emph.end>, and imi <lb></lb>tate him, as if I were his <emph type="italics"></emph>Zany<emph.end type="italics"></emph.end>; but what hath been effected in <lb></lb>my private thoughts by theſe arguments which I ſeem to alledg in <lb></lb>his favour, I would not have you to judg by what I ſay, whil'ſt <lb></lb>I am in the heat of acting my part in the Fable; but after I have <lb></lb>laid by my diſguiſe, for you may chance to find me different <lb></lb>from what you ſee me upon the Stage. </s><s>Now let us go on.</s></p><p type="main"><s><emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> and his followers produce another experiment like to <lb></lb><arrow.to.target n="marg293"></arrow.to.target> <lb></lb>that of the Projections, and it is of things that being ſeparated <pb xlink:href="040/01/132.jpg" pagenum="114"></pb>from the Earth, continue a good ſpace of time in the Air, ſuch <lb></lb>as are the Clouds, Birds of flight; and as of them it cannot be <lb></lb>ſaid that they are rapt or tranſparted by the Earth, having no ad <lb></lb>heſion thereto, it ſeems not poſſible, that they ſhould be able to <lb></lb>keep pace with the velocity thereof; nay it ſhould rather ſeem <lb></lb>to us, that they all ſwiftly move towards the Weſt: And if <lb></lb>being carried about by the Earth, paſſe our parallel in twenty <lb></lb>four hours, which yet is at leaſt ſixteen thouſand miles, how can <lb></lb>Birds follow ſuch a courſe or revolution? </s><s>Whereas on the con <lb></lb>trary, we ſee them fly as well towards the Eaſt, as towards the <lb></lb>Weſt, or any other part, without any ſenſible difference. </s><s>More <lb></lb><arrow.to.target n="marg294"></arrow.to.target> <lb></lb>over, if when we run a Horſe at his ſpeed, we feel the air beat <lb></lb>vehemently againſt our face, what an impetuous blaſt ought we <lb></lb>perpetually to feel from the Eaſt, being carried with ſo rapid a <lb></lb>courſe againſt the wind? </s><s>and yet no ſuch effect is perceived. </s><s>Take <lb></lb>another very ingenious argument inferred from the following ex <lb></lb><arrow.to.target n="marg295"></arrow.to.target> <lb></lb>periment. </s><s>The circular motion hath a faculty to extrude and diſ <lb></lb>ſipate from its Centre the parts of the moving body, whenſoever <lb></lb>either the motion is not very ſlow, or thoſe parts are not very <lb></lb>well faſtened together; and therefore, if <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> we ſhould turn <lb></lb>one of thoſe great wheels very faſt about, wherein one or more <lb></lb>men walking, crane up very great weights, as the huge maſſie <lb></lb>ſtone, uſed by the Callander for preſſing of Cloaths; or the <lb></lb>fraighted Barks which being haled on ſhore, are hoiſted out of <lb></lb>one river into another; in caſe the parts of that ſame Wheel ſo <lb></lb>ſwiftly turn'd round, be not very well joyn'd and pin'd together, <lb></lb>they would all be ſhattered to pieces; and though many ſtones or <lb></lb>other ponderous ſubſtances, ſhould be very faſt bound to its outward <lb></lb>Rimme, yet could they not reſiſt the impetuoſity, which with <lb></lb>great violence would hurl them every way far from the Wheel, <lb></lb>and conſequently from its Centre. </s><s>So that if the Earth did move <lb></lb>with ſuch and ſo much greater velocity, what gravity, what tena <lb></lb>city of lime or plaiſter would keep together Stones, Buildings, and <lb></lb>whole Cities, that they ſhould not be toſt into the Air by ſo pre <lb></lb>cipitous a motion? </s><s>And both men and beaſts, which are not fa <lb></lb>ſtened to the Earth, how could they reſiſt ſo great an <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end>? <lb></lb></s><s>Whereas, on the other ſide, we ſee both theſe, and far leſſe re <lb></lb>ſiſtances of pebles, ſands, leaves reſt quietly on the Earth, and <lb></lb>to return to it in falling, though with a very ſlow motion. </s><s>See <lb></lb>here, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> the moſt potent arguments, taken, to ſo ſpeak, <lb></lb>from things Terreſtrial; there remain thoſe of the other kind, <lb></lb>namely, ſuch as have relation to the appearances of Heaven, <lb></lb>which reaſons, to confeſſe the truth, tend more to prove the <lb></lb>Earth to be in the centre of the Univerſe, and conſequently, to <lb></lb>deprive it of the annual motion about the ſame, aſcribed unto it <pb xlink:href="040/01/133.jpg" pagenum="115"></pb>by <emph type="italics"></emph>Copernicus.<emph.end type="italics"></emph.end> Which arguments, as being of ſomewhat a diſte <lb></lb>rent nature, may be produced, after we have examined the <lb></lb>ſtrength of theſe already propounded.</s></p><p type="margin"><s><margin.target id="marg293"></margin.target><emph type="italics"></emph>An argument <lb></lb>taken from the <lb></lb>Clouds, and from <lb></lb>Birds.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg294"></margin.target><emph type="italics"></emph>An argument <lb></lb>taken from the air <lb></lb>which we feel to <lb></lb>beat upon us when <lb></lb>we run a Horſe at <lb></lb>full ſpeed.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg295"></margin.target><emph type="italics"></emph>An argument <lb></lb>taken from the <lb></lb>whirling of circu <lb></lb>lar motion, which <lb></lb>hath a faculty to <lb></lb>extrude and diſſi <lb></lb>pate.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>What ſay you <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end>? </s><s>do you think that <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> <lb></lb>is Maſter of, and knoweth how to unfold the <emph type="italics"></emph>Ptolomean<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ari <lb></lb>ſtotelian<emph.end type="italics"></emph.end> arguments? </s><s>Or do you think that any <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> is e <lb></lb>qually verſt in the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> demonſtrations?</s></p><p type="main"><s>SIMPL. </s><s>Were it not for the high eſteem, that the paſt diſcour <lb></lb>ſes have begot in me of the learning of <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> and of the a <lb></lb>cuteneſſe of <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> I would by their good leave have gone my <lb></lb>way without ſtaying for their anſwers; it ſeeming to me a thing <lb></lb>impoſſible, that ſo palpable experiments ſhould be contradicted; <lb></lb>and would, without hearing them farther, conſirm my ſelf in my <lb></lb>old perſwaſion; for though I ſhould be made to ſee that it was er <lb></lb>roneous, its being upheld by ſo many probable reaſons, would ren <lb></lb>der it excuſeable. </s><s>And if theſe are fallacies, what true demonſtra <lb></lb>tions were ever ſo fair?</s></p><p type="main"><s>SAGR. </s><s>Yet its good that we hear the reſponſions of <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end>; <lb></lb>which if they be true, muſt of neceſſity be more fair, and that by <lb></lb>inſinite degrees; and thoſe muſt be deformed, yea moſt deformed, <lb></lb>if the Metaphy ſical Axiome hold, That true and fair are one and <lb></lb><arrow.to.target n="marg296"></arrow.to.target> <lb></lb>the ſame thing; as alſo falſe and deformed. </s><s>Therefore <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> <lb></lb>let's no longer loſe time.</s></p><p type="margin"><s><margin.target id="marg296"></margin.target><emph type="italics"></emph>True and fair <lb></lb>are one and the <lb></lb>ſame, as alſo falſe <lb></lb>and deformed.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>The firſt Argument alledged by <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> if I well re <lb></lb>member it, was this. </s><s>The Earth cannot move circularly, becauſe <lb></lb>ſuch motion would be violent to the ſame, and therefore not per <lb></lb>petual: that it is violent, the reaſon was: Becauſe, that had it been <lb></lb>natural, its parts would likewiſe naturally move round, which is <lb></lb>impoſſible, for that it is natural for the parts thereof to move with a <lb></lb>right motion downwards. </s><s>To this my reply is, that I could glad <lb></lb>ly wiſh, that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> had more cleerly expreſt himſelf, where he <lb></lb><arrow.to.target n="marg297"></arrow.to.target> <lb></lb>ſaid; That its parts would likewiſe move circularly; for this mo <lb></lb>ving circularly is to be underſtood two wayes, one is, that every <lb></lb>particle or atome ſeparated from its <emph type="italics"></emph>Whole<emph.end type="italics"></emph.end> would move circularly <lb></lb>about its particular centre, deſcribing its ſmall Circulets; the other <lb></lb>is, that the whole Globe moving about its centre in twenty four <lb></lb>hours, the parts alſo would turn about the ſame centre in four and <lb></lb>twenty hours. </s><s>The firſt would be no leſſe an impertinency, than <lb></lb>if one ſhould ſay, that every part of the circumference of a Circle <lb></lb>ought to be a Circle; or becauſe that the Earth is Spherical, that <lb></lb>therefore every part thereof be a Globe, for ſo doth the <emph type="italics"></emph>Axiome<emph.end type="italics"></emph.end> <lb></lb>require: <emph type="italics"></emph>Eadem eſt ratio totius, & partium.<emph.end type="italics"></emph.end> But if he took it in <lb></lb>the other ſenſe, to wit, that the parts in imitation of the <emph type="italics"></emph>Whole<emph.end type="italics"></emph.end> <lb></lb>ſhould move naturally round the Centre of the whole Globe in <lb></lb>twenty four hours, I ſay, that they do ſo; and it concerns you, <pb xlink:href="040/01/134.jpg" pagenum="116"></pb>inſtead of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> to prove that they do not.</s></p><p type="margin"><s><margin.target id="marg297"></margin.target><emph type="italics"></emph>The anſwer to<emph.end type="italics"></emph.end> <lb></lb>Ariſtotles <emph type="italics"></emph>firſt ar <lb></lb>gument.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>This is proved by <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in the ſame place, when he <lb></lb>ſaith, that the natural motion of the parts is the right motion <lb></lb>downwards to the centre of the Univerſe; ſo that the circular <lb></lb>motion cannot naturally agree therewith.</s></p><p type="main"><s>SALV. </s><s>But do not you ſee, that thoſe very words carry in them <lb></lb>a confutation of this ſolution?</s></p><p type="main"><s>SIMPL. How? </s><s>and where?</s></p><p type="main"><s>SALV. </s><s>Doth not he ſay that the circular motion of the Earth <lb></lb>would be violent? </s><s>and therefore not eternal? </s><s>and that this is ab <lb></lb>ſurd, for that the order of the World is eternal?</s></p><p type="main"><s>SIMPL. </s><s>He ſaith ſo.</s></p><p type="main"><s>SALV. </s><s>But if that which is violent cannot be eternal, then by <lb></lb><arrow.to.target n="marg298"></arrow.to.target> <lb></lb>converſion, that which cannot be eternal, cannot be natural: but <lb></lb>the motion of the Earth downwards cannot be otherwiſe eternal; <lb></lb>therefore much leſſe can it be natural: nor can any other motion <lb></lb>be natural to it, ſave onely that which is eternal. </s><s>But if we make <lb></lb>the Earth move with a circular motion, this may be eternal to it, <lb></lb>and to its parts, and therefore natural.</s></p><p type="margin"><s><margin.target id="marg298"></margin.target><emph type="italics"></emph>That which is <lb></lb>violent, cannot be <lb></lb>eternal, and that <lb></lb>which cannot be e <lb></lb>ternal, cannot be <lb></lb>natural.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>The right motion is moſt natural to the parts of the <lb></lb>Earth, and is to them eternal; nor ſhall it ever happen that they <lb></lb>move not with a right motion; alwayes provided that the impe <lb></lb>diments be removed.</s></p><p type="main"><s>SALV. </s><s>You equivocate <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end>; and I will try to free you <lb></lb>from the equivoke. </s><s>Tell me, therefore, do you think that a <lb></lb>Ship which ſhould ſail from the Strait of <emph type="italics"></emph>Gibralter<emph.end type="italics"></emph.end> towards <emph type="italics"></emph>Pale <lb></lb>ſtina<emph.end type="italics"></emph.end> can eternally move towards that Coaſt? </s><s>keeping alwayes an <lb></lb>equal courſe?</s></p><p type="main"><s>SIMPL. </s><s>No doubtleſſe.</s></p><p type="main"><s>SALV. </s><s>And why not?</s></p><p type="main"><s>SIMPL. </s><s>Becauſe that Voyage is bounded and terminated be <lb></lb>tween the <emph type="italics"></emph>Herculean<emph.end type="italics"></emph.end> Pillars, and the ſhore of the <emph type="italics"></emph>Holy-land<emph.end type="italics"></emph.end>; and <lb></lb>the diſtance being limited, it is paſt in a finite time, unleſſe one by <lb></lb>returning back ſhould with a contrary motion begin the ſame Voy <lb></lb>age anew; but this would be an interrupted and no continued <lb></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"></emph>Ma <lb></lb>galanes<emph.end type="italics"></emph.end> by the <emph type="italics"></emph>Pacifick<emph.end type="italics"></emph.end> Ocean, the <emph type="italics"></emph>Moluccha's,<emph.end type="italics"></emph.end> the Cape <emph type="italics"></emph>di buona <lb></lb>Speranza,<emph.end type="italics"></emph.end> and from thence by the ſame Strait, and then again by <lb></lb>the <emph type="italics"></emph>Pacifick<emph.end type="italics"></emph.end> Ocean, &c. </s><s>do you believe that it may be perpe <lb></lb>tuated?</s></p><p type="main"><s>SIMPL. </s><s>It may; for this being a circumgyration, which re <lb></lb>turneth about its ſelf, with infinite replications, it may be perpetu <lb></lb>ated without any interruption.</s></p><p type="main"><s>SALV. </s><s>A Ship then may in this Voyage continue ſailing eter <lb></lb>nally.</s></p> <pb xlink:href="040/01/135.jpg" pagenum="117"></pb><p type="main"><s>SIMPL. </s><s>It may, in caſe the Ship were incorruptible, but the <lb></lb>Ship decaying, the Navigation muſt of neceſſity come to an end.</s></p><p type="main"><s>SALV. </s><s>But in the Mediterrane, though the Veſſel were incor <lb></lb>ruptible, yet could ſhe not ſail perpetually towards <emph type="italics"></emph>Paleſtina,<emph.end type="italics"></emph.end> that <lb></lb><arrow.to.target n="marg299"></arrow.to.target> <lb></lb>Voyage being determined. </s><s>Two things then are required, to the <lb></lb>end a moveable may without intermiſſion move perpetually; the <lb></lb>one is, that the motion may of its own nature be indeterminate and <lb></lb>infinite; the other, that the moveable be likewiſe incorruptible <lb></lb>and eternal.</s></p><p type="margin"><s><margin.target id="marg299"></margin.target><emph type="italics"></emph>Two things re <lb></lb>quiſite to the end a <lb></lb>motion may per <lb></lb>petuate it ſelf; an <lb></lb>unlimited ſpace, <lb></lb>and an incorrupti <lb></lb>ble moveable.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>All this is neceſſary.</s></p><p type="main"><s>SALV. </s><s>Therefore you may ſee how of your own accord you <lb></lb>have confeſſed it impoſſible that any moveable ſhould move eter <lb></lb>nally in a right line, in regard that right motion, whether it be up <lb></lb><arrow.to.target n="marg300"></arrow.to.target> <lb></lb>wards, or downwards, is by you your ſelf bounded by the circum <lb></lb>ference and centre; ſo that if a Moveable, as ſuppoſe the Earth <lb></lb>be eternal, yet foraſmuch as the right motion is not of its own na <lb></lb>ture eternall, but moſt ^{*}terminate, it cannot naturally ſuit with <lb></lb><arrow.to.target n="marg301"></arrow.to.target> <lb></lb>the Earth. </s><s>Nay, as was ſaid ^{*} yeſterday, <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> himſelf is <lb></lb><arrow.to.target n="marg302"></arrow.to.target> <lb></lb>conſtrained to make the Terreſtrial Globe eternally immoveable. <lb></lb></s><s>When again you ſay, that the parts of the Earth evermore move <lb></lb>downwards, all impediments being removed, you egregiouſly equi <lb></lb>vocate; for then, on the other ſide they muſt be impeded, contra <lb></lb>ried, and forced, if you would have them move; for, when they <lb></lb>are once fallen to the ground, they muſt be violently thrown up <lb></lb>wards, that they may a ſecond time fall; and as to the impedi <lb></lb>ments, theſe only hinder its arrival at the centre; but if there were <lb></lb>a <emph type="italics"></emph>Well,<emph.end type="italics"></emph.end> that did paſſe thorow and beyond the centre, yet would not <lb></lb>a clod of Earth paſſe beyond it, unleſſe inaſmuch as being tranſ <lb></lb>ported by its <emph type="italics"></emph>impetus,<emph.end type="italics"></emph.end> it ſhould paſſe the ſame to return thither a <lb></lb>gain, and in the end there to reſt. </s><s>As therefore to the defending, <lb></lb>that the motion by a right line doth or can agree naturally neither <lb></lb>to the Earth, nor to any other moveable, whil'ſt the Univerſe re <lb></lb>taineth its perfect order, I would have you take no further paines a <lb></lb>bout it, but (unleſſe you will grant them the circular motion) <lb></lb>your beſt way will be to defend and maintain their immobility.</s></p><p type="margin"><s><margin.target id="marg300"></margin.target><emph type="italics"></emph>Right motion <lb></lb>cannot be eternal, <lb></lb>and conſequently <lb></lb>cannot be natural <lb></lb>to the Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg301"></margin.target>* Terminatiſſimo.</s></p><p type="margin"><s><margin.target id="marg302"></margin.target>* By this expreſſi <lb></lb>on he every where <lb></lb>means the prece <lb></lb>ding Dialogue, or <lb></lb><emph type="italics"></emph>Giornata.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>As to their immoveableneſſe, the arguments of <emph type="italics"></emph>Ari <lb></lb>ſtotle,<emph.end type="italics"></emph.end> and moreover thoſe alledged by your ſelf ſeem in my opini <lb></lb>on neceſſarily to conclude the ſame, as yet; and I conceive it will <lb></lb>be a hard matter to refute them.</s></p><p type="main"><s>SALV. </s><s>Come we therefore to the ſecond Argument, which was, <lb></lb>That thoſe bodies, which we are aſſured do move circularly, have <lb></lb><arrow.to.target n="marg303"></arrow.to.target> <lb></lb>more than one motion, unleſſe it be the <emph type="italics"></emph>Primum Mobile<emph.end type="italics"></emph.end>; and <lb></lb>therefore, if the Earth did move circularly, it ought to have two <lb></lb>motions; from which alterations would follow in the riſing and <lb></lb>ſetting of the Fixed Stars: Which effect is not perceived to enſue. <pb xlink:href="040/01/136.jpg" pagenum="118"></pb>Therefore, &c. </s><s>The moſt proper and genuine anſwer to this Alle <lb></lb>gation is contained in the Argument it ſelf; and even <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> <lb></lb>puts it in our mouths, which it is impoſſible, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that you <lb></lb>ſhould not have ſeen.</s></p><p type="margin"><s><margin.target id="marg303"></margin.target><emph type="italics"></emph>The anſwer to <lb></lb>the ſecond argu <lb></lb>ment.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>I neither have ſeen it, nor do I yet apprehend it.</s></p><p type="main"><s>SALV. </s><s>This cannot be, ſure, the thing is ſo very plain.</s></p><p type="main"><s>SIMPL. </s><s>I will with your leave, caſt an eye upon the <emph type="italics"></emph>Text.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>We will command the <emph type="italics"></emph>Text<emph.end type="italics"></emph.end> 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></lb>I know the place perfectly well, which is in <emph type="italics"></emph>lib. 2. De Cælo, cap.<emph.end type="italics"></emph.end> <lb></lb>16. Here it is, <emph type="italics"></emph>Text<emph.end type="italics"></emph.end> 97. <emph type="italics"></emph>Preterea omnia, quæ feruntur latione <lb></lb>circulari ſubdeficere videntur, ac moveri pluribus una latione, <lb></lb>præter primam Sphæram; quare & Terram neceſſariam eſt, ſive <lb></lb>circa medium, ſive in medio poſita feratur, duabus moveri <lb></lb>lationibus. </s><s>Si autem hoc acciderit, neceſſariam eſt fieri muta <lb></lb>tiones, ac converſiones fixorum aſtrorum. </s><s>Hoc autem non vide <lb></lb>tur ficri, ſed ſemper eadem, apud eadem loca ipſius, & oriun <lb></lb>tur, & occidunt.<emph.end type="italics"></emph.end> [In Engliſh thus:] Furthermore all that are <lb></lb><arrow.to.target n="marg304"></arrow.to.target> <lb></lb>carried with circular motion, ſeem to ^{*} foreſlow, and to move <lb></lb>with more than one motion, except the firſt Sphere; wherefore <lb></lb>it is neceſſary that the Earth move with two motions, whether <lb></lb><arrow.to.target n="marg305"></arrow.to.target> <lb></lb>it be carried about the ^{*} middle, or placed in the middle. </s><s>But <lb></lb>if it be ſo, there would of neceſſity be alterations and converſi <lb></lb>ons made amongſt the fixed Stars. </s><s>But no ſuch thing is ſeen to <lb></lb>be done, but the ſame Star doth alwayes riſe and ſet in the ſame <lb></lb>place. </s><s>In all this I find not any falacy, and my thinks the argu <lb></lb>ment is very forcible.</s></p><p type="margin"><s><margin.target id="marg304"></margin.target>* Subdeſicere.</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></lb>in the fallacy of the Sillogiſme, and moreover, diſcovered ano <lb></lb>ther falſity. </s><s>Therefore obſerve. </s><s>The Poſitions, or if you will, <lb></lb>Concluſions, which <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> endeavours to oppoſe, are two; one <lb></lb>is that of thoſe, who placing the Earth in the midſt of the World, <lb></lb>do make it move in it ſelf about its own centre. </s><s>The other is of <lb></lb>thoſe, who conſtituting it far from the middle, do make it re <lb></lb>volve with a circular motion about the middle of the Univerſe. <lb></lb></s><s>And both theſe Poſitions he conjointly impugneth with one and <lb></lb>the ſame argument. </s><s>Now I affirm that he is out in both the one <lb></lb>and the other impugnation; and that his error againſt the firſt <lb></lb>Poſition is an Equivoke or Paralogiſme; and his miſtake touch <lb></lb><arrow.to.target n="marg306"></arrow.to.target> <lb></lb>ing the ſecond is a falſe conſequence. </s><s>Let us begin with the firſt <lb></lb>Aſſertion, which conſtituteth the Earth in the midſt of the <lb></lb>World, and maketh it move in it ſelf about its own centre; and <lb></lb><arrow.to.target n="marg307"></arrow.to.target> <lb></lb>let us confront it with the objection of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end>; ſaying, All <lb></lb>moveables, that move circularly, ſeem to ^{*} foreſlow, and move <lb></lb>with more than one Byas, except the firſt Sphere (that is <emph type="italics"></emph>the pri-<emph.end type="italics"></emph.end> <pb xlink:href="040/01/137.jpg" pagenum="119"></pb><emph type="italics"></emph>mum mobile<emph.end type="italics"></emph.end>) therefore the Earth moving about its own centre, <lb></lb>being placed in the middle, muſt of neceſſity have two byaſſes, <lb></lb>and foreſlow. </s><s>But if this were ſo, it would follow, that there <lb></lb>ſhould be a variation in the riſing and ſetting of the fixed Stars, <lb></lb>which we do not perceive to be done: Therefore the Earth doth <lb></lb>not move, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> Here is the Paralogiſme, and to diſcover it, I will <lb></lb>argue with <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in this manner. </s><s>Thou ſaiſt, oh <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> <lb></lb>that the Earth placed in the middle of the World, cannot move <lb></lb>in it ſelf (<emph type="italics"></emph>i. </s><s>e.<emph.end type="italics"></emph.end> upon its own <emph type="italics"></emph>axis<emph.end type="italics"></emph.end>) for then it would be requiſite <lb></lb>to allow it two byaſſes; ſo that, if it ſhould not be neceſſary to <lb></lb>allow it more than one Byas onely, thou wouldeſt not then hold <lb></lb>it impoſſible for it to move onely with that one; for thou would'ſt <lb></lb>unneceſſarily have conſined the impoſſibility to the plurality of <lb></lb>byaſſes, if in caſe it had no more but one, yet it could not move <lb></lb>with that. </s><s>And becauſe that of all the moveables in the World, <lb></lb>thou makeſt but one alone to move with one ſole byas; and all <lb></lb>the reſt with more than one; and this ſame moveable thou af <lb></lb>firmeſt to be the firſt Sphere, namely, that by which all the fix <lb></lb>ed and erratick Stars ſeem harmoniouſly to move from Eaſt to <lb></lb>Weſt, if in caſe the Earth may be that firſt Sphere, that by mo <lb></lb>ving with one by as onely, may make the Stars appear to move <lb></lb>from Eaſt to Weſt, thou wilt not deny them it: But he that af <lb></lb>firmeth, that the Earth being placed in the midſt of the World, <lb></lb>moveth about its own Axis, aſcribes unto it no other motion, <lb></lb>ſave that by which all the Stars appear to move from Eaſt to Weſt; <lb></lb>and ſo it cometh to be that firſt Sphere, which thou thy ſelf ac <lb></lb>knowledgeſt to move with but one by as onely. </s><s>It is therefore ne <lb></lb>ceſſary, oh <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> if thou wilt conclude any thing, that thou <lb></lb>demonſtrate, that the Earth being placed in the midſt of the <lb></lb>World, cannot move with ſo much as one by as onely; or elſe, <lb></lb>that much leſſe can the firſt Sphere have one ſole motion; for o <lb></lb>therwiſe thou doeſt in thy very Sillogiſme both commit the falacy, <lb></lb>and detect it, denying, and at that very time proving the ſame <lb></lb>thing. </s><s>I come now to the ſecond Poſition, namely, of thoſe <lb></lb>who placing the Earth far from the midſt of the Univerſe, make <lb></lb>it moveable about the ſame; that is, make it a Planet and erra <lb></lb>tick Star; againſt which the argument is directed, and as to <lb></lb>form is concludent, but faileth in matter. </s><s>For it being granted, <lb></lb>that the Earth doth in that manner move, and that with two by <lb></lb>aſſes, yet doth it not neceſſarily follow that though it were ſo, <lb></lb>it ſhould make alterations in the riſings and ſettings of the fixed <lb></lb>Stars, as I ſhall in its proper place declare. </s><s>And here I could <lb></lb>gladly excuſe <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end>; rather I could highly applaud him for ha <lb></lb>ving light upon the moſt ſubtil argument that could be produced <lb></lb>againſt the <emph type="italics"></emph>Copernican Hypotheſis<emph.end type="italics"></emph.end>; and if the objection be inge <pb xlink:href="040/01/138.jpg" pagenum="120"></pb>nious, and to outward appearance moſt powerful, you may ſee <lb></lb>how much more acute and ingenious the ſolution muſt be, and <lb></lb>not to be found by a wit leſſe piercing than that of <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end>; <lb></lb>and again from the difficulty in underſtanding it, you may argue <lb></lb>the ſo much greater difficulty in finding it. </s><s>But let us for the pre <lb></lb>ſent ſuſpend our anſwer, which you ſhall underſtand in due time <lb></lb>and place, after we have repeated the objection of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> and <lb></lb>that in his favour, much ſtrengthened. </s><s>Now paſſe we to <emph type="italics"></emph>Ari-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg308"></arrow.to.target> <lb></lb><emph type="italics"></emph>ſtotles<emph.end type="italics"></emph.end> third Argument, touching which we need give no farther <lb></lb>reply, it having been ſufficiently anſwered betwixt the diſcourſes <lb></lb>of yeſterday and to day: In as much as he urgeth, that the mo <lb></lb>tion of grave bodies is naturally by a right line to the centre; and <lb></lb>then enquireth, whether to the centre of the Earth, or to that <lb></lb>of the Univerſe, and concludeth that they tend naturally to the <lb></lb>centre of the Univerſe, but accidentally to that of the Earth. <lb></lb><arrow.to.target n="marg309"></arrow.to.target> <lb></lb>Therefore we may proceed to the fourth, upon which its requiſite <lb></lb>that we ſtay ſome time, by reaſon it is founded upon that expe <lb></lb>riment, from whence the greater part of the remaining argu <lb></lb>ments derive all their ſtrength. <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſaith therefore, that it is <lb></lb>a moſt convincing argument of the Earths immobility, to ſee <lb></lb>that projections thrown or ſhot upright, return perpendicularly <lb></lb>by the ſame line unto the ſame place from whence they were ſhot <lb></lb>or thrown. </s><s>And this holdeth true, although the motion be of a <lb></lb>very great height; which could never come to paſſe, did the <lb></lb>Earth move: for in the time that the projected body is moving <lb></lb>upwards and downwards in a ſtate of ſeparation from the Earth, <lb></lb>the place from whence the motion of the projection began, would <lb></lb>be paſt, by means of the Earths revolution, a great way to <lb></lb>wards the Eaſt, and look how great that ſpace was, ſo far from <lb></lb>that place would the projected body in its deſcent come to the <lb></lb>ground. </s><s>So that hither may be referred the argument taken from <lb></lb>a bullet ſhot from a Canon directly upwards; as alſo that other <lb></lb>uſed by <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ptolomy,<emph.end type="italics"></emph.end> of the grave bodies that falling <lb></lb>from on high, are obſerved to deſcend by a direct and perpendicu <lb></lb>lar line to the ſurface of the Earth. </s><s>Now that I may begin to untie <lb></lb>theſe knots, I demand of <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> that in caſe one ſhould deny <lb></lb>to <emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> that weights in falling freely from on <lb></lb>high, deſcend by a right and perpendicular line, that is, directly <lb></lb>to the centre, what means he would uſe to prove it?</s></p><p type="margin"><s><margin.target id="marg306"></margin.target>Ariſtotles <emph type="italics"></emph>argu <lb></lb>ment againſt the <lb></lb>Earths motion, is <lb></lb>defective in two <lb></lb>things<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg307"></margin.target>* The ſame word <lb></lb>which a little above <lb></lb>I tendred ſtay be <lb></lb>hind, as a bowle <lb></lb>when it meets with <lb></lb>ruls.</s></p><p type="margin"><s><margin.target id="marg308"></margin.target><emph type="italics"></emph>The anſwer to <lb></lb>the third argu <lb></lb>ment.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg309"></margin.target><emph type="italics"></emph>The anſwer to <lb></lb>the fourth argu <lb></lb>ment.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>The means of the ſenſes; the which aſſureth us, that <lb></lb>that Tower or other altitude, is upright and perpendicular, and <lb></lb>ſheweth us that that ſtone, or other grave body, doth ſlide along <lb></lb>the Wall, without inclining a hairs breadth to one ſide or ano <lb></lb>ther, and light at the foot thereof juſt under the place from whence <lb></lb>it was let fall.</s></p> <pb xlink:href="040/01/139.jpg" pagenum="121"></pb><p type="main"><s>SALV. </s><s>But if it ſhould happen that the Terreſtrial Globe did <lb></lb>move round, and conſequently carry the Tower alſo along with <lb></lb>it, and that the ſtone did then alſo grate and ſlide along the ſide of <lb></lb>the Tower, what muſt its motion be then?</s></p><p type="main"><s>SIMPL. </s><s>In this caſe we may rather ſay its motions: for it <lb></lb>would have one wherewith to deſcend from the top of the Tower <lb></lb>to the bottom, and ſhould neceſſarily have another to follow the <lb></lb>courſe of the ſaid Tower.</s></p><p type="main"><s>SALV. </s><s>So that its motion ſhould be compounded of two, to <lb></lb>wit, of that wherewith it meaſureth the Tower, and of that o <lb></lb>ther wherewith it followeth the ſame: From which compoſition <lb></lb>would follow, that the ſtone would no longer deſcribe that ſimple <lb></lb>right and perpendicular line, but one tranſverſe, and perhaps not <lb></lb>ſtreight.</s></p><p type="main"><s>SIMPL. </s><s>I can ſay nothing of its non-rectitude, but this I know <lb></lb>very well, that it would of neceſſity be tranſverſe, and different <lb></lb>from the other directly perpendicular, which it doth deſcribe, the <lb></lb>Earth ſtanding ſtill.</s></p><p type="main"><s>SALV. </s><s>You ſee then, that upon the meer obſerving the falling <lb></lb>ſtone to glide along the Tower, you cannot certainly affirm that <lb></lb>it deſcribeth a line which is ſtreight and perpendicular, unleſs you <lb></lb>firſt ſuppoſe that the Earth ſtandeth ſtill.</s></p><p type="main"><s>SIMPL. True; for if the Earth ſhould move, the ſtones mo <lb></lb>tion would be tranſverſe, and not perpendicular.</s></p><p type="main"><s>SALV. </s><s>Behold then the Paralogiſm of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ptolomey<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg310"></arrow.to.target> <lb></lb>to be evident and manifeſt, and diſcovered by you your ſelf, <lb></lb>wherein that is ſuppoſed for known, which is intended to be de <lb></lb>monſtrated.</s></p><p type="margin"><s><margin.target id="marg310"></margin.target><emph type="italics"></emph>The Paralogiſm <lb></lb>of<emph.end type="italics"></emph.end> Ariſtotle <emph type="italics"></emph>and<emph.end type="italics"></emph.end> <lb></lb>Ptolomey <emph type="italics"></emph>in ſup <lb></lb>poſing that for <lb></lb>known, which is in <lb></lb>queſtion.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>How can that be? </s><s>To me it appeareth that the <lb></lb>Syllogiſm is rightly demonſtrated without <emph type="italics"></emph>petitionem principii.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>You ſhall ſee how it is; anſwer me a little. </s><s>Doth he <lb></lb>not lay down the concluſion as unknown?</s></p><p type="main"><s>SIMPL. Unknown; why otherwiſe the demonſtrating it would <lb></lb>be ſuperfluous.</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 neceſſary that it ſhould; for otherwiſe it would be <lb></lb>a proving <emph type="italics"></emph>ignotum per æquè ignotum.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Our concluſion which is to be proved, and which is un <lb></lb>known, is it not the ſtability of the Earth?</s></p><p type="main"><s>SIMPL. </s><s>It is the ſame.</s></p><p type="main"><s>SALV. </s><s>The middle term, which ought to be known, is it not the <lb></lb>ſtreight and perpendicular deſcent of the ſtone?</s></p><p type="main"><s>SIMPL. </s><s>It is ſo.</s></p><p type="main"><s>SALV. </s><s>But was it not juſt now concluded, that we can have <lb></lb>no certain knowledg whether that ſame ſhall be direct and perpen <pb xlink:href="040/01/140.jpg" pagenum="122"></pb>dicular, unleſs we firſt know that the Earth ſtands ſtill? </s><s>Therefore <lb></lb>in your Syllogiſm the certainty of the middle term is aſſumed <lb></lb>from the uncertainty of the concluſion. </s><s>You may ſee then, what <lb></lb>and how great the Paralogiſm is.</s></p><p type="main"><s>SAGR. </s><s>I would, in favour of <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> defend <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> if it <lb></lb>were poſſible, or at leaſt better ſatisfie my ſelf concerning the <lb></lb>ſtrength of your illation. </s><s>You ſay, that the ſeeing the ſtone rake <lb></lb>along the Tower, is not ſufficient to aſſure us, that its motion is <lb></lb>perpendicular (which is the middle term of the Syllogiſm) unleſs <lb></lb>it be preſuppoſed, that the Earth ſtandeth ſtill, which is the con <lb></lb>cluſion to be proved: For that if the Tower did move together <lb></lb>with the Earth, and the ſtone did ſlide along the ſame, the motion <lb></lb>of the ſtone would be tranſverſe, and not perpendicular. </s><s>But I <lb></lb>ſhall anſwer, that ſhould the Tower move, it would be impoſſible <lb></lb>that the ſtone ſhould fall gliding along the ſide of it; and there <lb></lb>fore from its falling in that manner the ſtability of the Earth is in <lb></lb>ferred.</s></p><p type="main"><s>SIMPL. </s><s>It is ſo; for if you would have the ſtone in deſcend <lb></lb>ing to grate upon the Tower, though it were carried round by <lb></lb>the Earth, you muſt allow the ſtone two natural motions, to wit, <lb></lb>the ſtraight motion towards the Centre, and the circular about <lb></lb>the Centre, the which is impoſſible.</s></p><p type="main"><s>SALV. <emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> defenſe then conſiſteth in the impoſſibilitie, <lb></lb>or at leaſt in his eſteeming it an impoſſibility, that the ſtone ſhould <lb></lb>move with a motion mixt of right and circular: for if he did <lb></lb>not hold it impoſſible that the ſtone could move to the Centre, <lb></lb>and about the Centre at once, he muſt have underſtood, that it <lb></lb>might come to paſs that the cadent ſtone might in its deſcent, race <lb></lb>the Tower as well when it moved as when it ſtood ſtill; and con <lb></lb>ſequently he muſt have perceived, that from this grating nothing <lb></lb>could be inferred touching the mobility or immobility of the <lb></lb>Earth. </s><s>But this doth not any way excuſe <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end>; aſwell be <lb></lb>cauſe he ought to have expreſt it, if he had had ſuch a conceit, it <lb></lb>being ſo material a part of his Argument; as alſo becauſe it can <lb></lb>neither be ſaid that ſuch an effect is impoſſible, nor that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> <lb></lb>did eſteem it ſo. </s><s>The firſt cannot be affirmed, for that by and <lb></lb>by I ſhall ſhew that it is not onely poſſible, but neceſſary: nor <lb></lb><arrow.to.target n="marg311"></arrow.to.target> <lb></lb>much leſs can the ſecond be averred, for that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> himſelf <lb></lb>granteth fire to move naturally upwards in a right line, and to <lb></lb>move about with the diurnal motion, imparted by Heaven to the <lb></lb>whole Element of Fire, and the greater part of the Air: If there <lb></lb>fore he held it not impoſſible to mix the right motion upwards, <lb></lb>with the circular communicated to the Fire and Air from the con <lb></lb>cave of the Moon, much leſs ought he to account impoſſible the <lb></lb>mixture of the right motion downwards of the ſtone, with the <pb xlink:href="040/01/141.jpg" pagenum="123"></pb>circular which we preſuppoſe natural to the whole Terreſtrial <lb></lb>Globe, of which the ſtone is a part.</s></p><p type="margin"><s><margin.target id="marg311"></margin.target>Ariſtotle <emph type="italics"></emph>admit <lb></lb>teth that the Fire <lb></lb>moveth directly <lb></lb>upwards by na <lb></lb>ture, and round a <lb></lb>bout by participa <lb></lb>tion.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>I ſee no ſuch thing: for if the element of Fire re <lb></lb>volve round together with the Air, it is a very eaſie, yea a neceſſary <lb></lb>thing, that a ſpark of fire which from the Earth mounts upwards, <lb></lb>in paſſing thorow the moving air, ſhould receive the ſame motion, <lb></lb>being a body ſo thin, light, and eaſie to be moved: but that a <lb></lb>very heavy ſtone, or a Canon bullet, that deſcendeth from on <lb></lb>high, and that is at liberty to move whither it will, ſhould ſuffer <lb></lb>it ſelf to be tranſported either by the air or any other thing, is <lb></lb>altogether incredible. </s><s>Beſides that, we have the Experiment, <lb></lb>which is ſo proper to our purpoſe, of the ſtone let fall from the <lb></lb>round top of the Maſt of a ſhip, which when the ſhip lyeth ſtill, <lb></lb>falleth at the Partners of the Maſt; but when the ſhip ſaileth, falls <lb></lb>ſo far diſtant from that place, by how far the ſhip in the time of <lb></lb>the ſtones falling had run forward; which will not be a few fa <lb></lb>thoms, when the ſhips courſe is ſwift.</s></p><p type="main"><s>SALV. </s><s>There is a great diſparity between the caſe of the Ship <lb></lb><arrow.to.target n="marg312"></arrow.to.target> <lb></lb>and that of the Earth, if the Terreſtrial Globe be ſuppoſed to have <lb></lb>a diurnal motion. </s><s>For it is a thing very manifeſt, that the mo <lb></lb>tion of the Ship, as it is not natural to it, ſo the motion of all thoſe <lb></lb>things that are in it is accidental, whence it is no wonder that the <lb></lb>ſtone which was retained in the round top, being left at liberty, <lb></lb>deſcendeth downwards without any obligation to follow the mo <lb></lb>tion of the Ship. </s><s>But the diurnal converſion is aſcribed to the <lb></lb>Terreſtrial Globe for its proper and natural motion, and conſe <lb></lb>quently, it is ſo to all the parts of the ſaid Globe; and, as being <lb></lb>impreſs'd by nature, is indelible in them; and therefore that ſtone <lb></lb>that is on the top of the Tower hath an intrinſick inclination of <lb></lb>revolving about the Centre of its <emph type="italics"></emph>Whole<emph.end type="italics"></emph.end> in twenty four hours, and <lb></lb>this ſame natural inſtinct it exerciſeth eternally, be it placed in any <lb></lb>ſtate whatſoever. </s><s>And to be aſſured of the truth of this, you <lb></lb>have no more to do but to alter an antiquated impreſſion made <lb></lb>in your mind; and to ſay, Like as in that I hitherto holding it to <lb></lb>be the property of the Terreſtrial Globe to reſt immoveable about <lb></lb>its Centre, did never doubt or queſtion but that all whatſoever <lb></lb>particles thereof do alſo naturally remain in the ſame ſtate of reſt: <lb></lb>So it is reaſon, in caſe the Terreſtrial Globe did move round by <lb></lb>natural inſtinct in twenty four hours, that the intrinſick and natu <lb></lb>ral inclination of all its parts ſhould alſo be, not to ſtand ſtill, but <lb></lb><arrow.to.target n="marg313"></arrow.to.target> <lb></lb>to follow the ſame revolution. </s><s>And thus without running into <lb></lb>any inconvenience, one may conclude, that in regard the motion <lb></lb>conferred by the force of ^{*}Oars on the Ship, and by it on all the <lb></lb>things that are contained within her, is not natural but forreign, it <lb></lb>is very reaſonable that that ſtone, it being ſeparated from the ſhip, <pb xlink:href="040/01/142.jpg" pagenum="124"></pb>do reduce its ſelf to its natural diſpoſure, and return to exerciſe <lb></lb><arrow.to.target n="marg314"></arrow.to.target> <lb></lb>its pure ſimple inſtinct given it by nature. </s><s>To this I add, that <lb></lb>it's neceſſary, that at leaſt that part of the Air which is beneath the <lb></lb>greater heights of mountains, ſhould be tranſported and carried <lb></lb>round by the roughneſs of the Earths ſurface; or that, as being <lb></lb>mixt with many Vapours, and terrene Exhalations, it do na <lb></lb>turally follow the diurnal motion, which occurreth not in the <lb></lb>Air about the ſhip rowed by Oars: So that your arguing <lb></lb>from the ſhip to the Tower hath not the force of an illation; <lb></lb>becauſe that ſtone which falls from the round top of the Maſt, <lb></lb>entereth into a <emph type="italics"></emph>medium,<emph.end type="italics"></emph.end> which is unconcern'd in the motion <lb></lb>of the ſhip: but that which departeth from the top of the Tower, <lb></lb>finds a <emph type="italics"></emph>medium<emph.end type="italics"></emph.end> that hath a motion in common with the whole Ter <lb></lb>reſtrial Globe; ſo that without being hindred, rather being aſſiſted <lb></lb>by the motion of the air, it may follow the univerſal courſe of the <lb></lb>Earth.</s></p><p type="margin"><s><margin.target id="marg312"></margin.target><emph type="italics"></emph>The diſparity be <lb></lb>tween the fall of a <lb></lb>ſtone from the <lb></lb>round top of a ſhip, <lb></lb>and from the top <lb></lb>of a tower.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg313"></margin.target>*That you may not <lb></lb>ſuſpect my tranſla <lb></lb>tion, or wonder <lb></lb>what Oars have to <lb></lb>do with a ſhip, you <lb></lb>are to know that <lb></lb>the Author intends <lb></lb>the Gallies uſed in <lb></lb>the Mediterrane.</s></p><p type="margin"><s><margin.target id="marg314"></margin.target><emph type="italics"></emph>The part of the <lb></lb>Air inferiour to <lb></lb>the higher moun <lb></lb>tains doth follow <lb></lb>the motion of the <lb></lb>Earth.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>I cannot conceive that the air can imprint in a very <lb></lb><arrow.to.target n="marg315"></arrow.to.target> <lb></lb>great ſtone, or in a groſs Globe of Wood or Ball of Lead, as <lb></lb>ſuppoſe of two hundred weight, the motion wherewith its ſelf is <lb></lb>moved, and which it doth perhaps communicate to feathers, ſnow, <lb></lb>and other very light things: nay, I ſee that a weight of that na <lb></lb>ture, being expoſed to any the moſt impetuous wind, is not there <lb></lb>by removed an inch from its place; now conſider with your ſelf <lb></lb>whether the air will carry it along therewith.</s></p><p type="margin"><s><margin.target id="marg315"></margin.target><emph type="italics"></emph>The motion of the <lb></lb>Air apt to carry <lb></lb>with it light things <lb></lb>but not heavy.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>There is great difference between your experiment and <lb></lb>our caſe. </s><s>You introduce the wind blowing againſt that ſtone, <lb></lb>ſuppoſed in a ſtate of reſt, and we expoſe to the air, which already <lb></lb>moveth, the ſtone which doth alſo move with the ſame velocity; <lb></lb>ſo that the air is not to conferr a new motion upon it, but onely <lb></lb>to maintain, or to ſpeak better, not to hinder the motion already <lb></lb>acquired: you would drive the ſtone with a ſtrange and preter <lb></lb>natural motion, and we deſire to conſerve it in its natural. </s><s>If <lb></lb>you would produce a more pertinent experiment, you ſhould ſay, <lb></lb>that it is obſerved, if not with the eye of the forehead, yet with <lb></lb>that of the mind, what would evene, if an eagle that is carried by <lb></lb>the courſe of the wind, ſhould let a ſtone fall from its talons; <lb></lb>which, in regard that at its being let go, it went along with the <lb></lb>wind, and after it was let fall it entered into a <emph type="italics"></emph>medium<emph.end type="italics"></emph.end> that mo <lb></lb>ved with equal velocity, I am very confident that it would not be <lb></lb>ſeen to deſcend in its fall perpendicularly, but that following the <lb></lb>courſe of the wind, and adding thereto that of its particular gra <lb></lb>vity, it would move with a tranſverſe motion.</s></p><p type="main"><s>SIMPI. </s><s>But it would firſt be known how ſuch an experiment <lb></lb>may be made; and then one might judg according to the event. <lb></lb></s><s>In the mean time the effect of the ſhip doth hitherto incline to fa <lb></lb>vour our opinion.</s></p> <pb xlink:href="040/01/143.jpg" pagenum="125"></pb><p type="main"><s>SALV. </s><s>Well ſaid you <emph type="italics"></emph>hitherto,<emph.end type="italics"></emph.end> for perhaps it may anon change <lb></lb>countenance. </s><s>And that I may no longer hold you in ſuſpenſe, <lb></lb>tell me, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> do you really believe, that the Experiment of <lb></lb>the ſhip ſquares ſo very well with our purpoſe, as that it ought to <lb></lb>be believed, that that which we ſee happen in it, ought alſo to <lb></lb>evene in the Terreſtrial Globe?</s></p><p type="main"><s>SIMPL. </s><s>As yet I am of that opinion; and though you have <lb></lb>alledged ſome ſmall diſparities, I do not think them of ſo great <lb></lb>moment, as that they ſhould make me change my judgment.</s></p><p type="main"><s>SALV. </s><s>I rather deſire that you would continue therein, and <lb></lb>hold for certain, that the effect of the Earth would exactly anſwer <lb></lb>that of the ſhip: provided, that when it ſhall appear prejudicial to <lb></lb>your cauſe, you would not be humorous and alter your thoughts. <lb></lb></s><s>You may haply ſay, Foraſmuch as when the ſhip ſtands ſtill, the <lb></lb>ſtone falls at the foot of the Maſt, and when ſhe is under ſail, it <lb></lb>lights far from thence, that therefore by converſion, from the ſtones <lb></lb>falling at the foot is argued the ſhips ſtanding ſtill, and from its <lb></lb>falling far from thence is argued her moving; and becauſe that <lb></lb>which occurreth to the ſhip, ought likewiſe to befall the Earth: <lb></lb>that therefore from the falling of the ſtone at the foot of the Tow <lb></lb>er is neceſſarily inferred the immobility of the Terreſtrial Globe. <lb></lb></s><s>Is not this your argumentation?</s></p><p type="main"><s>SIMPL. </s><s>It is; and reduced into that conciſeneſs, as that it is <lb></lb>become moſt eaſie to be apprehended.</s></p><p type="main"><s>SALV. </s><s>Now tell me; if the ſtone let fall from the Round <lb></lb>top, when the ſhip is in a ſwift courſe, ſhould fall exactly in <lb></lb>the ſame place of the ſhip, in which it falleth when the ſhip is at <lb></lb>anchor, what ſervice would theſe experiments do you, in order to <lb></lb>the aſcertaining whether the veſſel doth ſtand ſtill or move?</s></p><p type="main"><s>SIMPL. </s><s>Juſt none: Like as, for exemple, from the beating of <lb></lb>the pulſe one cannot know whether a perſon be aſleep or awake, <lb></lb>ſeeing that the pulſe beateth after the ſame manner in ſleeping as <lb></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></lb>Ship?</s></p><p type="main"><s>SIMPL. </s><s>I have not; but yet I believe that thoſe Authors <lb></lb>which alledg the ſame, have accurately obſerved it; beſides that <lb></lb>the cauſe of the diſparity is ſo manifeſtly known, that it admits <lb></lb>of no queſtion.</s></p><p type="main"><s>SALV. </s><s>That it is poſſible that thoſe Authors inſtance in it, <lb></lb>without having made tryal of it, you your ſelf are a good teſti <lb></lb>mony, that without having examined it, alledg it as certain, and in <lb></lb>a credulous way remit it to their authority; as it is now not onely <lb></lb>poſſible, but very probable that they likewiſe did; I mean, did <lb></lb>remit the ſame to their Predeceſſors, without ever arriving at one <pb xlink:href="040/01/144.jpg" pagenum="126"></pb>that had made the experiment: for whoever ſhall examine the <lb></lb>ſame, ſhall find the event ſucceed quite contrary to what hath <lb></lb>been written of it: that is, he ſhall ſee the ſtone fall at all times <lb></lb>in the ſame place of the Ship, whether it ſtand ſtill, or move with <lb></lb>any whatſoever velocity. </s><s>So that the ſame holding true in the <lb></lb><arrow.to.target n="marg316"></arrow.to.target> <lb></lb>Earth, as in the Ship, one cannot from the ſtones falling perpen <lb></lb>dicularly at the foot of the Tower, conclude any thing touching <lb></lb>the motion or reſt of the Earth.</s></p><p type="margin"><s><margin.target id="marg316"></margin.target><emph type="italics"></emph>The stone falling <lb></lb>from the Mast of <lb></lb>a ſhip lights in the <lb></lb>ſame place, whe <lb></lb>ther the ſhip doth <lb></lb>move or ly still.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMPL. </s><s>If you ſhould refer me to any other means than to <lb></lb>experience, I verily believe our Diſputations would not come to <lb></lb>an end in haſte; for this ſeemeth to me a thing ſo remote from all <lb></lb>humane reaſon, as that it leaveth not the leaſt place for credulity <lb></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></lb>one proof thereof, and do you ſo confidently affirm it for true? <lb></lb></s><s>I for my part will return to my incredulity, and to the confidence <lb></lb>I had that the Experiment hath been tried by the principal Au <lb></lb>thors who made uſe thereof, and that the event ſucceeded as they <lb></lb>affirm.</s></p><p type="main"><s>SALV. </s><s>I am aſſured that the effect will enſue as I tell you; for ſo <lb></lb>it is neceſſary that it ſhould: and I farther add, that you know your <lb></lb>ſelf that it cannot fall out otherwiſe, however you feign or ſeem to <lb></lb>feign that you know it not. </s><s>Yet I am ſo good at taming of wits, <lb></lb>that I will make you confeſs the ſame whether you will or no. </s><s>But <lb></lb><emph type="italics"></emph>Sagredus<emph.end type="italics"></emph.end> ſtands very mute, and yet, if I miſtake not, I ſaw him <lb></lb>make an offer to ſpeak ſomewhat.</s></p><p type="main"><s>SAGR. </s><s>I had an intent to ſay ſomething, but to tell you true, I <lb></lb>know not what it was; for the curioſity that you have moved in me, <lb></lb>by promiſing that you would force <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> to diſcover the <lb></lb>knowledg which he would conceal from us, hath made me to de <lb></lb>poſe all other thoughts: therefore I pray you to make good your <lb></lb>vaunt.</s></p><p type="main"><s>SALV. </s><s>Provided that <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> do conſent to reply to what I <lb></lb>ſhall ask him, I will not fail to do it.</s></p><p type="main"><s>SIMPL. </s><s>I will anſwer what I know, aſſured that I ſhall not be <lb></lb>much put to it, for that of thoſe things which I hold to be falſe, <lb></lb>I think nothing can be known, in regard that Science reſpecteth <lb></lb>truths and not falſhoods.</s></p><p type="main"><s>SALV. </s><s>I deſire not that you ſhould ſay or reply, that you know <lb></lb>any thing, ſave that which you moſt aſſuredly know. </s><s>Therefore <lb></lb>tell me; If you had here a flat ſuperficies as polite as a Looking <lb></lb>glaſs, and of a ſubſtance as hard as ſteel, and that it were not pa <lb></lb>ralel to the Horizon, but ſomewhat inclining, and that upon it <lb></lb>you did put a Ball perfectly ſpherical, and of a ſubſtance grave and <pb xlink:href="040/01/145.jpg" pagenum="127"></pb>hard, as ſuppoſe of braſs; what think you it would do being let <lb></lb>go? </s><s>do not you believe (as for my part I do) that it would lie <lb></lb>ſtill?</s></p><p type="main"><s>SIMPL. </s><s>If that ſuperficies were inclining?</s></p><p type="main"><s>SALV. Yes; for ſo I have already ſuppoſed.</s></p><p type="main"><s>SIMPL. </s><s>I cannot conceive how it ſhould lie ſtill: nay, I am <lb></lb>confident that it would move towards the declivity with much pro <lb></lb>penſneſs.</s></p><p type="main"><s>SALV. </s><s>Take good heed what you ſay, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> for I am <lb></lb>confident that it would lie ſtill in what ever place you ſhould lay <lb></lb>it.</s></p><p type="main"><s>SIMPL. </s><s>So long as you make uſe of ſuch ſuppoſitions, <emph type="italics"></emph>Sal <lb></lb>viatus,<emph.end type="italics"></emph.end> I ſhall ceaſe to wonder if you inferr moſt abſurd con <lb></lb>cluſions.</s></p><p type="main"><s>SALV. </s><s>Are you aſſured, then, that it would freely move to <lb></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 becauſe I told you ſo, <lb></lb>(for I endeavoured to perſwade you to think the contrary) but of <lb></lb>your ſelf, and upon your natural judgment.</s></p><p type="main"><s>SIMPL. </s><s>Now I ſee what you would be at; you ſpoke not this <lb></lb>as really believing the ſame; but to try me, and to wreſt matter <lb></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></lb>move, and with what velocity? </s><s>But take notice that I inſtanced <lb></lb>in a Ball exactly round, and a plain exquiſitely poliſhed, that all <lb></lb>external and accidental impediments might be taken away. </s><s>And <lb></lb>ſo would I have you remove all obſtructions cauſed by the Airs re <lb></lb>ſiſtance to diviſion, and all other caſual obſtacles, if any other <lb></lb>there can be.</s></p><p type="main"><s>SIMPL. </s><s>I very well underſtand your meaning, and as to your <lb></lb>demand, I anſwer, that the Ball would continue to move <emph type="italics"></emph>in in <lb></lb>finitum,<emph.end type="italics"></emph.end> if the inclination of the plain ſhould ſo long laſt, and con <lb></lb>tinually with an accelerating motion; for ſuch is the nature of <lb></lb>ponderous moveables, that <emph type="italics"></emph>vires acquirant eundo<emph.end type="italics"></emph.end>: and the great <lb></lb>er the declivity was, the greater the velocity would be.</s></p><p type="main"><s>SALV. </s><s>But if one ſhould require that that Ball ſhould move <lb></lb>upwards on that ſame ſuperficies, do you believe that it would <lb></lb>ſo do?</s></p><p type="main"><s>SIMPL. </s><s>Not ſpontaneouſly; but being drawn, or violently <lb></lb>thrown, it may.</s></p><p type="main"><s>SALV. </s><s>And in caſe it were thruſt forward by the impreſſion of <lb></lb>ſome violent <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> from without, what and how great would <lb></lb>its motion be?</s></p><p type="main"><s>SIMPL. </s><s>The motion would go continually decreaſing and re <pb xlink:href="040/01/146.jpg" pagenum="128"></pb>tarding, as being contrary to nature; and would be longer or <lb></lb>ſhorter, according to the greater or leſs impulſe, and according to <lb></lb>the greater or leſs acclivity.</s></p><p type="main"><s>SALV. </s><s>It ſeems, then, that hitherto you have explained to me <lb></lb>the accidents of a moveable upon two different Planes; and that <lb></lb>in the inclining plane, the grave moveable doth ſpontaneouſly de <lb></lb>ſcend, and goeth continually accelerating, and that to retain it in <lb></lb>reſt, force muſt be uſed therein: but that on the aſcending plane, <lb></lb>there is required a force to thruſt it forward, and alſo to ſtay it in <lb></lb>reſt, and that the motion impreſſed goeth continually diminiſhing, <lb></lb>till that in the end it cometh to nothing. </s><s>You ſay yet farther, <lb></lb>that in both the one and the other caſe, there do ariſe differences <lb></lb>from the planes having a greater or leſs declivity or acclivity; ſo <lb></lb>that the greater inclination is attended with the greater velocity; <lb></lb>and contrariwiſe, upon the aſcending plane, the ſame moveable <lb></lb>thrown with the ſame force, moveth a greater diſtance, by how <lb></lb>much the elevation is leſs. </s><s>Now tell me, what would befall the <lb></lb>ſame moveable upon a ſuperficies that had neither acclivity nor <lb></lb>declivity?</s></p><p type="main"><s>SIMPL. </s><s>Here you muſt give me a little time to conſider of an <lb></lb>anſwer. </s><s>There being no declivity, there can be no natural incli <lb></lb>nation to motion: and there being no acclivity, there can be no <lb></lb>reſiſtance to being moved; ſo that there would ariſe an indiffe <lb></lb>rence between propenſion and reſiſtance of motion; therefore, <lb></lb>methinks it ought naturally to ſtand ſtill. </s><s>But I had forgot my <lb></lb>ſelf: it was but even now that <emph type="italics"></emph>Sagredus<emph.end type="italics"></emph.end> gave me to underſtand <lb></lb>that it would ſo do.</s></p><p type="main"><s>SALV. </s><s>So I think, provided one did lay it down gently: but <lb></lb>if it had an <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> given it towards any part, what would fol <lb></lb>low?</s></p><p type="main"><s>SIMP. </s><s>There would follow, that it ſhould move towards that <lb></lb>part.</s></p><p type="main"><s>SALV. </s><s>But with what kind of motion? </s><s>with the continually <lb></lb>accelerated, as in declining planes; or with the ſucceſſively re <lb></lb>tarded, as in thoſe aſcending.</s></p><p type="main"><s>SIMP. </s><s>I cannot tell how to diſcover any cauſe of acceleration, <lb></lb>or retardation, there being no declivity or acclivity.</s></p><p type="main"><s>SALV. Well: but if there be no cauſe of retardation, much <lb></lb>leſs ought there to be any cauſe of reſt. </s><s>How long therefore <lb></lb>would you have the moveable to move?</s></p><p type="main"><s>SIMP. </s><s>As long as that ſuperficies, neither inclined nor decli <lb></lb>ned ſhall laſt.</s></p><p type="main"><s>SALV. </s><s>Therefore if ſuch a ſpace were interminate, the motion <lb></lb>upon the ſame would likewiſe have no termination, that is, would <lb></lb>be perpetual.</s></p> <pb xlink:href="040/01/147.jpg" pagenum="129"></pb><p type="main"><s>SIMP. </s><s>I think ſo, if ſo be the moveable be of a matter <lb></lb>durable.</s></p><p type="main"><s>SALV. </s><s>That hath been already ſuppoſed, when it was ſaid, <lb></lb>that all external and accidental impediments were removed, and <lb></lb>the brittleneſſe of the moveable in this our caſe, is one of thoſe <lb></lb>impediments accidental. </s><s>Tell me now, what do you think is the <lb></lb>cauſe that that ſame Ball moveth ſpontaneouſly upon the inclining <lb></lb>plane, and not without violence upon the erected?</s></p><p type="main"><s>SIMP. </s><s>Becauſe the inclination of grave bodies is to move to <lb></lb>wards the centre of the Earth, and onely by violence upwards to <lb></lb>wards the circumference; and the inclining ſuperficies is that <lb></lb>which acquireth vicinity to the centre, and the aſcending one, <lb></lb>remoteneſſe.</s></p><p type="main"><s>SALV. </s><s>Therefore a ſuperficies, which ſhould be neither de <lb></lb>clining nor aſcending, ought in all its parts to be equally di <lb></lb>ſtant from the centre. </s><s>But is there any ſuch ſuperficies in the <lb></lb>World?</s></p><p type="main"><s>SIMP. </s><s>There is no want thereof: Such is our Terreſtrial <lb></lb>Globe, if it were more even, and not as it is rough and montai <lb></lb>nous; but you have that of the Water, at ſuch time as it is calm <lb></lb>and ſtill.</s></p><p type="main"><s>SALV. </s><s>Then a ſhip which moveth in a calm at Sea, is one of <lb></lb>thoſe moveables, which run along one of thoſe ſuperficies that <lb></lb>are neither declining nor aſcending, and therefore diſpoſed, in <lb></lb>caſe all obſtacles external and accidental were removed, to move <lb></lb>with the impulſe once imparted inceſſantly and uniformly.</s></p><p type="main"><s>SIMPL. </s><s>It ſhould ſeem to be ſo.</s></p><p type="main"><s>SALV. </s><s>And that ſtone which is on the round top, doth not it <lb></lb>move, as being together with the ſhip carried about by the cir <lb></lb>cumference of a Circle about the Centre; and therefore conſe <lb></lb>quently by a motion in it indelible, if all extern obſtacles be <lb></lb>removed? </s><s>And is not this motion as ſwift as that of the ſhip.</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 laſt <lb></lb>concluſion, if you are ſatisfied with the truth of all the pre <lb></lb>miſes.</s></p><p type="main"><s>SIMPL. </s><s>By my laſt concluſion, you mean, That that ſame <lb></lb>ſtone moving with a motion indelibly impreſſed upon it, is not to <lb></lb>leave, nay rather is to follow the ſhip, and in the end to light in <lb></lb>the ſelf ſame place, where it falleth when the ſhip lyeth ſtill; and <lb></lb>ſo I alſo grant it would do, in caſe there were no outward impe <lb></lb>diments that might diſturb the ſtones motion, after its being let <lb></lb>go, the which impediments are two, the one is the moveables <lb></lb>inability to break through the air with its meer <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> onely, it <lb></lb>being deprived of that of the ſtrength of Oars, of which it had <pb xlink:href="040/01/148.jpg" pagenum="130"></pb>been partaker, as part of the ſhip, at the time that it was upon <lb></lb>the Maſt; the other is the new motion of deſcent, which alſo <lb></lb>muſt needs be an hinderance of that other progreſſive motion.</s></p><p type="main"><s>SALV. </s><s>As to the impediment of the Air, I do not deny it <lb></lb>you; and if the thing falling were a light matter, as a feather, <lb></lb>or a lock of wool, the retardation would be very great, but in <lb></lb>an heavy ſtone is very exceeding ſmall. </s><s>And you your ſelf but <lb></lb>even now did ſay, that the force of the moſt impetuous wind <lb></lb>ſufficeth not to ſtir a great ſtone from its place; now do but con <lb></lb>ſider what the calmer air is able to do, being encountred by a <lb></lb>ſtone no more ſwift than the whole ſhip. </s><s>Nevertheleſſe, as I ſaid <lb></lb>before, I do allow you this ſmall effect, that may depend upon <lb></lb>ſuch an impediment; like as I know, that you will grant to me, <lb></lb>that if the air ſhould move with the ſame velocity that the ſhip <lb></lb>and ſtone hath, then the impediment would be nothing at all. <lb></lb></s><s>As to the other of the additional motion downwards; in the firſt <lb></lb>place it is manifeſt, that theſe two, I mean the circular, about <lb></lb>the centre, and the ſtreight, towards the centre, are not contra <lb></lb>ries, or deſtructive to one another, or incompatible. </s><s>Becauſe that <lb></lb>as to the moveable, it hath no repugnance at all to ſuch motions, <lb></lb>for you your ſelf have already confeſt the repugnance to be a <lb></lb>gainſt the motion which removeth from the centre, and the incli <lb></lb>nation to be towards the motion which approacheth to the centre. <lb></lb></s><s>Whence it doth of neceſſity follow, that the moveable hath nei <lb></lb>ther repugnance, nor propenſion to the motion which neither ap <lb></lb>proacheth, nor goeth from the centre, nor conſequently is there <lb></lb>any cauſe for the diminiſhing in it the faculty impreſſed. </s><s>And for <lb></lb>aſmuch as the moving cauſe is not one alone, which it hath at <lb></lb>tained by the new operation of retardation; but that they are <lb></lb>two, diſtinct from each other, of which, the gravity attends on <lb></lb>ly to the drawing of the moveable towards the centre, and the <lb></lb>vertue impreſs't to the conducting it about the centre, there re <lb></lb>maineth no occaſion of impediment.</s></p><p type="main"><s>SIMPL. </s><s>Your argumentation, to give you your due, is very <lb></lb>probable; but in reality it is invelloped with certain intricacies, <lb></lb>that are not eaſie to be extricated. </s><s>You have all along built upon <lb></lb><arrow.to.target n="marg317"></arrow.to.target> <lb></lb>a ſuppoſition, which the <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> Schools will not eaſily grant <lb></lb>you, as being directly contrary to <emph type="italics"></emph>Aristotle,<emph.end type="italics"></emph.end> and it is to take for <lb></lb>known and manifeſt, That the project ſeparated from the proji <lb></lb>cient, continueth the motion by <emph type="italics"></emph>vertue impreſſed<emph.end type="italics"></emph.end> on it by the <lb></lb>ſaid projicient, which <emph type="italics"></emph>vertue impreſſed<emph.end type="italics"></emph.end> is a thing as much dete <lb></lb>ſted in <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> Philoſophy, as the paſſage of any accident <lb></lb>from one ſubject into another. </s><s>Which doctrine doth hold, as I <lb></lb>believe it is well known unto you, that the project is carried by <lb></lb>the <emph type="italics"></emph>medium,<emph.end type="italics"></emph.end> which in our caſe happeneth to be the Air. </s><s>And <pb xlink:href="040/01/149.jpg" pagenum="131"></pb>therefore if that ſtone let fall from the round top, ought to fol <lb></lb>low the motion of the ſhip, that effect ſhould be aſcribed to the <lb></lb>Air, and not to the vertue impreſſed. </s><s>But you preſuppoſe that <lb></lb>the Air doth not follow the motion of the ſhip, but is tranquil. <lb></lb></s><s>Moreover, he that letteth it fall, is not to throw it, or to give <lb></lb>it <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> with his arm, but ought barely to open his hand and let <lb></lb>it go; and by this means, the ſtone, neither through the vertue <lb></lb>impreſſed by the projicient, nor through the help of the Air, <lb></lb>ſhall be able to follow the ſhips motion, and therefore ſhall be <lb></lb>left behind.</s></p><p type="margin"><s><margin.target id="marg317"></margin.target><emph type="italics"></emph>The project ac <lb></lb>cording to<emph.end type="italics"></emph.end> Ariſto <lb></lb>tle, <emph type="italics"></emph>is not moved by <lb></lb>vertue impreſſed, <lb></lb>but by the<emph.end type="italics"></emph.end> medium.</s></p><p type="main"><s>SALV. </s><s>I think then that you would ſay, that if the ſtone be <lb></lb>not thrown by the arm of that perſon, it is no longer a pro <lb></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"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſpeaks of the motion, the <lb></lb>moveable, and the mover of the projects, hath nothing to do <lb></lb>with the buſineſſe in hand; and if it concern not our purpoſe, <lb></lb>why do you alledg the ſame?</s></p><p type="main"><s>SIMP. </s><s>I produce it on the oceaſion of that impreſſed vertue, <lb></lb>named and introduced by you, which having no being in the <lb></lb>World, can be of no force; for <emph type="italics"></emph>non-entium nullæ ſunt operatio <lb></lb>nes<emph.end type="italics"></emph.end>; and therefore not onely of projected, but of all other pre <lb></lb>ternatural motions, the moving cauſe ought to be aſcribed to the <lb></lb><emph type="italics"></emph>medium,<emph.end type="italics"></emph.end> of which there hath been no due conſideration had; <lb></lb>and therefore all that hath been ſaid hitherto is to no purpoſe.</s></p><p type="main"><s>SALV. </s><s>Go to now, in good time. </s><s>But tell me, ſeeing that <lb></lb>your inſtance is wholly grounded upon the nullity of the vertue <lb></lb>impreſſed, if I ſhall demonſtrate to you, that the <emph type="italics"></emph>medium<emph.end type="italics"></emph.end> hath <lb></lb>nothing to do in the continuation of projects, after they are ſe <lb></lb>patated from the projicient, will you admit of the impreſſed ver <lb></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"></emph>medium<emph.end type="italics"></emph.end> being removed, I ſee not <lb></lb>how one can have recourſe to any thing elſe ſave the faculty im <lb></lb>preſſed by the mover.</s></p><p type="main"><s>SALV. </s><s>It would be well, for the removing, as much as is <lb></lb>poſſible, the occaſions of multiplying contentions, that you <lb></lb>would explain with as much diſtinctneſſe as may be, what is that <lb></lb>operation of the <emph type="italics"></emph>medium<emph.end type="italics"></emph.end> in continuing the motion of the project. <lb></lb><arrow.to.target n="marg318"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg318"></margin.target><emph type="italics"></emph>Operation of the<emph.end type="italics"></emph.end> <lb></lb>medium <emph type="italics"></emph>in continu <lb></lb>ing the motion of <lb></lb>the project.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>The projicient hath the ſtone in his hand, and with <lb></lb>force and violence throws his arm, with which jactation the <lb></lb>ſtone doth not move ſo much as the circumambient Air; ſo that <lb></lb>when the ſtone at its being forſaken by the hand, findeth it ſelf <lb></lb>in the Air, which at the ſame time moveth with impetouſity, it <lb></lb>is thereby born away; for, if the air did not operate, the ſtone <lb></lb>would fall at the foot of the projicient or thrower.</s></p> <pb xlink:href="040/01/150.jpg" pagenum="132"></pb><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"></emph>Many experi <lb></lb>ments, and rea <lb></lb>ſons againſt the <lb></lb>cauſe of the moti <lb></lb>on of projects, aſ <lb></lb>ſigned by<emph.end type="italics"></emph.end> Ariſtotle.</s></p><p type="main"><s>SALV. </s><s>And was you ſo credulous, as to ſuffer your ſelf to be <lb></lb>perſwaded to believe theſe fopperies, ſo long as you had your <lb></lb>ſenſes about you to confute them, and to underſtand the <lb></lb>truth thereof? </s><s>Therefore tell me, that great ſtone, and that <lb></lb>Canon bullet, which but onely laid upon a table, did continue <lb></lb>immoveable againſt the moſt impetuous winds, according as you a <lb></lb>little before did affirm, if it had been a ball of cork or other light <lb></lb>ſtuffe, think you that the wind would have removed it from its <lb></lb>place?</s></p><p type="main"><s>SIMP. Yes, and I am aſſured that it would have blown it <lb></lb>quite away, and with ſo much more velocity, by how much the <lb></lb>matter was lighter, for upon this reaſon we ſee the clouds to be <lb></lb>tranſported with a velocity equal to that of the wind that drives <lb></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 elſe but air moved.</s></p><p type="main"><s>SALV. </s><s>Then the moved air doth carry light things more <lb></lb>ſwiftly, and to a greater diſtance, 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 ſtone, and a <lb></lb>lock of cotton wool, which would move ſwiſteſt and fartheſt?</s></p><p type="main"><s>SIMP. </s><s>The ſtone by much; nay the wool would fall at my <lb></lb>feet.</s></p><p type="main"><s>SALV. But, if that which moveth the projected ſubſtance, af <lb></lb>ter it is delivered from the hand, be no other than the air moved <lb></lb>by the arm, and the moved air do more eaſily bear away light <lb></lb>than grave matters, how cometh it that the project of wool flieth <lb></lb>not farther, and ſwifter than that of ſtone? </s><s>Certainly it argu <lb></lb>eth that the ſtone hath ſome other impulſe beſides the motion of <lb></lb>the air. </s><s>Furthermore, if two ſtrings of equal length did hang <lb></lb>at yonder beam, and at the end of one there was faſtened a bul <lb></lb>let of lead, and a ball of cotton wool at the other, and both <lb></lb>were carried to an equal diſtance from the perpendicular, and <lb></lb>then let go; it is not to be doubted, but that both the one and <lb></lb>the other would move towards the perpendicular, and that being <lb></lb>carried by their own <emph type="italics"></emph>impetus,<emph.end type="italics"></emph.end> they would go a certain ſpace be <lb></lb>yond it, and afterwards return thither again. </s><s>But which of theſe <lb></lb>two pendent Globes do you think, would continue longeſt in mo <lb></lb>tion, before that it would come to reſt in its perpendicularity?</s></p><p type="main"><s>SIMP. </s><s>The ball of lead would ſwing to and again many times, <lb></lb>and that of wool but two or three at the moſt.</s></p><p type="main"><s>SALV. </s><s>So that that <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> and that <emph type="italics"></emph>mobility<emph.end type="italics"></emph.end> whatſoever is <lb></lb>the cauſe thereof, would conſerve its ſelf longer in grave ſub <lb></lb>ſtances, than light; I proceed now to another particular, and de <lb></lb>mand of you, why the air doth not carry away that Lemon <lb></lb>which is upon that ſame Table?</s></p> <pb xlink:href="040/01/151.jpg" pagenum="133"></pb><p type="main"><s>SIMP. </s><s>Becauſe that the air it ſelf is not moved</s></p><p type="main"><s>SALV. </s><s>It is requiſite then, that the projicient do confer mo <lb></lb>tion on the Air, with which it afterward moveth the project. </s><s>But <lb></lb>if ſuch a motion cannot be impreſſed [<emph type="italics"></emph>i. </s><s>e. </s><s>imparted<emph.end type="italics"></emph.end>] it being im <lb></lb>poſſible to make an accident paſſe out of one ſubject into another, <lb></lb>how can it paſſe from the arm into the Air? </s><s>Will you ſay that the <lb></lb>Air is not a ſubject different from the arm?</s></p><p type="main"><s>SIMP. </s><s>To this it is anſwered that the Air, in regard it is nei <lb></lb>ther heavy nor light in its own Region, is diſpoſed with facility to <lb></lb>receive every impulſe, and alſo to retain the ſame.</s></p><p type="main"><s>SALV. </s><s>But if thoſe <emph type="italics"></emph>penduli<emph.end type="italics"></emph.end> even now named, did prove <lb></lb>unto us, that the moveable, the leſſe it had of gravity, the leſſe <lb></lb>apt it was to conſerve its motion, how can it be that the Air <lb></lb>which in the Air hath no gravity at all, doth of it ſelf alone re <lb></lb>tain the motion acquired? </s><s>I believe, and know that you by this <lb></lb>time are of the ſame opinion, that the arm doth not ſooner re <lb></lb>turn to reſt, than doth the circumambient Air. </s><s>Let's go into the <lb></lb>Chamber, and with a towel let us agitate the Air as much as we <lb></lb>can, and then holding the cloth ſtill, let a little candle be <lb></lb>brought, that was lighted in the next room, or in the ſame place <lb></lb>let a leaf of beaten Gold be left at liberty to flie any wav, and you <lb></lb>ſhall by the calm vagation of them be aſſured that the Air is imme <lb></lb>diately reduced to tranquilty. </s><s>I could alledg many other experi <lb></lb>ments to the ſame purpoſe, but if one of theſe ſhould not ſuf <lb></lb>fice, I ſhould think your folly altogether incurable.</s></p><p type="main"><s>SAGR. </s><s>When an arrow is ſhot againſt the Wind, how incredi <lb></lb>ble a thing is it, that that ſame ſmall filament of air, impelled by <lb></lb>the bow-ſtring, ſhould in deſpite of fate go along with the arrow? <lb></lb></s><s>But I would willingly know another particular of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> to <lb></lb>which I intreat <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> would vouchſafe me an anſwer. </s><s>Sup <lb></lb>poſing that with the ſame Bow there were ſhot two arrows, one <lb></lb>juſt after the uſual manner, and the other ſide-wayes, placing it <lb></lb>long-wayes upon the Bow-ſtring, and then letting it flie, I would <lb></lb>know which of them would go fartheſt. </s><s>Favour me, I pray you <lb></lb>with an anſwer, though the queſtion may ſeem to you rather <lb></lb>ridiculous than otherwiſe; and excuſe me, for that I, who am, as <lb></lb>you ſee, rather blockiſh, than not, can reach no higher with my <lb></lb>ſpeculative faculty.</s></p><p type="main"><s>SIMPL. </s><s>I have never ſeen an arrow ſhot in that manner, yet <lb></lb>nevertheleſſe I believe, that it would not flie ſide-long, the <lb></lb>twentieth part of the ſpace that it goeth end-wayes.</s></p><p type="main"><s>SAGR. </s><s>And for that I am of the ſame opinion, hence it is, that <lb></lb>I have a doubt riſen in me, whether <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> doth not contradict <lb></lb>experience. </s><s>For as to experience, if I lay two arrows upon this <lb></lb>Table, in a time when a ſtrong Wind bloweth, one towards <pb xlink:href="040/01/152.jpg" pagenum="134"></pb>the courſe of the wind, and the other ſidelong, the wind will <lb></lb>quickly carry away this later, and leave the other where it was; <lb></lb>and the ſame to my ſeeming, ought to happen, if the Doctrine of <lb></lb><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> were true, of thoſe two ſhot out of a Bow: foraſmuch <lb></lb>as the arrow ſhot ſideways is driven by a great quantity of Air, <lb></lb>moved by the bowſtring, to wit by as much as the ſaid ſtring is <lb></lb>long, whereas the other arrow receiveth no greater a quantity of <lb></lb>air, than the ſmall circle of the ſtrings thickneſs. </s><s>And I cannot <lb></lb>imagine what may be the reaſon of ſuch a difference, but would <lb></lb>fain know the ſame.</s></p><p type="main"><s>SIMP. </s><s>The cauſe ſeemeth to me ſufficiently manifeſt; and it <lb></lb>is, becauſe the arrow ſhot endways, hath but a little quantity of <lb></lb>air to penetrate, and the other is to make its way through a quan <lb></lb>tity as great as its whole length.</s></p><p type="main"><s>SALV. </s><s>Then it ſeems the arrows ſhot, are to penetrate the air? <lb></lb></s><s>but if the air goeth along with them, yea, is that which carrieth <lb></lb>them, what penetration can they make therein? </s><s>Do you not ſee <lb></lb>that, in this caſe, the arrow would of neceſſity move with greater <lb></lb>velocity than the air? </s><s>and this greater velocity, what doth confer <lb></lb>it on the arrow? </s><s>Will you ſay the air giveth them a velocity <lb></lb>greater than its own? </s><s>Know then, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that the buſineſs <lb></lb>proceeds quite contrary to that which <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſaith, and that the </s></p><p type="main"><s><arrow.to.target n="marg320"></arrow.to.target> <lb></lb><emph type="italics"></emph>medium<emph.end type="italics"></emph.end> conferreth the motion on the project, is as falſe, as it is <lb></lb>true, that it is the onely thing which procureth its obſtruction; and <lb></lb>having known this, you ſhall underſtand without finding any thing <lb></lb>whereof to make queſtion, that if the air be really moved, it doth <lb></lb>much better carry the dart along with it longways, than endways, <lb></lb>for that the air which impelleth it in that poſture, is much, and in <lb></lb>this very little. </s><s>But ſhooting with the Bow, foraſmuch as the air <lb></lb>ſtands ſtill, the tranſverſe arrow, being to force its paſſage through <lb></lb>much air, comes to be much impeded, and the other that was nock't <lb></lb>eaſily overcometh the obſtruction of the ſmall quantity of air, <lb></lb>which oppoſeth it ſelf thereto.</s></p><p type="margin"><s><margin.target id="marg320"></margin.target><emph type="italics"></emph>The<emph.end type="italics"></emph.end> medium <emph type="italics"></emph>doth <lb></lb>impede and not cor <lb></lb>fer the motion of <lb></lb>projects.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>How many Propoſitions have I obſerved in <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> <lb></lb>(meaning ſtill in Natural Philoſophy) that are not onely falſe, <lb></lb>but falſe in ſuch ſort, that its diametrical contrary is true, as it <lb></lb>happens in this caſe. </s><s>But purſuing the point in hand, I think that <lb></lb><emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> is perſwaded, that, from ſeeing the ſtone always to fall <lb></lb>in the ſame place, he cannot conjecture either the motion or ſta <lb></lb>bility of the Ship: and if what hath been hitherto ſpoken, <lb></lb>ſhould not ſuffice, there is the Experiment of the <emph type="italics"></emph>medium<emph.end type="italics"></emph.end> which <lb></lb>may thorowly aſſure us thereof; in which experiment, the moſt <lb></lb>that could be ſeen would be, that the cadent moveable might be <lb></lb>left behind, if it were light, and that the air did not follow the <lb></lb>motion of the ſhip: but in caſe the air ſhould move with equal <pb xlink:href="040/01/153.jpg" pagenum="135"></pb>velocity, no imaginable diverſity could be found either in this, <lb></lb>or any other experiment whatſoever, as I am anon to tell you. <lb></lb></s><s>Now if in this caſe there appeareth no difference at all, what can <lb></lb>be pretended to be ſeen in the ſtone falling from the top of the <lb></lb>Tower, where the motion in gyration is not adventitious, and ac <lb></lb>cidental, but natural and eternal; and where the air exactly fol <lb></lb>loweth the motion of the Tower, and the Tower that of the Ter <lb></lb>reſtrial Globe? </s><s>have you any thing elſe to ſay, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> upon <lb></lb>this particular?</s></p><p type="main"><s>SIMP. </s><s>No more but this, that I ſee not the mobility of the <lb></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></lb>ſhew, that nothing can be concluded from the experiments alledg <lb></lb>ed by our adverſaries for convincing Arguments: as I think I <lb></lb>ſhall prove the others to be.</s></p><p type="main"><s>SAGR. </s><s>I beſeech you, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> before you proceed any far <lb></lb>ther, to permit me to ſtart certain queſtions, which have been <lb></lb>rouling in my fancy all the while that you with ſo much patience <lb></lb>and equanimity, was minutely explaining to <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> the expe <lb></lb>riment of the Ship.</s></p><p type="main"><s>SALV. </s><s>We are here met with a purpoſe to diſpute, and it's fit <lb></lb>that every one ſhould move the difficulties that he meets withall, <lb></lb>for this is the way to come to the knowledg of the truth. <lb></lb></s><s>Therefore ſpeak freely.</s></p><p type="main"><s>SAGR. </s><s>If it be true, that the <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> wherewith the ſhip moves, <lb></lb>doth remain indelibly impreſſ'd in the ſtone, after it is let fall from <lb></lb>the Maſt; and if it be farther true, that this motion brings no im <lb></lb>pediment or retardment to the motion directly downwards, na <lb></lb>tural to the ſtone: it's neceſſary, that there do an effect enſue of <lb></lb><arrow.to.target n="marg321"></arrow.to.target> <lb></lb>a very wonderful nature. </s><s>Let a Ship be ſuppoſed to ſtand ſtill, <lb></lb>and let the time of the falling of a ſtone from the Maſts Round-top <lb></lb>to the ground, be two beats of the pulſe; let the Ship afterwards <lb></lb>be under ſail, and let the ſame ſtone depart from the ſame place, <lb></lb>and it, according to what hath been premiſed, ſhall ſtill take up <lb></lb>the time of two pulſes in its fall, in which time the ſhip will have <lb></lb>run, ſuppoſe, twenty yards; To that the true motion of the ſtone <lb></lb>will be a tranſverſe line, conſiderably longer than the firſt ſtraight <lb></lb>and perpendicular line, which is the length of the ^{*} Maſt, and yet <lb></lb><arrow.to.target n="marg322"></arrow.to.target> <lb></lb>nevertheleſs the ^{*} ſtone will have paſt it in the ſame time. </s><s>Let <lb></lb>it be farther ſuppoſed, that the Ships motion is much more accele <lb></lb>rated, ſo that the ſtone in falling ſhall be to paſs a tranſverſe line <lb></lb>much longer than the other; and in ſum, increaſing the Ships ve <lb></lb><arrow.to.target n="marg323"></arrow.to.target> <lb></lb>locity as much as you will, the falling ſtone ſhall deſcribe its tranſ <lb></lb>verſe lines ſtill longer and longer, and yet ſhall paſs them all in <lb></lb>thoſe ſelf ſame two pulſes. </s><s>And in this faſhion, if a Canon were <pb xlink:href="040/01/154.jpg" pagenum="136"></pb>level'd on the top of a Tower, and ſhots were made therewith <lb></lb>point blank, that is, paralel to the Horizon, let the Piece have a <lb></lb>greater or leſs charge, ſo as that the ball may fall ſometimes a <lb></lb>thouſand yards diſtant, ſometimes four thouſand, ſometimes ſix, <lb></lb>ſometimes ten, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> and all theſe ſhots ſhall curry or finiſh their <lb></lb>ranges in times equal to each other, and every one equal to the <lb></lb>time which the ball would take to paſs from the mouth of the <lb></lb>Piece to the ground, being left, without other impulſe, to fall <lb></lb>ſimply downwards in a perpendicular line. </s><s>Now it ſeems a very <lb></lb>admirable thing, that in the ſame ſhort time of its falling perpen <lb></lb>dicularly down to the ground, from the height of, ſuppoſe, an <lb></lb>hundred yards, the ſame ball, being thruſt violently out of the <lb></lb>Piece by the Fire, ſhould be able to paſs one while four hundred, <lb></lb>another while a thouſand, another while four, another while ten <lb></lb>thouſand yards, ſo as that the ſaid ball in all ſhots made point <lb></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"></emph>An admirable <lb></lb>accident in the mo <lb></lb>tion of projects.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg322"></margin.target>*By the length of <lb></lb>the maſt he means <lb></lb>the diſtance be <lb></lb>tween the upper <lb></lb>deck and Round <lb></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 conſideration for its novelty is very pretty, and if <lb></lb>the effect be true, very admirable: and of the truth thereof, I <lb></lb>make no queſtion: and were it not for the accidental impediment <lb></lb>of the air, I verily believe, that, if at the time of the balls going <lb></lb>out of the Piece, another were let fall from the ſame height di <lb></lb>rectly downwards, they would both come to the ground at the <lb></lb>ſame inſtant, though that ſhould have curried ten thouſand <lb></lb>miles in its range, and this but an hundred onely: preſuppoſing <lb></lb>the ſurface of the Earth to be equal, which to be aſſured of, the <lb></lb>experiment may be made upon ſome lake. </s><s>As for the impediment <lb></lb>which might come from the air, it would conſiſt in retarding the <lb></lb>extreme ſwift motion of the ſhot. </s><s>Now, if you think fit, we will <lb></lb>proceed to the ſolution of the other Objections, ſeeing that <emph type="italics"></emph>Sim <lb></lb>plicius<emph.end type="italics"></emph.end> (as far as I can ſee) is convinc'd of the nullity of this firſt, <lb></lb>taken from things falling from on high downwards.</s></p><p type="main"><s>SIMP. </s><s>I find not all my ſcruples removed, but it may be the <lb></lb>fault is my own, as not being of ſo eaſie and quick an apprehenſion <lb></lb>as <emph type="italics"></emph>Sagredus.<emph.end type="italics"></emph.end> And it ſeems to me, that if this motion, of which <lb></lb>the ſtone did partake whilſt it was on the Round-top of the Ships <lb></lb>Maſt, be, as you ſay, to conſerve it ſelf indelibly in the ſaid ſtone, <lb></lb>even after it is ſeparated from the Ship, it would follow, that like <lb></lb>wiſe in caſe any one, riding a horſe that was upon his ſpeed, ſhould <lb></lb>let a bowl drop out of his hand, that bowl being fallen to the <lb></lb>ground would continue its motion and follow the horſes ſteps, <lb></lb>without tarrying behind him: the which effect, I believe, is not <lb></lb>to be ſeen, unleſs when he that is upon the horſe ſhould throw it <lb></lb>with violence that way towards which he runneth; but otherwiſe, <lb></lb>I believe it will ſtay on the ground in the ſame place where it <lb></lb>fell.</s></p> <pb xlink:href="040/01/155.jpg" pagenum="137"></pb><p type="main"><s>SALV. </s><s>I believe that you very much deceive your ſelf, and am <lb></lb>certain, that experience will ſhew you the contrary, and that the ball <lb></lb>being once arrived at the ground, will run together with the horſe, <lb></lb>not ſtaying behind him, unleſs ſo far as the aſperity and uneven <lb></lb>neſs of the Earth ſhall hinder it. </s><s>And the reaſon ſeems to me <lb></lb>very manifeſt: for if you, ſtanding ſtill, throw the ſaid ball a <lb></lb>long the ground, do you think it would not continue its motion <lb></lb>even after you had delivered it out of your hand? </s><s>and that for ſo <lb></lb>much a greater ſpace, by how much the ſuperficies were more <lb></lb>ſmooth, ſo that <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> 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"></emph>impetus<emph.end type="italics"></emph.end> with my <lb></lb>arm; but in the other caſe it is ſuppoſed, that he who is upon the <lb></lb>horſe, onely drops it out of his hand:</s></p><p type="main"><s>SALV. </s><s>So I deſire that it ſhould be: but when you throw it <lb></lb>with your arm, what other remaineth to the ball being once gone <lb></lb>out of your hand, than the motion received from your arm, which <lb></lb>motion being conſerved in the boul, it doth continue to carry it <lb></lb>forward? </s><s>Now, what doth it import, that that <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> be con <lb></lb>ferred on the ball rather from the arm than from the horſe? </s><s>Whilſt <lb></lb>you were on horſeback, did not your hand, and conſequently the <lb></lb>ball run as faſt as the horſe it ſelf? </s><s>Doubtleſs it did: therefore <lb></lb>in onely opening of the hand, the ball departs with the motion al <lb></lb>ready conceived, not from your arm, by your particular motion, <lb></lb>but from the motion dependant on the ſaid horſe, which cometh to <lb></lb>be communicated to you, to your arm, to your hand, and laſtly to <lb></lb>the ball. </s><s>Nay, I will tell you farther, that if the rider upon his <lb></lb>ſpeed fling the ball with his arm to the part contrary to the courſe, <lb></lb>it ſhall, after it is fallen to the ground, ſometimes (albeit thrown to <lb></lb>the contrary part) follow the courſe of the horſe, and ſometimes lie <lb></lb>ſtill on the ground; and ſhall onely move contrary to the ſaid <lb></lb>courſe, when the motion received from the arm, ſhall exceed that <lb></lb>of the carrier in velocity. </s><s>And it is a vanity, that of ſome, who <lb></lb>ſay that a horſeman is able to caſt a javelin thorow the air, that <lb></lb>way which the horſe runs, and with the horſe to follow and over <lb></lb>take the ſame; and laſtly, to catch it again. </s><s>It is, I ſay, a vanity, <lb></lb>for that to make the project return into the hand, it is requiſite to <lb></lb>caſt it upwards, in the ſame manner as if you ſtood ſtill. </s><s>For, let <lb></lb>the carrier be never ſo ſwift, provided it be uniform, and the pro <lb></lb>ject not over-light, it ſhall always fall back again into the hand of <lb></lb>the projicient, though never ſo high thrown.</s></p><p type="main"><s>SAGR. </s><s>By this Doctrine I come to know ſome Problems very <lb></lb><arrow.to.target n="marg324"></arrow.to.target> <lb></lb>curious upon this ſubject of projections; the firſt of which muſt <lb></lb>ſeem very ſtrange to <emph type="italics"></emph>Simplicius.<emph.end type="italics"></emph.end> And the Problem is this; I af <lb></lb>firm it to be poſſible, that the ball being barely dropt or let fall, <lb></lb>by one that any way runneth very ſwiftly, being arrived at the <pb xlink:href="040/01/156.jpg" pagenum="138"></pb>Earth, doth not onely follow the courſe of that perſon, but doth <lb></lb>much out go him. </s><s>Which Problem is connexed with this, that <lb></lb>the moveable being thrown by the projicient above the plane of <lb></lb>the Horizon, may acquire new velocity, greater by far than that <lb></lb>confer'd upon it by the projicient. </s><s>The which effect I have with <lb></lb>admiration obſerved, in looking upon thoſe who uſe the ſport of <lb></lb>tops, which, ſo ſoon as they are ſet out of the hand, are ſeen to <lb></lb>move in the air with a certain velocity, the which they afterwards <lb></lb>much encreaſe at their coming to the ground; and if whipping <lb></lb>them, they rub at any uneven place that makes them skip on high, <lb></lb>they are ſeen to move very ſlowly through the air, and falling a <lb></lb>gain to the Earth, they ſtill come to move with a greater velocity: <lb></lb>But that which is yet more ſtrange, I have farther obſerved, that <lb></lb>they not onely turn always more ſwiftly on the ground, than in <lb></lb>the air, but of two ſpaces both upon the Earth, ſometimes a mo <lb></lb>tion in the ſecond ſpace is more ſwift than in the firſt. </s><s>Now what <lb></lb>would <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> ſay to this?</s></p><p type="margin"><s><margin.target id="marg324"></margin.target><emph type="italics"></emph>Sundry curious <lb></lb>Problems, touch <lb></lb>ing the motions of <lb></lb>projects.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>He would ſay in the firſt place, that he had never made <lb></lb>ſuch an obſervation. </s><s>Secondly, he would ſay, that he did not be <lb></lb>lieve the ſame. </s><s>He would ſay again, in the third place, that if <lb></lb>you could aſſure him thereof, and demonſtratively convince him of <lb></lb>the ſame, 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></lb>ones. </s><s>But that I may make you underſtand this particular, you <lb></lb>muſt know, that if a perſon apprehend not a truth of himſelf, it <lb></lb>is impoſſible that others ſhould make him underſtand it: I may in <lb></lb>deed inſtruct you in thoſe things which are neither true nor falſe; <lb></lb>but the true, that is, the neceſſary, namely, ſuch as it is impoſſible <lb></lb>ſhould be otherwiſe, every common capacity either comprehendeth <lb></lb>them of himſelf, or elſe it is impoſſible he ſhould ever know them. <lb></lb></s><s>And of this opinion I am confident is <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> alſo: and there <lb></lb>fore I tell you, that the reaſons of the preſent Problems are known <lb></lb>by you, but it may be, not apprehended.</s></p><p type="main"><s>SIMP. </s><s>Let us, for the preſent, paſs by that controverſie, and <lb></lb>permit me to plead ignorance of theſe things you ſpeak of, and try <lb></lb>whether you can make me capable of underſtanding theſe Pro <lb></lb>blems.</s></p><p type="main"><s>SAGR. </s><s>This firſt dependeth upon another, which is, Whence <lb></lb>cometh it, that ſetting a top with the laſh, it runneth farther, and <lb></lb>conſequently with greater force, than when its ſet with the fin <lb></lb>gers?</s></p><p type="main"><s>SIMP. <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> alſo makes certain Problems about theſe kinds <lb></lb>of projects.</s></p><p type="main"><s>SALV. </s><s>He doth ſo; and very ingenious they are: particular <lb></lb>ly, That, Whence it cometh to paſs that round tops run better than <lb></lb>the ſquare?</s></p> <pb xlink:href="040/01/157.jpg" pagenum="139"></pb><p type="main"><s>SAGR. </s><s>And cannot you, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> give a reaſon for this, <lb></lb>without others prompting you?</s></p><p type="main"><s>SIMP. </s><s>Very good, I can ſo; but leave your jeering.</s></p><p type="main"><s>SAGR. </s><s>In like manner you do know the reaſon of this other <lb></lb>alſo. </s><s>Tell me therefore; know you that a thing which moveth, <lb></lb>being impeded ſtands ſtill?</s></p><p type="main"><s>SIMP. </s><s>I know it doth, if the impediment be ſo great as to <lb></lb>ſuffice.</s></p><p type="main"><s>SAGR. </s><s>Do you know, that moving upon the Earth is a greater <lb></lb>impediment to the moveable, than moving in the air, the Earth be <lb></lb>ing rough and hard, and the air ſoft and yielding?</s></p><p type="main"><s>SIMP. </s><s>And knowing this, I know that the top will turn faſter <lb></lb>in the air, than on the ground, ſo that my knowledg is quite con <lb></lb>trary to what you think it.</s></p><p type="main"><s>SAGR. </s><s>Fair and ſoftly, <emph type="italics"></emph>Simplicius.<emph.end type="italics"></emph.end> You know that in the <lb></lb>parts of a moveable, that turneth about its centre, there are found <lb></lb>motions towards all ſides; ſo that ſome aſcend, others deſcend; <lb></lb>ſome go forwards, others backwards?</s></p><p type="main"><s>SIMP. </s><s>I know it, and <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> taught me the ſame.</s></p><p type="main"><s>SAGR. </s><s>And with what demonſtration, I pray you?</s></p><p type="main"><s>SIMP. </s><s>With that of ſenſe.</s></p><p type="main"><s>SAGR. <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> then, hath made you ſee that which without <lb></lb>him you would not have ſeen? </s><s>Did he ever lend you his eyes? <lb></lb></s><s>You would ſay, that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> hath told, advertiſed, remembered <lb></lb>you of the ſame; and not taught you it. </s><s>When then a top, with <lb></lb>out changing place, turns round, (or in the childrens phraſe, ſleep <lb></lb>eth) not paralel, but erect to the Horizon, ſome of its parts aſcend, <lb></lb>and the oppoſite deſcend; the ſuperiour go one way, the infe <lb></lb>riour another. </s><s>Fancie now to your ſelf, a top, that without chan <lb></lb>ging place, ſwiftly turns round in that manner, and ſtands ſuſpen <lb></lb>ded in the air, and that in that manner turning, it be let fall to the <lb></lb>Earth perpendicularly, do you believe, that when it is arrived at <lb></lb>the ground, it will continue to turn round in the ſame manner, <lb></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 faſt.</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></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 uppermoſt, which <lb></lb>do move contrary to the inferiour; therefore you muſt inſtance <lb></lb>which it ſhall obey: for as to the parts aſcending and deſcending, <lb></lb>the one kind will not yield to the other; nor will they all go <lb></lb>downwards, being hindered by the Earth, nor upwards as being <lb></lb>heavy.</s></p> <pb xlink:href="040/01/158.jpg" pagenum="140"></pb><p type="main"><s>SIMP. </s><s>The top will run reeling along the floor towards that <lb></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></lb>thoſe which touch the ground?</s></p><p type="main"><s>SIMP. </s><s>Becauſe thoſe upon the ground happen to be impeded <lb></lb>by the roughneſs of the touch, that is, by the floors unevenneſs; <lb></lb>but the ſuperiour, which are in the tenuous and flexible air, are <lb></lb>hindred very little, if at all; and therefore the top will obey their <lb></lb>inclination.</s></p><p type="main"><s>SAGR. </s><s>So that that taction, if I may ſo ſay, of the neither <lb></lb>parts on the floor, is the cauſe that they ſtay, and onely the upper <lb></lb>parts ſpring the top forward.</s></p><p type="main"><s>SALV. </s><s>And therefore, if the top ſhould fall upon the ice, or <lb></lb>other very ſmooth ſuperficies, it would not ſo well run forward, but <lb></lb>might peradventure continue to revolve in it ſelf, (or ſleep) with <lb></lb>out acquiring any progreſſive motion.</s></p><p type="main"><s>SAGR. </s><s>It is an eaſie thing for it ſo to do; but yet neverthe <lb></lb>leſs, it would not ſo ſpeedily come to ſleep, as when it falleth on <lb></lb>a ſuperficies ſomewhat rugged. </s><s>But tell me, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> when <lb></lb>the top turning round about it ſelf, in that manner, is let fall, why <lb></lb>doth it not move forwards in the air, as it doth afterwards when it <lb></lb>is upon the ground?</s></p><p type="main"><s>SIMP. </s><s>Becauſe having air above it, and beneath, neither thoſe <lb></lb>parts, nor theſe have any where to touch, and not having more oc <lb></lb>caſion to go forward than backward, it falls perpendicularly.</s></p><p type="main"><s>SAGR. </s><s>So then the onely reeling about its ſelf, without other <lb></lb><emph type="italics"></emph>impetus,<emph.end type="italics"></emph.end> can drive the top forward, being arrived at the ground, <lb></lb>very nimbly. </s><s>Now proceed we to what remains. </s><s>That laſh, <lb></lb>which the driver tyeth to his Top-ſtick, and with which, winding <lb></lb>it about the top, he ſets it (<emph type="italics"></emph>i. </s><s>e.<emph.end type="italics"></emph.end> makes it go) what effect hath it on <lb></lb>the ſaid top?</s></p><p type="main"><s>SIMP. </s><s>It conſtrains it to turn round upon its toe, that ſo it may <lb></lb>free it ſelf from the Top-laſh.</s></p><p type="main"><s>SAGR. </s><s>So then, when the top arriveth at the ground, it cometh <lb></lb>all the way turning about its ſelf, by means of the laſh. </s><s>Hath it <lb></lb>not reaſon then to move in it ſelf more ſwiftly upon the ground, <lb></lb>than it did whilſt it was in the air?</s></p><p type="main"><s>SIMP. </s><s>Yes doubtleſs; for in the air it had no other impulſe <lb></lb>than that of the arm of the projicient; and if it had alſo the reel <lb></lb>ing, this (as hath been ſaid) in the air drives it not forward at all: <lb></lb>but arriving at the floor, to the motion of the arm is added the <lb></lb>progreſſion of the reeling, whereby the velocity is redoubled. </s><s>And <lb></lb>I know already very well, that the top skipping from the ground, <lb></lb>its velocity will deminiſh, becauſe the help of its circulation is <lb></lb>wanting; and returning to the Earth will get it again, and by that <pb xlink:href="040/01/159.jpg" pagenum="141"></pb>means move again faſter, than in the air. </s><s>It onely reſts for me to <lb></lb>underſtand, whether in this ſecond motion on the Earth it move <lb></lb>more ſwiftly, than in the firſt; for then it would move <emph type="italics"></emph>in infini <lb></lb>tum,<emph.end type="italics"></emph.end> alwayes accelerating.</s></p><p type="main"><s>SAGR. </s><s>I did not abſolutely affirm, that this ſecond motion is <lb></lb>more ſwift than the firſt; but that it may happen ſo to be ſome <lb></lb>times.</s></p><p type="main"><s>SIMP. </s><s>This is that, which I apprehend not, and which I <lb></lb>deſire to know.</s></p><p type="main"><s>SAGR. </s><s>And this alſo you know of your ſelf. </s><s>Therefore tell <lb></lb>me: When you let the top fall out of your hand, without ma <lb></lb>king it turn round (<emph type="italics"></emph>i. </s><s>e.<emph.end type="italics"></emph.end> ſetting it) what will it do at its coming to <lb></lb>the ground?</s></p><p type="main"><s>SIMP. Nothing, but there lie ſtill.</s></p><p type="main"><s>SAGR. </s><s>May it not chance, that in its fall to the ground it may <lb></lb>acquire a motion? </s><s>Think better on it.</s></p><p type="main"><s>SIMP. </s><s>Unleſſe we let it fall upon ſome inclining ſtone, as <lb></lb>children do playing at ^{*} <emph type="italics"></emph>Chioſa,<emph.end type="italics"></emph.end> and that falling ſide-wayes upon </s></p><p type="main"><s><arrow.to.target n="marg326"></arrow.to.target> <lb></lb>the ſame, it do acquire the motion of turning round upon its toe, <lb></lb>wherewith it afterwards continueth to move progreſſively on the <lb></lb>floor, I know not in what other manner it can do any thing but <lb></lb>lie ſtill where it falleth.</s></p><p type="margin"><s><margin.target id="marg326"></margin.target>* A Game in <emph type="italics"></emph>Italy,<emph.end type="italics"></emph.end> <lb></lb>which is, to glide <lb></lb>bullets down an <lb></lb>inclining ſtone, <lb></lb><emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>You ſee then that in ſome caſe it may acquire a new <lb></lb>revolution. </s><s>When then the top jerked up from the ground, falleth <lb></lb>down again, why may it not caſually hit upon the declivity of <lb></lb>ſome ſtone fixed in the floor, and that hath an inclination that <lb></lb>way towards which it moveth, and acquiring by that ſlip a new <lb></lb>whirle over and above that conferred by the laſh, why may it <lb></lb>not redouble its motion, and make it ſwifter than it was at its <lb></lb>firſt lighting upon the ground?</s></p><p type="main"><s>SIMP. </s><s>Now I ſee that the ſame may eaſily happen. </s><s>And I <lb></lb>am thinking that if the top ſhould turn the contrary way, in ar <lb></lb>riving at the ground, it would work a contrary effect, that is, <lb></lb>the motion of the accidental whirl would retard that of the pro <lb></lb>jicient.</s></p><p type="main"><s>SAGR. </s><s>And it would ſometimes wholly retard and ſtop it, in <lb></lb>caſe the revolution of the top were very ſwift. </s><s>And from hence a <lb></lb>riſeth the reſolution of that ſlight, which the more skilful Tennis <lb></lb>Players uſe to their advantage; that is, to gull their adverſary by <lb></lb>cutting (for ſo is their Phraſe) the Ball; which is, to return it <lb></lb>with a ſide Rachet, in ſuch a manner, that it doth thereby ac <lb></lb>quire a motion by it ſelf contrary to the projected motion, and ſo <lb></lb>by that means, at its coming to the ground, the rebound, which <lb></lb>if the ball did not turn in that manner, would be towards the <lb></lb>adverſary, giving him the uſual time to toſſe it back again, doth <pb xlink:href="040/01/160.jpg" pagenum="142"></pb>fail, and the ball runs tripping along the ground, or rebounds leſſe <lb></lb>than uſual, and breaketh the time of the return. </s><s>Hence it is <lb></lb><arrow.to.target n="marg327"></arrow.to.target> <lb></lb>that you ſee, thoſe who play at ^{*} Stool-ball, when they play in <lb></lb>a ſtony way, or a place full of. </s><s>holes and rubs that make the ball <lb></lb>trip an hundred ſeveral wayes, never ſuffering it to come neer the <lb></lb>mark, to avoid them all, they do not trundle the ball upon the <lb></lb>ground, but throw it, as if they were to pitch a quait. </s><s>But be <lb></lb>cauſe in throwing the ball, it iſſueth out of the hand with ſome <lb></lb>roling conferred by the fingers, when ever the hand is under the <lb></lb>ball, as it is moſt commonly held; whereupon the ball in its lighting <lb></lb>on the ground neer to the mark, between the motion of the pro <lb></lb>jicient and that of the roling, would run a great way from the <lb></lb>ſame: To make the ball ſtay, they hold it artificially, with their <lb></lb>hand uppermoſt, and it undermoſt, which in its delivery hath <lb></lb>a contrary twirl or roling conferred upon it by the fingers, by <lb></lb>means whereof in its coming to the ground neer the mark it ſtays <lb></lb>there, or runs very very little forwards. </s><s>But to return to our <lb></lb>principal problem which gave occaſion for ſtarting theſe others; I <lb></lb>ſay it is poſſible that a perſon carried very ſwiftly, may let a ball <lb></lb>drop out of his hand, that being come to the Earth, ſhall not <lb></lb>onely follow his motion, but alſo out-go it, moving with a great <lb></lb>er velocity. </s><s>And to ſee ſuch an effect, I deſire that the courſe <lb></lb>may be that of a Chariot, to which on the out-ſide let a decli <lb></lb>ning board be faſtened; ſo as that the neither part may be towards <lb></lb>the horſes, and the upper towards the hind Wheel. </s><s>Now, if in <lb></lb>the Chariots full career, a man within it, let a ball fall gliding a <lb></lb>long the declivity of that board, it ſhall in roling downward ac <lb></lb>quire a particular <emph type="italics"></emph>vertigo<emph.end type="italics"></emph.end> or turning, the which added to the <lb></lb>motion impreſſed by the Chariot, will carrie the ball along the <lb></lb>ground much faſter than the Chariot. </s><s>And if one accommodate <lb></lb>another declining board over againſt it, the motion of the Cha <lb></lb>riot may be qualified ſo, that the ball, gliding downwards along <lb></lb>the board, in its coming to the ground ſhall reſt immoveable, <lb></lb>and alſo ſhall ſometimes run the contrary way to the Chariot. </s><s>But <lb></lb>we are ſtrayed too far from the purpoſe, therefore if <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> <lb></lb>be ſatisfied with the reſolution of the firſt argnment againſt the <lb></lb>Earths mobility, taken from things falling perpendicularly, we <lb></lb>may paſſe to the reſt</s></p><p type="margin"><s><margin.target id="marg327"></margin.target>*A Game in <emph type="italics"></emph>Italy,<emph.end type="italics"></emph.end> <lb></lb>wherein they ſtrive <lb></lb>who ſhall trundle <lb></lb>or throw a wooden <lb></lb>bowle neereſt to an <lb></lb>aſſigned mark.</s></p><p type="main"><s>SALV. </s><s>The digreſſions made hitherto, are not ſo alienated <lb></lb>from the matter in hand, as that one can ſay they are wholly <lb></lb>ſtrangers to it. </s><s>Beſides theſe argumentations depend on thoſe <lb></lb>things that ſtart up in the fancy not of one perſon, but of three, <lb></lb>that we are: And moreover we diſcourſe for our pleaſure, nor <lb></lb>are we obliged to that ſtrictneſſe of one who <emph type="italics"></emph>ex profeſſo<emph.end type="italics"></emph.end> treateth <lb></lb>methodically of an argument, with an intent to publiſh the ſame. <pb xlink:href="040/01/161.jpg" pagenum="143"></pb>I will not conſent that our Poem ſhould be ſo confined to that <lb></lb>unity, as not to leave us fields open for Epſody's, which every <lb></lb>ſmall connection ſhould ſuffice to introduce; but with almoſt as <lb></lb>much liberry as if we were met to tell ſtories, it ſhall be lawful <lb></lb>for me to ſpeak, what ever your diſcourſe brings into my mind.</s></p><p type="main"><s>SAGR. </s><s>I like this motion very well; and ſince we are at this <lb></lb>liberty, let me take leave, before we paſſe any farther to ask of <lb></lb>you <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> whether you did ever conſider what that line may <lb></lb>be that is deſcribed by the grave moveable naturally falling down <lb></lb>from the top of a Tower; and if you have reflected on it, be <lb></lb>pleaſed to tell me what you think thereof.</s></p><p type="main"><s>SALV. </s><s>I have ſometimes conſidered of it, and make no que <lb></lb>ſtion, that if one could be certain of the nature of that motion <lb></lb>wherewith the grave body deſcendeth to approach the centre of <lb></lb>the Terreſtrial Globe, mixing it ſelf afterwards with the common <lb></lb>circular motion of the diurnal converſion; it might be exactly <lb></lb>found what kind of line that is, that the centre of gravity of the <lb></lb>moveable deſcribeth in thoſe two motions.</s></p><p type="main"><s>SAGR. </s><s>Touching the ſimple motion towards the centre de <lb></lb>pendent on the gravity, I think that one may confidently, with <lb></lb>out error, believe that it is by a right line, as it would be, were <lb></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></lb>experience rendereth us certain of the ſame.</s></p><p type="main"><s>SAGR. </s><s>But how doth experience aſſure us thereof, if we ne <lb></lb>ver ſee any motions but ſuch as are compoſed of the two, circular <lb></lb>and deſcending.</s></p><p type="main"><s>SALV. </s><s>Nay rather <emph type="italics"></emph>Sagredus<emph.end type="italics"></emph.end> we onely ſee the ſimple motion of <lb></lb>deſcent; ſince that other circular one common to the Earth, the <lb></lb>Tower and our ſelves remains imperceptible, and as if it never <lb></lb>were, and there remaineth perceptible to us that of the ſtone, one <lb></lb>ly not participated by us, and for this, ſenſe demonſtrateth that <lb></lb>it is by a right line, ever parallel to the ſaid Tower, which is <lb></lb>built upright and perpendicular upon the Terreſtrial ſurface.</s></p><p type="main"><s>SAGR. </s><s>You are in the right; and this was but too plainly de <lb></lb>monſtrated to me even now, ſeeing that I could not remember ſo <lb></lb>eaſie a thing; but this being ſo manifeſt, what more is it that you <lb></lb>ſay you deſire, for underſtanding the nature of this motion <lb></lb>downwards?</s></p><p type="main"><s>SALV. </s><s>It ſufficeth not to know that it is ſtreight, but its requi <lb></lb>ſite to know whether it be uniform, or irregular; that is, whe <lb></lb>ther it maintain alwayes one and the ſame velocity, or elſe goeth <lb></lb>retarding or accelerating.</s></p><p type="main"><s>SAGR. </s><s>It is already clear, that it goeth continually accelle <lb></lb>rating.</s></p> <pb xlink:href="040/01/162.jpg" pagenum="144"></pb><p type="main"><s>SALV. </s><s>Neither doth this ſuffice, but its requiſite to know ac <lb></lb>cording to what proportion ſuch accelleration is made; a Pro <lb></lb>blem, that I believe was never hitherto underſtood by any Phi <lb></lb>loſopher or Mathematician; although Philoſophers, and particu <lb></lb>larly the <emph type="italics"></emph>Peripateticks,<emph.end type="italics"></emph.end> have writ great and entire Volumes, <lb></lb>touching motion.</s></p><p type="main"><s>SIMP. </s><s>Philoſophers principally buſie themſelves about univer <lb></lb>ſals; they find the definitions and more common ſymptomes, o <lb></lb>mitting certain ſubtilties and niceties, which are rather curio <lb></lb>ſities to the Mathematicians. </s><s>And <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> did content himſelf <lb></lb>to deſine excellently what motion was in general; and of the lo <lb></lb>cal, to ſhew the principal qualities, to wit, that one is natural, <lb></lb>another violent; one is ſimple, another compound; one is <lb></lb>equal, another accellerate; and concerning the accelerate, con <lb></lb>tents himſelf to give the reaſon of acceleration, remitting the <lb></lb>finding out of the proportion of ſuch acceleration, and other <lb></lb>particular accidents to the Mechanitian, or other inferiour <lb></lb>Artiſt.</s></p><p type="main"><s>SAGR. </s><s>Very well <emph type="italics"></emph>Simplicius.<emph.end type="italics"></emph.end> But you <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> when you <lb></lb>deſcend ſometimes from the Throne of <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> Majeſty, <lb></lb>have you ever thrown away any of your hours in ſtudying to find <lb></lb>this proportion of the acceleration of the motion of deſcending <lb></lb>grave bodies?</s></p><p type="main"><s>SALV. </s><s>There was no need that I ſhould ſtudy for it, in regard <lb></lb>that the Academick our common friend, heretofore ſhewed me a <lb></lb>Treatiſe of his ^{*} <emph type="italics"></emph>De Motu,<emph.end type="italics"></emph.end> where this, and many other acci <lb></lb><arrow.to.target n="marg328"></arrow.to.target> <lb></lb>dents were demonſtrated. </s><s>But it would be too great a digreſſion, <lb></lb>if for this particular, we ſhould interrupt our preſent diſcourſe, <lb></lb>(which yet it ſelf is alſo no better than a digreſſion) and make as <lb></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></lb>cellent tract which <lb></lb>we give the firſt <lb></lb>place in our ſecond <lb></lb>Volume.</s></p><p type="main"><s>SAGR. </s><s>I am content to excuſe you from this narration for the <lb></lb>preſent, provided that this may be one of the Propoſitions reſer <lb></lb>ved to be examined amongſt the reſt in another particular meeting, <lb></lb>for that the knowledg thereof is by me very much deſired; and <lb></lb>in the mean time let us return to the line deſcribed by the grave <lb></lb>body in its fall from the top of the Tower to its baſe.</s></p><p type="main"><s>SALV. </s><s>If the right motion towards the centre of the Earth was <lb></lb>uniforme, the circular towards the Eaſt being alſo uniforme, you <lb></lb>would ſee compoſed of them both a motion by a ſpiral line, of <lb></lb>that kind with thoſe defined by <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> in his Book <emph type="italics"></emph>Dc Spira <lb></lb>libus<emph.end type="italics"></emph.end>; which are, when a point moveth uniformly upon a right <lb></lb>line, whileſt that line in the mean time turneth uniformly about <lb></lb>one of its extreme points fixed, as the centre of his gyration. <lb></lb></s><s>But becauſe the right motion of grave bodies falling, is continu <lb></lb>ally accelerated, it is neceſſary, that the line reſulting of the <pb xlink:href="040/01/163.jpg" pagenum="145"></pb>compoſition of the two motions do go alwayes receding with <lb></lb>greater and greater proportion from the circumference of that cir <lb></lb>cle, which the centre of the ſtones gravity would have deſigned, <lb></lb>if it had alwayes ſtaid upon the Tower; it followeth of neceſſity <lb></lb>that this receſſion at the firſt be but little, yea very ſinall, yea, <lb></lb>more, as ſmall as can be imagined, ſeeing that the deſcending <lb></lb>grave body departing from reſt, that is, from the privation of <lb></lb>motion, towards the bottom and entring into the right motion <lb></lb>downwards, it muſt needs paſſe through all the degrees of tardi <lb></lb>ty, that are betwixt reſt, and any aſſigned velocity; the which <lb></lb>degrees are infinite; as already hath been at large diſcourſed and <lb></lb>proved.</s></p><p type="main"><s>It being ſuppoſed therefore, that the progreſſe of the accele <lb></lb>ration being after this manner, and it being moreover true, that <lb></lb>the deſcending grave body goeth to terminate in the centre of the <lb></lb>Earth, it is neceſſary that the line of its mixt motion be ſuch, that <lb></lb><arrow.to.target n="marg329"></arrow.to.target> <lb></lb>it go continually receding with greater and greater proportion <lb></lb>from the top of the Tower, or to ſpeak more properly, from <lb></lb>the circumference of the circle deſcribed by the top of the Tower, <lb></lb>by means of the Earths converſion; but that ſuch receſſions be <lb></lb>leſſer and leſſer <emph type="italics"></emph>in infinitum<emph.end type="italics"></emph.end>; by how much the moveable finds it <lb></lb>ſelf to be leſſe and leſſe removed from the firſt term where it <lb></lb>reſted. </s><s>Moreover it is neceſſary, that this line of the compound <lb></lb>ed motion do go to terminate in the centre of the Earth. </s><s>Now <lb></lb>having preſuppoſed theſe two things, I come to deſcribe about <lb></lb>the centre A [<emph type="italics"></emph>in Fig. </s><s>1. of this ſecond Dialogue<emph.end type="italics"></emph.end>;] with the ſemi <lb></lb>diameter A B, the circle B I, repreſenting to me the Terreſtrial <lb></lb>Globe, and prolonging the ſemidiameter A B to C, I have de <lb></lb>ſcribed the height of the Tower B C; the which being carried <lb></lb>about by the Earth along the circumference B I, deſcribeth with <lb></lb>its top the arch C D: Dividing, in the next place, the line C A <lb></lb>in the middle at E; upon the centre E, at the diſtance E C, I de <lb></lb>ſcribe the ſemicircle C I A: In which, I now affirm, that it is very <lb></lb>probable that a ſtone falling from the top of the Tower C, doth <lb></lb>move, with a motion mixt of the circular, which is in common, <lb></lb>and of its peculiar right motion. </s><s>If therefore in the circumference <lb></lb>C D, certain equal parts C F, F G, G H, H L, be marked, and <lb></lb>from the points F, G, H, L, right lines be drawn towards the <lb></lb>centre A, the parts of them intercepted between the two cir <lb></lb>cumferences C D and B I, ſhall repreſent unto us the ſame <lb></lb>Tower C B, tranſported by the Terreſtrial Globe towards D I; <lb></lb>in which lines the points where they come to be interſected by the <lb></lb>arch of the ſemicircle C I, are the places by whichfrom time to <lb></lb>time the falling ſtone doth paſſe; which points go continually <lb></lb>with greater and greater proportion receding from the top of the <pb xlink:href="040/01/164.jpg" pagenum="146"></pb>Tower. </s><s>And this is the cauſe why the right motion made along <lb></lb>the ſide of the Tower appeareth to us more and more accelerate. <lb></lb></s><s>It appeareth alſo, how by reaſon of the infinite acuteneſſe of <lb></lb>the contact of thoſe two circles D C, C I, the receſſion of the <lb></lb>cadent moveable from the circumference C F D; namely, from <lb></lb>the top of the Tower, is towards the beginning extream ſmall, <lb></lb>which is as much as if one ſaid its motion downwards is very ſlow, <lb></lb>and more and more ſlow <emph type="italics"></emph>in infinitum,<emph.end type="italics"></emph.end> according to its vicinity to <lb></lb>the term C, that is to the ſtate of reſt. </s><s>And laſtly it is ſeen how <lb></lb>in the end this ſame motion goeth to terminate in the centre of the <lb></lb>Earth A.</s></p><p type="margin"><s><margin.target id="marg329"></margin.target><emph type="italics"></emph>The line deſcri <lb></lb>bed by a moveable <lb></lb>in its natural de <lb></lb>ſcent, the motion <lb></lb>of the Earth a <lb></lb>bout its own centre <lb></lb>being preſuppoſed, <lb></lb>would probably be <lb></lb>the circumference <lb></lb>of a circle.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I underſtand all this very well, nor can I perſwade my <lb></lb>ſelf that the falling moveable doth deſcribe with the centre of its <lb></lb>gravity any other line, but ſuch an one as this.</s></p><p type="main"><s>SALV. </s><s>But ſtay a little <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> for I am to acquaint you <lb></lb>alſo with three Obſervations of mine, that its poſſible will not diſ <lb></lb><arrow.to.target n="marg330"></arrow.to.target> <lb></lb>pleaſe you. </s><s>The firſt of which is, that if we do well conſider, the <lb></lb>moveable moveth not really with any more than onely one motion <lb></lb>ſimply circular, as when being placed upon the Tower, it moved <lb></lb>with one ſingle and circular motion. </s><s>The ſecond is yet more plea <lb></lb><arrow.to.target n="marg331"></arrow.to.target> <lb></lb>ſant; for, it moveth neither more nor leſſe then if it had ſtaid con <lb></lb>tinually upon the Tower, being that to the arches C F, F G, G H, <lb></lb>&c. </s><s>that it would have paſſed continuing alwayes upon the Tower, <lb></lb>the arches of the circumference C I are exactly equal, anſwering <lb></lb>under the ſame C F, F G, G H, &c. </s><s>Whence followeth the third <lb></lb><arrow.to.target n="marg332"></arrow.to.target> <lb></lb>wonder, That the true and real motion of the ſtone is never acce <lb></lb>lerated, but alwayes even and uniforme, ſince that all the equal ar <lb></lb>ches noted in the circumference C D, and their reſpondent ones <lb></lb>marked in the circumference C I, are paſt in equal times; ſo that <lb></lb>we are left at liberty to ſeek new cauſes of acceleration, or of o <lb></lb>ther motions, ſeeing that the moveable, as well ſtanding upon the <lb></lb>Tower, as deſcending thence, alwayes moveth in the ſame faſhion, <lb></lb>that is, circularly, with the ſame velocity, and with the ſame uni <lb></lb>formity. </s><s>Now tell me what you think of this my fantaſtical con <lb></lb>jecture.</s></p><p type="margin"><s><margin.target id="marg330"></margin.target><emph type="italics"></emph>A moveable fal <lb></lb>ting from the top of <lb></lb>the Tower, moveth <lb></lb>in the circumfe <lb></lb>rence of a circle.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg331"></margin.target><emph type="italics"></emph>It moveth neither <lb></lb>more nor leſſe, than <lb></lb>if it had ſtaid al <lb></lb>wayes there.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg332"></margin.target><emph type="italics"></emph>It moveth with <lb></lb>an uniform, not <lb></lb>an accelerate mo <lb></lb>tion.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I muſt tell you, that I cannot with words ſufficiently <lb></lb>expreſſe how admirable it ſeemeth to me; and for what at pre <lb></lb>ſent offereth it ſelf to my underſtanding, I cannot think that the <lb></lb>buſineſs happeneth otherwiſe; and would to God that all the <lb></lb>demonſtrations of Philoſophers were but half ſo probable as this. <lb></lb></s><s>However for my perfect ſatisfaction I would gladly hear how you <lb></lb>prove thoſe arches to be equal.</s></p><p type="main"><s>SALV. </s><s>The demonſtration is moſt eaſie. </s><s>Suppoſe to your ſelf <lb></lb>a line drawn from I to E. </s><s>And the Semidiameter of the circle CD, <lb></lb>that is, the line C A, being double the Semidiameter C E of the <pb xlink:href="040/01/165.jpg" pagenum="147"></pb>circle C I, the circumference ſhall be double to the circumference, <lb></lb>and every arch of the greater circle double to every like arch of <lb></lb>the leſſer; and conſequently, the half of the arch of the greater <lb></lb>circle, equal to the whole arch of the leſſe. </s><s>And becauſe the an <lb></lb>gle C E I made in the centre E of the leſſer circle, and which inſi <lb></lb>ſteth upon the arch C I, is double the angle C A D, made in the <lb></lb>centre A of the greater circle, to which the arch C D ſubtendeth; <lb></lb>therefore the arch C D is half of the arch of the greater circle like <lb></lb>to the arch C I, and therefore the two arches C D and C I are e <lb></lb>qual; and in the ſame manner we may demonſtrate of all their <lb></lb>parts. </s><s>But that the buſineſs, as to the motion of deſcending grave <lb></lb>bodies, proceedeth exactly thus, I will not at this time affirm; but <lb></lb>this I will ſay, that if the line deſcribed by the cadent moveable <lb></lb>be not exactly the ſame with this, it doth extream neerly reſemble <lb></lb>the ſame.</s></p><p type="main"><s>SAGR. </s><s>But I, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> am juſt now conſidering another par <lb></lb><arrow.to.target n="marg333"></arrow.to.target> <lb></lb>ticular very admirable; and this it is; That admitting theſe con <lb></lb>ſiderations, the right motion doth go wholly ^{*} mounting, and that <lb></lb><arrow.to.target n="marg334"></arrow.to.target> <lb></lb>Nature never makes uſe thereof, ſince that, even that that uſe, <lb></lb>which was from the beginning granted to it, which was of redu <lb></lb>cing the parts of integral bodies to their place, when they were <lb></lb>ſeparated from their whole, and therefore conſtituted in a depra <lb></lb>ved diſpoſition, is taken from it, and aſſigned to the circular <lb></lb>motion.</s></p><p type="margin"><s><margin.target id="marg333"></margin.target><emph type="italics"></emph>Right motion <lb></lb>ſeemeth wholly ex <lb></lb>cluded in nature.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg334"></margin.target>* Vadia del tutto a <lb></lb>monte, <emph type="italics"></emph>rendered in <lb></lb>the Latixe<emph.end type="italics"></emph.end> omni <lb></lb>no peſſum eat.</s></p><p type="main"><s>SALV. </s><s>This would neceſſarily follow, if it were concluded <lb></lb>that the Terreſtrial Globe moveth circularly; a thing, which I <lb></lb>pretend not to be done, but have onely hitherto attempted, as I <lb></lb>ſhall ſtill, to examine the ſtrength of thoſe reaſons, which have <lb></lb>been alledged by Philoſophers to prove the immobility of the <lb></lb>Earth, of which this firſt taken from things falling perpendicu <lb></lb>larly, hath begat the doubts, that have been mentioned; which <lb></lb>I know not of what force they may have ſeemed to <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end>; <lb></lb>and therefore before I paſſe to the examination of the remaining <lb></lb>arguments, it would be convenient that he produce what he hath <lb></lb>to reply to the contrary.</s></p><p type="main"><s>SIMP. </s><s>As to this firſt, I confeſſe indeed that I have heard <lb></lb>ſundry pretty notions, which I never thought upon before, and <lb></lb>in regard they are new unto me, I cannot have anſwers ſo ready <lb></lb>for them, but this argument taken from things falling perpendi <lb></lb>cularly, I eſteem it not one of the ſtrongeſt proofs of the mobi <lb></lb>lity of the Earth; and I know not what may happen touching the <lb></lb>ſhots of great Guns, eſpecially thoſe aimed contrary to the diur <lb></lb>nal motion.</s></p><p type="main"><s>SAGR. </s><s>The flying of the birds as much puzzleth me as the <lb></lb>objection of the Gun-ſhot, and all the other experiments above <pb xlink:href="040/01/166.jpg" pagenum="148"></pb>alledged. </s><s>For theſe birds which at their pleaſure flie for <lb></lb>wards and backwards, and wind to and again in a thouſand <lb></lb>faſhions, and, which more importeth, lie whole hours upon the <lb></lb>wing, theſe I ſay do not a little poſe me, nor do I ſee, how a <lb></lb>mongſt ſo many circumgyrations, they ſhould not loſe the motion <lb></lb>of the Earth, and how they ſhould be able to keep pace with <lb></lb>ſo great a velocity as that which they ſo far exceed with their flight.</s></p><p type="main"><s>SALV. </s><s>To ſpeak the truth, your ſcruple is not without reaſon, <lb></lb>and its poſſible <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> himſelf could not find an anſwer for it, <lb></lb>that was to himſelf entirely ſatisfactory; and therefore haply paſt <lb></lb>it over in ſilence albeit he was, indeed, very brief in examining <lb></lb>the other allegations of his adverſaries, I believe through his <lb></lb>height of wit, placed on greater aud ſublimer contemplations, <lb></lb>like as Lions are not much moved at the barking of little Dogs. <lb></lb></s><s>We will therefore reſerve the inſtance of birds to the laſt place, <lb></lb>and for the preſent, ſee if we can give <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> ſatisfaction in <lb></lb>the others, by ſhewing him in our wonted manner, that he him <lb></lb>ſelf hath their anſwers at hand, though upon firſt thoughts he doth <lb></lb>not diſcover them. </s><s>And to begin with the ſhots made at randome, <lb></lb>with the ſelf ſame piece, powder, and ball, the one towards the Eaſt, <lb></lb>the other towards the Weſt, let him tell me what it is that perſwades <lb></lb>him to think that the Range towards the Weſt (if the diurnal con <lb></lb>verſion belonged to the Earth) ought to be much longer than that <lb></lb>towards the Eaſt. <lb></lb><arrow.to.target n="marg335"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg335"></margin.target><emph type="italics"></emph>The reaſon why <lb></lb>a Gun ſhould ſiem <lb></lb>to carry farther to <lb></lb>wards the Weſt <lb></lb>than towards the <lb></lb>Eaſt.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I am moved ſo to think; becauſe in the ſhot made to <lb></lb>wards the Eaſt, the ball whil'ſt it is out of the piece, is follow <lb></lb>ed by the ſaid piece, the which being carried round by the Earth, <lb></lb>runneth alſo with much velocity towards the ſame part, where <lb></lb>upon the fall of the ball to the ground, cometh to be but little <lb></lb>diſtant from the piece. </s><s>On the contrary in the ſhot towards the <lb></lb>Weſt, before that the ball falleth to the ground, the piece is re <lb></lb>tired very far towards the Eaſt, by which means the ſpace be <lb></lb>tween the ball and the piece, that is Range, will appear longer <lb></lb>than the other, by how much the piece, that is the Earth, had <lb></lb>run in the time that both the bals were in the air.</s></p><p type="main"><s>SALV. </s><s>I could wiſh, that we did know ſome way to make an <lb></lb>experiment correſponding to the motion of theſe projects, as that <lb></lb>of the ſhip doth to the motion of things perpendicularly falling <lb></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"></emph>The experiment <lb></lb>of a running cha <lb></lb>riot to find out the <lb></lb>difference of Ran <lb></lb>ges.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I believe, that it would be a very oppoſite proof, to <lb></lb>take an open Chariot, and to accomodate therein a ^{*}Stock-bow <lb></lb>at half elevation, to the end the flight may prove the greateſt </s></p><p type="main"><s><arrow.to.target n="marg337"></arrow.to.target> <lb></lb>that my be, and whil'ſt the horſes ſhall run, to ſhoot firſt towards <lb></lb>the part whither you drive, and then another backwards towards <lb></lb>the contrary part, cauſing ſome one to mark diligently where <lb></lb>the Chariot was in that moment f time when the ſhaft came to <pb xlink:href="040/01/167.jpg" pagenum="149"></pb>the ground, as well in the one ſhot as in the other: for thus you <lb></lb>may ſee exactly how much one ſhaft flew farther than the other.</s></p><p type="margin"><s><margin.target id="marg337"></margin.target>* Baleſtrone da bol <lb></lb>zoni.</s></p><p type="main"><s>SIMP. </s><s>In my thoughts this experiment is very proper: and I <lb></lb>do not doubt but that the flight, that is, the ſpace between the <lb></lb>ſhaft and the place where the chariot was at the ſhafts fall, will be <lb></lb>leſs by much when one ſhooteth towards the chariots courſe, than <lb></lb>when one ſhooteth the contrary way. </s><s>For an example, let the <lb></lb>flight of it ſelf be three hundred yards, and the courſe of the cha <lb></lb>riot in the time whilſt the ſhaft ſtayeth in the air, an hundred <lb></lb>yards, therefore ſhooting towards the courſe, of the three hundred <lb></lb>yards of the flight, the chariot will have gone one hundred; ſo <lb></lb>then at the ſhafts coming to the ground, the ſpace between it and <lb></lb>the chariot, ſhall be but two hundred yards onely; but on the <lb></lb>contrary, in the other ſhoot, the chariot running contrary to the <lb></lb>ſhaft, when the ſhaft ſhall have paſſed its three hundred yards, and <lb></lb>the chariot its other hundred the contrary way, the diſtance inter <lb></lb>poſing ſhall be found to be four hundred yards.</s></p><p type="main"><s>SALV. </s><s>Is there any way to ſhoot ſo that theſe flights may be <lb></lb>equal?</s></p><p type="main"><s>SIMP. </s><s>I know no other way, unleſs by making the chariot to <lb></lb>ſtand ſtill.</s></p><p type="main"><s>SALV. </s><s>This we know; but I mean when the chariot runneth <lb></lb>in full carreer.</s></p><p type="main"><s>SIMP. </s><s>In that caſe you are to draw the Bow higher in ſhoot <lb></lb>ing forwards, and to ſlack it in ſhooting the contrary way.</s></p><p type="main"><s>SALV. </s><s>Then you ſee that there is one way more. </s><s>But how <lb></lb>much is the bow to be drawn, and how much ſlackened?</s></p><p type="main"><s>SIMP. </s><s>In our caſe, where we have ſuppoſed that the bow car <lb></lb>ried three hundred yards, it would be requiſite to draw it ſo, as <lb></lb>that it might carry four hundred, and in the other to ſlacken it ſo, <lb></lb>as that it might carry no more than two hundred. </s><s>For ſo each <lb></lb>of the flights would be but three hundred in relation to the chariot, <lb></lb>the which, with its courſe of an hundred yards which it ſubſtracts <lb></lb>from the ſhoot of four hundred, and addeth to that of two hun <lb></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 leſs intenſneſs of the <lb></lb>bow upon the ſhaft?</s></p><p type="main"><s>SIMP. </s><s>The ſtiffer bow carrieth it with greater velocity, and the <lb></lb>weaker with leſs; and the ſame ſhaft flieth ſo much farther at one <lb></lb>time than another, with how much greater velocity it goeth out of <lb></lb>the tiller at one time, than another.</s></p><p type="main"><s>SALV. </s><s>So that to make the ſhaft ſhot either way, to flie at e <lb></lb>qual diſtance from the running chariot, it is requiſite, that if in the <lb></lb>firſt ſhoot of the precedent example, it goeth out of the tiller with <lb></lb><emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> four degrees of velocity, that then in the other ſhoot it de <pb xlink:href="040/01/168.jpg" pagenum="150"></pb>part but with two onely: but if the ſame bow be uſed, it always <lb></lb>receiveth thence three degrees.</s></p><p type="main"><s>SIMP. </s><s>It doth ſo; and for this reaſon, ſhooting with the <lb></lb>ſame bow in the chariots courſe, the ſhoots cannot be equal.</s></p><p type="main"><s>SALV. </s><s>I had forgot to ask, with what velocity it is ſuppoſed in <lb></lb>this particular experiment, that the chariot runneth.</s></p><p type="main"><s>SIMP. </s><s>The velocity of the chariot muſt be ſuppoſed to be one <lb></lb>degree in compariſon to that of the bow, which is three,</s></p><p type="main"><s>SALV. </s><s>Very right, for ſo computation gives it. </s><s>But tell me, <lb></lb>when the chariot moveth, doth not all things in the ſame move <lb></lb>with the ſame velocity?</s></p><p type="main"><s>SIMP. </s><s>Yes doubtleſs.</s></p><p type="main"><s>SALV. </s><s>Then ſo doth the ſhaft alſo, and the bow, and the ſtring, <lb></lb>upon which the ſhaft is nock't.</s></p><p type="main"><s>SIMP. </s><s>They do ſo.</s></p><p type="main"><s>SALV. </s><s>Why then, in diſcharging the ſhaft towards the courſe <lb></lb>of the chariot, the bow impreſſeth its three degrees of velocity on <lb></lb>a ſhaft that had one degree of velocity before, by means of the <lb></lb>chariot which tranſported it ſo faſt towards that part; ſo that in <lb></lb>its going off it hath four degrees of velocity. </s><s>On the contrary, <lb></lb>in the other ſhoot, the ſame bow conferreth its ſame three degrees <lb></lb>of velocity on a ſhaft that moveth the contrary way, with one de <lb></lb>gree; ſo that in its departing from the bow-ſtring, it hath no more <lb></lb>left but onely two degrees of velocity. </s><s>But you your ſelf have <lb></lb>already ſaid, that the way to make the ſhoots equal, is to cauſe <lb></lb>that the ſhaft be let flie the firſt time with four degrees of velocity, <lb></lb>and the ſecond time with two. </s><s>Therefore without changing the <lb></lb>bow, the very courſe of the chariot is that which adjuſteth the <lb></lb><arrow.to.target n="marg338"></arrow.to.target> <lb></lb>flights, and the experiment doth ſo repreſent them to any one who <lb></lb>is not either wilfully or naturally incapable of reaſon. </s><s>Now <lb></lb>apply this diſcourſe to Gunnery, and you ſhall find, that whether the <lb></lb>Earth move or ſtand ſtill, the ſhots made with the ſame force, will <lb></lb>always curry equal ranges, to what part ſoever aimed. </s><s>The error <lb></lb>of <emph type="italics"></emph>Ariſtotle, Ptolomey, Iycho,<emph.end type="italics"></emph.end> your ſelf, and all the reſt, is ground <lb></lb>ed upon that fixed and ſtrong perſuaſion, that the Earth ſtandeth <lb></lb>ſtill, which you have not judgment nor power to depoſe, no not <lb></lb>when you have a deſire to argue of that which would enſue, pre <lb></lb>ſuppoſing the Earth to move. </s><s>And thus, in the other argument, <lb></lb>not conſidering that whil'ſt the ſtone is upon the Tower, it doth, <lb></lb>as to moving or not moving, the ſame that the Terreſtrial Globe <lb></lb>doth, becauſe you have concluded with your ſelf, that the Earth <lb></lb>ſtands ſtill, you always diſcourſe touching the fall of the ſtone, as <lb></lb>if it were to depart from reſt: whereas it behooveth to ſay, that <lb></lb>if the Earth ſtandeth ſtill, the ſtone departeth from reſt, and de <lb></lb>ſcendeth perpendicularly; but if the Earth do move, the ſtone <pb xlink:href="040/01/169.jpg" pagenum="151"></pb>likewiſe moveth with like velocity, nor doth it depart from reſt, <lb></lb>but from a motion equal to that of the Earth, wherewith it inter <lb></lb>mixeth the ſupervenient motion of deſcent, and of thoſe two com <lb></lb>poſeth a third which is tranſverſal or ſide-ways.</s></p><p type="margin"><s><margin.target id="marg338"></margin.target><emph type="italics"></emph>The ſolution of <lb></lb>the argument ta <lb></lb>ken from great <lb></lb>Guns ſhot towards <lb></lb>the East & Weſt.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>But for Gods ſake, if it move tranſverſly, how is it that <lb></lb>I behold it to move directly and perpendicularly? </s><s>This is no bet <lb></lb>ter than the denial of manifeſt ſenſe; and if we may not believe <lb></lb>ſenſe, at what other door ſhall we enter into diſquiſitions of Philo <lb></lb>ſophy?</s></p><p type="main"><s>SALV. </s><s>In reſpect to the Earth, to the Tower, and to our ſelves, <lb></lb>which all as one piece move with the diurnal motion together with <lb></lb>the ſtone, the diurnal motion is as if it never had been, and becom <lb></lb>eth inſenſible, imperceptible, and without any action at all; and <lb></lb>the onely motion which we can perceive, is that of which we par <lb></lb>take not, that is the deſcent gliding along the ſide of the Tower: <lb></lb>You are not the firſt that hath felt great repugnance in apprehen <lb></lb>ding this non-operating of motion upon things to which it is com <lb></lb>mon.</s></p><p type="main"><s>SAGR. </s><s>Now I do remember a certain conceipt, that came one <lb></lb><arrow.to.target n="marg339"></arrow.to.target> <lb></lb>day into my fancy, whilſt I ſailed in my voyage to <emph type="italics"></emph>Aleppo,<emph.end type="italics"></emph.end> whither <lb></lb>I went Conſul for our Countrey, and poſſibly it may be of ſome <lb></lb>uſe, for explaining this nullity of operation of common motion, <lb></lb>and being as if it never were to all the partakers thereof. </s><s>And if <lb></lb>it ſtand with the good liking of <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> I will reaſon with <lb></lb>him upon that which then I thought of by my ſelf alone.</s></p><p type="margin"><s><margin.target id="marg339"></margin.target><emph type="italics"></emph>A notable caſe <lb></lb>of<emph.end type="italics"></emph.end> Sagredus, <emph type="italics"></emph>to ſhew <lb></lb>the non-operating <lb></lb>of common motion.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>The novelty of the things which I hear, makes me not <lb></lb>ſo much a patient, as a greedy and curious auditor: therefore go <lb></lb>on.</s></p><p type="main"><s>SAGR. </s><s>If the neb of a writing pen, that I carried along with <lb></lb>me in the ſhip, through all my navigation from <emph type="italics"></emph>Venice<emph.end type="italics"></emph.end> to ^{*} <emph type="italics"></emph>Scan-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg340"></arrow.to.target> <lb></lb><emph type="italics"></emph>deron,<emph.end type="italics"></emph.end> had had a facultie of leaving viſible marks of its whole voy <lb></lb>age, what ſigns, what marks, what lines would it have left?</s></p><p type="margin"><s><margin.target id="marg340"></margin.target>* Aleſſandretta.</s></p><p type="main"><s>SIMP. </s><s>It would have left a line diſtended from <emph type="italics"></emph>Venice<emph.end type="italics"></emph.end> thither, <lb></lb>not perfectly ſtreight, or to ſay better, diſtended in a perfect arch <lb></lb>of a circle, but in ſome places more, in ſome leſs curved, according <lb></lb>as the veſſel had gone more or leſs fluctuating; but this its infle <lb></lb>cting in ſome places a fathom or two to the right hand or to the <lb></lb>left, upwards or downwards, in a length of many hundred miles, <lb></lb>would have brought but little alteration to the intire tract of the <lb></lb>line, ſo that it would have been hardly ſenſible; and without any <lb></lb>conſiderable error, might have been called the part of a perfect <lb></lb>arch.</s></p><p type="main"><s>SAGR. </s><s>So that the true and moſt exact motion of the neb of <lb></lb>my pen would have alſo been an arch of a perfect circle, if the <lb></lb>veſſels motion, the fluctuation of the billows ceaſing, had been <pb xlink:href="040/01/170.jpg" pagenum="152"></pb>calm and tranquill. </s><s>And if I had continually held that pen in <lb></lb>my hand, and had onely moved it ſometimes an inch or two this <lb></lb>way or that way, what alteration ſhould I have made in that its <lb></lb>principal, and very long tract or ſtroke?</s></p><p type="main"><s>SIMP. </s><s>Leſs than that which the declining in ſeveral places from <lb></lb>abſolute rectitude, but the quantity of a flea's eye makes in a right <lb></lb>line of a thouſand yards long.</s></p><p type="main"><s>SAGR. </s><s>If a Painter, then, at our launching from the Port, had <lb></lb>began to deſign upon a paper with that pen, and continued his <lb></lb>work till he came to <emph type="italics"></emph>Scanderon,<emph.end type="italics"></emph.end> he would have been able to have <lb></lb>taken by its motion a perfect draught of all thoſe figures perfectly <lb></lb>interwoven and ſhadowed on ſeveral ſides with countreys, build <lb></lb>ings, living creatures, and other things; albeit all the true, real, <lb></lb>and eſſential motion traced out by the neb of that pen, would <lb></lb>have been no other than a very long, but ſimple line: and as to <lb></lb>the proper operation of the Painter, he would have delineated the <lb></lb>ſame to an hair, if the ſhip had ſtood ſtill. </s><s>That therefore of the <lb></lb>huge long motion of the pen there doth remain no other marks, <lb></lb>than thoſe tracks drawn upon the paper, the reaſon thereof is be <lb></lb>cauſe the grand motion from <emph type="italics"></emph>Venice<emph.end type="italics"></emph.end> to <emph type="italics"></emph>Scanderon,<emph.end type="italics"></emph.end> was common to <lb></lb>the paper, the pen, and all that which was in the ſhip: but the petty <lb></lb>motions forwards and backwards, to the right, to the left, com <lb></lb>municated by the fingers of the Painter unto the pen, and not to <lb></lb>the paper, as being peculiar thereunto, might leave marks of it ſelf <lb></lb>upon the paper, which did not move with that motion. </s><s>Thus it <lb></lb>is likewiſe true, that the Earth moving, the motion of the ſtone in <lb></lb>deſcending downwards, was really a long tract of many hundreds <lb></lb>and thouſands of yards, and if it could have been able to have de <lb></lb>lineated in a calm air, or other ſuperficies, the track of its courſe, <lb></lb>it would have left behind an huge long tranſverſe line. </s><s>But that <lb></lb>part of all this motion which is common to the ſtone, the Tower, <lb></lb>and our ſelves, is imperceptible to us, and as if it had never been, <lb></lb>and that part onely remaineth obſervable, of which neither the <lb></lb>Tower nor we are partakers, which is in fine, that wherewith the <lb></lb>ſtone falling meaſureth the Tower.</s></p><p type="main"><s>SALV. </s><s>A moſt witty conceipt to clear up this point, which was <lb></lb>not a little difficult to many capacities. </s><s>Now if <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> will <lb></lb>make no farther reply, we may paſs to the other experiments, the <lb></lb>unfolding of which will receive no ſmall facility from the things <lb></lb>already declared.</s></p><p type="main"><s>SIMP. </s><s>I have nothing more to ſay: and I was well-nigh tranſ <lb></lb>ported with that delineation, and with thinking how thoſe ſtrokes <lb></lb>drawn ſo many ways, hither, thither, upwards, downwards, for <lb></lb>wards, backwards, and interwoven with thouſands of turnings, are <lb></lb>not eſſentially or really other, than ſmall pieces of one ſole line <pb xlink:href="040/01/171.jpg" pagenum="153"></pb>drawn all one way, and the ſame without any other alteration ſave <lb></lb>the declining the direct rectitude, ſometimes a very inſenſible mat <lb></lb>ter towards one ſide or another, and the pens moving its neb one <lb></lb>while ſofter, another while ſlower, but with very ſmall inequality. <lb></lb></s><s>And I think that it would in the ſame manner write a letter, and <lb></lb>that thoſe frollike penmen, who to ſhew their command of hand, <lb></lb>without taking their pen from the paper in one ſole ſtroke, with <lb></lb>infinite turnings draw a pleaſant knot, if they were in a boat that <lb></lb>did tide it along ſwiftly they would convert the whole motion <lb></lb>of the pen, which in reality is but one ſole line, drawn all towards <lb></lb>one and the ſame part, and very little curved, or declining from <lb></lb>perfect rectitude, into a knot or flouriſh. </s><s>And I am much pleaſed <lb></lb>that <emph type="italics"></emph>S agredus<emph.end type="italics"></emph.end> hath helped me to this conceit: therefore let us go <lb></lb>on, for the hope of meeting with more of them, will make me the <lb></lb>ſtricter in my attention.</s></p><p type="main"><s>SAGR. </s><s>If you have a curioſity to hear ſuch like ſubtilties, which <lb></lb><arrow.to.target n="marg341"></arrow.to.target> <lb></lb>occurr not thus to every one, you will find no want of them, eſpe <lb></lb>cially in this particular of Navigation; and do you not think that a <lb></lb>witty conceit which I met with likewiſe in the ſame voyage, when I <lb></lb>obſerved that the maſt of the ſhip, without either breaking or bend <lb></lb>ing, had made a greater voyage with its round-top, that is with its <lb></lb>top-gallant, than with its foot; for the round top being more diſtant <lb></lb>from the centre of the Earth than the foot is, it had deſcribed the <lb></lb>arch of a circle bigger than the circle by which the foot had paſſed.</s></p><p type="margin"><s><margin.target id="marg341"></margin.target><emph type="italics"></emph>Subtilties ſuffici <lb></lb>ently inſipid, ironi <lb></lb>cally, ſpoken and <lb></lb>taken from a cer <lb></lb>tain<emph.end type="italics"></emph.end> Encyclopædia.</s></p><p type="main"><s>SIMP. </s><s>And thus when a man walketh he goeth farther with <lb></lb>his head than with his feet.</s></p><p type="main"><s>SAGR. </s><s>You have found out the matter your ſelf by help of <lb></lb>your own mother-wit: But let us not interrupt <emph type="italics"></emph>Salviatus.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>It pleaſeth me to ſee <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> how he ſootheth up <lb></lb>himſelf in this conceit, if happly it be his own, and that he hath not <lb></lb>borrowed it from a certain little pamphlet of concluſions, where <lb></lb>there are a great many more ſuch fancies no leſs pleaſant & witty. <lb></lb></s><s>It followeth that we ſpeak of the peice of Ordinance mounted per <lb></lb><arrow.to.target n="marg342"></arrow.to.target> <lb></lb>pendicular to the Horizon, that is, of a ſhot towards our vertical <lb></lb>point, and to conclude, of the return of the ball by the ſame line <lb></lb>unto the ſame peice, though that in the long time which it is ſe <lb></lb>parated from the peice, the earth hath tranſported it many miles <lb></lb>towards the Eaſt; now it ſeemeth, that the ball ought to fall a like <lb></lb>diſtance from the peice towards the Weſt; the which doth not <lb></lb>happen: therefore the peice without having been moved did ſtay <lb></lb>expecting the ſame. </s><s>The anſwer is the ſame with that of the <lb></lb><arrow.to.target n="marg343"></arrow.to.target> <lb></lb>ſtone falling from the Tower; and all the fallacy, and equivocati <lb></lb>on conſiſteth in ſuppoſing ſtill for true, that which is in queſtion; <lb></lb>for the Opponent hath it ſtill fixed in his conceit that the <lb></lb>ball departs from its reſt, being diſcharged by the fire <pb xlink:href="040/01/172.jpg" pagenum="154"></pb>from the piece; and the departing from the ſtate of reſt, cannot <lb></lb>be, unleſſe the immobility of the Terreſtrial Globe be preſuppo <lb></lb>ſed, which is the concluſion of that was in diſpute; Therefore, <lb></lb>I reply, that thoſe who make the Earth moveable, anſwer, that <lb></lb>the piece, and the ball that is in it, partake of the ſame motion <lb></lb>with the Earth; nay that they have this together with her from <lb></lb>nature; and that therefore the ball departs in no other manner <lb></lb>from its quieſcence, but conjoyned with its motion about the cen <lb></lb>tre, the which by its projection upwards, is neither taken away, <lb></lb>nor hindered; and in this manner following, the univerſal motion <lb></lb>of the Earth towards the Eaſt, it alwayes keepeth perpendicular <lb></lb>over the ſaid piece, as well in its riſe as in its return. </s><s>And the <lb></lb>ſame you ſee to enſue, in making the experiment in a ſhip with <lb></lb>a bullet ſhot upwards perpendicularly with a Croſſe-bow, which <lb></lb>returneth to the ſame place whether the ſhip doth move, or ſtand <lb></lb>ſtill. <lb></lb><arrow.to.target n="marg344"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg342"></margin.target><emph type="italics"></emph>An inſtance a <lb></lb>gainst the diurnal <lb></lb>motion of the earth, <lb></lb>taken from the ſhot <lb></lb>of a Peece of Ordi <lb></lb>nance perpendicu <lb></lb>larly.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg343"></margin.target><emph type="italics"></emph>The anſwer to the <lb></lb>objection, ſhewing <lb></lb>the equivoke.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg344"></margin.target><emph type="italics"></emph>Another anſwer <lb></lb>to the ſame objecti <lb></lb>on.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>This ſatisfieth very well to all; but becauſe that I have <lb></lb>ſeen that <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> taketh pleaſure with certain ſubtilties to <lb></lb>puzzle his companions, I will demand of him whether, ſuppo <lb></lb>ſing for this time that the Earth ſtandeth ſtill, and the piece ere <lb></lb>cted upon it perpendicularly, directed to our Zenith, he do at all <lb></lb>queſtion that to be the true perpendicular ſhot, and that the ball <lb></lb>in departing, and in its return is to go by the ſame right line, <lb></lb>ſtill ſuppoſing all external and accidental impediments to be re <lb></lb>moved?</s></p><p type="main"><s>SIMP. </s><s>I underſtand that the matter ought to ſucceed exactly <lb></lb>in that manner.</s></p><p type="main"><s>SAGR. </s><s>But if the piece were placed, not perpendicularly, but <lb></lb>inclining towards ſome place, what would the motion of the ball <lb></lb>be? </s><s>Would it go haply, as in the other ſhot, by the perpendi <lb></lb>cular line, and return again by the ſame?</s></p><p type="main"><s>SIMP. </s><s>It would not ſo do; but iſſuing out of the piece, it <lb></lb>would purſue its motion by a right line which prolongeth the e <lb></lb>rect perpendicularity of the concave cylinder of the piece, unleſſe <lb></lb>ſo far as its own weight would make it decline from that erection <lb></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></lb>the motion of the ball, nor doth it, or would it move out of that <lb></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></lb>therefore placing the cylinder perpendicularly, and ſhooting the <lb></lb>ball upwards, it returneth by the ſame right line downwards; be <lb></lb>cauſe the motion of the ball dependent on its gravity is down <lb></lb>ward, by the ſame perpendicular. </s><s>The journey therefore of the <lb></lb>ball out of the piece, continueth or prolongeth the rectitude or <lb></lb>perpendicularity of that ſmall part of the ſaid journey, which it <lb></lb>made within the ſaid piece; is it not ſo?</s></p> <pb xlink:href="040/01/173.jpg" pagenum="155"></pb><p type="margin"><s><margin.target id="marg345"></margin.target><emph type="italics"></emph>Projects conti <lb></lb>nue their motion <lb></lb>by the right line <lb></lb>that followeth the <lb></lb>direction of the <lb></lb>motion, made to <lb></lb>gether with the <lb></lb>projicient, whil'ſt <lb></lb>they were conjoin'd <lb></lb>therewith.<emph.end type="italics"></emph.end></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></lb>Earth doth revolve about with a diurnal motion, carrying the <lb></lb>piece along with it, tell me what ſhall be the motion of the ball <lb></lb>within the cylinder, having given fire?</s></p><p type="main"><s>SIMP. </s><s>It ſhall be a ſtreight and perpendicular motion, the cylin <lb></lb>der being erected perpendicularly.</s></p><p type="main"><s>SAGR. </s><s>Conſider well what you ſay: for I believe that it will <lb></lb>not be perpendicular. </s><s>It would indeed be perpendicular, if the <lb></lb>Earth ſtood ſtill, for ſo the ball would have no other motion but <lb></lb>that proceeding from the fire. </s><s>But in caſe the Earth turns round, <lb></lb><arrow.to.target n="marg346"></arrow.to.target> <lb></lb>the ball that is in the piece, hath likewiſe a diurnal motion, ſo <lb></lb>that there being added to the ſame the impulſe of the fire, it mo <lb></lb>veth from the breech of the piece to the muzzle with two motions, <lb></lb>from the compoſition whereof it cometh to paſſe that the motion <lb></lb>made by the centre of the balls gravity is an inclining line. </s><s>And <lb></lb>for your clearer underſtanding the ſame, let the piece A C [<emph type="italics"></emph>in <lb></lb>Fig.<emph.end type="italics"></emph.end> 2.] be erected, and in it the ball B; it is manifeſt, that the <lb></lb>piece ſtanding immoveable, and fire being given to it, the ball <lb></lb>will make its way out by the mouth A, and with its centre, paſ <lb></lb>ſing thorow the the piece, ſhall have deſcribed the perpendicular <lb></lb>line B A, and it ſhall purſue that rectitude when it is out of the <lb></lb>piece, moving toward the Zenith. </s><s>But in caſe the Earth ſhould <lb></lb>move round, and conſequently carry the piece along with it, in <lb></lb>the time that the ball driven out of the piece ſhall move along <lb></lb>the cylinder, the piece being carried by the Earth, ſhall paſſe in <lb></lb>to the ſituation D E, and the ball B, in going off, would be at <lb></lb>the corniſh D, and the motion of the bals centre, would have <lb></lb>been according to the line B D, no longer perpendicular, but in <lb></lb>clining towards the Eaſt; and the ball (as hath been concluded) <lb></lb>being to continue its motion through the air, according to the <lb></lb>direction of the motion made in the piece, the ſaid motion ſhall <lb></lb>continue on according to the inclination of the line B D, and ſo <lb></lb>ſhall no longer be perpendicular, but inclined towards the Eaſt, <lb></lb>to which part the piece doth alſo move; whereupon the ball may <lb></lb>follow the motion of the Eerth, and of the piece. </s><s>Now <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> <lb></lb>you ſee it demonſtrated, that the Range which you took to be <lb></lb>perpendicular, is not ſo.</s></p><p type="margin"><s><margin.target id="marg346"></margin.target><emph type="italics"></emph>The revolution <lb></lb>of the Earth ſup <lb></lb>poſed, the ball in <lb></lb>the piece erected <lb></lb>perpendicularly, <lb></lb>doth not move by a <lb></lb>perpendicular, but <lb></lb>an inclined line.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I do not very well underſtand this buſineſs; do you, <lb></lb><emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end>?</s></p><p type="main"><s>SALV. </s><s>I apprehend it in part; but I have a certain kind of <lb></lb>ſcruple, which I wiſh I knew how to expreſs. </s><s>It ſeems to me, that <lb></lb>according to what hath been ſaid, if the Piece be erected perpen <lb></lb>dicular, and the Earth do move, the ball would not be to fall, as <lb></lb><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end> will have it, far from the Piece towards the <pb xlink:href="040/01/174.jpg" pagenum="156"></pb>Weſt, nor as you would have it, upon the Piece, but rather far <lb></lb>diſtant towards the Eaſt. </s><s>For according to your explanation, it <lb></lb>would have two motions, the which would with one conſent carry <lb></lb>it thitherward, to wit, the common motion of the Earth, which <lb></lb>carrieth the Piece and the ball from C A towards E D; and the <lb></lb>fire which carrieth it by the inclined line B D, both motions to <lb></lb>wards the Eaſt, and therefore they are ſuperiour to the motion of <lb></lb>the Earth.</s></p><p type="main"><s>SAGR. </s><s>Not ſo, Sir. </s><s>The motion which carrieth the ball to <lb></lb>wards the Eaſt, cometh all from the Earth, and the fire hath no <lb></lb>part at all therein: the motion which mounteth the ball upwards, <lb></lb>is wholly of fire, wherewith the Earth hath nothing to do. </s><s>And <lb></lb>that it is ſo, if you give not fire, the ball will never go out of the <lb></lb>Piece, nor yet riſe upwards a hairs breadth; as alſo if you make <lb></lb>the Earth immoveable, and give fire, the ball without any incli <lb></lb>nation ſhall go perpendicularly upwards. </s><s>The ball therefore ha <lb></lb>ving two motions, one upwards, and the other in gyration, of both <lb></lb>which the tranſverſe line B D is compounded, the impulſe upward <lb></lb>is wholly of fire, the circular cometh wholly from the Earth, and <lb></lb>is equal to the Earths motion: and being equal to it, the ball <lb></lb>maintaineth it ſelf all the way directly over the mouth of the <lb></lb>Piece, and at laſt falleth back into the ſame: and becauſe it al <lb></lb>ways obſerveth the erection of the Piece, it appeareth alſo conti <lb></lb>nually over the head of him that is near the Piece, and therefore <lb></lb>it appeareth to mount exactly perpendicular towards our Zenith, <lb></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></lb>regard the motion of the ball is very ſwift in the Piece, it ſeems <lb></lb>not poſſible, that in that moment of time the tranſpoſition of the <lb></lb>Piece from C A to A D ſhould confer ſuch an inclination upon <lb></lb>the tranſverſe line C D, that by means thereof, the ball when it <lb></lb>cometh afterwards into the air ſhould be able to follow the courſe <lb></lb>of the Earth.</s></p><p type="main"><s>SAGR. </s><s>You err upon many accounts; and firſt, the inclination <lb></lb>of the tranſverſe line C D, I believe it is much greater than you <lb></lb>take it to be, for I verily think that the velocity of the Earths mo <lb></lb>tion, not onely under the Equinoctial, but in our paralel alſo, is <lb></lb>greater than that of the ball whilſt it moveth in the Piece; ſo that <lb></lb>the interval C E would be abſolutely much bigger than the whole <lb></lb>length of the Piece, and the inclination of the tranſverſe line con <lb></lb>ſequently bigger than half a right angle: but be the velocity of <lb></lb>the Earth more, or be it leſs, in compariſon of the velocity of the <lb></lb>fire, this imports nothing; for if the velocity of the Earth be ſmall, <lb></lb>and conſequently the inclination of the tranſverſe line be little <lb></lb>alſo; there is then alſo need but of little inclination to make the <pb xlink:href="040/01/175.jpg" pagenum="157"></pb>ball ſuſpend it ſelf in its range directly over the Piece. </s><s>And in a <lb></lb>word, if you do but attentively conſider, you will comprehend, <lb></lb>that the motion of the Earth in transferring the Piece along with <lb></lb>it from C A to E D, conferreth upon the tranſverſe line C D, ſo <lb></lb>much of little or great inclination, as is required to adjuſt the <lb></lb>range to its perpendicularity. </s><s>But you err, ſecondly, in that you <lb></lb>referr the faculty of carrying the ball along with the Earth to the <lb></lb>impulſe of the fire, and you run into the ſame error, into which <lb></lb><emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> but even now ſeemed to have fallen; for the faculty <lb></lb>of following the motion of the Earth, is the primary and perpetual <lb></lb>motion, indelibly and inſeparably imparted to the ſaid ball, as to a <lb></lb>thing terreſtrial, and that of its own nature doth and ever ſhall <lb></lb>poſſeſs the ſame.</s></p><p type="main"><s>SALV. </s><s>Let us yield, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> for the buſineſs is juſt as he <lb></lb><arrow.to.target n="marg347"></arrow.to.target> <lb></lb>ſaith. </s><s>And now from this diſcourſe let us come to underſtand the <lb></lb>reaſon of a Venatorian Problem, of thoſe Fowlers who with their <lb></lb>guns ſhoot a bird flying; and becauſe I did imagine, that in regard <lb></lb>the bird flieth a great pace, therefore they ſhould aim their ſhot far <lb></lb>from the bird, anticipating its flight for a certain ſpace, and more <lb></lb>or leſs according to its velocity and the diſtance of the bird, that <lb></lb>ſo the bullet haſting directly to the mark aimed at, it might come <lb></lb>to arrive at the ſelf ſame time in the ſame point with its motion, <lb></lb>and the bird with its flight, and by that means one to encounter <lb></lb>the other: and asking one of them, if their practiſe was not ſo <lb></lb>to do; He told me, no; but that the ſlight was very eaſie and <lb></lb>certain, and that they took aim juſt in the ſame manner as if they <lb></lb>had ſhot at a bird that did ſit ſtill; that is, they made the flying <lb></lb>bird their mark, and by moving their fowling-piece they followed <lb></lb>her, keeping their aim ſtill full upon her, till ſuch time as they let <lb></lb>fly, and in this manner ſhot her as they did others ſitting ſtill. </s><s>It is <lb></lb>neceſſary therefore that that motion, though ſlow, which the fowl <lb></lb>ing-piece maketh in turning and following after the flight of the <lb></lb>bird do communicate it ſelf to the bullet alſo, and that it be joyned <lb></lb>with that of the fire; ſo that the ball hath from the fire the mo <lb></lb>tion directly upwards, and from the concave Cylinder of the barrel <lb></lb>the declination according to the flight of the Bird, juſt as was ſaid <lb></lb>before of the ſhot of a Canon; where the ball receiveth from the <lb></lb>fire a virtue of mounting upwards towards the Zenith, and from <lb></lb>the motion of the Earth its winding towards the Eaſt, and of both <lb></lb>maketh a compound motion that followeth the courſe of the <lb></lb>Earth, and that to the beholder ſeemeth onely to go directly up <lb></lb>wards, and return again downwards by the ſame line. </s><s>The hold <lb></lb>ing therefore of the gun continually directed towards the mark, <lb></lb>maketh the ſhoot hit right, and that you may keep your gun di <lb></lb>rected to the mark, in caſe the mark ſtands ſtill, you muſt alſo hold <pb xlink:href="040/01/176.jpg" pagenum="158"></pb>your gun ſtill; and if the mark ſhall move, the gun muſt be kept upon <lb></lb>the mark by moving. </s><s>And upon this dependeth the proper anſwer <lb></lb><arrow.to.target n="marg348"></arrow.to.target> <lb></lb>to the other argument taken from the ſhot of a Canon, at the <lb></lb>mark placed towards the South or North: wherein is alledged, <lb></lb>that if the Earth ſhould move, the ſhots would all range Weſt <lb></lb>ward of the mark, becauſe that in the time whilſt the ball, being <lb></lb>forc'd out of the Piece, goeth through the air to the mark, the ſaid <lb></lb>mark being carried toward the Eaſt, would leave the ball to the <lb></lb>Weſtward. </s><s>I anſwer therefore, demanding whether if the Ca <lb></lb>non be aimed true at the mark, and permitted ſo to continue, it <lb></lb>will conſtantly hit the ſaid mark, whether the Earth move or ſtand <lb></lb>ſtill? </s><s>It muſt be replied, that the aim altereth not at all, for if <lb></lb>the mark doth ſtand ſtill, the Piece alſo doth ſtand ſtill, and if it, <lb></lb>being tranſported by the Earths motion, doth move, the Piece doth <lb></lb>alſo move at the ſame rate, and, the aim maintained, the ſhot <lb></lb>proveth always true, as by what hath been ſaid above, is mani <lb></lb>feſt.</s></p><p type="margin"><s><margin.target id="marg347"></margin.target><emph type="italics"></emph>The manner how <lb></lb>Fowlers ſhoot birds <lb></lb>flying.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg348"></margin.target><emph type="italics"></emph>The anſwer to <lb></lb>the objection tak n <lb></lb>from the ſhots of <lb></lb>great Guns made <lb></lb>towards the North <lb></lb>and South.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Stay a little, I entreat you, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> till I have pro <lb></lb>pounded a certain conceit touching theſe ſhooters of birds flying, <lb></lb>whoſe proceeding I believe to be the ſame which you relate, and <lb></lb>believe the effect of hitting the bird doth likewiſe follow: but yet <lb></lb>I cannot think that act altogether conformable to this of ſhooting <lb></lb>in great Guns, which ought to hit as well when the piece and mark <lb></lb>moveth, as when they both ſtand ſtill; and theſe, in my opinion, <lb></lb>are the particulars in which they diſagree. </s><s>In ſhooting with a <lb></lb>great Gun both it and the mark move with equal velocity, being <lb></lb>both tranſported by the motion of the Terreſtrial Globe: and al <lb></lb>beit ſometimes the piece being planted more towards the Pole, <lb></lb>than the mark, and conſequently its motion being ſomewhat flow <lb></lb>er than the motion of the mark, as being made in a leſſer circle, <lb></lb>ſuch a difference is inſenſible, at that little diſtance of the piece <lb></lb>from the mark: but in the ſhot of the Fowler the motion of the <lb></lb>Fowling-piece wherewith it goeth following the bird, is very ſlow <lb></lb>in compariſon of the flight of the ſaid bird; whence me thinks it <lb></lb>ſhould follow, that that ſmall motion which the turning of the <lb></lb>Birding-piece conferreth on the bullet that is within it, cannot, <lb></lb>when it is once gone forth of it, multiply it ſelf in the air, untill it <lb></lb>come to equal the velocity of the birds flight, ſo as that the ſaid bullet <lb></lb>ſhould always keep direct upon it: nay, me thinketh the bird <lb></lb>would anticipate it and leave it behind. </s><s>Let me add, that in this <lb></lb>act, the air through which the bullet is to paſs, partaketh not of the <lb></lb>motion of the bird: whereas in the caſe of the Canon, both it, <lb></lb>the mark, and the intermediate air, do equally partake of the com <lb></lb>mon diurnal motion. </s><s>So that the true cauſe of the Marks-man <lb></lb>his hitting the mark, as it ſhould ſeem, moreover and beſides the <pb xlink:href="040/01/177.jpg" pagenum="159"></pb>following the birds flight with the piece, is his ſomewhat anticipa <lb></lb>ting it, taking his aim before it; as alſo his ſhooting (as I believe) <lb></lb>not with one bullet, but with many ſmall balls (called ſhot) the <lb></lb>which ſcattering in the air poſſeſs a great ſpace; and alſo the ex <lb></lb>treme velocity wherewith theſe ſhot, being diſcharged from the <lb></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"></emph>Sagredus<emph.end type="italics"></emph.end> anticipateth, <lb></lb>and out-goeth the dulneſs of mine; which perhaps would have <lb></lb><arrow.to.target n="marg349"></arrow.to.target> <lb></lb>light upon theſe diſparities, but not without long ſtudie. </s><s>Now <lb></lb>turning to the matter in hand, there do remain to be conſidered <lb></lb>by us the ſhots at point blank, towards the Eaſt and towards the <lb></lb>Weſt; the firſt of which, if the Earth did move, would always <lb></lb>happen to be too high above the mark, and the ſecond too low; <lb></lb>foraſmuch as the parts of the Earth Eaſtward, by reaſon of the di <lb></lb>urnal motion, do continually deſcend beneath the tangent paralel <lb></lb>to the Horizon, whereupon the Eaſtern ſtars to us appear to aſcend; <lb></lb>and on the contrary, the parts Weſtward do more and more aſ <lb></lb>cend, whereupon the Weſtern ſtars do in our ſeeming deſcend: <lb></lb>and therefore the ranges which are leveled according to the ſaid <lb></lb>tangent at the Oriental mark, (which whilſt the ball paſſeth <lb></lb>along by the tangent deſcendeth) ſhould prove too high, and the <lb></lb>Occidental too low by means of the elevation of the mark, whilſt <lb></lb>the ball paſſeth along the tangent. </s><s>The anſwer is like to the reſt: <lb></lb>for as the Eaſtern mark goeth continually deſcending, by reaſon <lb></lb>of the Earths motion, under a tangent that continueth immove <lb></lb>able; ſo likewiſe the piece for the ſame reaſon goeth continually <lb></lb>inclining, and with its mounture purſuing the ſaid mark: by <lb></lb>which means the ſhot proveth true.</s></p><p type="margin"><s><margin.target id="marg349"></margin.target><emph type="italics"></emph>The anſwer to the <lb></lb>Argument taken <lb></lb>from the ſhots at <lb></lb>point blanck to <lb></lb>wards the Eaſt & <lb></lb>Weſt.<emph.end type="italics"></emph.end></s></p><p type="main"><s>But here I think it a convenient opportunity to give notice of <lb></lb><arrow.to.target n="marg350"></arrow.to.target> <lb></lb>certain conceſſions, which are granted perhaps over liberally by <lb></lb>the followers of <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> unto their Adverſaries: I mean of <lb></lb>yielding to them certain experiments for ſure and certain, which <lb></lb>yet the Adverſaries themſelves had never made tryal of: as for <lb></lb>example, that of things falling from the round-top of a ſhip whilſt <lb></lb>it is in motion, and many others; amongſt which I verily believe, <lb></lb>that this of experimenting whether the ſhot made by a Canon to <lb></lb>wards the Eaſt proveth too high, and the Weſtern ſhot too low, <lb></lb>is one: and becauſe I believe that they have never made tryal <lb></lb>thereof, I deſire that they would tell me what difference they <lb></lb>think ought to happen between the ſaid ſhots, ſuppoſing the Earth <lb></lb>moveable, or ſuppoſing it moveable; and let <emph type="italics"></emph>Simplieius<emph.end type="italics"></emph.end> for this <lb></lb>time anſwer for them.</s></p><p type="margin"><s><margin.target id="marg350"></margin.target><emph type="italics"></emph>The followers of <lb></lb>Copernicus too <lb></lb>freely admit cer <lb></lb>tain propoſitions for <lb></lb>true, which are <lb></lb>very doubtfull.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I will not undertake to anſwer ſo confidently as another <lb></lb>more intelligent perhaps might do; but ſhall ſpeak what thus upon <lb></lb>the ſudden I think they would reply; which is in effect the ſame <pb xlink:href="040/01/178.jpg" pagenum="160"></pb>with that which hath been ſaid already, namely, that in caſe the <lb></lb>Earth ſhould move, the ſhots made Eaſtward would prove too <lb></lb>high, &c. </s><s>the ball, as it is probable, being to move along the tan <lb></lb>gent.</s></p><p type="main"><s>SALV. </s><s>But if I ſhould ſay, that ſo it falleth out upon triall, <lb></lb>how would you cenſure me?</s></p><p type="main"><s>SIMP. </s><s>It is neceſſary to proceed to experiments for the pro <lb></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 ſo <lb></lb>skilful, as to hit the mark at every ſhoot, in a diſtance of <emph type="italics"></emph>v.g.<emph.end type="italics"></emph.end> five <lb></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></lb>marks-man ſoever that would promiſe to come within a pace of <lb></lb>the mark,</s></p><p type="main"><s>SALV. </s><s>How can we then, with ſhots ſo uncertain, aſſure our <lb></lb>ſelves of that which is in diſpute?</s></p><p type="main"><s>SIMP. </s><s>We may be aſſured thereof two wayes; one, by ma <lb></lb>king many ſhots; the other, becauſe in reſpect of the great velo <lb></lb>city of the Earths motion, the deviation from the mark would in <lb></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></lb>the varying ſo much, yea and more, is granted to happen ordinarily <lb></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></lb>more than ſo. <lb></lb><arrow.to.target n="marg351"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg351"></margin.target><emph type="italics"></emph>A Computation <lb></lb>how much the ran <lb></lb>ges of great ſhot <lb></lb>ought to vary from <lb></lb>the marke, the <lb></lb>Earths motion be <lb></lb>ing granted.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Now I deſire that for our ſatisfaction we do make thus <lb></lb>in groſſe a ſlight calculation, if you conſent thereto, which will <lb></lb>ſtand us in ſtead likewiſe (if the computation ſucceed as I expect) <lb></lb>for a warning how we do in other occurrences ſuffer our ſelves, as <lb></lb>the ſaying is, to be taken with the enemies ſhouts, and ſurrender <lb></lb>up our belief to what ever firſt preſents it ſelf to our fancy. </s><s>And <lb></lb>now to give all advantages to the <emph type="italics"></emph>Peripateticks<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Tychonicks,<emph.end type="italics"></emph.end> <lb></lb>let us ſuppoſe our ſelves to be under the Equinoctial, there to ſhoot <lb></lb>a piece of Ordinance point blank Eaſtwards at a mark five hun <lb></lb>dred paces off. </s><s>Firſt, let us ſee thus (as I ſaid) in a level, what <lb></lb>time the ſhot after it is gone out of the Piece taketh to arrive at <lb></lb>the mark; which we know to be very little, and is certainly no <lb></lb>more than that wherein a travailer walketh two ſteps, which alſo <lb></lb>is leſs than the ſecond of a minute of an hour; for ſuppoſing <lb></lb>that the travailer walketh three miles in an hour, which are nine <lb></lb>thouſand paces, being that an hour containes three thouſand, ſix <lb></lb>hundred ſecond minutes, the travailer walketh two ſteps and an <lb></lb>half in a ſecond, a ſecond therefore is more than the time of the <lb></lb>balls motion. </s><s>And for that the diurnal revolution is twenty four <lb></lb>hours, the Weſtern horizon riſeth fifteen degrees in an hour, that <pb xlink:href="040/01/179.jpg" pagenum="161"></pb>is, fifteen firſt minutes of a degree, in one firſt minute of an hour; <lb></lb>that is, fifteen ſeconds of a degree, in one ſecond of an hour; and <lb></lb>becauſe one ſecond is the time of the ſhot, therefore in this time <lb></lb>the Weſtern horizon riſeth fifteen ſeconds of a degree, and ſo <lb></lb>much likewiſe the mark; and therefore fifteen ſeconds of that cir <lb></lb>cle, whoſe ſemidiameter is five hundred paces (for ſo much the di <lb></lb>ſtance of the mark from the Piece was ſuppoſed.) Now let us <lb></lb>look in the table of Arches and Chords (ſee here is <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> his <lb></lb>book) what part is the chord of fifteen ſeconds of the ſemidiame <lb></lb>ter, that is, five hundred paces. </s><s>Here you ſee the chord (or ſub <lb></lb>tenſe) of a firſt minute to be leſs than thirty of thoſe parts, of <lb></lb>which the ſemidiameter is an hundred thouſand. </s><s>Therefore the <lb></lb>chord of a ſecond minute ſhall be leſs then half of one of thoſe <lb></lb>parts, that is leſs than one of thoſe parts, of whichthe ſemidiame <lb></lb>ter is two hundred thouſand; and therefore the chord of fifteen <lb></lb>conds ſhall be leſs than fifteen of thoſe ſame two hundred thouſand <lb></lb>parts; but that which is leſs than <emph type="italics"></emph>(a)<emph.end type="italics"></emph.end> fifteen parts of two hun</s></p><p type="main"><s><arrow.to.target n="marg352"></arrow.to.target> <lb></lb>dred thouſand, is alſo more than that which is four centeſmes of <lb></lb>five hundred; therefore the aſcent of the mark in the time of the <lb></lb>balls motion is leſſe than four centeſmes, that is, than one twenty <lb></lb>fifth part of a pace; it ſhall be therefore <emph type="italics"></emph>(b)<emph.end type="italics"></emph.end> about two inches: <lb></lb>And ſo much conſequently ſhall be the variation of each Weſtern <lb></lb>ſhot, the Earth being ſuppoſed to have a diurnal motion. </s><s>Now if I <lb></lb>ſhall tell you, that this variation (I mean of falling two inches ſhort <lb></lb>of what they would do in caſe the Earth did not move) upon tri <lb></lb><arrow.to.target n="marg353"></arrow.to.target> <lb></lb>all doth happen in all ſhots, how will you convince me <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> <lb></lb>ſhewing me by an experiment that it is not ſo? </s><s>Do you not ſee <lb></lb>that it is impoſſible to confute me, unleſs you firſt find out a way <lb></lb>to ſhoot at a mark with ſo much exactneſſe, as never to miſſe an <lb></lb>hairs bredth? </s><s>For whilſt the ranges of great ſhot conſiſt of diffe <lb></lb>rent numbers of paces, as <emph type="italics"></emph>de facto<emph.end type="italics"></emph.end> they do, I will affirm that in <lb></lb>each of thoſe variations there is contained that of two inches cau <lb></lb>ſed by the motion of the Earth.</s></p><p type="margin"><s><margin.target id="marg352"></margin.target><emph type="italics"></emph>(a)<emph.end type="italics"></emph.end> That is, in <lb></lb>plainer termes the <lb></lb>fraction 15/200000, is <lb></lb>more than the fra <lb></lb>ction 4/50000, for di <lb></lb>viding the denomi <lb></lb>nators by their no <lb></lb>minators, and the <lb></lb>firſt produceth <lb></lb>13333 1/3 the other <lb></lb>but 12500.</s></p><p type="margin"><s><margin.target id="marg353"></margin.target><emph type="italics"></emph>(b)<emph.end type="italics"></emph.end> It ſhall be <lb></lb>neer 2 2/5 inches, ac <lb></lb>counting the pace <lb></lb>to be Geometrical, <lb></lb>containing 5 foot.</s></p><p type="main"><s>SAGR. </s><s>Pardon me, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> you are too liberal. </s><s>For I would <lb></lb><arrow.to.target n="marg354"></arrow.to.target> <lb></lb>tell the <emph type="italics"></emph>Peripateticks,<emph.end type="italics"></emph.end> that though every ſhot ſhould hit the very <lb></lb>centre of the mark, that ſhould not in the leaſt diſprove the motion <lb></lb>of the Earth. </s><s>For the Gunners are ſo conſtantly imployed in le <lb></lb>velling the ſight and gun to the mark, as that they can hit the ſame, <lb></lb>notwithſtanding the motion of the Earth. </s><s>And I ſay, that if the <lb></lb>Earth ſhould ſtand ſtill, the ſhots would not prove true; but the <lb></lb>Occidental would be too low, and the Oriental too high: now let <lb></lb><emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> diſprove me if he can.</s></p><p type="margin"><s><margin.target id="marg354"></margin.target><emph type="italics"></emph>It is demonſtra <lb></lb>ted with great ſub <lb></lb>tilty, that the <lb></lb>Earths motion ſup <lb></lb>poſed, Canon ſhot <lb></lb>ought not to vary <lb></lb>more than in reſt.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>This is a ſubtilty worthy of <emph type="italics"></emph>Sagredus:<emph.end type="italics"></emph.end> But whether <lb></lb>this variation be to be obſerved in the motion, or in the reſt of the <lb></lb>Earth, it muſt needs be very ſmall, it muſt needs be ſwallowed up <pb xlink:href="040/01/180.jpg" pagenum="162"></pb>in thoſe very great ones which ſundry accidents continually pro <lb></lb><arrow.to.target n="marg355"></arrow.to.target> <lb></lb>duce. </s><s>And all this hath been ſpoken and granted on good grounds <lb></lb>to <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> and only with an intent to advertiſe him how much <lb></lb>it importeth to be cautious in granting many experiments for true <lb></lb>to thoſe who never had tried them, but only eagerly alledged them <lb></lb>juſt as they ought to be for the ſerving their purpoſe: This is ſpo <lb></lb>ken, I ſay, by way of ſurpluſſage and Corollary to <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> for <lb></lb><arrow.to.target n="marg356"></arrow.to.target> <lb></lb>the real truth is, that as concerning theſe ſhots, the ſame ought ex <lb></lb>actly to befall aſwell in the motion as in the reſt of the Terreſtrial <lb></lb>Globe; as likewiſe it will happen in all the other experiments <lb></lb>that either have been or can be produced, which have at firſt bluſh <lb></lb>ſo mnch ſemblance of truth, as the antiquated opinion of the <lb></lb>Earths motion hath of equivocation.</s></p><p type="margin"><s><margin.target id="marg355"></margin.target><emph type="italics"></emph>It is requiſite to <lb></lb>be very cautious in <lb></lb>admitting experi <lb></lb>ments for true, to <lb></lb>thoſe who never <lb></lb>tried them.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg356"></margin.target><emph type="italics"></emph>Experiments and <lb></lb>arguments againſt <lb></lb>the Earths motion <lb></lb>ſeem ſo far con <lb></lb>cluding, as they lie <lb></lb>hid under equi <lb></lb>vokes.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>As for my part I am fully ſatisfied, and very well un <lb></lb>derſtand that who ſo ſhall imprint in his fancy this general com <lb></lb>munity of the diurnal converſion amongſt all things Terreſtrial, <lb></lb>to all which it naturally agreeth, aſwell as in the old conceit of its <lb></lb>reſt about the centre, ſhall doubtleſſe diſcern the fallacy and equi <lb></lb>voke which made the arguments produced ſeem eoncluding. <lb></lb></s><s>There yet remains in me ſome hæſitancy (as I have hinted be <lb></lb>fore) touching the flight of birds; the which having as it were an <lb></lb>animate faculty of moving at their pleaſure with a thouſand mo <lb></lb>tions, and to ſtay long in the Air ſeparated from the Earth, and <lb></lb>therein with moſt irregular windings to go fluttering to and again, <lb></lb>I cannot conceive how amongſt ſo great a confuſion of motions, <lb></lb>they ſhould be able to retain the firſt commune motion; and in <lb></lb>what manner, having once made any ſtay behind, they can get <lb></lb>it up again, and overtake the ſame with flying, and kcep pace <lb></lb>with the Towers and trees which hurry with ſo precipitant a courſe <lb></lb>towards the Eaſt; I ſay ſo precipitant, for in the great circle of <lb></lb>the Globe it is little leſſe than a thouſand miles an hour, whereof <lb></lb>the flight of the ſwallow I believe makes not fifty.</s></p><p type="main"><s>SALV. </s><s>If the birds were to keep pace with the courſe of the <lb></lb>trees by help of their wings, they would oſ neceſſity flie very faſt; <lb></lb>and if they were deprived of the univerſal converſion, they would <lb></lb>lag as far behind; and their flight would ſeem as furious towards <lb></lb>the Weſt, and to him that could diſcern the ſame, it would <lb></lb>much exceed the flight of an arrow; but I think we could not be <lb></lb>able to perceive it, no more than we ſee a Canon bullet, whil'ſt <lb></lb>driven by the fury of the fire, it flieth through the Air: But the <lb></lb>truth is that the proper motion of birds, I mean of their flight, <lb></lb>hath nothing to do with the univerſal motion, to which it is nei <lb></lb>ther an help, nor an hinderance; and that which maintaineth <lb></lb>the ſaid motion unaltered in the birds, is the Air it ſelf, thorough <lb></lb>which they flie, which naturally following the <emph type="italics"></emph>Vertigo<emph.end type="italics"></emph.end> of the <pb xlink:href="040/01/181.jpg" pagenum="163"></pb>Earth, like as it carrieth the clouds along with it, ſo it tranſporteth <lb></lb>birds and every thing elſe which is pendent in the ſame; in ſo much <lb></lb>that as to the buſineſſe of keeping pace with the Earth, the birds <lb></lb>need take no care thereof, but for that work might ſleep perpe <lb></lb>tually.</s></p><p type="main"><s>SAGR. </s><s>That the Air can carry the clouds along with it, as <lb></lb>being matters eaſie for their lightneſſe to be moved and deprived <lb></lb>of all other contrary inclination, yea more, as being matters that <lb></lb>partake alſo of the conditions and properties of the Earth; I com <lb></lb>prehend without any difficulty; but that birds, which as having <lb></lb>life, may move with a motion quite contrary to the diurnal, once <lb></lb>having ſurceaſed the ſaid motion, the Air ſhould reſtore them to <lb></lb>it, ſeems to me a little ſtrange, and the rather for that they are ſolid <lb></lb>and weighty bodies; and withal, we ſee; as hath been ſaid, ſtones <lb></lb>and other grave bodies to lie unmoved againſt the <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> of the <lb></lb>air; and when they ſuffer themſelves to be overcome thereby, <lb></lb>they never acquire ſo much velocity as the wind which carrieth <lb></lb>them.</s></p><p type="main"><s>SALV. </s><s>We aſcribe not ſo little force, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> to the moved <lb></lb>Air, which is able to move and bear before it ſhips full fraught, <lb></lb>to tear up trees by the roots, and overthrow Towers when it <lb></lb>moveth ſwiftly; and yet we cannot ſay that the motion of the <lb></lb>Air in theſe violent operations is neer ſo violent, as that of the <lb></lb>diurnal revolution.</s></p><p type="main"><s>SIMP. </s><s>You ſee then that the moved Air may alſo cotinue the <lb></lb>motion of projects, according to the Doctrine of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end>; and <lb></lb>it ſeemed to me very ſtrange that he ſhould have erred in this <lb></lb>particular.</s></p><p type="main"><s>SALV. </s><s>It may without doubt, in caſe it could continue it ſelf, <lb></lb>but lik as when the wind ceaſing neither ſhips go on, nor trees are <lb></lb>blown down, ſo the motion in the Air not continuing after the <lb></lb>ſtone is gone out of the hand, and the Air ceaſing to move, it <lb></lb>followeth that it muſt be ſomething elſe beſides the Air that ma <lb></lb>keth the projects to move.</s></p><p type="main"><s>SIMP. </s><s>But how upon the winds being laid, doth the ſhip ceaſe <lb></lb>to move? </s><s>Nay you may ſee that when the wind is down, and <lb></lb>the ſails furl'd, the veſſel continueth to run whole miles.</s></p><p type="main"><s>SALV. </s><s>But this maketh againſt your ſelf <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> for that <lb></lb>the wind being laid that filling the ſails drove on the ſhip, yet ne <lb></lb>vertheleſſe doth it without help of the <emph type="italics"></emph>medium<emph.end type="italics"></emph.end> continue its <lb></lb>courſe.</s></p><p type="main"><s>SIMP. </s><s>It might be ſaid that the water was the <emph type="italics"></emph>medium<emph.end type="italics"></emph.end> which <lb></lb>carried forward the ſhip, and maintain'd it in motion.</s></p><p type="main"><s>SALV. </s><s>It might indeed be ſo affirmed, if you would ſpeak <lb></lb>quite contrary to truth; for the truth is, that the water, by rea <pb xlink:href="040/01/182.jpg" pagenum="164"></pb>ſon of its great reſiſtance to the diviſion made by the hull of the <lb></lb>ſhip, doth with great noiſe reſiſt the ſame; nor doth it permit it <lb></lb>of a great while to acquire that velocity which the wind would <lb></lb>confer upon it, were the obſtacle of the water removed. </s><s>Per <lb></lb>haps <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> you have never conſidered with what fury the <lb></lb>water beſets a bark, whil'ſt it forceth its way through a ſtanding <lb></lb>water by help of Oars or Sails: for if you had ever minded that <lb></lb>effect, you would not now have produced ſuch an abſurdity. <lb></lb></s><s>And I am thinking that you have hitherto been one of thoſe who <lb></lb>to find out how ſuch things ſucceed, and to come to the know <lb></lb>ledg of natural effects, do not betake themſelves to a Ship, a <lb></lb>Croſſe-bow, or a piece of Ordinance, but retire into their ſtu <lb></lb>dies, and turn over Indexes and Tables to ſee whether <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> <lb></lb>hath ſpoken any thing thereof, and being aſſured of the true <lb></lb>ſenſe of the Text, neither deſire nor care for knowing any <lb></lb>more. <lb></lb><arrow.to.target n="marg357"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg357"></margin.target><emph type="italics"></emph>The great feli <lb></lb>city for which they <lb></lb>are much to be en <lb></lb>vied who perſwade <lb></lb>themſelves that <lb></lb>they know every <lb></lb>thing.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>This is a great felicity, and they are to be much en <lb></lb>vied for it. </s><s>For if knowledg be deſired by all, and if to be wiſe, <lb></lb>be to think ones ſelf ſo, they enjoy a very great happineſſe, for <lb></lb>that they may perſwade themſelves that they know and underſtand <lb></lb>all things, in ſcorn of thoſe who knowing, that they underſtand <lb></lb>not what theſe think they underſtand, and conſequently ſeeking <lb></lb>that they know not the very leaſt particle of what is knowable, <lb></lb>kill themſelves with waking and ſtudying, and conſume their days <lb></lb>in experiments and obſervations. </s><s>But pray you let us return to <lb></lb>our birds; touching which you have ſaid, that the Air being mo <lb></lb>ved with great velocity, might reſtore unto them that part of the <lb></lb>diurnal motion which amongſt the windings of their flight they <lb></lb>might have loſt; to which I reply, that the agitated Air ſeemeth <lb></lb>unable to confer on a ſolid and grave body, ſo great a velocity as <lb></lb>its own: And becauſe that of the Air is as great as that of the <lb></lb>Earth, I cannot think that the Air is able to make good the loſſe <lb></lb>of the birds retardation in flight.</s></p><p type="main"><s>SALV. </s><s>Your diſcourſe hath in it much of probability, and to <lb></lb>ſtick at trivial doubts is not for an acute wit; yet nevertheleſſe the <lb></lb>probability being removed, I believed that it hath not a jot more <lb></lb>force than the others already conſidered and reſolved.</s></p><p type="main"><s>SAGR. </s><s>It is moſt certain that if it be not neceſſatily conclu <lb></lb>dent, its efficacy muſt needs be juſt nothing at all, for it is <lb></lb>onely when the concluſion is neceſſary that the opponent hath no <lb></lb>thing to alledg on the contrary.</s></p><p type="main"><s>SALV. </s><s>Your making a greater ſcruple of this than of the other <lb></lb>inſtances dependeth, if I miſtake not, upon the birds being ani <lb></lb>mated, and thereby enabled to uſe their ſtrength at pleaſure a <lb></lb>gainſt the primary motion in-bred in terrene bodies: like as for <pb xlink:href="040/01/183.jpg" pagenum="165"></pb>example, we ſee them whil'ſt they are alive to fly upwards, a thing <lb></lb>altogether impoſſible for them to do as they are grave bodies; <lb></lb>whereas being dead they can onely fall downwards; and there <lb></lb>fore you hold that the reaſons that are of force in all the kinds of <lb></lb>projects above named, cannot take place in birds: Now this is <lb></lb>very true; and becauſe it is ſo, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> that doth not appear <lb></lb>to be done in thoſe projects, which we ſee the birds to do. </s><s>For if </s></p><p type="main"><s><arrow.to.target n="marg358"></arrow.to.target> <lb></lb>from the top of a Tower you let fall a dead bird and a live one, <lb></lb>the dead bird ſhall do the ſame that a ſtone doth, that is, it ſhall <lb></lb>firſt follow the general motion diurnal, and then the motion of <lb></lb>deſcent, as grave; but if the bird let fall, be a live, what ſhall <lb></lb>hinder it, (there ever remaining in it the diurnal motion) from <lb></lb>ſoaring by help of its wings to what place of the Horizon it ſhall <lb></lb>pleaſe? </s><s>and this new motion, as being peculiar to the bird, and <lb></lb>not participated by us, muſt of neceſſity be viſible to us; and if <lb></lb>it be moved by help of its wings towards the Weſt, what ſhall <lb></lb>hinder it from returning with a like help of its wings unto the <lb></lb>Tower. </s><s>And, becauſe, in the laſt place, the birds wending its <lb></lb>flight towards the Weſt was no other than a withdrawing from <lb></lb>the diurnal motion, (which hath, ſupppoſe ten degrees of velocity) <lb></lb>one degree onely, there did thereupon remain to the bird whil'ſt <lb></lb>it was in its flight nine degrees of velocity, and ſo ſoon as it did <lb></lb>alight upon the the Earth, the ten common degrees returned to it, <lb></lb>to which, by flying towards the Eaſt it might adde one, and with <lb></lb>thoſe eleven overtake the Tower. </s><s>And in ſhort, if we well con <lb></lb>ſider, and more narrowly examine the effects of the flight of <lb></lb>birds, they differ from the projects ſhot or thrown to any part of <lb></lb>the World in nothing, ſave onely that the projects are moved by an <lb></lb>external projicient, and the birds by an internal principle. </s><s>And <lb></lb><arrow.to.target n="marg359"></arrow.to.target> <lb></lb>here for a final proof of the nullity of all the experiments before <lb></lb>alledged, I conceive it now a time and place convenient to <lb></lb>demonſtrate a way how to make an exact trial of them all. <lb></lb></s><s>Shut your ſelf up with ſome friend in the grand Cabbin between <lb></lb>the decks of ſome large Ship, and there procure gnats, flies, and <lb></lb>ſuch other ſmall winged creatures: get alſo a great tub (or <lb></lb>other veſſel) full of water, and within it put certain fiſhes; let <lb></lb>alſo a certain bottle be hung up, which drop by drop letteth forth <lb></lb>its water into another bottle placed underneath, having a narrow <lb></lb>neck: and, the Ship lying ſtill, obſerve diligently how thoſe ſmall <lb></lb>winged animals fly with like velocity towards all parts of the Ca <lb></lb>bin; how the fiſhes ſwim indifferently towards all ſides; and how <lb></lb>the diſtilling drops all fall into the bottle placed underneath. </s><s>And <lb></lb>caſting any thing towards your friend, you need not throw it with <lb></lb>more force one way then another, provided the diſtances be equal: <lb></lb>and leaping, as the ſaying is, with your feet cloſed, you will reach <pb xlink:href="040/01/184.jpg" pagenum="166"></pb>as far one way as another. </s><s>Having obſerved all theſe particulars, <lb></lb>though no man doubteth that ſo long as the veſſel ſtands ſtill, they <lb></lb>ought to ſucceed in this manner; make the Ship to move with <lb></lb>what velocity you pleaſe; for (ſo long as the motion is uniforme, <lb></lb>and not fluctuating this way and that way) you ſhall not diſcern <lb></lb>any the leaſt alteration in all the forenamed effects; nor can you <lb></lb>gather by any of them whether the Ship doth move or ſtand ſtill. <lb></lb></s><s>In leaping you ſhall reach as far upon the floor, as before; nor for <lb></lb>that the Ship moveth ſhall you make a greater leap towards the <lb></lb>poop than towards the prow; howbeit in the time that you ſtaid <lb></lb>in the Air, the floor under your feet ſhall have run the contrary way <lb></lb>to that of your jump; and throwing any thing to your companion <lb></lb>you ſhall not need to caſt it with more ſtrength that it may reach <lb></lb>him, if he ſhall be towards the prow, and you towards the poop, <lb></lb>then if you ſtood in a contrary ſituation; the drops ſhall all diſtill <lb></lb>as before into the inferiour bottle and not ſo much as one ſhall <lb></lb>fall towards the poop, albeit whil'ſt the drop is in the Air, the Ship <lb></lb>ſhall have run many feet; the Fiſhes in their water ſhall not ſwim <lb></lb>with more trouble towards the fore-part, than towards the hinder <lb></lb>part of the tub; but ſhall with equal velocity make to the bait <lb></lb>placed on any ſide of the tub; and laſtly, the flies and gnats <lb></lb>ſhall continue their flight indifferently towards all parts; nor <lb></lb>ſhall they ever happen to be driven together towards the ſide of <lb></lb>the Cabbin next the prow, as if they were wearied with fol <lb></lb>lowing the ſwift courſe of the Ship, from which through their <lb></lb>ſuſpenſion in the Air, they had been long ſeparated; and if <lb></lb>burning a few graines of incenſe you make a little ſmoke, <lb></lb>you ſhall ſee it aſcend on high, and there in manner of a cloud <lb></lb>ſuſpend it ſelf, and move indifferently, not inclining more to one <lb></lb>ſide than another: and of this correſpondence of effects the cauſe <lb></lb>is for that the Ships motion is common to all the things contained <lb></lb>in it, and to the Air alſo; I mean if thoſe things be ſhut up in the <lb></lb>Cabbin: but in caſe thoſe things were above deck in the open Air, <lb></lb>and not obliged to follow the courſe of the Ship, differences more <lb></lb>or leſſe notable would be obſerved in ſome of the fore-named ef <lb></lb>fects, and there is no doubt but that the ſmoke would ſtay behind <lb></lb>as much as the Air it ſelf; the flies alſo, and the gnats being hin <lb></lb>dered by the Air would not be able to follow the motion of the <lb></lb>Ship, if they were ſeparated at any diſtance from it. </s><s>But keeping <lb></lb>neer thereto, becauſe the Ship it ſelf as being an unfractuous Fa <lb></lb>brick, carrieth along with it part of its neereſt Air, they would <lb></lb>follow the ſaid Ship without any pains or difficulty. </s><s>And for the <lb></lb>like reaſon we ſee ſometimes in riding poſt, that the troubleſome <lb></lb>flies and ^{*} hornets do follow the horſes flying ſometimes to one, <lb></lb><arrow.to.target n="marg360"></arrow.to.target> <lb></lb>ſometimes to another part of the body, but in the falling drops <pb xlink:href="040/01/185.jpg" pagenum="167"></pb>the difference would be very ſmall; and in the ſalts, and projecti <lb></lb>ons of grave bodies altogether imperceptible.</s></p><p type="margin"><s><margin.target id="marg358"></margin.target><emph type="italics"></emph>The anſwer to <lb></lb>the argument ta <lb></lb>ken from the flight <lb></lb>of birds contrary <lb></lb>to the motion of the <lb></lb>Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg359"></margin.target><emph type="italics"></emph>An experiment <lb></lb>with which alone <lb></lb>is ſhewn the nullity <lb></lb>of all the objecti <lb></lb>ons produced a <lb></lb>gainst the motion <lb></lb>of the Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg360"></margin.target>* Tafaris, <emph type="italics"></emph>borſe <lb></lb>flyes.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Though it came not into my thoughts to make triall of <lb></lb>theſe obſervations, when I was at Sea, yet am I confident that they <lb></lb>will ſucceed in the ſame manner, as you have related; in confirma <lb></lb>tion of which I remember that being in my Cabbin I have asked <lb></lb>an hundred times whether the Ship moved or ſtood ſtill; and <lb></lb>ſometimes I have imagined that it moved one way, when it ſteered <lb></lb>quite another way. </s><s>I am therefore as hitherto ſatisfied and con <lb></lb>vinced of the nullity of all thoſe experiments that have been pro <lb></lb>duced in proof of the negative part. </s><s>There now remains the ob <lb></lb>jection founded upon that which experience ſhews us, namely, that <lb></lb>a ſwift <emph type="italics"></emph>Vertigo<emph.end type="italics"></emph.end> or whirling about hath a faculty to extrude and <lb></lb>diſperſe the matters adherent to the machine that turns round; <lb></lb>whereupon many were of opinion, and <emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> amongſt the reſt, <lb></lb>that if the Earth ſhould turn round with ſo great velocity, the <lb></lb>ſtones and creatures upon it ſhould be toſt into the Skie, and <lb></lb>that there could not be a morter ſtrong enough to faſten buildings <lb></lb>ſo to their foundations, but that they would likewiſe ſuffer a like <lb></lb>extruſion.</s></p><p type="main"><s>SALV. </s><s>Before I come to anſwer this objection, I cannot but <lb></lb>take notice of that which I have an hundred times obſerved, and <lb></lb>not without laughter, to come into the minds of moſt men ſo ſoon <lb></lb>as ever they hear mention made of this motion of the Earth, which <lb></lb>is believed by them ſo fixt and immoveable, that they not only ne <lb></lb>ver doubted of that reſt, but have ever ſtrongly believed that all <lb></lb>other men aſwell as they, have held it to be created immoveable, <lb></lb>and ſo to have continued through all ſucceeding ages: and being <lb></lb><arrow.to.target n="marg361"></arrow.to.target> <lb></lb>ſetled in this perſwaſion, they ſtand amazed to hear that any one <lb></lb>ſhould grant it motion, as if, after that he had held it to be immo <lb></lb>veable, he had fondly thought it to commence its motion then <lb></lb>(and not till then) when <emph type="italics"></emph>Pythagoras<emph.end type="italics"></emph.end> (or whoever elſe was the firſt <lb></lb>hinter of its mobility) ſaid that it did move. </s><s>Now that ſuch a foo <lb></lb>liſh conceit (I mean of thinking that thoſe who admit the motion <lb></lb>of the Earth, have firſt thought it to ſtand ſtill from its creation, <lb></lb>untill the time of <emph type="italics"></emph>Pythagoras,<emph.end type="italics"></emph.end> and have onely made it moveable <lb></lb>after that <emph type="italics"></emph>Pythagor as<emph.end type="italics"></emph.end> eſteemed it ſo) findeth a place in the mindes <lb></lb>of the vulgar, and men of ſhallow capacities, I do not much won <lb></lb>der; but that ſuch perſons as <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> ſhould alſo <lb></lb>run into this childiſh miſtake, is to my thinking a more admirable <lb></lb>and unpardonable folly.</s></p><p type="margin"><s><margin.target id="marg361"></margin.target><emph type="italics"></emph>The ſtupidity of <lb></lb>ſome that think the <lb></lb>Earth to have be <lb></lb>gun to move, when<emph.end type="italics"></emph.end> <lb></lb>Pythagoras <emph type="italics"></emph>began <lb></lb>to affirme that it <lb></lb>did ſo.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>You believe then, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> that <emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> thought, that <lb></lb>in his Diſputation he was to maintain the ſtability of the Earth <lb></lb>againſt ſuch perſons, as granting it to have been immoveable, un <lb></lb>till the time of <emph type="italics"></emph>Pythagoras,<emph.end type="italics"></emph.end> did affirm it to have been but then <pb xlink:href="040/01/186.jpg" pagenum="168"></pb>made moveable, when the ſaid <emph type="italics"></emph>Pythagoras<emph.end type="italics"></emph.end> aſcribed unto it mo <lb></lb>tion.</s></p><p type="main"><s>SALV. </s><s>We can think no other, if we do but conſider the way <lb></lb><arrow.to.target n="marg362"></arrow.to.target> <lb></lb>he taketh to confute their aſſertion; the confutation of which <lb></lb>conſiſts in the demolition of buildings, and the toſſing of ſtones, <lb></lb>living creatures and men themſelves up into the Air. </s><s>And be <lb></lb>cauſe ſuch overthrows and extruſions cannot be made upon buil <lb></lb>dings and men, which were not before on the Earth, nor can men <lb></lb>be placed, nor buildings erected upon the Earth, unleſſe when it <lb></lb>ſtandeth ſtill; hence therefore it is cleer, that <emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> argueth a <lb></lb>gainſt thoſe, who having granted the ſtability of the Earth for <lb></lb>ſome time, that is, ſo long as living creatures, ſtones, and Maſons <lb></lb>were able to abide there, and to build Palaces and Cities, make it <lb></lb>afterwards precipitately moveable to the overthrow and deſtructi <lb></lb>of Edifices, and living creatures, &c. </s><s>For if he had undertook to <lb></lb>diſpute againſt ſuch as had aſcribed that revolution to the Earth <lb></lb>from its firſt creation, he would have confuted them by ſaying, <lb></lb>that if the Earth had alwayes moved, there could never have been <lb></lb>placed upon it either men or ſtones; much leſs could buildings <lb></lb>have been erected, or Cities founded, &c.</s></p><p type="margin"><s><margin.target id="marg362"></margin.target>Ariſtotle <emph type="italics"></emph>and<emph.end type="italics"></emph.end> <lb></lb>Ptolomy <emph type="italics"></emph>ſeem to <lb></lb>confute the mobili <lb></lb>ty of the Earth a <lb></lb>gainſt thoſe who <lb></lb>thought that it ha <lb></lb>ving a long time <lb></lb>ſtood still, did be <lb></lb>gin to move in the <lb></lb>time of<emph.end type="italics"></emph.end> Pythagoras</s></p><p type="main"><s>SIMP. </s><s>I do not well conceive theſe <emph type="italics"></emph>Ariſtotelick<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ptolo <lb></lb>maick<emph.end type="italics"></emph.end> inconveniences.</s></p><p type="main"><s>SALV. <emph type="italics"></emph>Ptolomey<emph.end type="italics"></emph.end> either argueth againſt thoſe who have eſteem <lb></lb>ed the Earth always moveable; or againſt ſuch as have held that <lb></lb>it ſtood for ſome time ſtill, and hath ſince been ſet on moving. <lb></lb></s><s>If againſt the firſt, he ought to ſay, that the Earth did not always <lb></lb>move, for that then there would never have been men, animals, or <lb></lb>edifices on the Earth, its <emph type="italics"></emph>vertigo<emph.end type="italics"></emph.end> not permitting them to ſtay <lb></lb>thereon. </s><s>But in that he arguing, ſaith that the Earth doth not <lb></lb>move, becauſe that beaſts, men, and houſes before plac'd on the <lb></lb>Earth would precipitate, he ſuppoſeth the Earth to have been once <lb></lb>in ſuch a ſtate, as that it did admit men and beaſts to ſtay, and <lb></lb>build thereon; the which draweth on the conſequence, that it <lb></lb>did for ſome time ſtand ſtill, to wit, was apt for the abode of a <lb></lb>nimals and erection of buildings. </s><s>Do you now conceive what I <lb></lb>would ſay?</s></p><p type="main"><s>SIMP. </s><s>I do, and I do not: but this little importeth to the <lb></lb>merit of the cauſe; nor can a ſmall miſtake of <emph type="italics"></emph>Ptolomey,<emph.end type="italics"></emph.end> com <lb></lb>mitted through inadvertencie be ſufficient to move the Earth, <lb></lb>when it is immoveable. </s><s>But omitting cavils, let us come to the <lb></lb>ſubſtance of the argument, which to me ſeems unanſwerable.</s></p><p type="main"><s>SALV. </s><s>And I, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> will drive it home, and re-inforce it, <lb></lb>by ſhewing yet more ſenſibly, that it is true that grave bodies <lb></lb>turn'd with velocity about a ſettled centre, do acquire an <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> <lb></lb>of moving, and receding to a diſtance from that centre, even <pb xlink:href="040/01/187.jpg" pagenum="169"></pb>then when they are in a ſtate of having a propenſion of moving <lb></lb>naturally to the ſame. </s><s>Tie a bottle that hath water in it, to <lb></lb>the end of a cord, and holding the other end faſt in your hand, <lb></lb>and making the cord and your arm the ſemi-diameter, and the <lb></lb>knitting of the ſhoulder the centre, ſwing the bottle very faſt a <lb></lb>bout, ſo as that it may deſcribe the circumference of a circle, <lb></lb>which, whether it be parallel to the Horizon, or perpendicular to <lb></lb>it, or any way inclined, it ſhall in all caſes follow, that the wa <lb></lb>ter will not fall out of the bottle: nay, he that ſhall ſwing it, <lb></lb>ſhall find the cord always draw, and ſtrive to go farther from the <lb></lb>ſhoulder. </s><s>And if you bore a hole in the bottom of the bottle, <lb></lb>you ſhall ſee the water ſpout forth no leſs upwards into the skie, <lb></lb>than laterally, and downwards to the Earth; and if inſtead of wa <lb></lb>ter, you ſhall put little pebble ſtones into the bottle, and ſwing it <lb></lb>in the ſame manner, you ſhall find that they will ſtrive in the like <lb></lb>manner againſt the cord. </s><s>And laſtly, we ſee boys throw ſtones <lb></lb>a great way, by ſwinging round a piece of a ſtick, at the end of <lb></lb>which the ſtone is let into a ſlit <emph type="italics"></emph>(which ſtick is called by them a <lb></lb>ſling;)<emph.end type="italics"></emph.end> all which are arguments of the truth of the concluſion, <lb></lb>to wit, that the <emph type="italics"></emph>vertigo<emph.end type="italics"></emph.end> or ſwing conferreth upon the moveable, <lb></lb>a motion towards the circumference, in caſe the motion be ſwift: <lb></lb>and therefore if the Earth revolve about its own centre, the mo <lb></lb>tion of the ſuperficies, and eſpecially towards the great circle, <lb></lb>as being incomparably more ſwift than thoſe before named, ought <lb></lb>to extrude all things up into the air.</s></p><p type="main"><s>SIMP. </s><s>The Argument ſeemeth to me very well proved and <lb></lb>inforced; and I believe it would be an hard matter to anſwer and <lb></lb>overthrow it.</s></p><p type="main"><s>SALV. </s><s>Its ſolution dependeth upon certain notions no leſs <lb></lb>known and believed by you, than by my ſelf: but becauſe they <lb></lb>come not into your mind, therefore it is that you perceive not the <lb></lb>anſwer; wherefore, without telling you it (for that you know the <lb></lb>ſame already) I ſhall with onely aſſiſting your memory, make you <lb></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></lb>hath made me almoſt think that you lean to that opinion of <emph type="italics"></emph>Pla-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg363"></arrow.to.target> <lb></lb><emph type="italics"></emph>to, Quòd noſtrum ſcire ſit quoddam reminiſci<emph.end type="italics"></emph.end>; therefore I intreat <lb></lb>you to free me from this doubt, by letting me know your judg <lb></lb>ment.</s></p><p type="margin"><s><margin.target id="marg363"></margin.target><emph type="italics"></emph>Our krowledg is <lb></lb>a kind of reminiſ <lb></lb>cence according to<emph.end type="italics"></emph.end> <lb></lb>Plato.</s></p><p type="main"><s>SALV. </s><s>What I think of the opinion of <emph type="italics"></emph>Plato,<emph.end type="italics"></emph.end> you may gather <lb></lb>from my words and actions. </s><s>I have already in the precedent con <lb></lb>ferences expreſly declared my ſelf more than once; I will purſue <lb></lb>the ſame ſtyle in the preſent caſe, which may hereafter ſerve you <lb></lb>for an example, thereby the more eaſily to gather what my opi <lb></lb>nion is touching the attainment of knowledg, when a time ſhall <pb xlink:href="040/01/188.jpg" pagenum="170"></pb>offer upon ſome other day: but I would not have <emph type="italics"></emph>Sagredus<emph.end type="italics"></emph.end> of <lb></lb>fended at this digreſſion.</s></p><p type="main"><s>SAGR. </s><s>I am rather very much pleaſed with it, for that I re <lb></lb>member that when I ſtudied Logick, I could never comprehend that <lb></lb>ſo much cry'd up and moſt potent demonſtration of <emph type="italics"></emph>Ariſtotle.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Let us go on therefore; and let <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> tell me <lb></lb>what that motion is which the ſtone maketh that is held faſt in the <lb></lb>ſlit of the ſling, when the boy ſwings it about to throw it a great <lb></lb>way?</s></p><p type="main"><s>SIMP. </s><s>The motion of the ſtone, ſo long as it is in the ſlit, is <lb></lb>circular, that is, moveth by the arch of a circle, whoſe ſtedfaſt <lb></lb>centre is the knitting of the ſhoulder, and its ſemi-diameter the arm <lb></lb>and ſtick.</s></p><p type="main"><s>SALV. </s><s>And when the ſtone leaveth the ſling, what is its mo <lb></lb>tion? </s><s>Doth it continue to follow its former circle, or doth it go <lb></lb>by another line?</s></p><p type="main"><s>SIMP. </s><s>It will continue no longer to ſwing round, for then it <lb></lb>would not go farther from the arm of the projicient, whereas <lb></lb>we ſee 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></lb>ver conſidered it before.</s></p><p type="main"><s>SALV. </s><s>Hark hither, <emph type="italics"></emph>Sagredus<emph.end type="italics"></emph.end>; this is the <emph type="italics"></emph>Quoddam reminiſci<emph.end type="italics"></emph.end> <lb></lb>in a ſubject well underſtood. </s><s>You have pauſed a great while, <lb></lb><emph type="italics"></emph>Simplicius.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>As far as I can ſee, the motion received in going out of <lb></lb>the ſling, can be no other than by a right line; nay, it muſt ne <lb></lb>ceſſarily be ſo, if we ſpeak of the pure adventitious <emph type="italics"></emph>impetus.<emph.end type="italics"></emph.end> I <lb></lb>was a little puzled to ſee it make an arch, but becauſe that arch <lb></lb>bended all the way upwards, and no other way, I conceive that <lb></lb><arrow.to.target n="marg364"></arrow.to.target> <lb></lb>that incurvation cometh from the gravity of the ſtone, which na <lb></lb>turally draweth it downwards. </s><s>The impreſſed <emph type="italics"></emph>impetus,<emph.end type="italics"></emph.end> I ſay, <lb></lb>without reſpecting the natural, is by a right line.</s></p><p type="margin"><s><margin.target id="marg364"></margin.target><emph type="italics"></emph>The motion im <lb></lb>preſſed by the pro <lb></lb>jicient is onely by a <lb></lb>right line.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>But by what right line? </s><s>Becauſe infinite, and towards <lb></lb>every ſide may be produced from the ſlit of the ſling, and from the <lb></lb>point of the ſtones ſeparation from the ſling.</s></p><p type="main"><s>SIMP. </s><s>It moveth by that line which goeth directly from the <lb></lb>motion which the ſtone made in the ſling.</s></p><p type="main"><s>SALV. </s><s>The motion of the ſtone whilſt it was in the ſlit, you <lb></lb>have affirmed already to be circular; now circularity oppoſeth <lb></lb>directneſs, there not being in the circular line any part that is di <lb></lb>rect or ſtreight.</s></p><p type="main"><s>SIMP I mean not that the projected motion is direct in re <lb></lb>ſpect of the whole circle, but in reference to that ultimate point, <lb></lb>where the circular motion determineth. </s><s>I know what I would <pb xlink:href="040/01/189.jpg" pagenum="171"></pb>ſay, but do not well know how to expreſs my ſelf.</s></p><p type="main"><s>SALV. </s><s>And I alſo perceive that you underſtand the buſineſs, <lb></lb>but that you have not the proper terms, wherewith to expreſs the <lb></lb>ſame. </s><s>Now theſe I can eaſily teach you; teach you, that is, as <lb></lb>to the words, but not as to the truths, which are things. </s><s>And that <lb></lb>you may plainly ſee that you know the thing I ask you, and onely <lb></lb>want language to expreſs it, tell me, when you ſhoot a bullet out <lb></lb>of a gun, towards what part is it, that its acquired <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> carri <lb></lb>eth it?</s></p><p type="main"><s>SIMP. </s><s>Its acquired <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> carrieth it in a right line, which <lb></lb>continueth the rectitude of the barrel, that is, which inclineth nei <lb></lb>ther to the right hand nor to the left, nor upwards not down <lb></lb>wards.</s></p><p type="main"><s>SALV. </s><s>Which in ſhort is aſmuch as to ſay, it maketh no angle <lb></lb>with the line of ſtreight motion made by the ſling.</s></p><p type="main"><s>SIMP. </s><s>So I would have ſaid.</s></p><p type="main"><s>SALV. </s><s>If then the line of the projects motion be to continue <lb></lb>without making an angle upon the circular line deſcribed by it, <lb></lb>whilſt it was with the projicient; and if from this circular motion it <lb></lb>ought to paſs to the right motion, what ought this right line to be?</s></p><p type="main"><s>SIMP. </s><s>It muſt needs be that which toucheth the circle in the <lb></lb>point of ſeparation, for that all others, in my opinion, being pro <lb></lb>longed would interſect the circumference, and by that means make <lb></lb>ſome angle therewith.</s></p><p type="main"><s>SALV. </s><s>You have argued very well, and ſhewn your ſelf half a <lb></lb>Geometrician. </s><s>Keep in mind therefore, that your true opinion <lb></lb>is expreſt in theſe words, namely, That the project acquireth an <lb></lb><emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> of moving by the Tangent, the arch deſcribed by the <lb></lb>motion of the projicient, in the point of the ſaid projects ſepara <lb></lb>tion from the projicient.</s></p><p type="main"><s>SIMP. </s><s>I underſtand you very well, and this is that which I <lb></lb>would ſay.</s></p><p type="main"><s>SALV. </s><s>Of a right line which toucheth a circle, which of its <lb></lb>points is the neareſt 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></lb>circumference of a circle, and the reſt without: and the points of <lb></lb>the circumference are all equidiſtant from the centre.</s></p><p type="main"><s>SALV. </s><s>Therefore a moveable departing from the contact, and <lb></lb>moving by the ſtreight Tangent, goeth continually farther and <lb></lb>farther from the contact, and alſo from the centre of the circle.</s></p><p type="main"><s>SIMP. </s><s>It doth ſo doubtleſs.</s></p><p type="main"><s>SALV. </s><s>Now if you have kept in mind the propoſitions, which <lb></lb>you have told me, lay them together, and tell me what you gather <lb></lb>from them.</s></p><p type="main"><s>SIMP. </s><s>I think I am not ſo forgetful, but that I do remember <pb xlink:href="040/01/190.jpg" pagenum="172"></pb><arrow.to.target n="marg365"></arrow.to.target> <lb></lb>them. </s><s>From the things premiſed I gather that the project ſwiftly <lb></lb>ſwinged round by the projicient, in its ſeparating from it, doth re <lb></lb>tain an <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> of continuing its motion by the right line, which <lb></lb>toucheth the circle deſcribed by the motion of the projicient in <lb></lb>the point of ſeparation, by which motion the project goeth con <lb></lb>tinually receding from the centre of the circle deſcribed by the <lb></lb>motion of the projicient.</s></p><p type="margin"><s><margin.target id="marg365"></margin.target><emph type="italics"></emph>The project mo <lb></lb>veth by the Tan <lb></lb>gent of the circle of <lb></lb>the motion prece <lb></lb>dent in the point of <lb></lb>ſeparation.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>You know then by this time the reaſon why grave bo <lb></lb>dies ſticking to the rim of a wheele, ſwiftly moved, are extruded <lb></lb>and thrown beyond the circumference to yet a farther diſtance <lb></lb>from the centre.</s></p><p type="main"><s>SIMP. </s><s>I think I underſtand this very well; but this new know <lb></lb>ledg rather increaſeth than leſſeneth my incredulity that the Earth <lb></lb>can turn round with ſo great velocity, without extruding up into <lb></lb>the sky, ſtones, animals, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>In the ſame manner that you have underſtood all this, <lb></lb>you ſhall, nay you do underſtand the reſt: and with recollecting <lb></lb>your ſelf, you may remember the ſame without the help of o <lb></lb>thers: but that we may loſe no time, I will help your memory <lb></lb>therein. </s><s>You do already know of your ſelf, that the circular mo <lb></lb>tion of the projicient impreſſeth on the project an <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> of mo <lb></lb>ving (when they come to ſeparate) by the right Tangent, the <lb></lb>circle of the motion in the point of ſeparation, and continuing a <lb></lb>long by the ſame the motion ever goeth receding farther and far <lb></lb>ther from the projicient: and you have ſaid, that the project <lb></lb>would continue to move along by that right line, if there were not <lb></lb>by its proper weight an inclination of deſcent added unto it; from <lb></lb>which the incurvation of the line of motion is derived. </s><s>It ſeems <lb></lb>moreover that you knew of your ſelf, that this incurvation al <lb></lb>ways bended towards the centre of the Earth, for thither do all <lb></lb>grave bodies tend. </s><s>Now I proceed a little farther, and ask you, whe <lb></lb>ther the moveable after its ſeparation, in continuing the right mo <lb></lb>tion goeth always equally receding from the centre, or if you will, <lb></lb>from the circumference of that circle, of which the precedent mo <lb></lb>tion was a part; which is as much as to ſay, Whether a moveable, <lb></lb>that forſaking the point of a Tangent, and moving along by the <lb></lb>ſaid Tangent, doth equally recede from the point of contact, and <lb></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></lb>recedeth very little from the circumference, wherewith it keepeth <lb></lb>a very narrow angle, but in its going farther and farther <lb></lb>off, the diſtance always encreaſeth with a greater proportion; ſo <lb></lb>that in a circle that ſhould have <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> ten yards of diameter, a point <lb></lb>of the Tangent that was diſtant from the contact but two palms, <lb></lb>would be three or four times as far diſtant from the circumference <pb xlink:href="040/01/191.jpg" pagenum="173"></pb>of the circle, as a point that was diſtant from the contaction one <lb></lb>palm, and the point that was diſtant half a palm, I likewiſe believe <lb></lb>would ſcarſe recede the fourth part of the diſtance of the ſecond: <lb></lb>fo that within an inch or two of the contact, the ſeparation of the <lb></lb>Tangent from the circumference is ſcarſe diſcernable.</s></p><p type="main"><s>SALV. </s><s>So that the receſſion of the project from the circumfe <lb></lb>rence of the precedent circular motion is very ſmall in the begin <lb></lb>ing?</s></p><p type="main"><s>SIMP. </s><s>Almoſt inſenſible.</s></p><p type="main"><s>SALV. </s><s>Now tell me a little; the project, which from the mo <lb></lb>tion of the projicient receiveth an <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> of moving along the <lb></lb>Tangent in a right line, and that would keep unto the ſame, did <lb></lb>not its own weight depreſs it downwards, how long is it after the <lb></lb>ſeparation, ere it begin to decline downwards.</s></p><p type="main"><s>SIMP. </s><s>I believe that it beginneth preſently; for it not ha <lb></lb>ving any thing to uphold it, its proper gravity cannot but ope <lb></lb>rate. <lb></lb><arrow.to.target n="marg366"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg366"></margin.target><emph type="italics"></emph>A grave project, <lb></lb>as ſoon as it is ſe <lb></lb>parated from the <lb></lb>projicient begineth <lb></lb>to decline.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>So that, if that ſame ſtone, which being extruded from <lb></lb>that wheel turn'd about very faſt, had as great a natural propen <lb></lb>ſion of moving towards the centre of the ſaid wheel, as it hath to <lb></lb>move towards the centre of the Earth, it would be an eaſie mat <lb></lb>ter for it to return unto the wheel, or rather not to depart from it; <lb></lb>in regard that upon the begining of the ſeparation, the receſſion be <lb></lb>ing ſo ſinall, by reaſon of the infinite acuteneſs of the angle of <lb></lb>contact, every very little of inclination that draweth it back to <lb></lb>wards the centie of the wheel, would be ſufficient to retain it up <lb></lb>on the rim or circumference.</s></p><p type="main"><s>SIMP. </s><s>I queſtion not, but that if one ſuppoſe that which nei <lb></lb>ther is, nor can be, to wit, that the inclination of thoſe grave bo <lb></lb>dies was to go towards the centre of the wheel, they would never <lb></lb>come to be extruded or ſhaken off.</s></p><p type="main"><s>SALV. </s><s>But I neither do, nor need to ſuppoſe that which is not; <lb></lb>for I will not deny but that the ſtones are extruded. </s><s>Yet I ſpeak <lb></lb>this by way of ſuppoſition, to the end that you might grant me <lb></lb>the reſt. </s><s>Now fancy to your ſelf, that the Earth is that great <lb></lb>wheel, which moved with ſo great velocity is to extrude the ſtones. <lb></lb></s><s>You could tell me very well even now, that the motion of proje <lb></lb>ction ought to be by that right line which toucheth the Earth in <lb></lb>the point of ſeparation: and this Tangent, how doth it notably <lb></lb>recede from the ſuperficies of the Terreſtrial Globe?</s></p><p type="main"><s>SIMP. </s><s>I believe, that in a thouſand yards, it will not recede <lb></lb>from the Earth an inch.</s></p><p type="main"><s>SALV. </s><s>And did you not ſay, that the project being drawn by <lb></lb>its own weight, declineth from the Tangent towards the centre of <lb></lb>the Earth?</s></p> <pb xlink:href="040/01/192.jpg" pagenum="174"></pb><p type="main"><s>SIMP. </s><s>I ſaid ſo, and alſo confeſſe the reſt: and do now plainly <lb></lb>underſtand that the ſtone will not ſeparate from the Earth, for <lb></lb>that its receſſion in the beginning would be ſuch, and ſo ſmall, <lb></lb>that it is a thouſand times exceeded by the inclination which the <lb></lb>ſtone hath to move towards the centre of the Earth, which cen <lb></lb>tre in this caſe is alſo the centre of the wheel. </s><s>And indeed it muſt <lb></lb>be confeſſed that the ſtones, the living creatures, and the other <lb></lb>grave bodies cannot be extruded; but here again the lighter things <lb></lb>beget in me a new doubt, they having but a very weak propenſion <lb></lb>of deſcent towards the centre; ſo that there being wanting in <lb></lb>them that faculty of withdrawing from the ſuperficies, I ſee not, <lb></lb>but that they may be extruded; and you know the rule, that <emph type="italics"></emph>ad <lb></lb>deſtruendum ſufficit unum.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAVL. </s><s>We will alſo give you ſatisfaction in this. </s><s>Tell me <lb></lb>therefore in the firſt place, what you underſtand by light matters, <lb></lb>that is, whether you thereby mean things really ſo light, as that <lb></lb>they go upwards, or elſe not abſolutely light, but of ſo ſmall gra <lb></lb>vity, that though they deſcend downwards, it is but very ſlowly; <lb></lb>for if you mean the abſolutely light, I will be readier than your <lb></lb>ſelf to admit their extruſion.</s></p><p type="main"><s>SIMP. </s><s>I ſpeak of the other ſort, ſuch as are feathers, wool, cot <lb></lb>ton, and the like; to lift up which every ſmall force ſufficeth: <lb></lb>yet nevertheleſſe we ſee they reſt on the Earth very quietly.</s></p><p type="main"><s>SALV. </s><s>This pen, as it hath a natural propenſion to deſcend to <lb></lb>wards the ſuperficies of the Earth, though it be very ſmall, yet I <lb></lb>muſt tell you that it ſufficeth to keep it from mounting upwards: <lb></lb>and this again is not unknown to you your ſelf; therefore tell me <lb></lb>if the pen were extruded by the <emph type="italics"></emph>Vertigo<emph.end type="italics"></emph.end> of the Earth, by what <lb></lb>line would it move?</s></p><p type="main"><s>SIMP. </s><s>By the tangent in the point of ſeparation.</s></p><p type="main"><s>SALV. </s><s>And when it ſhould be to return, and re-unite it ſelf to <lb></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></lb>Earth.</s></p><p type="main"><s>SALV. </s><s>So then here falls under our conſideration two moti <lb></lb>ons; one the motion of projection, which beginneth from the <lb></lb>point of contact, and proceedeth along the tangent; and the o <lb></lb>ther the motion of inclination downwards, which beginneth from <lb></lb>the project it ſelf, and goeth by the ſecant towards the centre; and <lb></lb>if you deſire that the projection follow, it is neceſſary that the <emph type="italics"></emph>im <lb></lb>petus<emph.end type="italics"></emph.end> by the tangent overcome the inclination by the ſecant: is it <lb></lb>not ſo?</s></p><p type="main"><s>SIMP. </s><s>So it ſeemeth to me.</s></p><p type="main"><s>SALV. </s><s>But what is it that you think neceſſary in the motion <lb></lb>of the projicient, to make that it may prevail over that inclina <pb xlink:href="040/01/193.jpg" pagenum="175"></pb>tion, from which enſueth the ſeparation and elongation of the <lb></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></lb>the ſame, that is, the ſame pen; now how can the ſame moveable <lb></lb>ſuperate and exceed it ſelf in motion?</s></p><p type="main"><s>SIMP. </s><s>I do not ſee how it can overcome or yield to it ſelf in <lb></lb>motion, unleſſe by moving one while faſter, and another while <lb></lb>ſlower.</s></p><p type="main"><s>SALV. </s><s>You ſee then, that you do know it. </s><s>If therefore the <lb></lb>projection of the pen ought to follow, and its motion by the tan <lb></lb>gent be to overcome its motion by the ſecant, what is it requiſite <lb></lb>that their velocities ſhould be?</s></p><p type="main"><s>SIMP. </s><s>It is requiſite that the motion by the tangent be greater <lb></lb>than that other by the ſecant. </s><s>But wretch that I am! Is it not <lb></lb>only many thouſand times greater than the deſcending motion of <lb></lb>the pen, but than that of the ſtone? </s><s>And yet like a ſimple fellow <lb></lb>I had ſuffered my ſelf to be perſwaded, that ſtones could not be <lb></lb>extruded by the revolution of the Earth. </s><s>I do therefore revoke <lb></lb>my former ſentence, and ſay, that if the Earth ſhould move, <lb></lb>ſtones, Elephants, Towers, and whole Cities would of neceſſity be <lb></lb>toſt up into the Air; and becauſe that that doth not evene, I con <lb></lb>clude that the Earth doth not move.</s></p><p type="main"><s>SALV. </s><s>Softly <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> you go on ſo faſt, that I begin to be <lb></lb>more afraid for you, than for the pen. </s><s>Reſt a little, and obſerve what <lb></lb>I am going to ſpeap. </s><s>If for the reteining of the ſtone or pen an <lb></lb>nexed to the Earths ſurface it were neceſſary that its motion of <lb></lb>deſcent were greater, or as much as the motion made by the tan <lb></lb>gent; you would have had reaſon to ſay, that it ought of neceſſity <lb></lb>to move as faſt, or faſter by the ſecant downwards, than by the <lb></lb>tangent Eaſtwards: But did not you tell me even now, that a <lb></lb>thouſand yards of diſtance by the tangent from the contact, do <lb></lb>remove hardly an inch from the circumference? </s><s>It is not ſuffici <lb></lb>ent therefore that the motion by the tangent, which is the ſame <lb></lb>with that of the diurnall <emph type="italics"></emph>Vertigo,<emph.end type="italics"></emph.end> (or haſty revolution) be fimply <lb></lb>more ſwift than the motion by the ſecant, which is the ſame with <lb></lb>that of the pen in deſcending; but it is requiſite that the ſame be <lb></lb>ſo much more ſwift as that the time which ſufficeth for the pen <lb></lb>to move <emph type="italics"></emph>v.g.<emph.end type="italics"></emph.end> a thouſand yards by the tangent, be inſufficient for <lb></lb>it to move one ſole inch by the ſecant. </s><s>The which I tell you ſhall <lb></lb>never be, though you ſhould make that motion never ſo ſwift, <lb></lb>and this never ſo ſlow.</s></p><p type="main"><s>SIMP. </s><s>And why might not that by the tangent be ſo ſwift, as <lb></lb>not to give the pen time to return to the ſurface of the Earth?</s></p><p type="main"><s>SALV. </s><s>Try whether you can ſtate the caſe in proper termes, <pb xlink:href="040/01/194.jpg" pagenum="176"></pb>and I will give you an anſwer. </s><s>Tell me therefore, how much do <lb></lb>you think ſufficeth to make that motion ſwifter than this?</s></p><p type="main"><s>SIMP. </s><s>I will ſay for example, that if that motion by the tan <lb></lb>gent were a million of times ſwifter than this by the ſecant, the <lb></lb>pen, yea, and the ſtone alſo would come to be extruded.</s></p><p type="main"><s>SALV. </s><s>You ſay ſo, and ſay that which is falſe, onely for <lb></lb>want, not of Logick, Phyſicks, or Metaphyſicks, but of Geome <lb></lb>try; for if you did but underſtand its firſt elements, you would <lb></lb>know, that from the centre of a circle a right line may be drawn <lb></lb>to meet the tangent, which interſecteth it in ſuch a manner, that <lb></lb>the part of the tangent between the contact and the ſecant, may <lb></lb>be one, two, or three millions of times greater than that part of <lb></lb>the ſecant which lieth between the tangent and the circumference, <lb></lb>and that the neerer and neerer the ſecant ſhall be to the contact, <lb></lb>this proportion ſhall grow greater and greater <emph type="italics"></emph>in infinitum<emph.end type="italics"></emph.end>; ſo <lb></lb>that it need not be feared, though the <emph type="italics"></emph>vertigo<emph.end type="italics"></emph.end> be ſwift, and the <lb></lb>motion downwards ſlow, that the pen or other lighter matter can <lb></lb>begin to riſe upwards, for that the inclination downwards always <lb></lb>exceedeth the velocity of the projection.</s></p><p type="main"><s>SAGR. </s><s>I do not perfectly apprehend this buſineſſe.</s></p><p type="main"><s>SALV. </s><s>I will give you a moſt univerſal yet very eaſie demon</s></p><p type="main"><s><arrow.to.target n="marg367"></arrow.to.target> <lb></lb>ſtration thereof. </s><s>Let a proportion be given between B A [<emph type="italics"></emph>in Fig.<emph.end type="italics"></emph.end> <lb></lb>3.] and C: And let B A be greater than C at pleaſure. </s><s>And let <lb></lb>there be deſcribed a circle, whoſe centre is D. </s><s>From which it is <lb></lb>required to draw a ſecant, in ſuch manner, that the tangent may <lb></lb>be in proportion to the ſaid ſecant, as B A to C. </s><s>Let A I be <lb></lb>ſuppoſed a third proportional to B A and C. </s><s>And as B I is to <lb></lb>I A, ſo let the diameter F E be to E G; and from the point G, <lb></lb>let there be drawn the tangent G H. </s><s>I ſay that all this is done as <lb></lb>was required; and as B A is to C, ſo is H G to G E. </s><s>And in re <lb></lb>gard that as B I is to I A, ſo is F E to E G; therefore by compo <lb></lb>ſition, as B A is to A I; ſo ſhall F G be to G E. </s><s>And becauſe C <lb></lb>is the middle proportion between <emph type="italics"></emph>B<emph.end type="italics"></emph.end> A and A I; and G H is a <lb></lb>middle term between F G and G E; therefore, as B A is to C, <lb></lb>ſo ſhall F G be to G H; that is H G to G E, which was to be <lb></lb>demonſtrated.</s></p><p type="margin"><s><margin.target id="marg367"></margin.target><emph type="italics"></emph>A geometrical <lb></lb>demonſtration to <lb></lb>prove the impoſſi <lb></lb>bility of extruſion <lb></lb>by means of the <lb></lb>terreſtrial<emph.end type="italics"></emph.end> vertigo.</s></p><p type="main"><s>SAGR. </s><s>I apprehend this demonſtration; yet nevertheleſſe, I <lb></lb>am not left wholly without hæſitation; for I find certain confu <lb></lb>ſed ſcruples role to and again in my mind, which like thick and <lb></lb>dark clouds, permit me not to diſcern the cleerneſſe and neceſſity <lb></lb>of the concluſion with that perſpicuity, which is uſual in Mathe <lb></lb>matical Demonſtrations. </s><s>And that which I ſtick at is this. </s><s>It is <lb></lb>true that the ſpaces between the tangent and the circumference do <lb></lb>gradually diminiſh <emph type="italics"></emph>in infinitum<emph.end type="italics"></emph.end> towards the contact; but it is alſo <lb></lb>true on the contrary, that the propenſion of the moveable to <pb xlink:href="040/01/195.jpg" pagenum="177"></pb>deſcending groweth leſs & leſs in it, the nearer it is to the firſt term <lb></lb>of its deſcent; that is, to the ſtate of reſt; as is manifeſt from that <lb></lb>which you declare unto us, demonſtrating that the deſcending grave <lb></lb>body departing from reſt, ought to paſſe thorow all the degrees of <lb></lb>tardity comprehended between the ſaid reſt, & any aſſigned degree <lb></lb>of velocity, the which grow leſs and leſs <emph type="italics"></emph>in infinitum.<emph.end type="italics"></emph.end> To which may <lb></lb>be added, that the ſaid velocity and propenſion to motion, doth for <lb></lb>another reaſon diminiſh to infinity; and it is becauſe the gravity of <lb></lb>the ſaid moveable may infinitely diminiſh. </s><s>So that the cauſes which <lb></lb>diminiſh the propenſion of aſcending, and conſequently favour <lb></lb>the projection, are two; that is, the levity of the moveable, and its <lb></lb>vicinity to the ſtate of reſt; both which are augmentable <emph type="italics"></emph>in infinit.<emph.end type="italics"></emph.end> <lb></lb>and theſe two on the contrary being to contract but with one ſole <lb></lb>cauſe of making the projection, I cannot conceive how it alone, al <lb></lb>though it alſo do admit of infinite augmentation, ſhould be able to <lb></lb>remain invincible againſt the union & confederacy of the others, w^{ch} <lb></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"></emph>Sagredus<emph.end type="italics"></emph.end>; and to explain it ſo as <lb></lb>that we may more cleerly apprehend it, for that you ſay that you <lb></lb>your ſelf have but a confuſed <emph type="italics"></emph>Idea<emph.end type="italics"></emph.end> of it, we will diſtinguiſh of the <lb></lb>ſame by reducing it into figure; which may alſo perhaps afford us <lb></lb>ſome caſe in reſolving the ſame. </s><s>Let us therefore [<emph type="italics"></emph>in Fig.<emph.end type="italics"></emph.end> 4.] draw <lb></lb>a perpendicular line towards the centre, and let it be AC, and to it <lb></lb>at right angles let there be drawn the Horizontal line A <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> upon <lb></lb>which the motion of the projection ought to be made; now the pro <lb></lb>ject would continue to move along the ſame with an even motion, if <lb></lb>ſo be its gravity did not incline it downwards. </s><s>Let us ſuppoſe from <lb></lb>the point A a right line to be drawn, that may make any angle at <lb></lb>pleaſure with the line A B; which let be A E, and upon A<emph type="italics"></emph>B<emph.end type="italics"></emph.end> let us <lb></lb>mark ſome equal ſpaces AF, FH, HK, and from them let us let fall <lb></lb>the perpendiculars FG, HI, K L, as far as AE. </s><s>And becauſe, as al <lb></lb>ready hath been ſaid, the deſcending grave body departing from reſt, <lb></lb>goeth from time to time acquiring a greater degree of velocity, <lb></lb>according as the ſaid time doth ſucceſſively encreaſe; we may con <lb></lb>ceive the ſpaces AF, FH, HK, to repreſent unto us equal times; and <lb></lb>the perpendiculars FG, HI, KL, degrees of velocity acquired in the <lb></lb>ſaid times; ſo that the degree of velocity acquired in the whole time <lb></lb>A K, is as the line K L, in reſpect to the degree H I, acquired in the <lb></lb>time AH, and the degree FG in the time AF; the which degrees KL, <lb></lb>HI, FG, are (as is manifeſt) the ſame in proportion, as the times K A, <lb></lb>HA, F A, and if other perpendiculars were drawn from the points <lb></lb>marked at pleaſure in the line F A, one might ſucceſſively find de <lb></lb>grees leſſe and leſſe <emph type="italics"></emph>in infinitum,<emph.end type="italics"></emph.end> proceeding towards the point A, <lb></lb>repreſenting the firſt inſtant of time, and the firſt ſtate of reſt. </s><s>And <lb></lb>this retreat towards A, repreſenteth the firſt propenſion to the <pb xlink:href="040/01/196.jpg" pagenum="178"></pb>motion of deſcent, diminiſhed <emph type="italics"></emph>in infinitum<emph.end type="italics"></emph.end> by the approach of <lb></lb>the moveable to the firſt ſtate of reſt, which approximation is <lb></lb>augmentable <emph type="italics"></emph>in infinitum.<emph.end type="italics"></emph.end> Now let us find the other diminution <lb></lb>of velocity, which likewiſe may proceed to infinity, by the di <lb></lb>minution of the gravity of the moveable, and this ſhall be repre <lb></lb>ſented by drawing other lines from the point A, which contein <lb></lb>angles leſſe than the angle B A E, which would be this line A D, <lb></lb>the which interſecting the parallels K L, H I, F G, in the points <lb></lb>M, N, and O, repreſent unto us the degrees F O, H N, K M, <lb></lb>acquired in the times A F, A H, A K, leſſe than the other de <lb></lb>grees F G, H I, K L, acquired in the ſame times; but theſe <lb></lb>latter by a moveable more ponderous, and thoſe other by a <lb></lb>moveable more <emph type="italics"></emph>light.<emph.end type="italics"></emph.end> And it is manifeſt, that by the retreat of <lb></lb>the line E A towards A B, contracting the angle E A B (the <lb></lb>which may be done <emph type="italics"></emph>in infinitum,<emph.end type="italics"></emph.end> like as the gravity may <emph type="italics"></emph>in infi <lb></lb>nitum<emph.end type="italics"></emph.end> be diminiſhed) the velocity of the cadent moveable may <lb></lb>in like manner be diminiſhed <emph type="italics"></emph>in infinitum,<emph.end type="italics"></emph.end> and ſo conſequently <lb></lb>the cauſe that impeded the projection; and therefore my thinks <lb></lb>that the union of theſe two reaſons againſt the projection, dimi <lb></lb>niſhed to infinity, cannot be any impediment to the ſaid proje <lb></lb>ction. </s><s>And couching the whole argument in its ſhorteſt terms, we <lb></lb>will ſay, that by contracting the angle E A B, the degrees of ve <lb></lb>locity L K, I H, G F, are diminiſhed; and moreover by the re <lb></lb>treat of the parallels K L, H I, F G, towards the angle A, the <lb></lb>fame degrees are again diminiſhed; and both theſe diminutions <lb></lb>extend to infinity: Therefore the velocity of the motion of de <lb></lb>ſcent may very well diminiſh ſo much, (it admitting of a twoſold <lb></lb>diminution <emph type="italics"></emph>in infinitum<emph.end type="italics"></emph.end>) as that it may not ſuffice to reſtore the <lb></lb>moveable to the circumference of the wheel, and thereupon may <lb></lb>occaſion the projection to be hindered and wholly obviated.</s></p><p type="main"><s>Again on the contrary, to impede the projection, it is neceſ <lb></lb>ſary that the ſpaces by which the project is to deſcend for the <lb></lb>reuniting it ſelf to the Wheel, be made ſo ſhort and cloſe toge <lb></lb>ther, that though the deſcent of the moveable be retarded, yea <lb></lb>more, diminiſhed <emph type="italics"></emph>in infinitum,<emph.end type="italics"></emph.end> yet it ſufficeth to reconduct it thither: <lb></lb>and therefore it would be requiſite, that you find out a diminuti <lb></lb>on of the ſaid ſpaces, not only produced to infinity, but to ſuch an <lb></lb>infinity, as that it may ſuperate the double infinity that is made in <lb></lb>the diminution of the velocity of the deſcending moveable. </s><s>But <lb></lb>how can a magnitude be diminiſhed more than another, which <lb></lb>hath a twofold diminution <emph type="italics"></emph>in infinitum<emph.end type="italics"></emph.end>? </s><s>Now let <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> ob <lb></lb>ſerve how hard it is to philoſophate well in nature, without <emph type="italics"></emph>Geo <lb></lb>metry.<emph.end type="italics"></emph.end> The degrees of velocity diminiſhed <emph type="italics"></emph>in infinitum,<emph.end type="italics"></emph.end> as well <lb></lb>by the diminution of the gravity of the moveable, as by the ap <lb></lb>proxination to the firſt term of the motion, that is, to the ſtate <pb xlink:href="040/01/197.jpg" pagenum="179"></pb>of reſt, are alwayes determinate, and anſwer in proportion to the <lb></lb>parallels comprehended between two right lines that concur in <lb></lb>an angle, like to the angle B A E, or B A D, or any other <lb></lb>infinitely more acute, alwayes provided it be rectilineall <lb></lb>But the diminution of the ſpaces thorow which the moveable is <lb></lb>to be conducted along the circumference of the wheel, is propor <lb></lb>tionate to another kind of diminution, comprehended between <lb></lb>lines that contain an angle infinitely more narrow and acute, than <lb></lb>any rectilineal angle, how acute ſoever, which is that in our pre <lb></lb>ſent caſe. </s><s>Let any point be taken in the perpendicular A C, and <lb></lb>making it the centre, deſcribe at the diſtance C A, an arch A M P, <lb></lb>the which ſhall interſect the parallels that determine the degrees of <lb></lb>velocity, though they be very minute, and comprehended within <lb></lb>a moſt acute rectilineal angle; of which parallels the parts that <lb></lb>lie between the arch and the tangent A B, are the quantities of <lb></lb>the ſpaces, and of the returns upon the wheel, alwayes leſſer (and <lb></lb>with greater proportion leſſer, by how much neerer they approach <lb></lb>to the contact) than the ſaid parallels of which they are parts. <lb></lb></s><s>The parallels comprehended between the right lines in retiring to <lb></lb>wards the angle diminiſh alwayes at the ſame rate, as <emph type="italics"></emph>v.g.<emph.end type="italics"></emph.end> A H be <lb></lb>ing divided in two equal parts in F, the parallel H I ſhall be dou <lb></lb>ble to F G, and ſub-dividing F A, in two equal parts, the paral <lb></lb>lel produced from the point of the diviſion ſhall be the half of <lb></lb>F G; and continuing the ſub-diviſion <emph type="italics"></emph>in infinitum,<emph.end type="italics"></emph.end> the ſubſequent <lb></lb>parallels ſhall be alwayes half of the next preceding; but it doth <lb></lb>not ſo fall out in the lines intercepted between the tangent and <lb></lb>the circumference of the circle: For if the ſame ſub-diviſion be <lb></lb>made in F A; and ſuppoſing for example, that the parallel which <lb></lb>cometh from the point H, were double unto that which commeth <lb></lb>from F, this ſhall be more then double to the next following, and <lb></lb>continually the neerer we come towards the contact A, we ſhall <lb></lb>find the precedent lines contein the next following three, four, <lb></lb>ten, an hundred, a thouſand, an hundred thouſand, an hundred <lb></lb>millions of times, and more <emph type="italics"></emph>in infinitum.<emph.end type="italics"></emph.end> The brevity therefore of <lb></lb>ſuch lines is ſo reduced, that it far exceeds what is requiſite to make <lb></lb>the project, though never ſo light, return, nay more, continue <lb></lb>unremoveable upon the circumference.</s></p><p type="main"><s>SAGR. </s><s>I very well comprehend the whole diſcourſe, and upon <lb></lb>what it layeth all its ſtreſſe, yet nevertheleſſe methinks that he <lb></lb>that would take pains to purſue it, might yet ſtart ſome further <lb></lb>queſtions, by ſaying, that of thoſe two cauſes which render the <lb></lb>deſcent of the moveable ſlower and ſlower <emph type="italics"></emph>in infinitum,<emph.end type="italics"></emph.end> it is mani <lb></lb>feſt, that that which dependeth on the vicinity to the firſt term of <lb></lb>the deſcent, increaſeth alwayes in the ſame proportion, like as the <lb></lb>parallels alwayes retain the ſame proportion to each other, &c. <pb xlink:href="040/01/198.jpg" pagenum="180"></pb>but that the diminution of the ſame velocity, dependent on the <lb></lb>diminution of the gravity of the moveable (which vvas the ſecond <lb></lb>cauſe) doth alſo obſerve the ſame proportion, doth not ſo plainly <lb></lb>appear, And vvho ſhall aſſure us that it doth not proceed accor <lb></lb>ding to the proportion of the lines intercepted between the ſecant, <lb></lb>and the circumference; or vvhether vvith a greater proportion?</s></p><p type="main"><s>SALV. </s><s>I have aſſumed for a truth, that the velocities of movea <lb></lb>bles deſcending naturally, vvill follovv the proportion of their gra <lb></lb>vities, with the favour of <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> who doth <lb></lb>in many places affirm the ſame, as a propoſition manifeſt: You, <lb></lb>in favour of my adverſary, bring the ſame into queſtion, and ſay <lb></lb>that its poſſible that the velocity increaſeth with greater propor <lb></lb>tion, yea and greater <emph type="italics"></emph>in infinitum<emph.end type="italics"></emph.end> than that of the gravity; ſo that <lb></lb>all that hath been ſaid falleth to the ground: For maintaining <lb></lb>whereof, I ſay, that the proportion of the velocities is much leſſe <lb></lb>than that of the gravities; and thereby I do not onely ſupport <lb></lb>but confirme the premiſes. </s><s>And for proof of this I appeal unto <lb></lb>experience, which will ſhew us, that a grave body, howbeit thirty <lb></lb>or fourty times bigger then another; as for example, a ball of <lb></lb>lead, and another of ſugar, will not move much more than twice <lb></lb>as faſt. </s><s>Now if the projection would not be made, albeit the ve <lb></lb>locity of the cadent body ſhould diminiſh according to the pro <lb></lb>portion of the gravity, much leſſe would it be made ſo long as the <lb></lb>velocity is but little diminiſhed, by abating much from the gravi <lb></lb>ty. </s><s>But yet ſuppoſing that the velocity diminiſheth with a propor <lb></lb>tion much greater than that wherewith the gravity decreaſeth, nay <lb></lb>though it were the ſelf-ſame wherewith thoſe parallels conteined <lb></lb>between the tangent and circumference do decreaſe, yet cannot I <lb></lb>ſee any neceſſity why I ſhould grant the projection of matters of <lb></lb>never ſo great levity; yea I farther averre, that there could no ſuch <lb></lb>projection follow, meaning alwayes of matters not properly and <lb></lb>abſolutely light, that is, void of all gravity, and that of their own <lb></lb>natures move upwards, but that deſcend very ſlowly, and <lb></lb>have very ſmall gravity. </s><s>And that which moveth me ſo to think <lb></lb>is, that the diminution of gravity, made according to the propor <lb></lb>tion of the parallels between the tangent and the circumference, <lb></lb>hath for its ultimate and higheſt term the nullity of weight, as thoſe <lb></lb>parallels have for their laſt term of their diminution the contact it <lb></lb>ſelf, which is an indiviſible point: Now gravity never diminiſheth <lb></lb>ſo far as to its laſt term, for then the moveable would ceaſe to be <lb></lb>grave; but yet the ſpace of the reverſion of the project to the <lb></lb>circumference is reduced to the ultimate minuity, which is when <lb></lb>the moveable reſteth upon the circumference in the very point of <lb></lb>contact; ſo as that to return thither it hath no need of ſpace: <lb></lb>and therefore let the propenſion to the motion of deſcent be ne <pb xlink:href="040/01/199.jpg" pagenum="181"></pb>ver ſo ſmall, yet is it alwayes more than ſufficient to reconduct the <lb></lb>moveable to the circumference, from which it is diſtant but its leaſt <lb></lb>ſpace, that is, nothing at all.</s></p><p type="main"><s>SAGR. </s><s>Your diſcourſe, I muſt confeſs, is very accurate; and <lb></lb>yet no leſs concluding than it is ingenuous; and it muſt be gran <lb></lb>ted that to go about to handle natural queſtions, without <emph type="italics"></emph>Geome <lb></lb>try,<emph.end type="italics"></emph.end> is to attempt an impoſſibility.</s></p><p type="main"><s>SALV. </s><s>But <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> will not ſay ſo; and yet I do not think <lb></lb>that he is one of thoſe <emph type="italics"></emph>Peripateticks<emph.end type="italics"></emph.end> that diſſwade their Diſciples <lb></lb>from ſtudying the <emph type="italics"></emph>Mathematicks,<emph.end type="italics"></emph.end> as Sciences that vitiate the rea <lb></lb>ſon, and render it leſſe apt for contemplation.</s></p><p type="main"><s>SIMP. </s><s>I would not do ſo much wrong to <emph type="italics"></emph>Plato,<emph.end type="italics"></emph.end> but yet I may <lb></lb>truly ſay with <emph type="italics"></emph>Aristotle,<emph.end type="italics"></emph.end> that he too much loſt himſelf in, and too <lb></lb>much doted upon that his <emph type="italics"></emph>Geometry<emph.end type="italics"></emph.end>: for that in concluſion theſe <lb></lb>Mathematical ſubtilties <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> are true in abſtract, but applied <lb></lb>to ſenſible and Phyſical matter, they hold not good. </s><s>For the <lb></lb>Mathematicians will very well demonſtrate for example, that <lb></lb><emph type="italics"></emph>Sphæratangit planum in puncto<emph.end type="italics"></emph.end>; a poſition like to that in diſpute, <lb></lb>but when one cometh to the matter, things ſucceed quite another <lb></lb>way. </s><s>And ſo I may ſay of theſe angles of contact, and theſe <lb></lb>proportions; which all evaporate into Air, when they are applied <lb></lb>to things material and ſenſible.</s></p><p type="main"><s>SALV. </s><s>You do not think then, that the tangent toucheth the <lb></lb>ſuperficies of the terreſtrial Globe in one point only?</s></p><p type="main"><s>SIMP. No, not in one ſole point; but I believe that a right <lb></lb>line goeth many tens and hundreds of yards touching the ſurface <lb></lb>not onely of the Earth, but of the water, before it ſeparate from <lb></lb>the ſame.</s></p><p type="main"><s>SALV. </s><s>But if I grant you this, do not you perceive that it ma <lb></lb>keth ſo much the more againſt your cauſe? </s><s>For if it be ſuppoſed <lb></lb>that the tangent was ſeparated from the terreſtrial ſuperficies, yet <lb></lb>it hath been however demonſtrated that by reaſon of the great a <lb></lb>cuity of the angle of contingence (if happily it may be call'd an <lb></lb>angle) the project would not ſeparate from the ſame; how much <lb></lb>leſſe cauſe of ſeparation would it have, if that angle ſhould be <lb></lb>wholly cloſed, and the ſuperficies and the tangent become all one? <lb></lb><arrow.to.target n="marg368"></arrow.to.target> <lb></lb>Perceive you not that the Projection would do the ſame thing up <lb></lb>on the ſurface of the Earth, which is aſmuch as to ſay, it would <lb></lb>do juſt nothing at all? </s><s>You ſee then the power of truth, which <lb></lb>while you ſtrive to oppoſe it, your own aſſaults themſelves uphold <lb></lb>and defend it. </s><s>But in regard that you have retracted this errour, <lb></lb>I would be loth to leave you in that other which you hold, namely, <lb></lb>that a material Sphere doth not touch a plain in one ſole point: <lb></lb>and I could wiſh ſome few hours converſation with ſome perſons <lb></lb>converſant in <emph type="italics"></emph>Geometry,<emph.end type="italics"></emph.end> might make you a little more intelligent <pb xlink:href="040/01/200.jpg" pagenum="182"></pb>amongſt thoſe who know nothing thereof. </s><s>Now to ſhew you how <lb></lb>great their errour is who ſay, that a Sphere <emph type="italics"></emph>v.g.<emph.end type="italics"></emph.end> of braſſe, doth not <lb></lb>touch a plain <emph type="italics"></emph>v.g.<emph.end type="italics"></emph.end> of ſteel in one ſole point, Tell me what con <lb></lb>ceipt you would entertain of one that ſhould conſtantly aver, that <lb></lb>the Sphere is not truly a Sphere.</s></p><p type="margin"><s><margin.target id="marg368"></margin.target><emph type="italics"></emph>The truth <lb></lb>ſometimes gaines <lb></lb>ſtrength by con <lb></lb>tradiction.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I would eſteem him wholly devoid of reaſon.</s></p><p type="main"><s>SALV. </s><s>He is in the ſame caſe who ſaith that the material Sphere <lb></lb><arrow.to.target n="marg369"></arrow.to.target> <lb></lb>doth not touch a plain, alſo material, in one onely point; for to <lb></lb>ſay this is the ſame, as to affirm that the Sphere is not a Sphere. <lb></lb></s><s>And that this is true, tell me in what it is that you conſtitute the <lb></lb>Sphere to conſiſt, that is, what it is that maketh the Sphere differ <lb></lb>from all other ſolid bodies.</s></p><p type="margin"><s><margin.target id="marg369"></margin.target><emph type="italics"></emph>The sphere al <lb></lb>though material, <lb></lb>toucheth the mate <lb></lb>rial plane but in <lb></lb>one point onely.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I believe that the eſſence of a Sphere conſiſteth in ha <lb></lb><arrow.to.target n="marg370"></arrow.to.target> <lb></lb>ving all the right lines produced from its centre to the circumfe <lb></lb>rence, equal.</s></p><p type="margin"><s><margin.target id="marg370"></margin.target><emph type="italics"></emph>The definition of <lb></lb>the ſphere.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>So that, if thoſe lines ſhould not be equal, there ſame <lb></lb>ſolidity would be no longer a ſphere?</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 amongſt the <lb></lb>many lines that may be drawn between two points, that may be <lb></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 underſtand that this onely right line ſhall <lb></lb>again of neceſſity be the ſhorteſt of them all?</s></p><p type="main"><s>SIMP. </s><s>I know it, and alſo have a demonſtration thereof, pro <lb></lb>duced by a great <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> Philoſopher, and as I take it, if my <lb></lb>memory do not deceive me, he alledgeth it by way of reprehending <lb></lb><emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> that ſuppoſeth it as known, when it may be demon <lb></lb>ſtrated.</s></p><p type="main"><s>SALV. </s><s>This muſt needs be a great Mathematician, that knew <lb></lb>how to demonſtrate that which <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> neither did, nor could <lb></lb>demonſtrate. </s><s>And if you remember his demonſtration, I would <lb></lb>gladly hear it: for I remember very well, that <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> in his <lb></lb>Books, <emph type="italics"></emph>de Sphærà & Cylindro,<emph.end type="italics"></emph.end> placeth this Propoſition amongſt the <lb></lb><emph type="italics"></emph>Poſtulata<emph.end type="italics"></emph.end>; and I verily believe that he thought it demonſtrated.</s></p><p type="main"><s>SIMP. </s><s>I think I ſhall remember it, for it is very eaſie and <lb></lb>ſhort.</s></p><p type="main"><s>SALV. </s><s>The diſgrace of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> and the honour of this Phi <lb></lb>loſopher ſhall be ſo much the greater.</s></p><p type="main"><s>SIMP. </s><s>I will deſcribe the Figure of it. </s><s>Between the points <lb></lb><arrow.to.target n="marg371"></arrow.to.target> <lb></lb>A and B, [<emph type="italics"></emph>in Fig.<emph.end type="italics"></emph.end> 5.] draw the right line A B, and the curve line <lb></lb>A C B, of which we will prove the right to be the ſhorter: and <lb></lb>the proof is this; take a point in the curve-line, which let be C, <lb></lb>and draw two other lines, A C and C B, which two lines together; <lb></lb>are longer than the ſole line A B, for ſo demonſtrateth <emph type="italics"></emph>Euelid.<emph.end type="italics"></emph.end> <pb xlink:href="040/01/201.jpg" pagenum="183"></pb>But the curve-line A C B, is greater than the two right-lines A C, <lb></lb>and C B; therefore, <emph type="italics"></emph>à fortiori,<emph.end type="italics"></emph.end> the curve-line A C B, is much <lb></lb>greater than the right line A B, which was to be demonſtrated. <lb></lb><arrow.to.target n="marg372"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg371"></margin.target><emph type="italics"></emph>The demonſtra <lb></lb>tion of a Peripate <lb></lb>tick, to prove the <lb></lb>right line to be the <lb></lb>ſhorteſt of all lines.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg372"></margin.target><emph type="italics"></emph>The Paralogiſm <lb></lb>of the ſame Peripa <lb></lb>tetick, which pro <lb></lb>veth<emph.end type="italics"></emph.end> ignotum per <lb></lb>ignotius.</s></p><p type="main"><s>SALV. </s><s>I do not think that if one ſhould ranſack all the Para <lb></lb>logiſms of the world, there could be found one more commodious <lb></lb>than this, to give an example of the moſt ſolemn fallacy of all <lb></lb>fallacies, namely, than that which proveth <emph type="italics"></emph>ignotum per ignotius.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>How ſo?</s></p><p type="main"><s>SALV. </s><s>Do you ask me how ſo? </s><s>The unknown concluſion <lb></lb>which you deſire to prove, is it not, that the curved line A C B, is <lb></lb>longer than the right line A B; the middle term which is taken <lb></lb>for known, is that the curve-line A C B, is greater than the two <lb></lb>lines A C and C B, the which are known to be greater than A B; <lb></lb>And if it be unknown whether the curve-line be greater than the <lb></lb>ſingle right-line A B, ſhall it not be much more unknown whether <lb></lb>it be greater than the two right lines A C & C B, which are known <lb></lb>to be greater than the ſole line A B, & yet you aſſume it as known?</s></p><p type="main"><s>SIMP. </s><s>I do not yet very well perceive wherein lyeth the fal <lb></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></lb>known by <emph type="italics"></emph>Euclid<emph.end type="italics"></emph.end>) and in as much as the curve line is longer than <lb></lb>the two right lines A C and B C, ſhall it not not be much greater <lb></lb>than the ſole right line A B?</s></p><p type="main"><s>SIMP. </s><s>It ſhall ſo.</s></p><p type="main"><s>SALV. </s><s>That the curve-line A C B, is greater than the right <lb></lb>line A B, is the concluſion more known than the middle term, <lb></lb>which is, that the ſame curve-line is greater than the two right <lb></lb>lines A C and C B. </s><s>Now when the middle term is leſs known <lb></lb>than the concluſion, it is called a proving <emph type="italics"></emph>ignotum per ignotius.<emph.end type="italics"></emph.end> <lb></lb>But to return to our purpoſe, it is ſufficient that you know the <lb></lb>right line to be the ſhorteſt of all the lines that can be drawn be <lb></lb>tween two points. </s><s>And as to the principal concluſion, you ſay, <lb></lb>that the material ſphere doth not touch the ſphere in one ſole <lb></lb>point. </s><s>What then is its contact?</s></p><p type="main"><s>SIMP. </s><s>It ſhall be a part of its ſuperficies.</s></p><p type="main"><s>SALV. </s><s>And the contact likewiſe of another ſphere equal to the <lb></lb>firſt, ſhall be alſo a like particle of its ſuperficies?</s></p><p type="main"><s>SIMP. </s><s>There is no reaſon vvhy it ſhould be othervviſe.</s></p><p type="main"><s>SALV. </s><s>Then the tvvo ſpheres vvhich touch each other, ſhall <lb></lb>touch vvith the tvvo ſame particles of a ſuperficies, for each of them <lb></lb>agreeing to one and the ſame plane, they muſt of neceſſity agree <lb></lb>in like manner to each other. </s><s>Imagine now that the two ſpheres </s></p><p type="main"><s><arrow.to.target n="marg373"></arrow.to.target> <lb></lb>[<emph type="italics"></emph>in Fig.<emph.end type="italics"></emph.end> 6.] whoſe centres are A and B, do touch one another: <lb></lb>and let their centres be conjoyned by the right line A B, which <lb></lb>paſſeth through the contact. </s><s>It paſſeth thorow the point C, and <pb xlink:href="040/01/202.jpg" pagenum="184"></pb>another point in the contact being taken as D, conjoyn the two <lb></lb>right lines A D and B D, ſo as that they make the triangle A D B; <lb></lb>of which the two ſides A D and D B ſhall be equal to the other one <lb></lb>A C B, both thoſe and this containing two ſemidiameters, which <lb></lb>by the definition of the ſphere are all equal: and thus the right <lb></lb>line A B, drawn between the two centres A and B, ſhall not be the <lb></lb>ſhorteſt of all, the two lines A D and D B being equal to it: which <lb></lb>by your own conceſſion is abſurd.</s></p><p type="margin"><s><margin.target id="marg373"></margin.target><emph type="italics"></emph>A demon ſtration <lb></lb>that the ſphere tou <lb></lb>cheth the plane but <lb></lb>in one point.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>This demonſtration holdeth in the abſtracted, but not in <lb></lb>the material ſpheres.</s></p><p type="main"><s>SALV. </s><s>Inſtance then wherein the fallacy of my argument con <lb></lb>ſiſteth, if as you ſay it is not concluding in the material ſpheres, but <lb></lb>holdeth good in the immaterial and abſtracted. <lb></lb><arrow.to.target n="marg374"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg374"></margin.target><emph type="italics"></emph>Why the ſphere in <lb></lb>abſtract, toucheth <lb></lb>the plane onely in <lb></lb>one point, and not <lb></lb>the material in <lb></lb>conerete.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>The material ſpheres are ſubject to many accidents, <lb></lb>which the immaterial are free from. </s><s>And becauſe it cannot be, <lb></lb>that a ſphere of metal paſſing along a plane, its own weight ſhould <lb></lb>not ſo depreſs it, as that the plain ſhould yield ſomewhat, or that <lb></lb>the ſphere it ſelf ſhould not in the contact admit of ſome impreſſi <lb></lb>on. </s><s>Moreover, it is very hard for that plane to be perfect, if for <lb></lb>nothing elſe, yet at leaſt for that its matter is porous: and per <lb></lb>haps it will be no leſs difficult to find a ſphere ſo perfect, as that <lb></lb>it hath all the lines from the centre to the ſuperficies, exactly <lb></lb>equal.</s></p><p type="main"><s>SALV. </s><s>I very readily grant you all this that you have ſaid; but <lb></lb>it is very much beſide our purpoſe: for whilſt you go about to <lb></lb>ſhew me that a material ſphere toucheth not a material plane in <lb></lb>one point alone, you make uſe of a ſphere that is not a ſphere, and <lb></lb>of a plane that is not a plane; for that, according to what you <lb></lb>ſay, either theſe things cannot be found in the world, or if they <lb></lb>may be found, they are ſpoiled in applying them to work the effect. <lb></lb></s><s>It had been therefore a leſs evil, for you to have granted the con <lb></lb>cluſion, but conditionally, to wit, that if there could be made of <lb></lb>matter a ſphere and a plane that were and could continue perfect, <lb></lb>they would touch in one ſole point, and then to have denied that <lb></lb>any ſuch could be made.</s></p><p type="main"><s>SIMP. </s><s>I believe that the propoſition of Philoſophers is to be <lb></lb>underſtood in this ſenſe; for it is not to be doubted, but that the <lb></lb>imperfection of the matter, maketh the matters taken in con <lb></lb>crete, to diſagree with thoſe taken in abſtract.</s></p><p type="main"><s>SALV. What, do they not agree? </s><s>Why, that which you your <lb></lb>ſelf ſay at this inſtant, 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 ſay, that through the imperfection of the <lb></lb>matter, that body which ought to be perfectly ſpherical, and that <lb></lb>plane which ought to be perfectly level, do not prove to be the <pb xlink:href="040/01/203.jpg" pagenum="185"></pb>ſame in concrete, as they are imagined to be in abſtract?</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></lb>to a material plane, youapply an imperfect Sphere to an imperfect <lb></lb>plane, & theſe you ſay do not touch only in one point. </s><s>But I muſt <lb></lb>tell you, that even in abſtract an immaterial Sphere, that is, not a <lb></lb>perfect Sphere, may touch an immaterial plane, that is, not a per <lb></lb>fect plane, not in one point, but with part of its ſuperficies, ſo that <lb></lb>hitherto that which falleth out in concrete, doth in like manner <lb></lb>hold true in abſtract. </s><s>And it would be a new thing that the com <lb></lb>putations and rates made in abſtract numbers, ſhould not after <lb></lb>wards anſwer to the Coines of Gold and Silver, and to the mer <lb></lb>chandizes in concrete. </s><s>But do you know <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> how this <lb></lb>commeth to paſſe? </s><s>Like as to make that the computations agree <lb></lb>with the Sugars, the Silks, the Wools, it is neceſſary that the <lb></lb>accomptant reckon his tares of cheſts, bags, and ſuch other things: <lb></lb>So when the <emph type="italics"></emph>Geometricall Philoſopher<emph.end type="italics"></emph.end> would obſerve in concrete <lb></lb>the effects demonſtrated in abſtract, he muſt defalke the impedi <lb></lb>ments of the matter, and if he know how to do that, I do aſſure <lb></lb>you, the things ſhall jump no leſſe exactly, than <emph type="italics"></emph>Arithmstical<emph.end type="italics"></emph.end> <lb></lb>computations. </s><s>The errours therefore lyeth neither in abſtract, nor <lb></lb>in concrete, nor in <emph type="italics"></emph>Geometry,<emph.end type="italics"></emph.end> nor in <emph type="italics"></emph>Phyſicks,<emph.end type="italics"></emph.end> but in the Calcula <lb></lb>tor, that knoweth not how to adjuſt his accompts. </s><s>Therefore if <lb></lb>you had a perfect Sphere and plane, though they were material, <lb></lb>you need not doubt but that they would touch onely in one point. <lb></lb></s><s>And if ſuch a Sphere was and is impoſſible to be procured, it was <lb></lb>much beſides the purpoſe to ſay, <emph type="italics"></emph>Quod Sphæra ænea non tangit in <lb></lb>puncto.<emph.end type="italics"></emph.end> Furthermore, if I grant you <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that in matter a <lb></lb>figure cannot be procured that is perfectly ſpherical, or perfectly <lb></lb>level: Do you think there may be had two materiall bodies, <lb></lb>whoſe ſuperficies in ſome part, and in ſome ſort are incurvated as <lb></lb>irregularly as can be deſired?</s></p><p type="margin"><s><margin.target id="marg375"></margin.target><emph type="italics"></emph>Things are ex <lb></lb>actly the ſame in <lb></lb>abſtract as in con <lb></lb>crete.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>Of theſe I believe that there is no want.</s></p><p type="main"><s>SALV. </s><s>If ſuch there be, then they alſo will touch in one ſole <lb></lb><arrow.to.target n="marg376"></arrow.to.target> <lb></lb>point; for this contact in but one point alone is not the ſole and <lb></lb>peculiar priviledge of the perfect Sphere and perfect plane. </s><s>Nay, he <lb></lb>that ſhould proſecute this point with more ſubtil contemplations <lb></lb>would finde that it is much harder to procure two bodies that <lb></lb><arrow.to.target n="marg377"></arrow.to.target> <lb></lb>touch with part of their ſnperſicies, than with one point onely. <lb></lb></s><s>For if two ſuperficies be required to combine well together, it is <lb></lb>neceſſary either, that they be both exactly plane, or that if one be <lb></lb>convex, the other be concave; but in ſuch a manner concave, <lb></lb>that the concavity do exactly anſwer to the convexity of the other: <lb></lb>the which conditions are much harder to be found, in regard of <lb></lb>their too narrow determination, than thoſe others, which in their <lb></lb>caſuall latitude are infinite.</s></p> <pb xlink:href="040/01/204.jpg" pagenum="186"></pb><p type="margin"><s><margin.target id="marg376"></margin.target><emph type="italics"></emph>Contact in a ſin <lb></lb>gle point is not pe <lb></lb>culiar to the per <lb></lb>fect Spheres onely? <lb></lb></s><s>but belongeth to all <lb></lb>curved figures.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg377"></margin.target><emph type="italics"></emph>It is more diffi <lb></lb>cult to find Figures <lb></lb>that touch with a <lb></lb>part of their ſur <lb></lb>face, than in one <lb></lb>ſole point.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>You believe then, that two ſtones, or two pieces of I <lb></lb>ron taken at chance, and put together, do for the moſt part touch <lb></lb>in one ſole point?</s></p><p type="main"><s>SALV. </s><s>In caſual encounters, I do not think they do; as well <lb></lb>becauſe for the moſt part there will be ſome ſmall yielding filth <lb></lb>upon them, as becauſe that no diligence is uſed in applying them <lb></lb>without ſtriking one another; and every ſmall matter ſufficeth to <lb></lb>make the one ſuperficies yield ſomewhat to the other; ſo that <lb></lb>they interchangeably, at leaſt in ſome ſmall particle, receive ſigure <lb></lb>from the impreſſion of each other. </s><s>But in caſe their ſuperficies <lb></lb>were very terſe and polite, and that they were both laid upon a <lb></lb>table, that ſo one might not preſſe upon the other, and gently put <lb></lb>towards one another, I queſtion not, but that they might be <lb></lb>brought to the ſimple contact in one onely point.</s></p><p type="main"><s>SAGR. </s><s>It is requiſite, with your permiſſion, that I propound a <lb></lb>certain ſcruple of mine, which came into my minde, whil'ſt I heard <lb></lb>propoſed by <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> the impoſſibility of finding a materiall <lb></lb>and ſolid body, that is, perfectly of a Spherical figure, and whil'ſt <lb></lb>J law <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> in a certain manner, not gainſaying, to give his <lb></lb>conſent thereto; therefore I would know, whether there would <lb></lb>be the ſame difficulty in forming a ſolid of ſome other figure, that <lb></lb>is, to expreſſe my ſelf better, whether there is more difficulty in <lb></lb>reducing a piece of Marble into the figure of a perfect Sphere, than <lb></lb>into a perfect Pyramid, or into a perfect Horſe, or into a perfect <lb></lb>Graſſe-hopper?</s></p><p type="main"><s>SALV. </s><s>To this I will make you the firſt anſwer: and in the <lb></lb>firſt place, I will acquit my ſelf of the aſſent which you think I <lb></lb>gave to <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> which was only for a time; for I had it alſo in <lb></lb>my thoughts, betore I intended to enter upon any other matter, to <lb></lb>ſpeak that, which, it may be, is the ſame, or very like to that which <lb></lb>you are about to ſay, And anſwering to your firſt queſtion, I ſay, <lb></lb><arrow.to.target n="marg378"></arrow.to.target> <lb></lb>that if any figure can be given to a Solid, the Spherical is the eaſi <lb></lb>eſt of all others, as it is likewiſe the moſt ſimple, and holdeth the <lb></lb>ſame place amongſt ſolid figures, as the Circle holdeth amongſt <lb></lb><arrow.to.target n="marg379"></arrow.to.target> <lb></lb>the ſuperficial. </s><s>The deſcription of which Circle, as being more ea <lb></lb>ſie than all the reſt, hath alone been judged by <emph type="italics"></emph>Mathematicians<emph.end type="italics"></emph.end> <lb></lb>worthy to be put amongſt the ^{*} <emph type="italics"></emph>poſtulata<emph.end type="italics"></emph.end> belonging to the deſcri <lb></lb><arrow.to.target n="marg380"></arrow.to.target> <lb></lb>ption of all other figures. </s><s>And the formation of the Sphere is <lb></lb>ſo very eaſie, that if in a plain plate of hard metal you take an <lb></lb>empty or hollow circle, within which any Solid goeth caſually re <lb></lb>volving that was before but groſly rounded, it ſhall, without any <lb></lb>other artifice be reduced to a Spherical figure, as perfect as is poſ <lb></lb>ſible for it to be; provided, that that ſame Solid be not leſſe than <lb></lb>the Sphere that would paſſe thorow that Circle. </s><s>And that which is <lb></lb>yet more worthy of our conſideration is, that within the ſelf-ſame <pb xlink:href="040/01/205.jpg" pagenum="187"></pb>incavity one may form Spheres of ſeveral magnitudes. </s><s>But what <lb></lb><arrow.to.target n="marg381"></arrow.to.target> <lb></lb>is required to the making of an Horſe, or (as you ſay) of a Graſs <lb></lb>hopper, I leave to you to judge, who know that there are but few <lb></lb>ſtatuaries in the world able to undertake ſuch a piece of work. <lb></lb></s><s>And I think that herein <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> will not diſſent from me.</s></p><p type="margin"><s><margin.target id="marg378"></margin.target><emph type="italics"></emph>The Sphericall <lb></lb>Figure is eaſier to <lb></lb>be made than any <lb></lb>other.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg379"></margin.target><emph type="italics"></emph>The circular Fi <lb></lb>gure only is placed <lb></lb>amongst the<emph.end type="italics"></emph.end> poſtu <lb></lb>lata <emph type="italics"></emph>of Mathema <lb></lb>ticians.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg380"></margin.target>* Demands or <lb></lb>Petitions.</s></p><p type="margin"><s><margin.target id="marg381"></margin.target><emph type="italics"></emph>Sphericall Fi <lb></lb>gures of ſundry <lb></lb>magnitudes may <lb></lb>be made with one <lb></lb>onely inſtrument.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I know not whether I do at all diffent from you; my <lb></lb>opinion is this, that none of the afore-named figures can be per <lb></lb>fectly obteined; but for the approaching as neer as is poſſible to <lb></lb>the moſt perfect degree, I believe that it is incomparably more ea <lb></lb>ſie to reduce the Solid into a Spherical figure, than into the ſhape <lb></lb>of an Horſe, or Graſſe-hopper?</s></p><p type="main"><s>SAGR. </s><s>And this greater difficulty, wherein think you doth it <lb></lb>depend?</s></p><p type="main"><s>SIMP. </s><s>Like as the great facility in forming the Sphere ariſeth <lb></lb><arrow.to.target n="marg382"></arrow.to.target> <lb></lb>from its abſolute ſimplicity and uniformity ſo the great irregu <lb></lb>larity rendereth the conſtruction of all other figures difficult.</s></p><p type="margin"><s><margin.target id="marg382"></margin.target><emph type="italics"></emph>Irregular forms <lb></lb>difficult to be in <lb></lb>troduced.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Therefore the irregularity being the cauſe of the diffi <lb></lb>culty, than the figure of a ſtone broken with an hammer by <lb></lb>chance, ſhall be one of the figures that are difficult to be introdu <lb></lb>ced, it being perhaps more irregular than that of the horſe?</s></p><p type="main"><s>SIMP. </s><s>So it ſhould be.</s></p><p type="main"><s>SAGR. </s><s>But tell me; that figure what ever it is which the ſtone <lb></lb>hath, hath it the ſame in perfection, or no?</s></p><p type="main"><s>SIMP. </s><s>What it hath, it hath ſo perfectly, that nothing can be <lb></lb>more exact.</s></p><p type="main"><s>SAGR. Then, if of figures that are irregular, and conſequent <lb></lb>ly hard to be procured, there are yet infinite which are moſt per <lb></lb>fectly obteined, with what reaſon can it be ſaid, that the moſt <lb></lb>ſimple, and conſequently the moſt eaſie of all, is impoſſible to be <lb></lb>procured?</s></p><p type="main"><s>SALV. Gentlemen, with your favour, I may ſay that we have <lb></lb>ſallied out into a diſpute not much more worth than the wool of a <lb></lb>goat; and whereas our argumentations ſhould continually be con <lb></lb>verſant about ſerious and weighty points, we conſume our time in <lb></lb><arrow.to.target n="marg383"></arrow.to.target> <lb></lb>frivolous and impertinent wranglings. </s><s>Let us call to minde, I pray <lb></lb>you, that the ſearch of the worlds conſtitution, is one of the grea <lb></lb>teſt and nobleſt Problems that are in nature; and ſo much the <lb></lb>greater, inaſmuch as it is directed to the reſolving of that other; <lb></lb>to wit, of the cauſe of the Seas ebbing and flowing, enquired in <lb></lb>to by all the famous men, that have hitherto been in the world, <lb></lb>and poſſibly found out by none of them. </s><s>Therefore if we have <lb></lb>nothing more remaining for the full confutation of the argument <lb></lb>taken from the Earths <emph type="italics"></emph>vertigo,<emph.end type="italics"></emph.end> which was the laſt, alledged to <lb></lb>prove its immobility upon its own centre, let us paſſe to the ex <lb></lb>amination of thoſe things that are alledged for, and againſt the <lb></lb><emph type="italics"></emph>Annual Motion.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/206.jpg" pagenum="188"></pb><p type="margin"><s><margin.target id="marg383"></margin.target><emph type="italics"></emph>The conſtitution <lb></lb>of the Univerſe is <lb></lb>one of the moſt no <lb></lb>ble Problems.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I would not have you, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> meaſure our wits by <lb></lb>the ſcale of yours: you, who uſe to be continually buſied about <lb></lb>the ſublimeſt contemplations, eſteem thoſe notions frivolous and <lb></lb>below you, which we think matters worthy of our profoundeſt <lb></lb>thoughts: yet ſometimes for our ſatisfaction do not diſdain to <lb></lb>ſtoop ſo low as to give way a little to our curioſity. </s><s>As to the <lb></lb>refutation of the laſt argument, taken from the extruſions of the <lb></lb>diurnal <emph type="italics"></emph>vertigo,<emph.end type="italics"></emph.end> far leſs than what hath been ſaid, would have <lb></lb>given me ſatisfaction: and yet the things ſuperfluouſly ſpoken, <lb></lb>ſeemed to me ſo ingenious, that they have been ſo far from wea <lb></lb>rying my fancy, as that they have, by reaſon of their novelty, en <lb></lb>tertained me all along with ſo great delight, that I know not how <lb></lb>to deſire greater: Therefore, if you have any other ſpeculation <lb></lb>to add, produce it, for I, as to my own particular, ſhall gladly <lb></lb>hearken to it.</s></p><p type="main"><s>SALV. </s><s>I have always taken great delight in thoſe things which <lb></lb>I have had the fortune to diſcover, and next to that, which is my <lb></lb>chief content, I find great pleaſure in imparting them to ſome <lb></lb>friends, that apprehendeth and ſeemeth to like them: Now, in re <lb></lb>gard you are one of theſe, ſlacking a little the reins of my ambi <lb></lb>tion, which is much pleaſed when I ſhew my ſelf more perſpi <lb></lb>cacious, than ſome other that hath the reputation of a ſharp <lb></lb>ſight, I will for a full and true meaſure of the paſt diſpute, pro <lb></lb>duce another fallacy of the Sectators of <emph type="italics"></emph>Ptolomey<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> <lb></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-paſſed, and granted to <emph type="italics"></emph>Ptolomey,<emph.end type="italics"></emph.end> <lb></lb>as an effect indubitable, that the extruſion of the ſtone proceed <lb></lb>ing from the velocity of the wheel turn'd round upon its centre, <lb></lb>the cauſe of the ſaid extruſion encreaſeth in proportion, as the ve <lb></lb>locity of the <emph type="italics"></emph>vertigo<emph.end type="italics"></emph.end> (or whirling) is augmented: from whence <lb></lb>it was inferred, that the velocity of the Earth's <emph type="italics"></emph>vertigo<emph.end type="italics"></emph.end> being <lb></lb>very much greater than that of any machin whatſoever, that we <lb></lb>can make to turn round artificially; the extruſion of ſtones, of <lb></lb>animals, &c. </s><s>would conſequently be far more violent. </s><s>Now, I <lb></lb>obſerve that there is a great fallacy in this diſcourſe, in that we do <lb></lb>compare theſe velocities indifferently and abſolutely to one ano <lb></lb>ther. </s><s>It's true, that if I compare the velocities of the ſame wheel, <lb></lb>or of two wheels equal to each other, that which ſhall be more <lb></lb>ſwiftly turn'd round, ſhall extrude the ſtone with greater vio <lb></lb>lence; and the velocity encreaſing, the cauſe of the projection <lb></lb>ſhall likewiſe encreaſe: but when the velocity is augmented, not <lb></lb>by encreaſing the velocity in the ſame wheel, which would be by <lb></lb>cauſing it to make a greater number of revolutions in equal times; <lb></lb>but by encreaſing the diameter, and making the wheel greater, ſo <lb></lb>as that the converſion taking up the ſame time in the leſſer wheel, <pb xlink:href="040/01/207.jpg" pagenum="189"></pb>as in the greater, the velocity is greater onely in the bigger wheel, <lb></lb><arrow.to.target n="marg384"></arrow.to.target> <lb></lb>for that its circumference is bigger; there is no man that thinketh <lb></lb>that the cauſe of the extruſion in the great wheel will encreaſe ac <lb></lb>cording to the proportion of the velocity of its circumference, to <lb></lb>the velocity of the circumference of the other leſſer wheel; for that <lb></lb>this is moſt falſe, as by a moſt expeditious experiment I ſhall thus <lb></lb>groſly declare: We may ſling a ſtone with a ſtick of a yard long, <lb></lb>farther than we can do with a ſtick ſix yards long, though <lb></lb>the motion of the end of the long ſtick, that is of the ſtone placed <lb></lb>in the ſlit thereof, were more than double as ſwift as the mo <lb></lb>tion of the end of the other ſhorter ſtick, as it would be if <lb></lb>the velocities were ſuch that the leſſer ſtick ſhould turn thrice <lb></lb>round in the time whilſt the greater is making one onely con <lb></lb>verſion.</s></p><p type="margin"><s><margin.target id="marg384"></margin.target><emph type="italics"></emph>The cauſe of the <lb></lb>projection increaſ <lb></lb>eth not according <lb></lb>to the proportion of <lb></lb>the velocity, in <lb></lb>creaſed by making <lb></lb>the wheel bigger.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>This which you tell me, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> muſt, I ſee, needs <lb></lb>ſucceed in this very manner; but I do not ſo readily apprehend <lb></lb>the cauſe why equal velocities ſhould not operate equally in <lb></lb>extruding projects, but that of the leſſer wheel much more than <lb></lb>the other of the greater wheel; therefore I intreat you to tell me <lb></lb>how this cometh to paſs.</s></p><p type="main"><s>SIMP. Herein, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> you ſeem to differ much from your <lb></lb>ſelf, for that you were wont to penetrate all things in an inſtant, <lb></lb>and now you have overlook'd a fallacy couched in the experiment <lb></lb>of the ſtick, which I my ſelf have been able to diſcover: and this <lb></lb>is the different manner of operating, in making the projection one <lb></lb>while with the ſhort ſling and another while with the long one, <lb></lb>for if you will have the ſtone fly out of the ſlit, you need not con <lb></lb>tinue its motion uniformly, but at ſuch time as it is at the ſwifteſt, <lb></lb>you are to ſtay your arm, and ſtop the velocity of the ſtick; where <lb></lb>upon the ſtone which was in its ſwifteſt motion, flyeth out, and <lb></lb>moveth with impetuoſity: but now that ſtop cannot be made in <lb></lb>the great ſtick, which by reaſon of its length and flexibility, doth <lb></lb>not entirely obey the check of the arm, but continueth to accom <lb></lb>pany the ſtone for ſome ſpace, and holdeth it in with ſo much leſs <lb></lb>force, and not as if you had with a ſtiff ſling ſent it going with a <lb></lb>jerk: for if both the ſticks or ſlings ſhould be check'd by one and <lb></lb>the ſame obſtacle, I do believe they would fly aſwell out of the <lb></lb>one, as out of the other, howbeit their motions were equally <lb></lb>ſwift.</s></p><p type="main"><s>SAGR. </s><s>With the permiſſion of <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> I will anſwer ſome <lb></lb>thing to <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> in regard he hath addreſſed himſelf to me; <lb></lb>and I ſay, that in his diſcourſe there is ſomewhat good <lb></lb>and ſomewhat bad: good, becauſe it is almoſt all true; <lb></lb>bad, becauſe it doth not agree with our caſe: Truth is, that when <lb></lb>that which carrieth the ſtones with velocity, ſhall meet with a <pb xlink:href="040/01/208.jpg" pagenum="190"></pb>check that is immoveable, they ſhall fly out with great impetuo <lb></lb>ſity: the ſame effect following in that caſe, which we ſee dayly <lb></lb>to fall out in a boat that running a ſwift courſe, runs a-ground, or <lb></lb>meets with ſome ſudden ſtop, for all thoſe in the boat, being ſur <lb></lb><arrow.to.target n="marg385"></arrow.to.target> <lb></lb>prized, ſtumble forwards, and fall towards the part whither the <lb></lb>boat ſteered. </s><s>And in caſe the Earth ſhould meet with ſuch a <lb></lb>check, as ſhould be able to reſiſt and arreſt its <emph type="italics"></emph>vertigo,<emph.end type="italics"></emph.end> then indeed <lb></lb>I do believe that not onely beaſts, buildings and cities, but moun <lb></lb>tains, lakes and ſeas would overturn, and the globe it ſelf would <lb></lb>go near to ſhake in pieces; but nothing of all this concerns our <lb></lb>preſent purpoſe, for we ſpeak of what may follow to the motion <lb></lb>of the Earth, it being turn'd round uniformly, and quietly about <lb></lb>its own centre, howbeit with a great velocity. </s><s>That likewiſe <lb></lb>which you ſay of the ſlings, is true in part; but was not alledged <lb></lb>by <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> as a thing that punctually agreed with the matter <lb></lb>whereof we treat, but onely, as an example, for ſo in groſs it may <lb></lb>prompt us in the more accurate conſideration of that point, whe <lb></lb>ther, the velocity increaſing at any rate, the cauſe of the proje <lb></lb>ction doth increaſe at the ſame rate: ſo that <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> if a wheel of <lb></lb>ten yards diameter, moving in ſuch a manner that a point of its <lb></lb>circumference will paſs an hundred yards in a minute of an hour, <lb></lb>and ſo hath an <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> able to extrude a ſtone, that ſame <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> <lb></lb>ſhall be increaſed an hundred thouſand times in a wheel of a million <lb></lb>of yards diameter; the which <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> denieth, and I incline to his <lb></lb>opinion; but not knowing the reaſon thereof, I have requeſted it <lb></lb>of him, and ſtand impatiently expecting it.</s></p><p type="margin"><s><margin.target id="marg385"></margin.target><emph type="italics"></emph>Graming the di <lb></lb>urnal<emph.end type="italics"></emph.end> vertigo <emph type="italics"></emph>of <lb></lb>the Earth, & that <lb></lb>by ſome ſudden ſtop <lb></lb>or obſtacle it were <lb></lb>arreſted, houſes, <lb></lb>mountains them <lb></lb>ſelves, and perhaps <lb></lb>the whole Globe <lb></lb>would be ſhaken n <lb></lb>pieces.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>I am ready to give you the beſt ſatisfaction, that my <lb></lb>abilities will give leave: And though in my firſt diſcourſe you <lb></lb>thought that I had enquired into things eſtranged from our pur <lb></lb>poſe, yet nevertheleſſe I believe that in the ſequel of the diſpute, <lb></lb>you will find that they do not prove ſo. </s><s>Therefore let <emph type="italics"></emph>Sagredus<emph.end type="italics"></emph.end> <lb></lb>tell me wherein he hath obſerved that the reſiſtance of any move <lb></lb>able to motion doth conſiſt.</s></p><p type="main"><s>SAGR. </s><s>I ſee not for the preſent that the moveable hath any <lb></lb>internal reſiſtance to motion, unleſſe it be its natural inclination <lb></lb>and propenſion to the contrary motion, as in grave bodies, that <lb></lb>have a propenſion to the motion downwards, the reſiſtance is to <lb></lb>the motion upwards; and I ſaid an internal reſiſtance, becauſe <lb></lb>of this, I think, it is you intend to ſpeak, and not of the external <lb></lb>reſiſtances, which are many and accidental.</s></p><p type="main"><s>SALV. </s><s>It is that indeed I mean, and your nimbleneſſe of wit <lb></lb>hath been too hard for my craftineſſe, but if I have been too <lb></lb>ſhort in asking the queſtion, I doubt whether <emph type="italics"></emph>Sagredus<emph.end type="italics"></emph.end> hath been <lb></lb>full enough in his anſwer to ſatisſie the demand; and whether <lb></lb>there be not in the moveable, beſides the natural inclination to the <pb xlink:href="040/01/209.jpg" pagenum="191"></pb>contrary term, another intrinſick and natural quality, which ma <lb></lb><arrow.to.target n="marg386"></arrow.to.target> <lb></lb>keth it averſe to motion. </s><s>Therefore tell me again; do you not <lb></lb>think that the inclination <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> of grave bodies to move down <lb></lb>wards, is equal to the reſiſtance of the ſame to the motion of pro <lb></lb>jection upwards?</s></p><p type="margin"><s><margin.target id="marg386"></margin.target><emph type="italics"></emph>The inclination of <lb></lb>grave bodies to the <lb></lb>motion downwards, <lb></lb>is equal to their <lb></lb>reſiſtance to the <lb></lb>motion upwards.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I believe that it is exactly the ſame. </s><s>And for this reaſon <lb></lb>I ſee that two equal weights being put into a ballance, they do <lb></lb>ſtand ſtill in <emph type="italics"></emph>equilibrium,<emph.end type="italics"></emph.end> the gravity of the one reſiſting its be <lb></lb>ing raiſed by the gravity wherewith the other preſſing down <lb></lb>wards would raiſe it.</s></p><p type="main"><s>SALV. </s><s>Very well; ſo that if you would have one raiſe up the <lb></lb>other, you muſt encreaſe the weight of that which depreſſeth, <lb></lb>or leſſen the weight of the other. </s><s>But if the reſiſtance to aſcend <lb></lb>ing motion cunſiſt onely in gravity, how cometh it to paſſe, that <lb></lb><arrow.to.target n="marg387"></arrow.to.target> <lb></lb>in ballances of unequal arms, to wit in the ^{*} <emph type="italics"></emph>Stiliard,<emph.end type="italics"></emph.end> a weight <lb></lb>ſometimes of an hundred pounds, with its preſſion downwards, <lb></lb>doth not ſuffice to raiſe up on of four pounds; that ſhall counter <lb></lb>poiſe with it, nay this of four, deſcending ſhall raiſe up that <lb></lb>of an hundred; for ſuch is the effect of the pendant weight upon <lb></lb>the weight which we would weigh? </s><s>If the reſiſtance to motion <lb></lb>reſideth onely in the gravity, how can the arm with its weight of <lb></lb>four pounds onely, reſiſt the weight of a ſack of wool, or bale of <lb></lb>ſilk, which ſhall be eight hundred, or a thouſand weight; yea <lb></lb>more, how can it overcome the ſack with its moment, and raiſe <lb></lb>it up? </s><s>It muſt therefore be confeſt <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> that here it maketh <lb></lb>uſe of ſome other reſiſtance, and other force, beſides that of <lb></lb>ſimple gravity.</s></p><p type="margin"><s><margin.target id="marg387"></margin.target>* A portable bal <lb></lb>lance wherewith <lb></lb>market-people <lb></lb>weigh their com <lb></lb>modities, giving it <lb></lb>gravity by remo <lb></lb>ving the weight <lb></lb>farther from the <lb></lb>cock: call'd by the <lb></lb>Latines, <emph type="italics"></emph>Campana <lb></lb>trutina.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>It muſt needs be ſo; therefore tell me what this ſe <lb></lb>cond virtue ſhould be.</s></p><p type="main"><s>SALV. </s><s>It is that which was not in the ballance of equal <lb></lb>arms; you ſee then what variety there is in the Stiliard; and up <lb></lb>on this doubtleſſe dependeth the cauſe of the new effect.</s></p><p type="main"><s>SAGR. </s><s>I think that your putting me to it a ſecond time, hath <lb></lb>made me remember ſomething that may be to the purpoſe. </s><s>In <lb></lb>both theſe beams the buſineſs is done by the weight, and by the <lb></lb>motion; in the ballance, the motions are equal, and therefore the <lb></lb>one weight muſt exceed it in gravity before it can move it; in the <lb></lb>ſtiliard, the leſſer weight will not move the greater, unleſs when <lb></lb>this latter moveth little, as being ſlung at a leſſer diſtance, and the <lb></lb>other much, as hanging at a greater diſtance from the lacquet or <lb></lb>cock. </s><s>It is neceſſary therefore to conclude, that the leſſer weight <lb></lb>overcometh the reſiſtance of the greater, by moving much, whilſt <lb></lb>the other is moved but little.</s></p><p type="main"><s>SALV. </s><s>Which is as much as to ſay, that the velocity of the <lb></lb>moveable leſs grave, compenſateth the gravity of the moveable <lb></lb>more grave and leſs ſwift. <pb xlink:href="040/01/210.jpg" pagenum="192"></pb><arrow.to.target n="marg388"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg388"></margin.target><emph type="italics"></emph>The greater velo <lb></lb>city exactly com <lb></lb>penſates thegreater <lb></lb>gravity.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>But do you think that the velocity doth fully make <lb></lb>good the gravity? </s><s>that is, that the moment and force of a move <lb></lb>able of <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> four pounds weight, is as great as that of one of an <lb></lb>hundred weight, whenſoever that the firſt hath an hundred degrees <lb></lb>of velocity, and the later but four onely?</s></p><p type="main"><s>SALV. </s><s>Yes doubtleſs, as I am able by many experiments to <lb></lb>demonſtrate: but for the preſent, let this onely of the ſtiliard <lb></lb>ſuffice: in which you ſee that the light end of the beam is then <lb></lb>able to ſuſtain and equilibrate the great Wool ſack, when its di <lb></lb>ſtance from the centre, upon which the ſtiliard reſteth and turn <lb></lb>eth, ſhall ſo much exceed the leſſer diſtance, by how much the ab <lb></lb>ſolute gravity of the Wool-ſack exceedeth that of the pendent <lb></lb>weight. </s><s>And we ſee nothing that can cauſe this inſufficiencie in <lb></lb>the great ſack of Wool, to raiſe with its weight the pendent <lb></lb>weight ſo much leſs grave, ſave the diſparity of the motions which <lb></lb>the one and the other ſhould make, whilſt that the Wool ſack by <lb></lb>deſcending but one inch onely, will raiſe the pendent weight an <lb></lb>hundred inclies: (ſuppoſing that the ſack did weigh an hundred <lb></lb>times as much, and that the diſtance of the ſmall weight from the <lb></lb>centre of the beam were an hundred times greater, than the di <lb></lb>ſtance between the ſaid centre and the point of the ſacks ſuſpenſi <lb></lb>on.) And again, the pendent weight its moving the ſpace of an <lb></lb>hundred inches, in the time that the ſack moveth but one inch <lb></lb>onely, is the ſame as to ſay, that the velocity of the motion of the <lb></lb>little pendent weight, is an hundred times greater than the velo <lb></lb>city of the motion of the ſack. </s><s>Now fix it in your belief, as a <lb></lb>true and manifeſt axiom, that the reſiſtance which proceedeth from <lb></lb>the velocity of motion, compenſateth that which dependeth on <lb></lb>the gravity of another moveable: So that conſequently, a move <lb></lb>able of one pound, that moveth with an hundred degrees of ve <lb></lb>locity, doth as much reſiſt all obſtruction, as another moveable <lb></lb>of an hundred weight, whoſe velocity is but one degree onely. <lb></lb></s><s>And two equal moveables will equally reſiſt their being moved, <lb></lb>if that they ſhall be moved with equal velocity: but if one be <lb></lb>to be moved more ſwiftly than the other, it ſhall make greater re <lb></lb>ſiſtance, according to the greater velocity that ſhall be conferred <lb></lb>on it. </s><s>Theſe things being premiſed, let us proceed to the expla <lb></lb>nation of our Problem; and for the better underſtanding of <lb></lb>things, let us make a ſhort Scheme thereof. </s><s>Let two unequal <lb></lb>wheels be deſcribed about this centre A, [<emph type="italics"></emph>in Fig.<emph.end type="italics"></emph.end> 7.] and let the <lb></lb>circumference of the leſſer be B G, and of the greater C E H, and <lb></lb>let the ſemidiameter A B C, be perpendicular to the Horizon; and <lb></lb>by the points B and C, let us draw the right lined Tangents B F <lb></lb>and C D; and in the arches B G and C E, take two equal parts <lb></lb>B G and C E: and let the two wheels be ſuppoſed to be turn'd <pb xlink:href="040/01/211.jpg" pagenum="193"></pb>round upon their centres with equal velocities, ſo as that two mo <lb></lb>veables, which ſuppoſe for example to be two ſtones placed in the <lb></lb>points B and C, come to be carried along the circumferences B G <lb></lb>and C E, with equal velocities; ſo that in the ſame time that the <lb></lb>ſtone B ſhall have run the arch B G, the ſtone C will have paſt the <lb></lb>arch C E. </s><s>I ſay now, that the whirl or <emph type="italics"></emph>vertigo<emph.end type="italics"></emph.end> of the leſſer wheel <lb></lb>is much more potent to make the projection of the ſtone B, than <lb></lb>the <emph type="italics"></emph>vertigo<emph.end type="italics"></emph.end> of the bigger wheel to make that of the ſtone C. <lb></lb></s><s>Therefore the projection, as we have already declared, being to be <lb></lb>made along the tangent, when the ſtones B and C are to ſeparate <lb></lb>from their wheels, and to begin the motion of projection from the <lb></lb>points B and C, then ſhall they be extruded by the <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> con <lb></lb>ceived from the <emph type="italics"></emph>vertigo<emph.end type="italics"></emph.end> by (or along) the tangents B F and C D. <lb></lb></s><s>The two ſtones therefore have equal impetuoſities of running a <lb></lb>long the tangents B F and C D, and would run along the ſame, if <lb></lb>they were not turn'd aſide by ſome other force: is it not ſo <emph type="italics"></emph>Sa <lb></lb>gredus<emph.end type="italics"></emph.end>?</s></p><p type="main"><s>SAGR. </s><s>In my opinion the buſineſſe is as you ſay.</s></p><p type="main"><s>SALV. </s><s>But what force, think you, ſhould that be which averts <lb></lb>the ſtones from moving by the tangents, along which they are cer <lb></lb>tainly driven by the <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> of the <emph type="italics"></emph>vertigo.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>It is either their own gravity, or elſe ſome glutinous <lb></lb>matter that holdeth them faſt and cloſe to the wheels.</s></p><p type="main"><s>SALV. </s><s>But for the diverting of a moveable from the motion <lb></lb>to which nature inciteth it, is there not required greater or leſſer <lb></lb>force, according as the deviation is intended to be greater or leſ <lb></lb>ſer? </s><s>that is, according as the ſaid moveable in its deviation hath a <lb></lb>greater or leſſer ſpace to move in the ſame time?</s></p><p type="main"><s>SAGR. </s><s>Yes certainly: for it was concluded even now, that to <lb></lb>make a moveable to move; the movent vertue muſt be increaſed <lb></lb>in proportion to the velocity wherewith it is to move.</s></p><p type="main"><s>SALV. </s><s>Now conſider, that for the deviating the ſtone upon <lb></lb>the leſſe wheel from the motion of projection, which it would <lb></lb>make by the tangent B F, and for the holding of it faſt to the <lb></lb>wheel, it is required, that its own gravity draw it back the whole <lb></lb>length of the ſecant F G, or of the perpendicular raiſed from the <lb></lb>point G, to the line B F, whereas in the greater wheel the retracti <lb></lb>on needs to be no more than the ſecant D E, or the perpendicu <lb></lb>lar let fall from the tangent D G to the point E, leſſe by much <lb></lb>than F G, and alwayes leſſer and leſſer according as the wheel is <lb></lb>made bigger. </s><s>And foraſmuch as theſe retractions (as I may call <lb></lb>them) are required to be made in equal times, that is, whil'ſt the <lb></lb>wheels paſſe the two equal arches B G and C E, that of the ſtone <lb></lb>B, that is, the retraction F G ought to be more ſwift than the o <lb></lb>ther D E; and therefore much greater force will be required for <pb xlink:href="040/01/212.jpg" pagenum="194"></pb>holding faſt the ſtone B to its little wheel, than for the holding <lb></lb>the ſtone C to its great one, which is as much as to ſay, that ſuch <lb></lb>a ſmall thing will impede the extruſion in the great wheel, as will <lb></lb>not at all hinder it in the little one. </s><s>It is manifeſt therefore that <lb></lb>the more the wheel augmenteth, the more the cauſe of the pro <lb></lb>jection diminiſheth.</s></p><p type="main"><s>SAGR. </s><s>From this which I now underſtand, by help of your mi <lb></lb>nute diſſertation, I am induced to think, that I am able to ſatisfie <lb></lb>my judgment in a very few words. </s><s>For equal <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> being im <lb></lb>preſſed on both the ſtones that move along the tangents, by the <lb></lb>equal velocity of the two wheels, we ſee the great circumference, <lb></lb>by means of its ſmall deviation from the tangent, to go ſeconding, <lb></lb>as it were, and in a fair way refraining in the ſtone the appetite, if <lb></lb>I may ſo ſay, of ſeparating from the circumference; ſo that any <lb></lb>ſmall retention, either of its own inclination, or of ſome glutina <lb></lb>tion ſufficeth to hold it faſt to the wheel. </s><s>Which, again, is not a <lb></lb>ble to work the like effect in the little wheel, which but little pro <lb></lb>ſecuting the direction of the tangent, ſeeketh with too much ea <lb></lb>gerneſſe to hold faſt the ſtone; and the reſtriction and glutination <lb></lb>not being ſtronger than that which holdeth the other ſtone faſt to </s></p><p type="main"><s><arrow.to.target n="marg389"></arrow.to.target> <lb></lb>the greater wheel, it ^{*} breaks looſe, and runneth along the tan <lb></lb>gent. </s><s>Therefore I do not only finde that all thoſe have erred, <lb></lb>who have believed the cauſe of the projection to increaſe accor <lb></lb>ding to the augmentation of the <emph type="italics"></emph>vertigo's<emph.end type="italics"></emph.end> velocity; but I am <lb></lb>further thinking, that the projection diminiſhing in the inlarging of <lb></lb>the wheel, ſo long as the ſame velocity is reteined in thoſe wheels; <lb></lb>it may poſſibly be true, that he that would make the great wheel <lb></lb>extrude things like the little one, would be forced to increaſe <lb></lb>them as much in velocity, as they increaſe in diameter, which he <lb></lb>might do, by making them to finiſh their converſions in equal <lb></lb>times; and thus we may conclude, that the Earths revolution or <lb></lb><emph type="italics"></emph>vertigo<emph.end type="italics"></emph.end> would be no more able to extrude ſtones, than any little <lb></lb>wheel that goeth ſo ſlowly, as that it maketh but one turn in twen <lb></lb>ty four hours.</s></p><p type="margin"><s><margin.target id="marg389"></margin.target>* Strappar la ca <lb></lb>vezza, <emph type="italics"></emph>is to break <lb></lb>the bridle.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>We will enquire no further into this point for the pre <lb></lb>ſent: let it ſuffice that we have abundantly (if I deceive not my <lb></lb>ſelf) demonſtrated the invalidity of the argument, which at firſt <lb></lb>ſight ſeemed very concluding, and was ſo held by very famous <lb></lb>men: and I ſhall think my time and words well beſtowed, if I <lb></lb>have but gained ſome belief in the opinion of <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> I will <lb></lb>not ſay or the Earths mobility, but only that the opinion of thoſe <lb></lb>that believe it, is not ſo ridiculous and fond, as the rout of vulgar <lb></lb>Philoſophers eſteem it.</s></p><p type="main"><s>SIMP. </s><s>The anſwers hitherto produced againſt the arguments <lb></lb>brought againſt this <emph type="italics"></emph>Diurnal Revolution<emph.end type="italics"></emph.end> of the Earth taken from <pb xlink:href="040/01/213.jpg" pagenum="195"></pb>grave bodies falling from the top of a Tower, and from proje <lb></lb>ctions made perpendicularly upwards, or according to any inclina <lb></lb>tion ſidewayes towards the Eaſt, Weſt, North, South, &c. </s><s>have <lb></lb>ſomewhat abated in me the antiquated incredulity I had conceived <lb></lb>againſt that opinion: but other greater doubts run in my mind <lb></lb>at this very inſtant, which I know not in the leaſt how to free my <lb></lb>ſelf of, and haply you your ſelf will not be able to reſolve them; <lb></lb>nay, its poſſible you may not have heard them, for they are very <lb></lb>modern. </s><s>And theſe are the objections of two Authours, that <emph type="italics"></emph>ex <lb></lb>profeſſo<emph.end type="italics"></emph.end> write againſt <emph type="italics"></emph>Copernicus.<emph.end type="italics"></emph.end> Some of which are read in a <lb></lb><arrow.to.target n="marg390"></arrow.to.target> <lb></lb>little Tract of natural concluſions; The reſt are by a great both <lb></lb>Philoſopher and Mathematician, inſerted in a Treatiſe which he <lb></lb>hath written in favour of <emph type="italics"></emph>Aristotle,<emph.end type="italics"></emph.end> and his opinion touching the <lb></lb>inalterability of the Heavens, where he proveth, that not onely <lb></lb>the Comets, but alſo the new ſtars, namely, that <emph type="italics"></emph>anno<emph.end type="italics"></emph.end> 1572. in <lb></lb><emph type="italics"></emph>Caſſiopeia,<emph.end type="italics"></emph.end> and that <emph type="italics"></emph>anno<emph.end type="italics"></emph.end> 1604. in <emph type="italics"></emph>Sagittarius<emph.end type="italics"></emph.end> were not above the <lb></lb>Spheres of the Planets, but abſolutely beneath the concave of <lb></lb>the Moon in the Elementary Sphere, and this he demonſtrateth a <lb></lb>gainſt <emph type="italics"></emph>Tycho, Kepler,<emph.end type="italics"></emph.end> and many other Aftronomical Obſervators, <lb></lb>and beateth them at their own weapon; to wit, the Doctrine of <lb></lb>Parallaxes. </s><s>If you like thereof, I will give you the reaſons of <lb></lb>both theſe Authours, for I have read them more than once, <lb></lb>with attention; and you may examine their ſtrength, and give <lb></lb>your opinion thereon.</s></p><p type="margin"><s><margin.target id="marg390"></margin.target><emph type="italics"></emph>Other objections <lb></lb>of two modern Au <lb></lb>thors against<emph.end type="italics"></emph.end> Co <lb></lb>pernicus.</s></p><p type="main"><s>SALV. </s><s>In regard that our principal end is to bring upon the <lb></lb>ſtage, and to conſider what ever hath been ſaid for, or againſt the <lb></lb>two Syſtemes, <emph type="italics"></emph>Ptolomaick,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Copernican,<emph.end type="italics"></emph.end> it is not good to omit <lb></lb>any thing that hath been written on this ſubject.</s></p><p type="main"><s>SIMP. </s><s>I will begin therefore with the objections which I finde <lb></lb>in the Treatiſe of Concluſions, and afterwards proceed to the <lb></lb><arrow.to.target n="marg391"></arrow.to.target> <lb></lb>reſt. </s><s>In the firſt place then, he beſtoweth much paines in calcu <lb></lb>lating exactly how many miles an hour a point of the terreſtrial <lb></lb>Globe ſituate under the Equinoctial, goeth, and how many miles <lb></lb>are paſt by other points ſituate in other parallels: and not being <lb></lb>content with finding out ſuch motions in horary times, he findeth <lb></lb>them alſo in a minute of an hour; and not contenting himſelf <lb></lb>with a minute, he findes them alſo in a ſecond minute; yea more, <lb></lb>he goeth on to ſhew plainly, how many miles a Cannon bullet <lb></lb>would go in the ſame time, being placed in the concave of the Lu <lb></lb><arrow.to.target n="marg392"></arrow.to.target> <lb></lb>nar Orb, ſuppoſing it alſo as big as <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> himſelf repreſenteth <lb></lb>it, to take away all ſubterfuges from his adverſary. </s><s>And having <lb></lb>made this moſt ingenious and exquiſite ſupputation, he ſheweth, <lb></lb>that a grave body falling from thence above would conſume more <lb></lb>than ſix dayes in attaining to the centre of the Earth, to which all <lb></lb>grave bodies naturally move. </s><s>Now if by the abſolute Divine <pb xlink:href="040/01/214.jpg" pagenum="196"></pb>Power, or by ſome Angel, a very great Cannon bullet were carri <lb></lb>ed up thither, and placed in our Zenith or vertical point, and from <lb></lb>thence let go at liberty, it is in his, and alſo in my opinion, a moſt <lb></lb>incredible thing that it, in deſcending downwards, ſhould all the <lb></lb>way maintain it ſelf in our vertical line, continuing to turn round <lb></lb>with the Earth, about its centre, for ſo many dayes, deſcribing <lb></lb>under the Equinoctial a Spiral line in the plain of the great circle <lb></lb>it ſelf: and under other Parallels, Spiral lines about Cones, and <lb></lb>under the Poles falling by a ſimple right line. </s><s>He, in the next <lb></lb>place, ſtabliſheth and confirmeth this great improbability by pro <lb></lb>ving, in the way of interrogations, many difficulties impoſſible to <lb></lb>be removed by the followers of <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end>; and they are, if I do <lb></lb>well remember-----.</s></p><p type="margin"><s><margin.target id="marg391"></margin.target><emph type="italics"></emph>The firſt obje <lb></lb>ction of the mo <lb></lb>dern Author of <lb></lb>the little tract of<emph.end type="italics"></emph.end> <lb></lb>Concluſions.</s></p><p type="margin"><s><margin.target id="marg392"></margin.target><emph type="italics"></emph>A Cannon bul <lb></lb>let would ſpend <lb></lb>more than ſix days <lb></lb>in falling from the <lb></lb>Concave of the <lb></lb>Moon to the cen <lb></lb>tre of the Earth, <lb></lb>according to the o <lb></lb>pinion of that mo <lb></lb>dern Author of the<emph.end type="italics"></emph.end> <lb></lb>Concluſions.</s></p><p type="main"><s>SALV. </s><s>Take up a little, good <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> and do not load me <lb></lb>with ſo many novelties at once: I have but a bad memory, and <lb></lb>therefore I muſt not go too faſt. </s><s>And in regard it cometh into <lb></lb>my minde, that I once undertook to calculate how long time ſuch a <lb></lb>grave body falling from the concave of the Moon, would be in <lb></lb>paſſing to the centre of the Earth, and that I think I remember <lb></lb>that the time would not be ſo long; it would be fit that you ſhew <lb></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"></emph>à fortiori,<emph.end type="italics"></emph.end> a ſuffi <lb></lb>cient advantage for his adverſaries, ſuppoſing that the velocity of <lb></lb>the body falling along the vertical line, towards the centre of the <lb></lb>Earth, were equal to the velocity of its circular motion, which it <lb></lb>made in the grand circle of the concave of the Lunar Orb. <lb></lb></s><s>Which by equation would come to paſſe in an hour, twelve thou <lb></lb>ſand ſix hundred German miles, a thing which indeed ſavours of <lb></lb>impoſſibility: Yet nevertheleſſe, to ſhew his abundant caution, <lb></lb>and to give all advantages to his adverſaries, he ſuppoſeth it for <lb></lb>true, and concludeth, that the time oſ the fall ought however to <lb></lb>be more than ſix dayes.</s></p><p type="main"><s>SALV. </s><s>And is this the ſum of his method? </s><s>And doth he by <lb></lb>this demonſtration prove the time of the fall to be above ſix <lb></lb>dayes?</s></p><p type="main"><s>SAGR. </s><s>Me thinks that he hath behaved himſelf too modeſtly, <lb></lb>for that having it in the power of his will to give what velocity he <lb></lb>pleaſed to ſuch a deſcending body, and might aſwell have made it <lb></lb>ſix moneths, nay, ſix years in falling to the Earth, he is content <lb></lb>with ſix dayes. </s><s>But, good <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> ſharpen my appetite a lit <lb></lb>tle, by telling me in what manner you made your computation, in <lb></lb>regard you ſay, that you have heretofore caſt it up: for I am con <lb></lb>fident that if the queſtion had not required ſome ingenuity in <lb></lb>working it, you would never have applied your minde unto <lb></lb>it.</s></p> <pb xlink:href="040/01/215.jpg" pagenum="197"></pb><p type="main"><s>SALV. </s><s>It is not enough, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> that the ſubjects be noble <lb></lb>and great, but the buſineſſe conſiſts in handling it nobly. </s><s>And <lb></lb>who knoweth not, that in the diſſection of the members of <lb></lb>a beaſt, there may be diſcovered infinite wonders of provident <lb></lb>and prudent Nature; and yet for one, that the Anatomiſt diſ <lb></lb>ſects, the butcher cuts up a thouſand. </s><s>Thus I, who am now <lb></lb>ſeeking how to ſatisfie your demand, cannot tell with which of the <lb></lb>two ſhapes I had beſt to appear on the Stage; but yet, taking <lb></lb>heart from the example of <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> his Authour, I will, with <lb></lb>out more delays, give you an account (if I have not forgot) how <lb></lb>I proceeded. </s><s>But before I go any further, I muſt not omit to tell <lb></lb>you, that I much fear that <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> hath not faithfully related <lb></lb>the manner how this his Authour found, that the Cannon bul <lb></lb>let in coming from the concave of the Moon to the centre of the <lb></lb>Earth, would ſpend more than fix dayes: for if he had ſuppo <lb></lb>ſed that its velocity in deſcending was equal to that of the <lb></lb>concave (as <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> ſaith he doth ſuppoſe) he would have <lb></lb>ſhewn himſelf ignorant of the firſt, and more ſimple principles <lb></lb>of <emph type="italics"></emph>Geometry<emph.end type="italics"></emph.end>; yea, I admire that <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> in admitting the <lb></lb>ſuppoſition which he ſpeaketh of, doth not ſee the monſtrous ab <lb></lb>ſurdity that is couched in it.</s></p><p type="main"><s>SIMP. </s><s>Its poſſible that I may have erred in relating it; but <lb></lb>that I ſee any fallacy in it, I am ſure is not true.</s></p><p type="main"><s>SALV. </s><s>Perhaps I did not rightly apprehend that which you <lb></lb>ſaid, Do you not ſay, that this Authour maketh the velocity <lb></lb>of the bullet in deſcending equall to that which it had in tur <lb></lb>ning round, being in the concave of the Moon, and that com <lb></lb>ming down with the ſame velocity, it would reach to the centre <lb></lb>in ſix 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 ſhamefull errour therein? <lb></lb></s><s>But queſtionleſſe you diſſemble it: For it cannot be, but that <lb></lb>you ſhould know that the ſemidiameter of the Circle is leſſe than <lb></lb><arrow.to.target n="marg393"></arrow.to.target> <lb></lb>the ſixth part of the circumference; and that conſequently, the <lb></lb>time in which the moveable ſhall paſſe the ſemidiameter, ſhall be <lb></lb>leſſe than the ſixth part of the time; in which, being moved <lb></lb>with the ſame velocity, it would paſſe the circumference; and <lb></lb>that therefore the bullet deſcending with the velocity, where <lb></lb>with it moved in the concave, will arrive in leſſe than four hours <lb></lb>at the centre, ſuppoſing that in the concave one revolution <lb></lb>ſhould be conſummate in twenty four hours, as he muſt of ne <lb></lb>ceſſity have ſuppoſed it, for to keep it all the way in the ſame <lb></lb>vertical line.</s></p><p type="margin"><s><margin.target id="marg393"></margin.target><emph type="italics"></emph>A ſhamefull <lb></lb>errour in the Ar <lb></lb>gument taken from <lb></lb>the bullets falling <lb></lb>out of the Moons <lb></lb>concave.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>Now I thorowly perceive the miſtake: but yet I <lb></lb>would not lay it upon him undeſervedly, for it's poſſible that I <pb xlink:href="040/01/216.jpg" pagenum="198"></pb>may have erred in rehearſing his Argument, and to avoid running <lb></lb>into the ſame miſtakes for the future, I could wiſh I had his <lb></lb>Book; and if you had any body to ſend for it, I would take it <lb></lb>for a great favour.</s></p><p type="main"><s>SAGR. </s><s>You ſhall not want a Lacquey that will runne for it <lb></lb>with all ſpeed: and he ſhall do it preſently, without loſing any <lb></lb>time; in the mean time <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> may pleaſe to oblige us with his <lb></lb>computation.</s></p><p type="main"><s>SIMP. </s><s>If he go, he ſhall finde it lie open upon my Desk, <lb></lb>together with that of the other Author, who alſo argueth a <lb></lb>gainſt <emph type="italics"></emph>Copernicus.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>We will make him bring that alſo for the more cer <lb></lb>tainty: and in the interim <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> ſhall make his calculation: I <lb></lb>have diſpatch't away a meſſenger.</s></p><p type="main"><s>SALV. </s><s>Above all things it muſt be conſidered, that the motion <lb></lb>of deſcending grave bodies is not uniform, but departing from <lb></lb><arrow.to.target n="marg394"></arrow.to.target> <lb></lb>reſt they go continually accelerating: An effect known and ob <lb></lb>ſerved by all men, unleſſe it be by the forementioned modern Au <lb></lb>thour, who not ſpeaking of acceleration, maketh it even and u <lb></lb>niforme. </s><s>But this general notion is of no avail, if it be not known <lb></lb>according to what proportion this increaſe of velocity is made; a <lb></lb>concluſion that hath been until our times unknown to all <emph type="italics"></emph>Philoſo <lb></lb>phers<emph.end type="italics"></emph.end>; and was firſt found out & demonſtrated by the ^{*} <emph type="italics"></emph>Academick,<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg395"></arrow.to.target> <lb></lb>our common friend, who in ſome of his ^{*} writings not yet publiſh <lb></lb><arrow.to.target n="marg396"></arrow.to.target> <lb></lb>ed, but in familiarity ſhewn to me, and ſome others of his ac <lb></lb>quaintance he proveth, how that the acceleration of the right mo <lb></lb>tion of grave bodies, is made according to the numbers uneven <lb></lb>beginning <emph type="italics"></emph>ab unitate,<emph.end type="italics"></emph.end> that is, any number of equal times being aſ <lb></lb>ſigned, if in the firſt time the moveable departing from reſt ſhall <lb></lb><arrow.to.target n="marg397"></arrow.to.target> <lb></lb>have paſſed ſuch a certain ſpace, as for example, an ell, in the ſe <lb></lb>cond time it ſhall have paſſed three ells, in the third five, in the <lb></lb>fourth ſeven, and ſo progreſſively, according to the following odd <lb></lb>numbers; which in ſhort is the ſame, as if I ſhould ſay, that the <lb></lb>ſpaces paſſed by the moveable departing from its reſt, are unto <lb></lb><arrow.to.target n="marg398"></arrow.to.target> <lb></lb>each other in proportion double to the proportion of the times, <lb></lb>in which thoſe ſpaces are meaſured; or we will ſay, that the <lb></lb>ſpaces paſſed are to each other, as the ſquares of their times.</s></p><p type="margin"><s><margin.target id="marg394"></margin.target><emph type="italics"></emph>An exact com <lb></lb>pute of the time of <lb></lb>the fall of the Ca <lb></lb>non bullet from the <lb></lb>Moons concave to <lb></lb>the Earths centre.<emph.end type="italics"></emph.end></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 theſe <emph type="italics"></emph>Wri <lb></lb>tings,<emph.end type="italics"></emph.end> he every <lb></lb>where meanes his <lb></lb>Dialogues, <emph type="italics"></emph>De mo <lb></lb>tu,<emph.end type="italics"></emph.end> which I promiſe <lb></lb>to give you in my <lb></lb>ſecond Volume.</s></p><p type="margin"><s><margin.target id="marg397"></margin.target><emph type="italics"></emph>Acceleration of <lb></lb>the natural motion <lb></lb>of grave bodies is <lb></lb>made according to <lb></lb>the odde numbers <lb></lb>beginning at unity.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg398"></margin.target><emph type="italics"></emph>The ſpaces paſt <lb></lb>by the falling <lb></lb>grave body are as <lb></lb>the ſquares of their <lb></lb>times.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>This is truly admirable: and do you ſay that there is <lb></lb>a Mathematical demonſtration for it?</s></p><p type="main"><s>SALV. Yes, purely Mathematical; and not onely for this, but <lb></lb>for many other very admirable paſſions, pertaining to natural mo <lb></lb>tions, and to projects alſo, all invented, and demonſtrated by <emph type="italics"></emph>Our<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg399"></arrow.to.target> <lb></lb><emph type="italics"></emph>Friend,<emph.end type="italics"></emph.end> and I have ſeen and conſidered them all to my very great <lb></lb>content and admiration, ſeeing a new compleat Doctrine to ſpring <lb></lb>up touching a ſubject, upon which have been written hundreds of <pb xlink:href="040/01/217.jpg" pagenum="199"></pb>Volumes; and yet not ſo much as one of the infinite admirable <lb></lb>concluſions that thoſe his writings contain, hath ever been ob <lb></lb>ſerved, or underſtood by any one, before <emph type="italics"></emph>Our Friend<emph.end type="italics"></emph.end> made <lb></lb>them out.</s></p><p type="margin"><s><margin.target id="marg399"></margin.target><emph type="italics"></emph>An intire and <lb></lb>new Science of the<emph.end type="italics"></emph.end> <lb></lb>Academick <emph type="italics"></emph>concer <lb></lb>ning local motion.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>You make me loſe the deſire I had to underſtand <lb></lb>more in our diſputes in hand, onely that I may hear ſome of <lb></lb>thoſe demonſtrations which you ſpeak of; therefore either give <lb></lb>them me preſently, or at leaſt promiſe me upon your word, to <lb></lb>appoint a particular conference concerning them, at which <emph type="italics"></emph>Sim <lb></lb>plicius<emph.end type="italics"></emph.end> alſo may be preſent, if he ſhall have a mind to hear the <lb></lb>paſſions and accidents of the primary effect in Nature.</s></p><p type="main"><s>SIMP. </s><s>I ſhall undoubtedly be much pleaſed therewith, though <lb></lb>indeed, as to what concerneth Natural Philoſophy, I do not think <lb></lb>that it is neceſſary to deſcend unto minute particularities, a gene <lb></lb>ral knowledg of the definition of motion, and of the diſtin <lb></lb>ction of natural and violent, even and accelerate, and the like, <lb></lb>ſufficing: For if this were not ſufficient, I do not think that <emph type="italics"></emph>Ari <lb></lb>ſtotle<emph.end type="italics"></emph.end> would have omitted to have taught us what ever more was <lb></lb>neceſſary.</s></p><p type="main"><s>SALV. </s><s>It may be ſo. </s><s>But let us not loſe more time about <lb></lb>this, which I promiſe to ſpend half a day apart in, for your ſatis <lb></lb>faction; nay, now I remember, I did promiſe you once before to <lb></lb>ſatisfie you herein. </s><s>Returning therefore to our begun calcula <lb></lb>tion of the time, wherein the grave cadent body would paſs from <lb></lb>the concave of the Moon to the centre of the Earth, that we may <lb></lb>not proceed arbitrarily and at randon, but with a Logical method, <lb></lb>we will firſt attempt to aſcertain our ſelves by experiments often <lb></lb>repeated, in how long time a ball <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> of Iron deſcendeth to the <lb></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 ſuch a determinate <lb></lb>weight, and let it be the ſame wherewith we intend to make the <lb></lb>computation of the time of deſcent 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></lb>hundred, of a thouſand pounds, will all meaſure the ſame hundred <lb></lb>yards in the ſame time.</s></p><p type="main"><s>SIMP. </s><s>But this I cannot believe, nor much leſs doth <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> <lb></lb>think ſo, who writeth, that the velocities of deſcending grave <lb></lb>bodies, are in the ſame proportion to one another, as their gra <lb></lb>vities.</s></p><p type="main"><s>SALV. </s><s>If you will admit this for true, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> you muſt be <lb></lb><arrow.to.target n="marg400"></arrow.to.target> <lb></lb>lieve alſo, that two balls of the ſame matter, being let fall in the <lb></lb>ſame moment, one of an hundred pounds, and another of one, <lb></lb>from an altitude of an hundred yards, the great one arriveth at the <lb></lb>ground, before the other is deſcended but one yard onely: Now <lb></lb>bring your fancy, if you can, to imagine, that you ſee the great <pb xlink:href="040/01/218.jpg" pagenum="200"></pb>ball got to the ground, when the little one is ſtill within leſs than <lb></lb>a yard of the top of the Tower.</s></p><p type="margin"><s><margin.target id="marg400"></margin.target><emph type="italics"></emph>The error of<emph.end type="italics"></emph.end> Ari <lb></lb>ſtotle <emph type="italics"></emph>in affirming, <lb></lb>falling grave bo <lb></lb>dies to move accor <lb></lb>ding to the propor <lb></lb>tion of their gravi <lb></lb>ties.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>That this propoſition is moſt falſe, I make no doubt in <lb></lb>the world; but yet that yours is abſolutely true, I cannot well <lb></lb>aſſure my ſelf: nevertheleſs, I believe it, ſeeing that you ſo re <lb></lb>ſolutely affirm it; which I am ſure you would not do, if you had <lb></lb>not certain experience, or ſome clear demonſtration thereof.</s></p><p type="main"><s>SALV. </s><s>I have both: and when we ſhall handle the buſineſs <lb></lb>of motions apart, I will communicate them: in the interim, that <lb></lb>we may have no more occaſions of interrupting our diſcourſe, we <lb></lb>will ſuppoſe, that we are to make our computation upon a ball of <lb></lb><arrow.to.target n="marg401"></arrow.to.target> <lb></lb>Iron of an hundred <emph type="italics"></emph>(a)<emph.end type="italics"></emph.end> pounds, the which by reiterated experi <lb></lb>ments deſcendeth from the altitude of an hundred <emph type="italics"></emph>(b)<emph.end type="italics"></emph.end> yards, in <lb></lb>five ſecond-minutes of an hour. </s><s>And becauſe, as we have ſaid, <lb></lb>the ſpaces that are meaſured by the cadent moveable, increaſe in <lb></lb>double proportion; that is, according to the ſquares of the times, <lb></lb>being that the time of one firſt-minute is duodecuple to the time <lb></lb>of five ſeconds, if we multiply the hundred yards by the ſquare of <lb></lb>12, that is by 144, we ſhall have 14400, which ſhall be the num <lb></lb>ber of yards that the ſame moveable ſhall paſs in one firſt-minute <lb></lb>of an hour: and following the ſame rule becauſe one hour is 60 <lb></lb>minutes, multiplying 14400, the number of yards paſt in one mi <lb></lb>nute, by the ſquare of 60, that is, by 3600, there ſhall come forth <lb></lb>51840000, the number of yards to be paſſed in an hour, which <lb></lb>make 17280 miles. </s><s>And deſiring to know the ſpace that the ſaid <lb></lb>ball would paſs in 4 hours, let us multiply 17280 by 16, (which <lb></lb>is the ſquare of 4) and the product will be 276480 miles: which <lb></lb>number is much greater than the diſtance from the Lunar concave <lb></lb>to the centre of the Earth, which is but 196000 miles, making the <lb></lb>diſtance of the concave 56 ſemidiameters of the Earth, as that mo <lb></lb>dern Author doth; and the ſemidiameter of the Earth 3500 miles, <lb></lb><arrow.to.target n="marg402"></arrow.to.target> <lb></lb>of 3000 ^{*}<emph type="italics"></emph>Braces<emph.end type="italics"></emph.end> to a †mile, which are our <emph type="italics"></emph>Italian<emph.end type="italics"></emph.end> miles.</s></p><p type="margin"><s><margin.target id="marg401"></margin.target><emph type="italics"></emph>(a) (b)<emph.end type="italics"></emph.end> Note that <lb></lb>theſe Calculations <lb></lb>are made in <emph type="italics"></emph>Itali <lb></lb>an<emph.end type="italics"></emph.end> weights and <lb></lb>meaſures. </s><s>And 100 <lb></lb>pounds <emph type="italics"></emph>Haverdu <lb></lb>poiſe<emph.end type="italics"></emph.end> make 131 <emph type="italics"></emph>l. <lb></lb></s><s>Florentine.<emph.end type="italics"></emph.end> And <lb></lb>100 Engliſh yards <lb></lb>makes 150 2/5 Braces <lb></lb><emph type="italics"></emph>Florent.<emph.end type="italics"></emph.end> ſo that the <lb></lb>brace or yard of <lb></lb>our <emph type="italics"></emph>Author<emph.end type="italics"></emph.end> is 3/4 <lb></lb>of cur yard.</s></p><p type="margin"><s><margin.target id="marg402"></margin.target>* The <emph type="italics"></emph>Italian<emph.end type="italics"></emph.end> mea <lb></lb>ſure which I com <lb></lb>monly tranſl te <lb></lb>yards.</s></p><p type="main"><s>Therefore, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that ſpace from the concave of the Moon <lb></lb>to the centre of the Earth, which your Accomptant ſaid could <lb></lb><arrow.to.target n="marg403"></arrow.to.target> <lb></lb>not be paſſed under more than ſix days, you ſee that (computing <lb></lb>by experience, and not upon the fingers ends) that it ſhall be paſ <lb></lb>ſed in much leſs than four hours; and making the computation <lb></lb>exact, it ſhall be paſſed by the moveable in 3 hours, 22 <emph type="italics"></emph>min. </s><s>prim.<emph.end type="italics"></emph.end> <lb></lb>and 4 ſeconds.</s></p><p type="margin"><s><margin.target id="marg403"></margin.target>† The <emph type="italics"></emph>Italian<emph.end type="italics"></emph.end> mile <lb></lb>is 1000/1056 of our mile.</s></p><p type="main"><s>SAGR. </s><s>I beſeech you, dear Sir, do not defraud me of this ex <lb></lb>act calculation, for it muſt needs be very excellent.</s></p><p type="main"><s>SALV. </s><s>So indeed it is: therefore having (as I have ſaid) by <lb></lb>diligent tryal obſerved, that ſuch a moveable paſſeth in its deſcent, <lb></lb>the height of 100 yards in 5 ſeconds of an hour, we will ſay, if <lb></lb>100 yards are paſſed in 5 ſeconds; in how many ſeconds ſhall <pb xlink:href="040/01/219.jpg" pagenum="201"></pb>588000000 yards (for ſo many are in 56 diameters of the Earth) <lb></lb>be paſſed? </s><s>The rule for this work is, that the third number muſt <lb></lb>be multiplied by the ſquare of the ſecond, of which doth come <lb></lb>14700000000, which ought to be divided by the firſt, that is, by <lb></lb>100, and the root ſquare of the quotient, that is, 12124 is the <lb></lb>number ſought, namely 12124 <emph type="italics"></emph>min. </s><s>ſecun.<emph.end type="italics"></emph.end> of an hour, which are <lb></lb>3 hours, 22 <emph type="italics"></emph>min. </s><s>prim.<emph.end type="italics"></emph.end> and 4 ſeconds.</s></p><p type="main"><s>SAGR. </s><s>I have ſeen the working, but I know nothing of the <lb></lb>reaſon for ſo 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, becauſe it <lb></lb>is very eaſie. </s><s>Let us mark theſe three numbers with the Letters <lb></lb>A firſt, B ſecond, C <lb></lb><figure id="id.040.01.219.1.jpg" xlink:href="040/01/219/1.jpg"></figure> <lb></lb>third. </s><s>A and C are the <lb></lb>numbers of the ſpaces, <lb></lb>B is the number of the <lb></lb>time; the fourth number <lb></lb>is ſought, of the time <lb></lb>alſo. </s><s>And becauſe we <lb></lb>know, that look what <lb></lb>proportion the ſpace A, <lb></lb>hath to the ſpuace C, the <lb></lb>ſame proportion ſhall the <lb></lb>ſquare of the time B <lb></lb>have to the ſqare of the <lb></lb>time, which is ſought. <lb></lb></s><s>Therefore by the Golden Rule, let the number C be multi <lb></lb>plied by the ſquare of the number B, and let the product be di <lb></lb>vided by the number A, and the quotient ſhall be the ſquare of <lb></lb>the number ſought, and its ſquare root ſhall be the number it ſelf <lb></lb>that is ſought. </s><s>Now you ſee how eaſie it is to be underſtood.</s></p><p type="main"><s>SAGR. </s><s>So are all truths, when once they are found out, but the <lb></lb>difficulty lyeth in finding them. </s><s>I very well apprehend it, and kindly <lb></lb>thank you. </s><s>And if there remain any other curioſity touching this <lb></lb>point, I pray you let us hear it; for if I may ſpeak my mind, I <lb></lb>will with the favour of <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that from your diſcourſes I al <lb></lb>wayes learn ſome new motion, but from thoſe of his Philoſo <lb></lb>phers, I do not remember that I have learn't any thing of mo <lb></lb>ment.</s></p><p type="main"><s>SALV. </s><s>There might be much more ſaid touching theſe local <lb></lb>motions; but according to agreement, we will reſerve it to a par <lb></lb>ticular conference, and for the preſent I will ſpeak ſomething <lb></lb>touching the Author named by <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> who thinketh he hath <lb></lb>given a great advantage to the adverſe party in granting that, that <lb></lb>Canon bullet in falling from the concave of the Moon may de <lb></lb>ſcend with a velocity equal to the velocity wherewith it would <pb xlink:href="040/01/220.jpg" pagenum="202"></pb>turn round, ſtaying there above, and moving along with the di <lb></lb>urnal converſion. </s><s>Now I tell him, that that ſame ball falling from <lb></lb>the concave unto the centre, will acquire a degree of velocity <lb></lb>much more than double the velocity of the diurnal motion of the <lb></lb>Lunar concave; and this I will make out by ſolid and not imper <lb></lb><arrow.to.target n="marg404"></arrow.to.target> <lb></lb>tinent ſuppoſitions. </s><s>You muſt know therefore that the grave <lb></lb>body falling and acquiring all the way new velocity according <lb></lb>to the proportion already mentioned, hath in any whatſoever <lb></lb>place of the line of its motion ſuch a degree of velocity, that if it <lb></lb>ſhould continue to move therewith, uniformly without farther <lb></lb>encreaſing it; in another time like to that of its deſcent, it would <lb></lb>paſſe a ſpace double to that paſſed in the line of the precedent <lb></lb>motion of deſcent. </s><s>And thus for example, if that ball in coming <lb></lb>from the concave of the Moon to its centre hath ſpent three hours, <lb></lb>22 min. <emph type="italics"></emph>prim.<emph.end type="italics"></emph.end> and 4 ſeconds, I ſay, that being arrived at the cen <lb></lb>tre, it ſhall find it ſelf conſtituted in ſuch a degree of velocity, that <lb></lb>if with that, without farther encreaſing it, it ſhould continue to <lb></lb>move uniformly, it would in other 3 hours, 22 min. <emph type="italics"></emph>prim.<emph.end type="italics"></emph.end> and <lb></lb>4 ſeconds, paſſe double that ſpace, namely as much as the whole <lb></lb>diameter of the Lunar Orb; and becauſe from the Moons con <lb></lb>cave to the centre are 196000 miles, which the ball paſſeth in 3 <lb></lb>hours 22 <emph type="italics"></emph>prim.<emph.end type="italics"></emph.end> min. </s><s>and 4 ſeconds, therefore (according to what <lb></lb>hath been ſaid) the ball continuing to move with the velocity <lb></lb>which it is found to have in its arrival at the centre, it would <lb></lb>paſſe in other 3 hours 22 min. </s><s>prim. </s><s>and 4 ſeconds, a ſpace dou <lb></lb>ble to that, namely 392000 miles; but the ſame continuing in <lb></lb>the concave of the Moon, which is in circuit 1232000 miles, and <lb></lb>moving therewith in a diurnal motion, it would make in the ſame <lb></lb>time, that is in 3 hours 22 min. </s><s>prim. </s><s>and 4 ſeconds, 172880 <lb></lb>miles, which are fewer by many than the half of the 392000 <lb></lb>miles. </s><s>You ſee then that the motion in the concave is not as the <lb></lb>modern Author ſaith, that is, of a velocity impoſſible for the fall <lb></lb>ing ball to partake of, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg404"></margin.target><emph type="italics"></emph>The falling move <lb></lb>able if it move with <lb></lb>a degree of veloci <lb></lb>ty acquired in a <lb></lb>like time with an <lb></lb>uniform motion, it <lb></lb>ſhall paß a ſpace <lb></lb>double to that paſ <lb></lb>ſed with the acce <lb></lb>leratedmotion.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>The diſcourſe would paſs for current, and would give <lb></lb>me full ſatisfaction, if that particular was but ſalved, of the mo <lb></lb>ving of the moveable by a double ſpace to that paſſed in falling <lb></lb>in another time equal to that of the deſcent, in caſe it doth continue <lb></lb>to move uniformly with the greateſt degree of velocity acquired <lb></lb>in deſcending. </s><s>A propoſition which you alſo once before ſuppo <lb></lb>ſed as true, but never demonſtrated.</s></p><p type="main"><s>SALV. </s><s>This is one of the demonſtrations of <emph type="italics"></emph>Our Friend,<emph.end type="italics"></emph.end> and <lb></lb>you ſhall ſee it in due time; but for the preſent, I will with ſome <lb></lb>conjectures (not teach you any thing that is new, but) remember you <lb></lb>of a certain contrary opinion, and ſhew you, that it may haply ſo be. <lb></lb></s><s>A bullet of lead hanging in a long and fine thread faſtened to the <pb xlink:href="040/01/221.jpg" pagenum="203"></pb>roof, if we remove it far from perpendicularity, and then let it go, <lb></lb>have you not obſerved that, it declining, will paſs freely, and well <lb></lb>near as far to the other ſide of the perpendicular?</s></p><p type="main"><s>SAGR. </s><s>I have obſerved it very well, and find (eſpecially if the <lb></lb>plummet be of any conſiderable weight) that it riſeth ſo little leſs <lb></lb>than it deſcended, ſo that I have ſometimes thought, that the a <lb></lb>ſcending arch is equal to that deſcending, and thereupon made it <lb></lb>a queſtion whether the vibrations might not perpetuate themſelves; <lb></lb>and I believe that they might, if that it were poſſible to remove <lb></lb><arrow.to.target n="marg405"></arrow.to.target> <lb></lb>the impediment of the Air, which reſiſting penetration, doth ſome <lb></lb>ſmall matter retard and impede the motion of the <emph type="italics"></emph>pendulum,<emph.end type="italics"></emph.end> <lb></lb>though indeed that impediment is but ſmall: in favour of which <lb></lb>opinion the great number of vibrations that are made before the <lb></lb>moveable wholly ceaſeth to move, ſeems to plead.</s></p><p type="margin"><s><margin.target id="marg405"></margin.target><emph type="italics"></emph>The motion of <lb></lb>grave<emph.end type="italics"></emph.end> penduli <lb></lb><emph type="italics"></emph>might be perpetua <lb></lb>ted, impediments <lb></lb>being removed.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>The motion would not be perpetual, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> al <lb></lb>though the impediment of the Air were totally removed, becauſe <lb></lb>there is another much more abſtruſe.</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></lb>other?</s></p><p type="main"><s>SALV. </s><s>You will be pleaſed when you hear it, but I ſhall not <lb></lb>tell it you till anon: in the mean time, let us proceed. </s><s>I have <lb></lb>propoſed the obſervation of this <emph type="italics"></emph>Pendulum,<emph.end type="italics"></emph.end> to the intent, that you <lb></lb>ſhould underſtand, that the <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> acquired in the deſcending <lb></lb>arch, where the motion is natural, is of it ſelf able to drive the <lb></lb>ſaid ball with a violent motion, as far on the other ſide in the like <lb></lb>aſcending arch; if ſo, I ſay, of it ſelf, all external impediments <lb></lb>being removed: I believe alſo that every one takes it for granted, <lb></lb>that as in the deſcending arch the velocity all the way increaſeth, <lb></lb>till it come to the loweſt point, or its perpendicularity; ſo from <lb></lb>this point, by the other aſcending arch, it all the wav diminiſheth, <lb></lb>untill it come to its extreme and higheſt point: and diminiſhing <lb></lb>with the ſame proportions, where with it did before increaſe, ſo that <lb></lb>the dgrees of the velocities in the points equidiſtant from the point <lb></lb>of perpendicularity, are equal to each other. </s><s>Hence it ſeemeth <lb></lb>to me (arguing with all due modeſty) that I might eaſily be induced <lb></lb>to believe, that if the Terreſtrial Globe were bored thorow the <lb></lb><arrow.to.target n="marg406"></arrow.to.target> <lb></lb>centre, a Canon bullet deſcending through that Well, would ac <lb></lb>quire by that time it came to the centre, ſuch an impulſe of velo <lb></lb>city, that, it having paſſed beyond the centre, would ſpring it up <lb></lb>wards the other way, as great a ſpace, as that was wherewith it had <lb></lb>deſcended, all the way beyond the centre diminiſhing the velocity <lb></lb>with decreaſements like to the increaſements acquired in the de <lb></lb>ſcent: and the time ſpent in this ſecond motion of aſcent, I be <lb></lb>lieve, would be equal to the time of deſcent. </s><s>Now if the move <lb></lb>able by diminiſhing that its greateſt degree of velocity which it <pb xlink:href="040/01/222.jpg" pagenum="204"></pb>had in the centre, ſucceſſively until it come to total extinction, <lb></lb>do carry the moveable in ſuch a time ſuch a certain ſpace, as it had <lb></lb>gone in ſuch a like quantity of time, by the acquiſt of velocity <lb></lb>from the total privation of it until it came to that its greateſt degree; <lb></lb>it ſeemeth very reaſonable, that if it ſhould move always with the <lb></lb>ſaid greateſt degree of velocity it would paſs, in ſuch another <lb></lb>quantity of time, both thoſe ſpaces: For if we do but in our <lb></lb>mind ſucceſſively divide thoſe velocities into riſing and falling <lb></lb>degrees, as <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> theſe numbers in the margine; ſo that the <lb></lb>firſt ſort unto 10 be ſuppoſed the increaſing velocities, and the <lb></lb>others unto 1, be the decreaſing; and let thoſe of the time <lb></lb>of the deſcent, and the others of the time of the aſcent being <lb></lb>added all together, make as many, as if one of the two ſums of <lb></lb>them had been all of the greateſt degrees, and therefore the <lb></lb>whole ſpace paſſed by all the degrees of the increaſing veloci <lb></lb>ties, and decreaſing, (which put together is the whole diame <lb></lb>ter) ought to be equal to the ſpace paſſed by the greateſt velo <lb></lb>cities, that are in number half the aggregate of the increaſing <lb></lb>and decreaſing velocities. </s><s>I know that I have but obſcurely <lb></lb>expreſſed my ſelf, and I wiſh I may be underſtood.</s></p><p type="margin"><s><margin.target id="marg406"></margin.target><emph type="italics"></emph>If the Terreſtrial <lb></lb>Globe were perfo <lb></lb>rated, a grave bo <lb></lb>dy deſcending by <lb></lb>that bore, would <lb></lb>paß and aſcend as <lb></lb>far beyond the cen <lb></lb>tre, as it did de <lb></lb>ſcend.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I think I underſtand you very well; and alſo that I <lb></lb>can in a few words ſhew, that I do underſtand you. </s><s>You had <lb></lb>a mind to ſay, that the motion begining from reſt, and all the <lb></lb>way increaſing the velocity with equal augmentations, ſuch as <lb></lb>are thoſe of continuate numbers begining at 1, rather at 0, <lb></lb>which repreſenteth the ſtate of reſt, diſpoſed as in the margine: <lb></lb>and continued at pleaſure, ſo as that the leaſt degree may be 0, <lb></lb>and the greateſt <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> 5, all theſe degrees of velocity wherewith <lb></lb>the moveable is moved, make the ſum of 15; but if the <lb></lb>moveable ſhould move with as many degrees in number as <lb></lb>theſe are, and each of them equal to the biggeſt, which is 5, the <lb></lb>aggregate of all theſe laſt velocities would be double to the <lb></lb>others, namely 30. And therefore the moveable moving with <lb></lb>a like time, but with uniform velocity, which is that of the <lb></lb>higheſt degree 5, ought to paſs a ſpace double to that which it <lb></lb>paſſeth in the accelerate time, which beginneth at the ſtate of reſt.</s></p><p type="main"><s>SALV. </s><s>According to your quick and piercing way of appre <lb></lb>hending things, you have explained the whole buſineſs with more <lb></lb>plainneſs than I my ſelf; and put me alſo in mind of adding ſome <lb></lb>thing more: for in the accelerate motion, the augmentation be <lb></lb>ing continual, you cannot divide the degrees of velocity, which <lb></lb>continually increaſe, into any determinate number, becauſe chan <lb></lb>ging every moment, they are evermore infinite. </s><s>Therefore we <lb></lb>ſhall be the better able to exemplifie our intentions by deſcribing <lb></lb>a Triangle, which let be this A B C, [<emph type="italics"></emph>in Fig.<emph.end type="italics"></emph.end> 8.] taking in the <pb xlink:href="040/01/223.jpg" pagenum="205"></pb>ſide A C, as many equal parts as we pleaſe, A D, D E, E F, F G, <lb></lb>and drawing by the points D, E, F, G, right lines parallel to the baſe <lb></lb>B C. </s><s>Now let us imagine the parts marked in the line A C, to be <lb></lb>equal times, and let the parallels drawn by the points D, E, F, G, <lb></lb>repreſent unto us the degrees of velocity accelerated, and increaſ <lb></lb>ing equally in equal times; and let the point A be the ſtate of reſt, <lb></lb>from which the moveable departing, hath <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> in the time A D, <lb></lb>acquired the degree of velocity D H, in the ſecond time we will <lb></lb>ſuppoſe, that it hath increaſed the velocity from D H, as far as to <lb></lb>E I, and ſo ſuppoſing it to have grown greater in the ſucceeding <lb></lb>times, according to the increaſe of the lines F K, G L, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> but <lb></lb><arrow.to.target n="marg407"></arrow.to.target> <lb></lb>becauſe the acceleration is made continually from moment to mo <lb></lb>ment, and not disjunctly from one certain part of time to another; <lb></lb>the point A being put for the loweſt moment of velocity, that is, <lb></lb>for the ſtate of reſt, and A D for the firſt inſtant of time follow <lb></lb>ing; it is manifeſt, that before the acquiſt of the degree of velocity <lb></lb>D H, made in the time A D, the moveable muſt have paſt by <lb></lb>infinite other leſſer and leſſer degrees gained in the infinite inſtants <lb></lb>that are in the time D A, anſwering the infinite points that are in <lb></lb>the line D A; therefore to repreſent unto us the infinite degrees <lb></lb>of velocity that precede the degree D H, it is neceſſary to imagine <lb></lb>infinite lines ſucceſſively leſſer and leſſer, which are ſuppoſed to <lb></lb>be drawn by the infinite points of the line D A, and parallels to <lb></lb>D H, the which infinite lines repreſent unto us the ſuperficies of <lb></lb>the Triangle A H D, and thus we may imagine any ſpace paſſed <lb></lb>by the moveable, with a motion which begining at reſt, goeth uni <lb></lb>formly accelerating, to have ſpent and made uſe of infinite degrees <lb></lb>of velocity, increaſing according to the infinite lines that begin <lb></lb>ing from the point A, are ſuppoſed to be drawn parallel to the <lb></lb>line H D, and to the reſt I E, K F, L G, the motion continuing as <lb></lb>far as one will.</s></p><p type="margin"><s><margin.target id="marg407"></margin.target><emph type="italics"></emph>The acceleration <lb></lb>of grave bodies na <lb></lb>turally deſcendent, <lb></lb>increaſeth from <lb></lb>moment to moment.<emph.end type="italics"></emph.end></s></p><p type="main"><s>Now let us compleat the whole Parallelogram A M B C, and let <lb></lb>us prolong as far as to the ſide thereof B M, not onely the Parallels <lb></lb>marked in the Triangle, but thoſe infinite others imagined to be <lb></lb>drawn from all the points of the ſide A C; and like as B C, was <lb></lb>the greateſt of thoſe infinite parallels of the Triangle, repreſent <lb></lb>ing unto us the greateſt degree of velocity acquired by the move <lb></lb>able in the accelerate motion, and the whole ſuperficies of the ſaid <lb></lb>Triangle, was the maſs and ſum of the whole velocity, wherewith <lb></lb>in the time A C it paſſed ſuch a certain ſpace, ſo the parallelogram <lb></lb>is now a maſs and aggregate of a like number of degrees of ve <lb></lb>locity, but each equal to the greateſt B C, the which maſs of ve <lb></lb>locities will be double to the maſs of the increaſing velocities in <lb></lb>the Triangle, like as the ſaid Parallelogram is double to the Tri <lb></lb>angle: and therefore if the moveable, that falling did make uſe <pb xlink:href="040/01/224.jpg" pagenum="206"></pb>of the accelerated degrees of velocity, anſwering to the triangle <lb></lb>A B C, hath paſſed in ſuch a time ſuch a ſpace, it is very reaſonable <lb></lb>and probable, that making uſe of the uniform velocities anſwering <lb></lb>to the parallelogram, it ſhall paſſe with an even motion in the <lb></lb>ſame time a ſpace double to that paſſed by the accelerate mo <lb></lb>tion.</s></p><p type="main"><s>SAGR. </s><s>I am entirely ſatisfied. </s><s>And if you call this a probable <lb></lb>Diſcourſe, what ſhall the neceſſary demonſtrations be? </s><s>I wiſh <lb></lb>that in the whole body of common Philoſophy, I could find one <lb></lb>that was but thus concludent. <lb></lb><arrow.to.target n="marg408"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg408"></margin.target><emph type="italics"></emph>In natural Sci <lb></lb>ences it is not ne <lb></lb>ceſſary to ſeek Ma <lb></lb>thematicall evi <lb></lb>dence.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>It is not neceſſary in natural Philoſophy to ſeek exqui <lb></lb>ſite Mathematical evidence.</s></p><p type="main"><s>SAGR. </s><s>But this point of motion, is it not a natural queſtion? <lb></lb></s><s>and yet I cannot find that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> hath demonſtrated any the <lb></lb>leaſt accident of it. </s><s>But let us no longer divert our intended <lb></lb>Theme, nor do you fail, I pray you <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> to tell me that <lb></lb>which you hinted to me to be the cauſe of the <emph type="italics"></emph>Pendulum's<emph.end type="italics"></emph.end> qui <lb></lb>eſcence, beſides the reſiſtance of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> ro penetration.</s></p><p type="main"><s>SALV. </s><s>Tell me; of two <emph type="italics"></emph>penduli<emph.end type="italics"></emph.end> hanging at unequal diſtan <lb></lb>ces, doth not that which is faſtned to the longer threed make its <lb></lb>vibrations more ſeldome?</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"></emph>The<emph.end type="italics"></emph.end> pendulum <lb></lb><emph type="italics"></emph>hanging at a long <lb></lb>er threed, maketh <lb></lb>its vibrations more <lb></lb>ſeldome than the<emph.end type="italics"></emph.end> <lb></lb>pendulum <emph type="italics"></emph>hanging <lb></lb>at a ſhorter threed.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. Yes, if they be moved to equall diſtances from their <lb></lb>perpendicularity.</s></p><p type="main"><s>SALV. </s><s>This greater or leſſe elongation importeth nothing at <lb></lb>all, for the ſame <emph type="italics"></emph>pendulum<emph.end type="italics"></emph.end> alwayes maketh its reciprocations in e <lb></lb>quall times, be they longer or ſhorter, that is, though the <emph type="italics"></emph>pendulum<emph.end type="italics"></emph.end></s></p><p type="main"><s><arrow.to.target n="marg410"></arrow.to.target> <lb></lb>be little or much removed from its perpendicularity, and if they <lb></lb>are not abſolutely equal, they are inſenſibly different, as expe <lb></lb>rience may ſhew you: and though they were very unequal, yet <lb></lb>would they not diſcountenance, but favour our cauſe. </s><s>There <lb></lb>fore let us draw the perpendicular A B [<emph type="italics"></emph>in Fig.<emph.end type="italics"></emph.end> 9.] and hang from <lb></lb>the point A, upon the threed A C, a plummet C, and another up <lb></lb>on the ſame threed alſo, which let be E, and the threed A C, being <lb></lb>removed from its perpendicularity, and then letting go the plum <lb></lb>mets C and E, they ſhall move by the arches C B D, E G F, and <lb></lb>the plummet E, as hanging at a leſſer diſtance, and withall, as <lb></lb>(by what you ſaid) leſſe removed, will return back again faſter, <lb></lb>and make its vibrations more frequent than the plummet C, and <lb></lb>therefore ſhall hinder the ſaid plummet C, from running ſo much <lb></lb>farther towards the term D, as it would do, if it were free: and <lb></lb>thus the plummet E bringing unto it in every vibration continuall <lb></lb><arrow.to.target n="marg411"></arrow.to.target> <lb></lb>impediment, it ſhall finally reduce it to quieſcence. </s><s>Now the <lb></lb>ſame threed, (taking away the middle plummet) is a compoſition <lb></lb>of many grave <emph type="italics"></emph>penduli,<emph.end type="italics"></emph.end> that is, each of its parts is ſuch a <emph type="italics"></emph>pendu <lb></lb>lum<emph.end type="italics"></emph.end> faſtned neerer and neerer to the point A, and therefore diſpo <pb xlink:href="040/01/225.jpg" pagenum="207"></pb>ſed to make its vibrations ſucceſſively more and more frequent; <lb></lb>and conſequently is able to bring a continual impediment to the <lb></lb>plummet C; and for a proof that this is ſo, if we do but obſerve <lb></lb>the thread A C, we ſhall ſee it diſtended not directly, but in an <lb></lb>arch; and if inſtead of the thread we take a chain, we ſhall diſ <lb></lb>cern the effect more perſectly; and eſpecially removing the gra <lb></lb><arrow.to.target n="marg412"></arrow.to.target> <lb></lb>vity C, to a conſiderable diſtance from the perpendicular A B, for <lb></lb>that the chain being compoſed of many looſe particles, and each of <lb></lb>them of ſome weight, the arches A E C, and A F D, will appear <lb></lb>notably incurvated. </s><s>By reaſon therefore, that the parts of the <lb></lb>chain, according as they are neerer to the point A, deſire to make <lb></lb>their vibrations more frequent, they permit not the lower parts of <lb></lb>the ſaid chain to ſwing ſo far as naturally they would: and by <lb></lb>continual detracting from the vibrations of the plummet C, they <lb></lb>finally make it ceaſe to move, although the impediment of the air <lb></lb>might be removed.</s></p><p type="margin"><s><margin.target id="marg410"></margin.target><emph type="italics"></emph>The vibrations <lb></lb>of the ſame<emph.end type="italics"></emph.end> pen <lb></lb>dulum <emph type="italics"></emph>are made <lb></lb>with the ſame fre <lb></lb>quency, whether <lb></lb>they be ſmall or <lb></lb>great.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg411"></margin.target><emph type="italics"></emph>The cauſe which <lb></lb>impedeth the<emph.end type="italics"></emph.end> pen <lb></lb>dulum, <emph type="italics"></emph>and redu <lb></lb>ceth it to reſt.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg412"></margin.target><emph type="italics"></emph>The thread or <lb></lb>chain to which a<emph.end type="italics"></emph.end> <lb></lb>pendulum <emph type="italics"></emph>is faſt <lb></lb>ned, maketh an <lb></lb>arch, and doth not <lb></lb>ſtretch it ſelfe <lb></lb>ſtreight out in its <lb></lb>vibrations.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>The books are now come; here take them <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> <lb></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 againſt the <lb></lb>diurnal motion of the Earth, he having firſt confuted the annual. <lb></lb><emph type="italics"></emph>Motus terræ annuus aſſerrere<emph.end type="italics"></emph.end> Copernicanos <emph type="italics"></emph>cogit converſionem e <lb></lb>juſdem quotidianam; alias idem terræ Hemiſphærium continenter <lb></lb>ad Solem eſſet converſum obumbrato ſemper averſo. [In Engliſh <lb></lb>thus:]<emph.end type="italics"></emph.end> The annual motion of the Earth doth compell the <emph type="italics"></emph>Co <lb></lb>pernicans<emph.end type="italics"></emph.end> to aſſert the daily converſion thereof; otherwiſe the <lb></lb>ſame Hemiſphere of the Earth would be continually turned to <lb></lb>wards the Sun, the ſhady ſide being always averſe. </s><s>And ſo one <lb></lb>half of the Earth would never come to ſee the Sun.</s></p><p type="main"><s>SALV. </s><s>I find at the very ſirſt ſight, that this man hath not rightly <lb></lb>apprehended the <emph type="italics"></emph>Copernican Hypotheſis,<emph.end type="italics"></emph.end> for if he had but taken <lb></lb>notice how he alwayes makes the Axis of the terreſtrial Globe <lb></lb>perpetually parallel to it ſelf, he would not have ſaid, that one <lb></lb>half of the Earth would never ſee the Sun, but that the year <lb></lb>would be one entire natural day, that is, that thorow all parts of <lb></lb>the Earth there would be ſix moneths day, and ſix moneths night, <lb></lb>as it now befalleth to the inhabitants under the Pole, but let <lb></lb>this miſtake be forgiven him, and let us come to what remai <lb></lb>neth.</s></p><p type="main"><s>SIMP. </s><s>It followeth, <emph type="italics"></emph>Hanc autem gyrationem Terræ im <lb></lb>poſſibilem eſſe ſic demonſtramus.<emph.end type="italics"></emph.end> Which ſpeaks in Engliſh thus: <lb></lb>That this gyration of the Earth is impoſſible we thus demonſtrate. <lb></lb></s><s>That which enſueth is the declaration of the following figure, <lb></lb>wherein is delineated many deſcending grave bodies, and aſcend <lb></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 ſee them, I pray you. </s><s>Oh! what fine figures, <pb xlink:href="040/01/226.jpg" pagenum="208"></pb>what birds, what balls, and what other pretty things are here?</s></p><p type="main"><s>SIMP. </s><s>Theſe are balls which come from the concave of the <lb></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-fiſh, which here at <emph type="italics"></emph>Venice<emph.end type="italics"></emph.end> they <lb></lb>call <emph type="italics"></emph>buovoli<emph.end type="italics"></emph.end>; and this alſo came from the Moons concave.</s></p><p type="main"><s>SAGR. Indeed, it ſeems then, that the Moon hath a great pow <lb></lb><arrow.to.target n="marg413"></arrow.to.target> <lb></lb>er over theſe Oyſter-fiſhes, which we call ^{*} <emph type="italics"></emph>armed ſiſbes.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg413"></margin.target>* Peſci armai, <emph type="italics"></emph>or<emph.end type="italics"></emph.end> <lb></lb>armati.</s></p><p type="main"><s>SIMP. </s><s>And this is that calculation, which I mentioned, of this <lb></lb>Journey in a natural day, in an hour, in a firſt minute, and in a <lb></lb>ſecond, which a point of the Earth would make placed under the <lb></lb>Equinoctial, and alſo in the parallel of 48 <emph type="italics"></emph>gr.<emph.end type="italics"></emph.end> And then followeth <lb></lb>this, which I doubted I had committed ſome miſtake in reciting, <lb></lb>therefore let us read it. <emph type="italics"></emph>His poſitis, neceſſe est, terra circulariter <lb></lb>mota, omnia ex aëre eidem, &c. </s><s>Quod ſi haſce pilas æquales po <lb></lb>nemus pondere, magnitudine, gravitate, & in concavo Sphæræ Lu <lb></lb>naris poſitas libero deſcenſui permittamus, ſi motum deorſum æque <lb></lb>mus celeritate motui circum, (quod tamen ſecus eſt, cum pila A, <lb></lb>&c.) elabentur minimum (ut multum cedamus adverſariis) dies <lb></lb>ſex: quo tempore ſexies circa terram, &c. [In Engliſb thus.]<emph.end type="italics"></emph.end> <lb></lb>Theſe things being ſuppoſed, it is neceſſary, the Earth being cir <lb></lb>cularly moved, that all things from the air to the ſame, &c. </s><s>So <lb></lb>that if we ſuppoſe theſe balls to be equal in magnitude and gra <lb></lb>vity, and being placed in the concave of the Lunar Sphere, we <lb></lb>permit them a free deſcent, and if we make the motion down <lb></lb>wards equal in velocity to the motion about, (which nevertheleſs <lb></lb>is otherwiſe, if the ball A, &c.) they ſhall be falling at leaſt (that <lb></lb>we may grant much to our adverſaries) ſix dayes; in which time <lb></lb>they ſhall be turned ſix 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></lb>perſon. </s><s>From hence you may collect <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> with what cau <lb></lb>tion they ought to proceed, who would give themſelves up to be <lb></lb>lieve others in thoſe things, which perhaps they do not believe <lb></lb>themſelves. </s><s>For me thinks it a thing impoſſible, but that this Au <lb></lb>thor was adviſed, that he did deſign to himſelf a circle, whoſe dia <lb></lb>meter (which amongſt Mathematicians, is leſſe than one third part <lb></lb>of the circumference) is above 72 times bigger than it ſelf: an <lb></lb>errour that affirmeth that to be conſiderably more than 200, <lb></lb>which is leſſe than one.</s></p><p type="main"><s>SAGR. </s><s>It may be, that theſe Mathematical proportions, which <lb></lb>are true in abſtract, being once applied in concrete to Phyſical and <lb></lb>Elementary circles, do not ſo exactly agree: And yet, I think, <lb></lb>that the Cooper, to find the ſemidiameter of the bottom, which he <lb></lb>is to fit to the Cask, doth make uſe of the rule of Mathematicians <lb></lb>in abſtract, although ſuch bottomes be things meerly material, <pb xlink:href="040/01/227.jpg" pagenum="209"></pb>and concrete: therefore let <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> plead in excuſe of this <lb></lb>Author; and whether he chinks that the Phyſicks can differ ſo <lb></lb>very much from the Mathematicks.</s></p><p type="main"><s>SIMP. </s><s>The ſubſtractions are in my opinion inſufficient to ſalve <lb></lb>this difference, which is ſo extreamly too great to be reconciled: <lb></lb>and in this caſe I have no more to ſay but that, <emph type="italics"></emph>Quandoque bonus <lb></lb>dormitet Homerus.<emph.end type="italics"></emph.end> But ſuppoſing the calculation of ^{*} <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg414"></arrow.to.target> <lb></lb>to be more exact, and that the time of the deſcent of the ball <lb></lb>were no more than three hours; yet me thinks, that coming from <lb></lb>the concave of the Moon, which is ſo great a diſtance off, it would <lb></lb>be an admirable thing, that it ſhould have an inſtinct of maintain <lb></lb>ing it ſelf all the way over the ſelf-ſame point of the Earth, over <lb></lb>which it did hang in its departure thence and not rather be left a <lb></lb>very great way behind.</s></p><p type="margin"><s><margin.target id="marg414"></margin.target>* Not <emph type="italics"></emph>Sagre <lb></lb>dus,<emph.end type="italics"></emph.end> as the Latine <lb></lb>ha hit.</s></p><p type="main"><s>SALV. </s><s>The effect may be admirable, and not admirable, but <lb></lb>natural and ordinary, according as the things precedent may fall <lb></lb>out. </s><s>For if the ball (according to the Authors ſuppoſitions) <lb></lb>whilſt it ſtaid in the concave of the Moon, had the circular motion <lb></lb>of twenty four hours together with the Earth, and with the reſt of <lb></lb>the things contained within the ſaid Concave; that very vertue <lb></lb>which made it turn round before its deſcent, will continue it in <lb></lb>the ſame motion in its deſcending. </s><s>And ſo far it is from not keep <lb></lb>ing pace with the motion of the Earth, and from ſtaying behind, <lb></lb>that it is more likely to out-go it; being that in its approaches to <lb></lb>the Earth, the motion of gyration is to be made with circles con <lb></lb>tinually leſſer and leſſer; ſo that the ball retaining in it ſelf that <lb></lb>ſelf-ſame velocity which it had in the concave, it ought to antici <lb></lb>pate, as I have ſaid, the <emph type="italics"></emph>vertigo<emph.end type="italics"></emph.end> or converſion of the Earth. </s><s>But <lb></lb>if the ball in the concave did want that circulation, it is not obli <lb></lb>ged in deſcending to maintain it ſelf perpendicularly over that <lb></lb>point of the Earth, which was juſt under it when the deſcent be <lb></lb>gan. </s><s>Nor will <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> or any of his followers affirm the <lb></lb>ſame.</s></p><p type="main"><s>SIMP. </s><s>But the Author maketh an objection, as you ſee, de <lb></lb>manding on what principle this circular motion of grave and light <lb></lb>bodies, doth depend: that is, whether upon an internal or an ex <lb></lb>ternal principle.</s></p><p type="main"><s>SALV. </s><s>Keeping to the Probleme of which we ſpeak, I ſay, <lb></lb>that that very principle which made the ball turn round, whil'ſt it <lb></lb>was in the Lunar concave, is the ſame that maintaineth alſo the <lb></lb>circulation in the deſcent: yet I leave the Author at liberty to <lb></lb>make it internal or external at his pleaſure.</s></p><p type="main"><s>SIMP. </s><s>The Author proveth, that it can neither be inward nor <lb></lb>outward.</s></p><p type="main"><s>SALV. </s><s>And I will ſay then, that the ball in the concave did <pb xlink:href="040/01/228.jpg" pagenum="210"></pb>not move, and ſo he ſhall not be bound to ſhew how that in deſ <lb></lb>cending it continueth all the way vertically over one point, for <lb></lb>that it will not do any ſuch thing.</s></p><p type="main"><s>SIMP. </s><s>Very well; But if grave bodies, and light can have no <lb></lb>principle, either internal or external of moving circularly, than <lb></lb>neither can the terreſtrial Globe move with a circular motion: and <lb></lb>thus you have the intent of the Author.</s></p><p type="main"><s>SALV. </s><s>I did not ſay, that the Earth had no principle, either <lb></lb>interne, or externe to the motion of gyration, but I ſay, that I do <lb></lb>not know which of the two it hath; and yet my not knowing it <lb></lb>hath not a power to deprive it of the ſame; but if this Author <lb></lb>can tell by what principle other mundane bodies are moved round, <lb></lb>of whoſe motion there is no doubt; I ſay, that that which ma <lb></lb>keth the Earth to move, is a vertue, like to that, by which <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> <lb></lb>and <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> are moved, and wherewith he believes that the ſtarry <lb></lb>Sphere it ſelf alſo doth move; and if he will but aſſure me, who is <lb></lb>the mover of one of theſe moveables, I will undertake to be able <lb></lb>to tell him who maketh the Earth to move. </s><s>Nay more; I will <lb></lb>undertake to do the ſame, if he can but tell me, who moveth the <lb></lb>parts of the Earth downwards.</s></p><p type="main"><s>SIMP. </s><s>The cauſe of this is moſt manifeſt, and every one knows <lb></lb>that it is gravity.</s></p><p type="main"><s>SALV. </s><s>You are out, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> you ſhould ſay, that every <lb></lb>one knowes, that it is called Gravity: but I do not queſtion you <lb></lb>about the name, but the eſſence of the thing, of which eſſence <lb></lb>you know not a tittle more than you know the eſſence of the <lb></lb>mover of the ſtars in gyration; unleſſe it be the name that hath <lb></lb>been put to this, and made familiar, and domeſtical, by the many <lb></lb><arrow.to.target n="marg415"></arrow.to.target> <lb></lb>experiences which we ſee thereof every hour in the day,: but not <lb></lb>as if we really underſtand any more, what principle or vertue that <lb></lb>is which moveth a ſtone downwards, than we know who moveth <lb></lb>it upwards, when it is ſeparated from the projicient, or who mo <lb></lb>veth the Moon round, except (as I have ſaid) onely the name, <lb></lb>which more particularly and properly we have aſſigned to the mo <lb></lb>tion of deſcent, namely, Gravity; whereas for the cauſe of cir <lb></lb>cular motion, in more general termes, we aſſign the <emph type="italics"></emph>Vertue impreſ <lb></lb>ſed,<emph.end type="italics"></emph.end> and call the ſame an <emph type="italics"></emph>Intelligence,<emph.end type="italics"></emph.end> either aſſiſting, or informing; <lb></lb>and to infinite other motions we aſcribe Nature for their cauſe.</s></p><p type="margin"><s><margin.target id="marg415"></margin.target><emph type="italics"></emph>We know no more <lb></lb>who moveth grave <lb></lb>bodies downwards; <lb></lb>than who moveth <lb></lb>the Stars round, <lb></lb>nor know we any <lb></lb>thing of theſe cau <lb></lb>ſes, more than the <lb></lb>names impoſed on <lb></lb>them by us.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>It is my opinion, that this Author asketh far leſſe than <lb></lb>that, to which you deny to make anſwer; for he doth not ask <lb></lb>what is nominally and particularly the principle that moveth <lb></lb>grave and light bodies circularly, but whatſoever it be, he deſi <lb></lb>reth to know, whether you think it intrinſecal, or extrinſecal: <lb></lb>For howbeit, <emph type="italics"></emph>v. </s><s>gr.<emph.end type="italics"></emph.end> I do not know, what kind of thing that gravity <lb></lb>is, by which the Earth deſcendeth; yet I know that it is an intern <pb xlink:href="040/01/229.jpg" pagenum="211"></pb>principle, ſeeing that if it be not hindered, it moveth ſpontane <lb></lb>ouſly: and on the contrary, I know that the principle which mo <lb></lb>veth it upwards, is external, although that I do not know, what <lb></lb>thing that vertue is, impreſſed on it by the projicient.</s></p><p type="main"><s>SALV. </s><s>Into how many queſtions muſt we excurre, if we would <lb></lb>decide all the difficulties, which ſucceſſively have dependance one <lb></lb>upon another! You call that an external (and you alſo call it a <lb></lb>preternatural and violent) principle, which moveth the grave pro <lb></lb>ject upwards; but its poſſible that it may be no leſſe interne and <lb></lb>natural, than that which moveth it downwards; it may peradven <lb></lb><arrow.to.target n="marg416"></arrow.to.target> <lb></lb>ture be called external and violent, ſo long as the moveable is joy <lb></lb>ned to the projicient; but being ſeparated, what external thing <lb></lb>remaineth for a mover of the arrow, or ball? </s><s>In ſumme, it muſt <lb></lb>neceſſarliy be granted, that that vertue which carrieth ſuch a move <lb></lb>able upwards, is no leſſe interne, than that which moveth it down <lb></lb>wards; and I think the motion of grave bodies aſcending by the <lb></lb><emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> conceived, to be altogether as natural, as the motion of <lb></lb>deſcent depending on gravity.</s></p><p type="margin"><s><margin.target id="marg416"></margin.target><emph type="italics"></emph>The vertue which <lb></lb>carrieth grave pro <lb></lb>jects upwards, is <lb></lb>no leſſe natural to <lb></lb>them, than the <lb></lb>gravity which mo <lb></lb>veth them down <lb></lb>wards.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I will never grant this; for the motion of deſcent hath <lb></lb>its principle internal, natural, and perpetual, and the motion of <lb></lb>aſcent hath its principle externe, violent, and finite.</s></p><p type="main"><s>SALV. </s><s>If you refuſe to grant me, that the principles of the <lb></lb>motions of grave bodies downwards and upwards, are equally in <lb></lb><arrow.to.target n="marg417"></arrow.to.target> <lb></lb>ternal and natural; what would you do, if I ſhould ſay, that they <lb></lb>may alſo be the ſame in number?</s></p><p type="margin"><s><margin.target id="marg417"></margin.target><emph type="italics"></emph>Contrary prin <lb></lb>ciples cannot natu <lb></lb>rally reſide in the <lb></lb>ſame ſubject.<emph.end type="italics"></emph.end></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 deſire you your ſelf to be the Judge: Therefore <lb></lb>tell me, Do you believe that in the ſame natural body, there may <lb></lb>reſide 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></lb>Earth, of Lead, of Gold, and in ſum, of the moſt ponderous mat <lb></lb>ters; that is, to what motion do you believe that their interne <lb></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></lb>the centre of the Univerſe, and of the Earth, whither, if they be <lb></lb>not hindered, it will carry them.</s></p><p type="main"><s>SALV. </s><s>So that, if the Terreſtrial Globe were bored thorow, <lb></lb>and a Well made that ſhould paſſe through the centre of it, a <lb></lb>Cannon bullet being let fall into the ſame, as being moved by a <lb></lb>natural and intrinſick principle, would paſſe to the centre; and it <lb></lb>would make all this motion ſpontaneouſly, and by intrinſick prin <lb></lb>ciple, is it not ſo?</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"></pb>it will paſſe any further, or elſe that there it would immediately <lb></lb>ſtand ſtill, 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></lb>further.</s></p><p type="main"><s>SALV. </s><s>But this motion beyond the centre, would it not be up <lb></lb>wards, and according to your aſſertion preternatural, and violent? <lb></lb></s><s>And yet on what other principle do you make it to depend, but <lb></lb>only upon the ſelf ſame, which did carry the ball to the centre, <lb></lb>and which you called intrinſecal, and natural? </s><s>Finde, if you can, <lb></lb>another external projicient, that overtaketh it again to drive it <lb></lb>upwards. </s><s>And this that hath been ſaid of the motion thorow <lb></lb>the centre, is alſo ſeen by us here above; for the interne <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg418"></arrow.to.target> <lb></lb>of a grave body falling along a declining ſuperficies, if the ſaid <lb></lb>ſuperficies be reflected the other way, it ſhall carry it, without a <lb></lb>jot interrupting the motion, alſo upwards. </s><s>A ball of lead that <lb></lb>hangeth by a thread, being removed from its perpendicularity, de <lb></lb>ſcendeth ſpontaneouſly, as being drawn by its internal inclination, <lb></lb>and without any interpoſure of reſt, paſſeth beyond the loweſt <lb></lb>point of perpendicularity: and without any additional mover, <lb></lb>moveth upwards. </s><s>I know that you will not deny, but that the <lb></lb>principle of grave bodies that moveth them downwards, is no leſs <lb></lb>natural, and intrinſecal, than that principle of light bodies, which <lb></lb>moveth them upwards: ſo that I propoſe to your conſideration a <lb></lb>ball of lead, which deſcending through the Air from a great al <lb></lb>titude, and ſo moving by an intern principle, and comming to a <lb></lb>depth of water, continueth its deſcent, and without any other ex <lb></lb>terne mover, ſubmergeth a great way; and yet the motion of <lb></lb>deſcent in the water is preternatural unto it; but yet nevertheleſs <lb></lb>dependeth on a principle that is internal, and not external to the <lb></lb>ball. </s><s>You ſee it demonſtrated then, that a moveable may be <lb></lb>moved by one and the ſame internal principle, with contrary mo <lb></lb>tions.</s></p><p type="margin"><s><margin.target id="marg418"></margin.target><emph type="italics"></emph>The natural mo <lb></lb>tion changeth it <lb></lb>ſelfe into that <lb></lb>which is called pre <lb></lb>ternatural and vi <lb></lb>olent.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I believe there are ſolutions to all theſe objections, <lb></lb>though for the preſent I do not remember them; but however it <lb></lb>be, the Author continueth to demand, on what principle this cir <lb></lb>cular motion of grave and light bodies dependeth; that is, whe <lb></lb>ther on a principle internal, or external; and proceeding for <lb></lb>wards, ſheweth, that it can be neither on the one, nor on the other, <lb></lb>ſaying; <emph type="italics"></emph>Si ab externo; Deuſne illum excitat per continuum mira <lb></lb>culum? </s><s>an verò Angelus, an aër? </s><s>Et hunc quidem multi aſſig <lb></lb>nant. </s><s>Sed contra----[In Engliſh thus]<emph.end type="italics"></emph.end> If from an externe prin <lb></lb>ciple; Whether God doth not excite it by a continued Miracle? <lb></lb></s><s>or an Angel, or the Air? </s><s>And indeed many do aſſign this. </s><s>But <lb></lb>on the contrary-----.</s></p><p type="main"><s>SALV. </s><s>Trouble not your ſelf to read his argument; for I am <pb xlink:href="040/01/231.jpg" pagenum="213"></pb>none of thoſe who aſcribe that principle to the ambient air. </s><s>As <lb></lb>to the Miracle, or an Angel, I ſhould rather incline to this ſide; for <lb></lb>that which taketh beginning from a Divine Miracle, or from an <lb></lb>Angelical operation; as for inſtance, the tranſportation of a Can <lb></lb>non ball or bullet into the concave of the Moon, doth in all pro <lb></lb>bability depend on the vertue of the ſame principle for perform <lb></lb>ing the reſt. </s><s>But, as to the Air, it ſerveth my turn, that it doth <lb></lb>not hinder the circular motion of the moveables, which we did <lb></lb>ſuppoſe to move thorow it. </s><s>And to prove that, it ſufficeth (nor is <lb></lb>more required) that it moveth with the ſame motion, and finiſh <lb></lb>eth its circulations with the ſame velocity, that the Terreſtrial <lb></lb>Globe doth.</s></p><p type="main"><s>SIMP. </s><s>And he likewiſe makes his oppoſition to this alſo; <lb></lb>demanding who carrieth the air about, Nature, or Violence? <lb></lb></s><s>And proveth, that it cannot be Nature, alledging that that is con <lb></lb>trary to truth, experience, and to <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> himſelf.</s></p><p type="main"><s>SALV. </s><s>It is not contrary to <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> in the leaſt, who writeth <lb></lb>no ſuch thing; and this Author aſcribes theſe things to him with <lb></lb>two exceſſive courteſie. </s><s>It's true, he ſaith, and for my part I <lb></lb>think he ſaith well, that the part of the air neer to the Earth, be <lb></lb>ing rather a terreſtrial evaporation, may have the ſame nature, <lb></lb>and naturally follow its motion; or, as being contiguous to it, <lb></lb>may follow it in the ſame manner, as the Peripateticks ſay, that <lb></lb>the ſuperiour part of it, and the Element of fire, follow the mo <lb></lb>tion of the Lunar Concave, ſo that it lyeth upon them to declare, <lb></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"></emph>Copernicus<emph.end type="italics"></emph.end> maketh only <lb></lb>the inferiour part of the Air to move, and ſuppoſeth the upper <lb></lb>part thereof to want the ſaid motion, he cannot give a reaſon, how <lb></lb>that quiet air can be able to carry thoſe grave bodies along with <lb></lb>it, and make them keep pace with the motion of the Earth.</s></p><p type="main"><s>SALV. <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> will ſay, that this natural propenſion of the <lb></lb><arrow.to.target n="marg419"></arrow.to.target> <lb></lb>elementary bodies to ſollow the motion of the Earth, hath a li <lb></lb>mited Sphere, out of which ſuch a natural inclination would ceaſe; <lb></lb>beſides that, as I have ſaid, the Air is not that which carrieth the <lb></lb>moveables along with it; which being ſeparated from the Earth, <lb></lb>do follow its motion; ſo that all the objections come to nothing, <lb></lb>which this Author produceth to prove, that the Air cannot cauſe <lb></lb>ſuch effects.</s></p><p type="margin"><s><margin.target id="marg419"></margin.target><emph type="italics"></emph>The propenſion <lb></lb>of elementary bo <lb></lb>dies to follow the <lb></lb>Earth, hath a li <lb></lb>mited Sphere of <lb></lb>activity.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>To ſhew therefore, that that cannot be, it will be neceſ <lb></lb>ſary to ſay, that ſuch like effects depend on an interne principle, <lb></lb>againſt which poſition, <emph type="italics"></emph>oboriuntur difficillimæ, immò inextricabiles <lb></lb>quæſtiones ſecundæ,<emph.end type="italics"></emph.end> of which ſort are theſe that follow. <emph type="italics"></emph>Princi <lb></lb>pium illud internum vel eſt accidens, vel ſubſtantia. </s><s>Si primum; <lb></lb>quale nam illud? </s><s>nam qualitas locomotiva circum, hactenus nulla<emph.end type="italics"></emph.end> <pb xlink:href="040/01/232.jpg" pagenum="214"></pb><emph type="italics"></emph>videtur agnita. (In Engliſh thus:)<emph.end type="italics"></emph.end> Contrary to which poſition <lb></lb>there do ariſe moſt difficult, yea inextricable ſecond queſtions, <lb></lb>ſuch as theſe; That intern principle is either an accident, or a <lb></lb>ſubſtance. </s><s>If the firſt; what manner of accident is it? </s><s>For a <lb></lb>locomotive quality about the centre, ſeemeth to be hitherto ac <lb></lb>knowledged by none.</s></p><p type="main"><s>SALV. How, is there no ſuch thing acknowledged? </s><s>Is it not <lb></lb>known to us, that all theſe elementary matters move round, to <lb></lb>gether with the Earth? </s><s>You ſee how this Author ſuppoſeth for <lb></lb>true, that which is in queſtion.</s></p><p type="main"><s>SIMP. </s><s>He ſaith, that we do not ſee the ſame; and me thinks, <lb></lb>he hath therein reaſon on his ſide.</s></p><p type="main"><s>SALV. </s><s>We ſee it not, becauſe we turn round together with <lb></lb>them.</s></p><p type="main"><s>SIMP. </s><s>Hear his other Argument. <emph type="italics"></emph>Quæ etiam ſi eſſet, quo <lb></lb>modo tamen inveniretur in rebus tam contrariis? </s><s>in igne, ut in a <lb></lb>quâ; in aëre, ut in terra; in viventibus, ut in anima carentibus? <lb></lb>[in Engliſh thus:]<emph.end type="italics"></emph.end> Which although it were, yet how could it be <lb></lb>found in things ſo contrary? </s><s>in the fire, as in the water? </s><s>in the <lb></lb>air, as in the earth? </s><s>in living creatures, as in things wanting <lb></lb>life?</s></p><p type="main"><s>SALV. </s><s>Suppoſing for this time, that water and fire are contra <lb></lb>ries; as alſo the air and earth; (of which yet much may be ſaid) <lb></lb>the moſt that could follow from thence would be, that thoſe mo <lb></lb>tions cannot be common to them, that are contrary to one ano <lb></lb>ther: ſo that <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> the motion upwards, which naturally agreeth <lb></lb>to fire, cannot agree to water; but that, like as it is by nature con <lb></lb>trary to fire: ſo to it that motion ſuiteth, which is contrary to the <lb></lb>motion of fire, which ſhall be the motion <emph type="italics"></emph>deorſùm<emph.end type="italics"></emph.end>; but the cir <lb></lb>cular motion, which is not contrary either to the motion <emph type="italics"></emph>ſurſùm,<emph.end type="italics"></emph.end> <lb></lb>or to the motion <emph type="italics"></emph>deorſùm,<emph.end type="italics"></emph.end> but may mix with both, as <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> <lb></lb>himſelf affirmeth, why may it not equally ſuit with grave bodies <lb></lb>and with light? </s><s>The motions in the next place, which cannot be <lb></lb>common to things alive, and dead, are thoſe which depend on the <lb></lb>ſoul: but thoſe which belong to the body, in as much as it is ele <lb></lb>mentary, and conſequently participateth of the qualities of the e <lb></lb>lements, why may not they be common as well to the dead corps, <lb></lb>as to the living body? </s><s>And therefore, if the circular motion be <lb></lb>proper to the elements, it ought to be common to the mixt bodies <lb></lb>alſo.</s></p><p type="main"><s>SAGR. </s><s>It muſt needs be, that this Author holdeth, that a dead <lb></lb>cat, falling from a window, it is not poſſible that a live cat alſo <lb></lb>could fall; it not being a thing convenient, that a carcaſe ſhould <lb></lb>partake of the qualities which ſuit with things alive.</s></p><p type="main"><s>SALV. </s><s>Therefore the diſcourſe of this Author concludeth <pb xlink:href="040/01/233.jpg" pagenum="215"></pb>nothing againſt one that ſhould affirm, that the principle of the cir <lb></lb>cular motions of grave and light bodies is an intern accident: I <lb></lb>know not how he may prove, that it cannot be a ſubſtance.</s></p><p type="main"><s>SIMP. </s><s>He brings many Arguments againſt this. </s><s>The firſt of <lb></lb>which is in theſe words: <emph type="italics"></emph>Si ſecundum (nempè, ſi dieas tale princi <lb></lb>pium eſſe ſubſtantiam) illud eſt aut materia, aut forma, aut compo <lb></lb>ſitum. </s><s>Sed repugnant iterum tot diverſæ rerum naturæ, quales <lb></lb>ſunt aves, limaces, ſaxa, ſagittæ, nives, fumi, grandines, piſces, <lb></lb>&c. </s><s>quæ tamen omnia ſpecie & genere differentia, moverentur à <lb></lb>naturâ ſuâ circulariter, ipſa naturis diverſiſſima, &c. [In Engliſh <lb></lb>thus]<emph.end type="italics"></emph.end> If the ſecond, (that is, if you ſhall ſay that this principle is <lb></lb>a ſubſtance) it is either matter, or form, or a compound of both. <lb></lb></s><s>But ſuch diverſe natures of things are again repugnant, ſuch as are <lb></lb>birds, ſnails, ſtones, darts, ſnows, ſmoaks, hails, fiſhes, &c. </s><s>all <lb></lb>which notwithſtanding their differences in ſpecies and kind, are <lb></lb>moved of their own nature circularly, they being of their natures <lb></lb>moſt different, &c.</s></p><p type="main"><s>SALV. </s><s>If theſe things before named are of diverſe natures, and <lb></lb>things of diverſe natures cannot have a motion in common, it muſt <lb></lb>follow, if you would give ſatisfaction to all, that you are to think <lb></lb>of, more than two motions onely of upwards and downwards: and <lb></lb>if there muſt be one for the arrows, another for the ſnails, another <lb></lb>for the ſtones, and another for fiſhes; then are you to bethink your <lb></lb>ſelf of worms, topazes and muſhrums, which are not leſs different <lb></lb>in nature from one another, than ſnow and hail.</s></p><p type="main"><s>SIMP. </s><s>It ſeems that you make a jeſt of theſe Arguments.</s></p><p type="main"><s>SALV. </s><s>No indeed, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> but it hath been already an <lb></lb>ſwered above, to wit, that if one motion, whether downwards or <lb></lb>upwards, can agree with all thoſe things afore named, a circular <lb></lb>motion may no leſs agree with them: and as you are a <emph type="italics"></emph>Peripate <lb></lb>tick,<emph.end type="italics"></emph.end> do not you put a greater difference between an elementary <lb></lb>comet and a celeftial ſtar, than between a fiſh and a bird? </s><s>and <lb></lb>yet both thoſe move circularly. </s><s>Now propoſe your ſecond Ar <lb></lb>gument.</s></p><p type="main"><s>SIMP. <emph type="italics"></emph>Si terra ſtaret per voluntatem Dei, rotaréntne cætera, an <lb></lb>non? </s><s>ſi hoc, falſum eſt à naturâ gyrare; ſi illud, redeunt priores <lb></lb>quæſtiones. </s><s>Et ſanè mirum eſſet, quòd Gavia piſciculo, Alauda <lb></lb>nidulo ſuo, & corvus limaci, petraque, etiam volans, imminere <lb></lb>non poſſet. [Which I thus render<emph.end type="italics"></emph.end>:] If the Earth be ſuppoſed to <lb></lb>ſtand ſtill by the will of God, ſhould the reſt of bodies turn round <lb></lb>or no? </s><s>If not, then it's falſe that they are revolved by nature; if <lb></lb>the other, the former queſtions will return upon us. </s><s>And <lb></lb>truly it would be ſtrange that the Sea-pie ſhould not be able to <lb></lb>hover over the ſmall fiſh, the Lark over her neſt, and the Crow o <lb></lb>ver the ſnail and rock, though flying.</s></p> <pb xlink:href="040/01/234.jpg" pagenum="216"></pb><p type="main"><s>SALV. </s><s>I would anſwer for my ſelf in general terms, that if <lb></lb>it were appointed by the will of God, that the Earth ſhould ceaſe <lb></lb>from its diurnal revolution, thoſe birds would do what ever ſhould <lb></lb>pleaſe the ſame Divine will. </s><s>But if this Author deſire a more <lb></lb>particular anſwer, I ſhould tell him, that they would do quite con <lb></lb>trary to what they do now, if whilſt they, being ſeparated from <lb></lb>the Earth, do bear themſelves up in the air, the Terreſtrial Globe <lb></lb>by the will of God, ſhould all on a ſudden be put upon a precipi <lb></lb>tate motion; it concerneth this Author now to aſcertain us what <lb></lb>would in this caſe ſucceed.</s></p><p type="main"><s>SAGR. </s><s>I pray you, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> at my requeſt to grant to this <lb></lb>Author, that the Earth ſtanding ſtill by the will of God, the other <lb></lb>things, ſeparated from it, would continue to turn round of their <lb></lb>own natural motion, and let us hear what impoſſibilities or incon <lb></lb>veniences would follow: for I, as to my own particular, do not <lb></lb>ſee how there can be greater diſorders, than theſe produced by the <lb></lb>Author himſelf, that is, that Larks, though they ſhould flie, could <lb></lb>not be able to hover over their neſts, nor Crows over ſnails, or <lb></lb>rocks: from whence would follow, that Crows muſt ſuffer for <lb></lb>want of ſnails, and young Larks muſt die of hunger, and cold, not <lb></lb>being able to be fed or ſheltered by the wings of the old ones. <lb></lb></s><s>This is all the ruine that I can conceive would follow, ſuppoſing <lb></lb>the Authors ſpeech to be true. </s><s>Do you ſee, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> if grea <lb></lb>ter inconveniences would happen?</s></p><p type="main"><s>SIMP. </s><s>I know not how to diſcover greater; but it is very cre <lb></lb>dible, that the Author beſides theſe, diſcovered other diſorders in <lb></lb>Nature, which perhaps in reverend reſpect of her, he was not will <lb></lb>ing to inſtance in. </s><s>Therefore let us proceed to the third Obje <lb></lb>ction. <emph type="italics"></emph>Inſuper quî fit, ut istæ res tam variæ tantùm moveantur <lb></lb>ab Occaſu in Ortum, parallelæ ad Æquatorem? </s><s>ut ſemper movean <lb></lb>tur, nunquam quieſcant? [which ſpeaks to this ſenſe:]<emph.end type="italics"></emph.end> Moreover, <lb></lb>how comes it to paſs that theſe things, ſo diverſe, are onely moved <lb></lb>from the Weſt towards the Eaſt, parallel to the Æquinoctial? <lb></lb></s><s>that they always move, and never reſt?</s></p><p type="main"><s>SALV. </s><s>They move from Weſt to Eaſt parallel to the Æqui <lb></lb>noctial without ceaſing, in the ſame manner as you believe the <lb></lb>fixed ſtars to move from Eaſt to Weſt, parallel to the Æquinocti <lb></lb>al, without ever reſting.</s></p><p type="main"><s>SIMP. <emph type="italics"></emph>Quarè, quò ſunt altiores, celeriùs; quò humiliores, tar <lb></lb>diùs? (i. </s><s>e.)<emph.end type="italics"></emph.end> Why are the higher the ſwifter, and the lower the <lb></lb>ſlower?</s></p><p type="main"><s>SALV. </s><s>Becauſe that in a Sphere or circle, that turns about up <lb></lb>on its own centre, the remoter parts deſcribe greater circuits, and <lb></lb>the parts nearer at hand deſcribe leſſer in the ſame time.</s></p><p type="main"><s>SIMP. <emph type="italics"></emph>Quare, quæ Æquinoctiali propriores, in majori; quæ<emph.end type="italics"></emph.end> <pb xlink:href="040/01/235.jpg" pagenum="217"></pb><emph type="italics"></emph>remotiores, in minori circulo feruntur? [ſcilicet:]<emph.end type="italics"></emph.end> Why are <lb></lb>thoſe near the Æquinoctial carried about in a greater circle, and <lb></lb>thoſe which are remote in a leſſer?</s></p><p type="main"><s>SALV. </s><s>To imitate the ſtarry Sphere, in which thoſe neareſt <lb></lb>to the Æquinoctial, move in greater circles, than the more re <lb></lb>mote.</s></p><p type="main"><s>SIMP. <emph type="italics"></emph>Quarè Pila eadem ſub Æquinoctiali tota circa centrum <lb></lb>terr æ, ambitu maximo, celeritate incredibili; ſub Polo verò circa <lb></lb>centrum proprium, gyro nullo, tarditate ſupremâ volveretur? <lb></lb>[That is:]<emph.end type="italics"></emph.end> Why is the ſame ball under the Æquinoctial wholly <lb></lb>turned round the centre of the Earth in the greateſt circumfe <lb></lb>rence, with an incredible celerity; but under the Pole about its <lb></lb>own centre, in no circuite, but with the ultimate degree of tar <lb></lb>dity?</s></p><p type="main"><s>SALV. </s><s>To imitate the ſtars of the Firmament, that would do <lb></lb>the like if they had the diurnal motion.</s></p><p type="main"><s>SIMP. <emph type="italics"></emph>Quare eadem res, pila v. </s><s>g. </s><s>plumbea, ſi ſemel terram <lb></lb>circuivit, deſcripto circulo maximo, eandem ubique non circum <lb></lb>migret ſecundùm circulum maximum, ſed tranſlata extra Æquino <lb></lb>ctialem in circulis minoribus agetur? [Which ſpeaketh thus:]<emph.end type="italics"></emph.end> <lb></lb>Why doth not the ſame thing, as for example, a ball of lead <lb></lb>turn round every where according to the ſame great circle, if once <lb></lb>deſcribing a great circle, it hath incompaſſed the Earth, but being <lb></lb>removed from the Æquinoctial, doth move in leſſer circles?</s></p><p type="main"><s>SALV. </s><s>Becauſe ſo would, nay, according to the doctrine of <lb></lb><emph type="italics"></emph>Ptolomey,<emph.end type="italics"></emph.end> ſo have ſome fixed ſtars done, which once were very <lb></lb>near the Æquinoctial, and deſcribed very vaſt circles, and now that <lb></lb>they are farther off, deſcribe leſſer.</s></p><p type="main"><s>SAGR. </s><s>If I could now but keep in mind all theſe fine no <lb></lb>tions, I ſhould think that I had made a great purchaſe; I muſt <lb></lb>needs intreat you, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> to lend me this Book, for there can <lb></lb>not chuſe but be a ſea of rare and ingenious matters contained in <lb></lb>it.</s></p><p type="main"><s>SIMP. </s><s>I will preſent you with it.</s></p><p type="main"><s>SAGR. </s><s>Not ſo, Sir; I would not deprive you of it: but are <lb></lb>the Queries yet at an end?</s></p><p type="main"><s>SIMP. </s><s>No Sir; hearken therefore. <emph type="italics"></emph>Si latio circularis gra <lb></lb>vibus & levibus eſt naturalis, qualis eſt ea quæ fit ſecundùm line <lb></lb>am rectam? </s><s>Nam ſi naturalis, quomodo & is motus qui circum est, <lb></lb>naturalis eſt, cùm ſpecie differat à recto? </s><s>Si violentus, quî fit, ut <lb></lb>miſſile ignitum ſurſùm evolans ſcintilloſum caput ſurſùm à terrâ, <lb></lb>non autem circum volvatur, &c. [Which take in our idiom:]<emph.end type="italics"></emph.end> If <lb></lb>a circular lation is natural to heavy and light things, what is that <lb></lb>which is made according to a right line? </s><s>For if it be natural, how <lb></lb>then is that motion which is about the centre natural, ſeeing it <pb xlink:href="040/01/236.jpg" pagenum="218"></pb>differs in ſpecies from a right motion? </s><s>If it be violent, how is it <lb></lb>that a fiery dart flying upwards, ſparkling over our heads at a di <lb></lb>ſtance from the Earth, but not turning about, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg420"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg420"></margin.target><emph type="italics"></emph>Of the mixt mo <lb></lb>tion we ſee not the <lb></lb>part that is circu <lb></lb>lar, becauſe we <lb></lb>partake thereof.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>It hath been ſaid already very often, that the circular <lb></lb>motion is natural to the whole, and to its parts, whilſt they are in <lb></lb>perfect diſpoſure, and the right is to reduce to order the parts <lb></lb>diſordered; though indeed it is better to ſay, that neither the <lb></lb>parts ordered or diſordered ever move with a right motion, but <lb></lb>with one mixed, which might as well be averred meerly circular: <lb></lb>but to us but one part onely of this motion is viſible and obſer <lb></lb>vable, that is, the part of the right, the other part of the circular <lb></lb>being imperceptible to us, becauſe we partake thereof. </s><s>And this <lb></lb>anſwers to the rays which move upwards, and round about, but we <lb></lb>cannot diſtinguiſh their circular motion, for that, with that we our <lb></lb>ſelves move alſo. </s><s>But I believe that this Author never thought <lb></lb>of this mixture; for you may ſee that he reſolutely ſaith, that the <lb></lb>rays go directly upwards, and not at all in gyration.</s></p><p type="main"><s>SIMP. <emph type="italics"></emph>Quare centrum ſphære delapſæ ſub Æquatore ſpiram de <lb></lb>ſcribit in ejus plano: ſub aliis parallelis ſpiram deſcribit in cono? <lb></lb></s><s>ſub Polo deſcendit in axe lineam gyralem, decurrens in ſuperficie <lb></lb>cylindricâ conſignatam<emph.end type="italics"></emph.end>? (In Engliſh to this purpoſe:) Why doth <lb></lb>the centre of a falling Globe under the Æquinoctial deſcribe a <lb></lb>ſpiral line in the plane of the Æquator; and in other parallels <lb></lb>a ſpiral about a Cone; and under the Pole deſcend in the <lb></lb>axis deſcribing a gyral line, running in a Cylindrical Superſi <lb></lb>cies?</s></p><p type="main"><s>SALV. </s><s>Becauſe of the lines drawn from the Centre to the cir <lb></lb>cumference of the ſphere, which are thoſe by which <emph type="italics"></emph>graves<emph.end type="italics"></emph.end> de <lb></lb>fcend, that which terminates in the Æquinoctial deſigneth a cir <lb></lb>cle, and thoſe that terminate in other parallels deſcribe conical <lb></lb>ſuperficies; now the axis deſcribeth nothing at all, but continueth <lb></lb>in its own being. </s><s>And if I may give you my judgment freely, I <lb></lb>will ſay, that I cannot draw from all theſe Queries, any ſenſe that <lb></lb>interfereth with the motion of the Earth; for if I demand of this <lb></lb>Author, (granting him that the Earth doth not move) what would <lb></lb>follow in all theſe particulars, ſuppoſing that it do move, as <emph type="italics"></emph>Co <lb></lb>pernicus<emph.end type="italics"></emph.end> will have it; I am very confident, that he would ſay that <lb></lb>all theſe effects would happen, that he hath objected, as inconve <lb></lb>niences to diſprove its mobility: ſo that in this mans opinion ne <lb></lb>ceſſary conſequences are accounted abſurdities: but I beſeech <lb></lb>you, if there be any more, diſpatch them, and free us ſpeedily <lb></lb>from this weariſom task.</s></p><p type="main"><s>SIMP. </s><s>In this which follows he oppoſes <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> & his Sectators, <lb></lb>who affirm, that the motion of the parts ſeparated from their whole, <lb></lb>is onely to unite themſelves to their whole; but that the moving <pb xlink:href="040/01/237.jpg" pagenum="219"></pb>circularly along with the vertigenous diurnal revolution is abſo <lb></lb>lutely natural: againſt which he objecteth, ſaying, that according <lb></lb>to theſe mens opinion; <emph type="italics"></emph>Si tota terra, unà cum aquâ in nihilum <lb></lb>redigeretur, nulla grando aut pluvia è nube decideret, ſed natu <lb></lb>raliter tantùm circumferetur, neque ignis ullus, aut igneum aſcen <lb></lb>deret, cùm illorum non improbabili ſententià ignis nullus ſit ſuprà.<emph.end type="italics"></emph.end> <lb></lb>[Which I tranſlate to this ſenſe:] If the whole Earth, together <lb></lb>with the Water were reduced into nothing, no hail or rain would <lb></lb>fall from the clouds, but would be onely naturally carried round; <lb></lb>neither any fire or fiery thing would aſcend, ſeeing to theſe that men <lb></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 Philoſopher is admirable, and <lb></lb>worthy of great applauſe, for he is not content to provide for <lb></lb>things that might happen, the courſe of Nature continuing, but <lb></lb>will ſhew hic care in what may follow from thoſe things that he <lb></lb>very well knows ſhall never come to paſs. </s><s>I will grant him there <lb></lb>fore, (that I may get ſom pretty paſſages out of him) that if the <lb></lb>Earth and Water ſhould be reduced to nothing, there would be no <lb></lb>more hails or rains, nor would igneal matters aſcend any longer <lb></lb>upwards, but would continually turn round: what will follow? <lb></lb></s><s>what will the Philoſopher ſay then?</s></p><p type="main"><s>SIMP. </s><s>The objection is in the words which immediately fol <lb></lb>low; here they are: <emph type="italics"></emph>Quibus tamen experientia & ratio adver <lb></lb>ſatur.<emph.end type="italics"></emph.end> Which nevertheleſs (ſaith he) is contrary to experience and <lb></lb>reaſon.</s></p><p type="main"><s>SALV. </s><s>Now I muſt yield, ſeeing he hath ſo great an advan <lb></lb>tage of me as experience, of which I am unprovided. </s><s>For as yet <lb></lb>I never had the fortune to ſee the Terreſtrial Globe and the ele <lb></lb>ment of Water turn'd to nothing, ſo as to have been able to ob <lb></lb>ſerve what the hail and water did in that little Chaos. </s><s>But he <lb></lb>perhaps tells us for our inſtruction 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></lb>this perſon, to ask him, whether when this Globe vaniſhed, it car <lb></lb>ried away with it the common centre of gravity, as I believe it did; <lb></lb>in which caſe, I think that the hail and water would remain inſen <lb></lb>ſate and ſtupid amongſt the clouds, without knowing what to do <lb></lb>with themſelves. </s><s>It might be alſo, that attracted by that great <lb></lb>void <emph type="italics"></emph>Vacuum,<emph.end type="italics"></emph.end> left by the Earths abſenting, all the ambients would <lb></lb>be rarified, and particularly, the air, which is extreme eaſily drawn, <lb></lb>and would run thither with very great haſte to fill it up. </s><s>And <lb></lb>perhaps the more ſolid and material bodies, as birds, (for there <lb></lb>would in all probability be many of them ſcattered up and down <lb></lb>in the air) would retire more towards the centre of the great va <lb></lb>cant ſphere; (for it ſeemeth very reaſonable, that ſubſtances that <pb xlink:href="040/01/238.jpg" pagenum="220"></pb>under ſmall bulk contain much matter, ſhould have narrower pla <lb></lb>ces aſſigned them, leaving the more ſpacious to the more rarified) <lb></lb>and there being dead of hunger, and reſolved into Earth, would <lb></lb>form a new little Globe, with that little water, which at that time <lb></lb>was among the clouds. </s><s>It might be alſo, that thoſe matters as <lb></lb>not beholding the light, would not perceive the Earths departure, <lb></lb>but like blind things, would deſcend according to their uſual cuſtom <lb></lb>to the centre, whither they would now go, if that globe did not <lb></lb>hinder them. </s><s>And laſtly, that I may give this Philoſopher a leſs <lb></lb>irreſolute anſwer, I do tell him, that I know as much of what <lb></lb>would follow upon the annihilation of the Terreſtrial Globe, as <lb></lb>he would have done that was to have followed in and about the <lb></lb>ſame, before it was created. </s><s>And becauſe I am certain he will <lb></lb>ſay, that he would never have been able to have known any of <lb></lb>all thoſe things which experience alone hath made him knowing <lb></lb>in, he ought not to deny me pardon, and to excuſe me if I know <lb></lb>not that which he knows, touching what would enſue upon the <lb></lb>annihilation of the ſaid Globe: for that I want that experience <lb></lb>which he hath. </s><s>Let us hear if he have any thing elſe to ſay.</s></p><p type="main"><s>SIMP. </s><s>There remains this figure, which repreſents the Terre <lb></lb>ſtrial Globe with a great cavity about its centre, full of air; and <lb></lb>to ſhew that <emph type="italics"></emph>Graves<emph.end type="italics"></emph.end> move not downwards to unite with the Ter <lb></lb>reſtrial Globe, as <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> ſaith, he conſtituteth this ſtone in <lb></lb>the centre; and demandeth, it being left at liberty, what it would <lb></lb>do; and he placeth another in the ſpace of this great vacuum, and <lb></lb>asketh the ſame queſtion. </s><s>Saying, as to the firſt: <emph type="italics"></emph>Lapis in centro <lb></lb>conſtitutus, aut aſcendet ad terram in punctum aliquod, aut non. </s><s>Si <lb></lb>ſecundum; falſum est, partes ob ſolam ſejunctionem à toto, ad il <lb></lb>lud moveri. </s><s>Si primum; omnis ratio & experientia renititur, <lb></lb>neque gravia in ſuœ gravitatis centro conquieſcent. </s><s>Item ſi ſu <lb></lb>ſpenſus lapis, liberatus decidat in centrum, ſeparabit ſe à toto, con <lb></lb>tra<emph.end type="italics"></emph.end> Copernicum<emph type="italics"></emph>: ſi pendeat, refragatur omnis experientia, cùm <lb></lb>videamus integros fornices corruere.<emph.end type="italics"></emph.end> (Wherein he ſaith:) The <lb></lb>ſtone placed in the centre, either aſcendeth to the Earth in ſome <lb></lb>point, or no. </s><s>If the ſecond, it is falſe that the parts ſeparated <lb></lb>from the whole, move unto it. </s><s>If the firſt; it contradicteth all <lb></lb>reaſon and experience, nor doth the grave body reſt in the centre <lb></lb>of its gravity. </s><s>And if the ſtone being ſuſpended in the air, be let <lb></lb>go, do deſcend to the centre, it will ſeparate from its whole, con <lb></lb>trary to <emph type="italics"></emph>Copernicus:<emph.end type="italics"></emph.end> if it do hang in the air, it contradicteth all <lb></lb>experience: ſince we ſee whole Vaults to fall down.</s></p><p type="main"><s>SALV. </s><s>I will anſwer, though with great diſadvantage to my <lb></lb>ſelf, ſeeing I have to do with one who hath ſeen by experience, <lb></lb>what theſe ſtones do in this great Cave: a thing, which for my <lb></lb>part I have not ſeen; and will ſay, that things grave have an exi <pb xlink:href="040/01/239.jpg" pagenum="221"></pb>ſtence before the common centre of gravity: ſo that it is not one </s></p><p type="main"><s><arrow.to.target n="marg421"></arrow.to.target> <lb></lb>centre alone, which is no other than indiviſible point, and therefore <lb></lb>of no efficacie, that can attract unto it grave matters; but that thoſe <lb></lb>matters conſpiring naturally to unite, form to themſelves a com <lb></lb>mon centre, which is that about which parts of equal moment <lb></lb>conſiſt: ſo that I hold, that if the great aggregate of grave bo <lb></lb><arrow.to.target n="marg422"></arrow.to.target> <lb></lb>dies were gathered all into any one place, the ſmall parts that were <lb></lb>ſeparated from their whole, would follow the ſame, and if they <lb></lb>were not hindered, would penetrate wherever they ſhould find <lb></lb>parts leſs grave than themſelves: but coming where they ſhould <lb></lb>meet with matters more grave, they would deſcend no farther. <lb></lb></s><s>And therefore I hold, that in the Cave full of air, the whole Vault <lb></lb>would preſs, and violently reſt it ſelf onely upon that air, in caſe <lb></lb>its hardneſs could not be overcome and broken by its gravity; but <lb></lb>looſe ſtones, I believe, would deſcend to the centre, and not ſwim <lb></lb>above in the air: nor may it be ſaid, that they move not to their <lb></lb>whole, though they move whither all the parts of the whole <lb></lb>would transfer themſelves, if all impediments were removed.</s></p><p type="margin"><s><margin.target id="marg421"></margin.target><emph type="italics"></emph>Things grave are <lb></lb>before the centre of <lb></lb>gravity.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg422"></margin.target><emph type="italics"></emph>The great maſs <lb></lb>of grave bodies be <lb></lb>ing transferred out <lb></lb>of their place, the <lb></lb>ſeparated parts <lb></lb>would follow that <lb></lb>maß.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>That which remaineth, is a certain Errour which he ob <lb></lb>ſerveth in a Diſciple of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> who making the Earth to <lb></lb>move with an annual motion, and a diurnal, in the ſame manner <lb></lb>as the Cart-wheel moveth upon the circle of the Earth, and in it <lb></lb>ſelf, did conſtitute the Terreſtrial Globe too great, or the great <lb></lb>Orb too little; for that 365 revolutions of the Æquinoctial, are <lb></lb>leſs by far than the circumference of the great Orb.</s></p><p type="main"><s>SALV. </s><s>Take notice that you miſtake, and tell us the direct <lb></lb>contrary to what muſt needs be written in that Book; for you <lb></lb>ſhould ſay, that that ſame <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Author did conſtitute the <lb></lb>Terreſtrial Globe too little, and the great Orb too big; and not <lb></lb>the Terreſtrial Globe too big, and the annual too little.</s></p><p type="main"><s>SIMP. </s><s>The miſtake is not mine; ſee here the words of the <lb></lb>Book. <emph type="italics"></emph>Non videt, quòd vel circulum annuum æquo minorem, vel <lb></lb>orbem terreum juſto multò fabricet majorem.<emph.end type="italics"></emph.end> (In Engliſh thus:) <lb></lb>He ſeeth not, that he either maketh the annual circle equal to the <lb></lb>leſs, or the Terreſtrial Orb much too big.</s></p><p type="main"><s>SALV. </s><s>I cannot tell whether the firſt Author erred or no, ſince <lb></lb>the Author of this Tractate doth not name him; but the error of <lb></lb>this Book is certain and unpardonable, whether that follower of <lb></lb><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> erred or not erred; for that your Author paſſeth by ſo <lb></lb>material an error, without either detecting or correcting it. </s><s>But <lb></lb>let him be forgiven this fault, as an error rather of inadvertencie, <lb></lb>than of any thing elſe: Farthermore, were it not, that I am al <lb></lb>ready wearied and tired with talking and ſpending ſo mnch time <lb></lb>with very little profit, in theſe frivolous janglings and alterca <lb></lb>tions, I could ſhew, that it is not impoſſible for a circle, though <pb xlink:href="040/01/240.jpg" pagenum="222"></pb><arrow.to.target n="marg423"></arrow.to.target> <lb></lb>no bigger than a Cart-wheel, with making not 365, but leſſe than <lb></lb>20 revolutions, to deſcribe and meaſure the circumference, not <lb></lb>onely of the grand Orb, but of one a thouſand times greater; <lb></lb>and this I ſ y to ſhew, that there do not want far greater ſubtil <lb></lb>ties, than this wherewith your Author goeth about to detect the <lb></lb>errour of <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end>: but I pray you, let us breath a little, that <lb></lb>ſo we may proceed to the other Philoſopher, that oppoſeth of the <lb></lb>ſame <emph type="italics"></emph>Copernicus.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg423"></margin.target><emph type="italics"></emph>It is not impoſſi <lb></lb>ble with the cir <lb></lb>cumference of a <lb></lb>ſmall circle few <lb></lb>times revolved to <lb></lb>meaſure and de <lb></lb>ſcribe a line bigger <lb></lb>than any great cir <lb></lb>cle what ſoever.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>To confeſſe the truth, I ſtand as much in need of re <lb></lb>ſpite as either of you; though I have onely wearied my eares: <lb></lb>and were it not that I hope to hear more ingenious things from <lb></lb>this other Author, I queſtion whether I ſhould not go my ways, to <lb></lb><arrow.to.target n="marg424"></arrow.to.target> <lb></lb>take the air in my ^{*} Pleaſure-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></lb>for this is a moſt accompliſhed Philoſopher, and a great Mathema <lb></lb>tician, and hath confuted <emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end> in the buſineſſe of the Comets, <lb></lb>and new Stars. <lb></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></lb>the <emph type="italics"></emph>Author<emph.end type="italics"></emph.end> is <emph type="italics"></emph>Sci <lb></lb>pie Claramontius.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Perhaps he is the ſame with the Author of the Book, <lb></lb>called <emph type="italics"></emph>Anti-Tycho<emph.end type="italics"></emph.end>?</s></p><p type="main"><s>SIMP. </s><s>He is the very ſame: but the confutation of the new <lb></lb>Stars is not in his <emph type="italics"></emph>Anti-Tycho,<emph.end type="italics"></emph.end> onely ſo far as he proveth, that they <lb></lb>were not prejudicial to the inalterability and ingenerability of the <lb></lb>Heavens, as I told you before; but after he had publiſhed his <lb></lb><emph type="italics"></emph>Anti-Tycho,<emph.end type="italics"></emph.end> having found out, by help of the Parallaxes, a way to <lb></lb>demonſtrate, that they alſo are things elementary, and contained <lb></lb>within the concave of the Moon, he hath writ this other Book, <lb></lb><emph type="italics"></emph>de tribus uovis Stellis, &c.<emph.end type="italics"></emph.end> and therein alſo inſerted the Argu <lb></lb>ments againſt <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end>: I have already ſhewn you what he <lb></lb>harh written touching theſe new Stars in his <emph type="italics"></emph>Anti-Tycho,<emph.end type="italics"></emph.end> where he <lb></lb>denied not, but that they were in the Heavens; but he proved, that <lb></lb>their production altered not the inalterability of the Heavens, and <lb></lb>that he did, with a Diſcourſe purely philoſophical, in the ſame man <lb></lb>ner as you have already heard. </s><s>And I then forgot to tell you, how <lb></lb>that he afterwards did finde out a way to remove them out of the <lb></lb>Heavens; for he proceeding in this confutation, by way of com <lb></lb>putations and parallaxes, matters little or nothing at all under <lb></lb>ſtood by me, I did not mention them to you, but have bent all my <lb></lb>ſtudies upon theſe arguments againſt the motion of the Earth, <lb></lb>which are purely natural.</s></p><p type="main"><s>SALV. </s><s>I underſtand you very well: and it will be convenient <lb></lb>after we have heard what he hath to ſay againſt <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> that <lb></lb>we hear, or ſee at leaſt the manner wherewith he, by way of Pa <lb></lb>rallaxes, proveth thoſe new ſtars to be elementary, which ſo many <lb></lb>famous Aſtronomers conſtitute to be all very high, and amongſt <lb></lb>the ſtars of the Firmament; and as this Author accompliſheth ſuch <pb xlink:href="040/01/241.jpg" pagenum="223"></pb>an enterprize of pulling the new ſtars out of heaven, and placing <lb></lb>them in the elementary Sphere, he ſhall be worthy to be highly <lb></lb>exalted, and transferred himſelf amongſt the ſtars, or at leaſt, <lb></lb>that his name be by fame eternized amongſt them. </s><s>Yet before we <lb></lb>enter upon this, let us hear what he alledgeth againſt the opinion <lb></lb>of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> and do you begin to recite his Arguments.</s></p><p type="main"><s>SIMP. </s><s>It will not be neceſſary that we read them <emph type="italics"></emph>ad verbum,<emph.end type="italics"></emph.end> <lb></lb>becauſe they are very prolix; but I, as you may ſee, in reading <lb></lb>them ſeveral times attentively, have marked in the margine thoſe <lb></lb>words, wherein the ſtrength of his arguments lie, and it will <lb></lb>ſuffice to read them. </s><s>The ſirſt Argument beginneth here. <emph type="italics"></emph>Et<emph.end type="italics"></emph.end></s></p><p type="main"><s><arrow.to.target n="marg426"></arrow.to.target> <lb></lb><emph type="italics"></emph>primo, ſi opinio Copernici recipiatur, Criterium naturalis Philo <lb></lb>ſophiæ, ni prorſus tollatur, vehementer ſaltem labefactari <lb></lb>videtur.<emph.end type="italics"></emph.end> [In our Idiom thus] And firſt, if <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> his opinion <lb></lb>be imbraced, the <emph type="italics"></emph>Criterium<emph.end type="italics"></emph.end> of natural Philoſophy will be, if not <lb></lb>wholly ſubverted, yet at leaſt extreamly ſhaken.</s></p><p type="margin"><s><margin.target id="marg426"></margin.target><emph type="italics"></emph>The opinion of<emph.end type="italics"></emph.end> <lb></lb>Copernicus <emph type="italics"></emph>over <lb></lb>throws the<emph.end type="italics"></emph.end> Crite <lb></lb>rium <emph type="italics"></emph>of Philoſophy<emph.end type="italics"></emph.end></s></p><p type="main"><s>Which, according to the opinion of all the ſects of Philoſophers <lb></lb>requireth, that Senſe and Experience be our guides in philoſopha <lb></lb>ting: But in the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> poſition the Senſes are greatly delu <lb></lb>ded, whil'ſt that they viſibly diſcover neer at hand in a pure <emph type="italics"></emph>Medi <lb></lb>um,<emph.end type="italics"></emph.end> the graveſt bodies to deſcend perpendicularly downwards, ne <lb></lb>ver deviating a ſingle hairs breadth from rectitude; and yet accor <lb></lb>ding to the opinion of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> the ſight in ſo manifeſt a thing <lb></lb>is deceived, and that motion is not reall ſtraight, but mixt of <lb></lb>right and circular.</s></p><p type="main"><s>SALV. </s><s>This is the firſt argument, that <emph type="italics"></emph>Ariſtotle, Ptolomy,<emph.end type="italics"></emph.end> and <lb></lb>all their followers do produce; to which we have abundant <lb></lb>ly anſwered, and ſhewn the Paralogiſme, and with ſufficient <lb></lb>plainneſſe proved, that the motion in common to us and other mo <lb></lb>veables, is, as if there were no ſuch thing; but becauſe true con <lb></lb>cluſions meet with a thouſand accidents, that confirme them, I <lb></lb><arrow.to.target n="marg427"></arrow.to.target> <lb></lb>will, with the favour of this Philoſopher, adde ſomething more; <lb></lb>and you <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> perſonating him, anſwer me to what I ſhall <lb></lb>ask you: And firſt tell me, what effect hath that ſtone upon you, <lb></lb><arrow.to.target n="marg428"></arrow.to.target> <lb></lb>which falling from the top of the Tower, is the cauſe that you per <lb></lb>ceive that motion; for if its fall doth operate upon you neither <lb></lb>more nor leſſe, than its ſtanding ſtill on the Towers top, you <lb></lb>doubtleſſe could not diſcern its deſcent, or diſtinguiſh its moving <lb></lb>from its lying ſtill.</s></p><p type="margin"><s><margin.target id="marg427"></margin.target><emph type="italics"></emph>Common motion <lb></lb>is, as if it never <lb></lb>were.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg428"></margin.target><emph type="italics"></emph>The argument <lb></lb>taken from things <lb></lb>falling perpendicu <lb></lb>larly, another way <lb></lb>confuted.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I comprehend its moving, in relation to the Tower, <lb></lb>for that I ſee it one while juſt againſt ſuch a mark in the ſaid <lb></lb>Tower, and another while againſt another lower, and ſo ſucceſ <lb></lb>ſively, till that at laſt I perceive it arrived at the ground.</s></p><p type="main"><s>SALV. </s><s>Then if that ſtone were let fall from the tallons of an <lb></lb>Eagle flying, and ſhould deſcend thorow the ſimple inviſible Air, <pb xlink:href="040/01/242.jpg" pagenum="224"></pb>and you had no other object viſible and ſtable, wherewith to make <lb></lb>compariſons to that, you could not perceive its motion?</s></p><p type="main"><s>SIMP. No, nor the ſtone it ſelf; for if I would ſee it, when <lb></lb><arrow.to.target n="marg429"></arrow.to.target> <lb></lb>it is at the higheſt, I muſt raiſe up my head, and as it deſcendeth <lb></lb>I muſt hold it lower and lower, and in a word, muſt continually <lb></lb>move either that, or my eyes, following the motion of the ſaid <lb></lb>ſtone.</s></p><p type="margin"><s><margin.target id="marg429"></margin.target><emph type="italics"></emph>Whence the mo <lb></lb>tion of a cadent bo <lb></lb>dy is collected.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>You have now rightly anſwered: you know then that <lb></lb><arrow.to.target n="marg430"></arrow.to.target> <lb></lb>the ſtone lyeth ſtill, when without moving your eye, you alwayes <lb></lb>ſee it before you; and you know that it moveth, when for the <lb></lb>keeping it in ſight, you muſt move the organ of ſight, the eye. </s><s>So <lb></lb>then when ever without moving your eye, you continually be <lb></lb>hold an object in the ſelf ſame aſpect, you do always judge it <lb></lb>immoveable.</s></p><p type="margin"><s><margin.target id="marg430"></margin.target><emph type="italics"></emph>The motion of <lb></lb>the eye argueth <lb></lb>the motion of the <lb></lb>object looked on.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I think it muſt needs be ſo.</s></p><p type="main"><s>SALV. </s><s>Now fancy your ſelf to be in a ſhip, and to have fixed <lb></lb>your eye on the point of the Sail-yard: Do you think, that be <lb></lb>cauſe the ſhip moveth very faſt, you muſt move your eye, to keep <lb></lb>your ſight alwayes upon the point of the Sail-yard, and to fol <lb></lb>low its motion?</s></p><p type="main"><s>SIMP. </s><s>I am certain, that I ſhould need to make no change at <lb></lb>all; and that not only in the ſight; but if I had aimed a Musket <lb></lb>at it, I ſhould never have need, let the ſhip move how it will, <lb></lb>to ſtir it an hairs breadth to keep it full upon the ſame.</s></p><p type="main"><s>SALV. </s><s>And this happens becauſe the motion, which the Ship <lb></lb>conferreth on the Sail-yard, it conferreth alſo upon you, and upon <lb></lb>your eye; ſo that you need not ſtir it a jot to behold the top of <lb></lb>the Sail-yard: and conſequently, it will ſeem to you immovea <lb></lb>able. </s><s>Now this Diſcourſe being applied to the revolution of the <lb></lb>Earth, and to the ſtone placed in the top of the Tower, in which <lb></lb>you cannot diſcern any motion, becauſe that you have that mo <lb></lb>tion which is neceſſary for the following of it, in common with it <lb></lb>from the Earth; ſo that you need not move your eye. </s><s>When a <lb></lb>gain there is conferred upon it the motion of deſcent, which is its <lb></lb>particular motion, and not yours, and that it is intermixed with the <lb></lb>circular, that part of the circular which is common to the ſtone, <lb></lb>and to the eye, continueth to be imperceptible, and the right one <lb></lb>ly is perceived, for that to the perception of it, you muſt follow it <lb></lb>with your eye, looking lower and lower. </s><s>I wiſh for the undecei <lb></lb>ving of this Philoſopher, that I could adviſe him, that ſome time <lb></lb><arrow.to.target n="marg431"></arrow.to.target> <lb></lb>or other going by water, he would carry along with him a Veſſel <lb></lb>of reaſonable depth full of water, and prepare a ball of wax, or <lb></lb>other matter that would deſcend very ſlowly to the bottome, ſo <lb></lb>that in a minute of an hour, it would ſcarce ſink a yard; and that <lb></lb>rowing the boat as faſt as could be, ſo that in a minute of an hour <pb xlink:href="040/01/243.jpg" pagenum="225"></pb>it ſhould run above an hundred yards, he would let the ball ſub <lb></lb>merge into the water, & freely deſcend, & diligently obſerve its mo <lb></lb>tion. </s><s>If he would but do thus, he ſhould ſee, firſt, that it would go in a <lb></lb>direct line towards that point of the bottom of the veſſel, whither it <lb></lb>would tend, if the boat ſhould ſtand ſtill; & to his eye, and in rela <lb></lb>tion to the veſſel, that motion would appear moſt ſtraight and per <lb></lb>pendicular, and yet he could not ſay, but that it would be compoſed <lb></lb>of the right motion downwards, and of the circular about the ele <lb></lb>ment of water. </s><s>And if theſe things befall in matters not natural, <lb></lb>and in things that we may experiment in their ſtate of reſt; & then <lb></lb>again in the contrary ſtate of motion, and yet as to appearance no <lb></lb>diverſity at all is diſcovered, & that they ſeem to deceive our ſenſe <lb></lb>what can we diſtinguiſh touching the Earth, which hath been per <lb></lb>petually in the ſame conſtitution, as to motion and reſt? </s><s>And in <lb></lb>what time can we experiment whether any difference is diſcernable <lb></lb>amongſt theſe accidents of local motion, in its diverſe ſtates of mo <lb></lb>tion and reſt, 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"></emph>An experiment <lb></lb>that ſheweth how <lb></lb>the common motion <lb></lb>is imperceptible.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Theſe Diſcourſes have ſomewhat whetted my ſtomack, <lb></lb>which thoſe fiſhes, and ſnails had in part nauſeated; and the former <lb></lb>made me call to minde the correction of an errour, that hath ſo <lb></lb>much appearance of truth, that I know not whether one of a <lb></lb>thouſand would refuſe to admit it as unqueſtionable. </s><s>And it was <lb></lb>this, that ſailing into <emph type="italics"></emph>Syria,<emph.end type="italics"></emph.end> and carrying with me a very good <lb></lb><emph type="italics"></emph>Teleſcope,<emph.end type="italics"></emph.end> that had been beſtowed on me by our <emph type="italics"></emph>Common Friend,<emph.end type="italics"></emph.end> <lb></lb>who not many dayes before had invented, I propoſed to the Ma <lb></lb>riners, that it would be of great benefit in Navigation to make uſe <lb></lb>of it upon the round top of a ſhip, to diſcover and kenne Veſſels <lb></lb>afar off. </s><s>The benefit was approved, but there was objected the <lb></lb><arrow.to.target n="marg432"></arrow.to.target> <lb></lb>difficulty of uſing it, by reaſon of the Ships continual fluctuation; <lb></lb>and eſpecially on the round top, where the agitation is ſo much <lb></lb>greater, and that it would be better for any one that would make <lb></lb>uſe thereof to ſtand at the Partners upon the upper Deck, where <lb></lb>the toſſing is leſſe than in any other place of the Ship. </s><s>I (for I <lb></lb>will not conceal my errour) concurred in the ſame opinion, and <lb></lb>for that time ſaid no more: nor can I tell you by what hints I was <lb></lb>moved to return to ruminate with my ſelf upon this buſineſſe, and <lb></lb>in the end came to diſcover my ſimplicity (although excuſable) in <lb></lb>admitting that for true, which is moſt falſe; falſe I ſay, that the <lb></lb>great agitation of the basket or round top, in compariſon of the <lb></lb>ſmall one below, at the partners of the Maſt, ſhould render the <lb></lb>uſe of the <emph type="italics"></emph>Teleſcope<emph.end type="italics"></emph.end> more difficult in finding out the object.</s></p><p type="margin"><s><margin.target id="marg432"></margin.target><emph type="italics"></emph>An ingenuous <lb></lb>conſideration a <lb></lb>bout the poſſibility <lb></lb>of uſing the<emph.end type="italics"></emph.end> Teleſ <lb></lb>cope <emph type="italics"></emph>with as much <lb></lb>facility on the <lb></lb>round top of the <lb></lb>Maſt of a ſhip, <lb></lb>as on the Deck.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>I ſhould have accompanied the Mariners, and your ſelf <lb></lb>at the beginning.</s></p><p type="main"><s>SIMP. </s><s>And ſo ſhould I have done, and ſtill do: nor can I be <lb></lb>lieve, if I ſhould think of it an hundred years, that I could under <lb></lb>ſtand it otherwiſe.</s></p> <pb xlink:href="040/01/244.jpg" pagenum="226"></pb><p type="main"><s>SAGR. </s><s>I may then, it ſeems, for once prove a Maſter to you both. <lb></lb></s><s>And becauſe the proceeding by interrogatories doth in my opinion <lb></lb>much dilucidate things, beſides the pleaſure which it affords of con <lb></lb>founding our companion, forcing from him that which he thought he <lb></lb>knew not, I will make uſe of that artifice. </s><s>And firſt, I ſuppoſe that the <lb></lb>Ship, Gally, or other Veſſel, which we would diſcover, is a great way <lb></lb>off, that is, four, ſix, ten, or twenty ^{*} miles, for that to kenne thoſe <lb></lb><arrow.to.target n="marg433"></arrow.to.target> <lb></lb>neer at hand there is no need of theſe Glaſſes: & conſequently, the <lb></lb><emph type="italics"></emph>Teleſcope<emph.end type="italics"></emph.end> may at ſuch a diſtance of four or ſix miles conveniently <lb></lb>diſcover the whole Veſſel, & a muchgreater bulk. </s><s>Now I demand <lb></lb>what for ſpecies, & how many for number are the motions that are <lb></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></lb>from the ſtrict Sea <lb></lb>Diallect, which <lb></lb>denominatesall di <lb></lb>ſtances by Leagues.</s></p><p type="main"><s>SALV. </s><s>We will ſuppoſe that the Ship goeth towards the Eaſt. <lb></lb></s><s>Firſt, in a calme Sea, it would have no other motion than <lb></lb><arrow.to.target n="marg434"></arrow.to.target> <lb></lb>this of progreſſion, but adding the undulation of the Waves, <lb></lb>there ſhall reſult thence one, which alternately hoyſting and low <lb></lb>ering the poop and prow, maketh the round top, to lean forwards <lb></lb>and backwards; other waves driving the veſſel ſidewayes, bow the <lb></lb>Maſt to the Starboard and Larboard; others, may bring the ſhip <lb></lb>ſomewhat abovt, and bear her away by the Miſne from Eaſt, one <lb></lb><arrow.to.target n="marg435"></arrow.to.target> <lb></lb>while towards the ^{*} Northeaſt; another while toward the South <lb></lb>eaſt; others bearing her up by the Carine may make her onely to <lb></lb>riſe, and fall; and in ſum, theſe motions are for ſpecies two, one <lb></lb>that changeth the direction of the <emph type="italics"></emph>Teleſcope<emph.end type="italics"></emph.end> angularly, the other <lb></lb>lineally, without changing angle, that is, alwayes keeping the <lb></lb>tube of the Inſtrument parallel to its ſelf.</s></p><p type="margin"><s><margin.target id="marg434"></margin.target><emph type="italics"></emph>Different moti <lb></lb>ons depending on <lb></lb>the fluctuation of <lb></lb>the Ship.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg435"></margin.target>* <emph type="italics"></emph>Greco,<emph.end type="italics"></emph.end> which <lb></lb>the Latine Tran <lb></lb>ſlator according to <lb></lb>his uſual careleſſe <lb></lb>neſſe (to call it no <lb></lb>worſe) tranſlates <lb></lb><emph type="italics"></emph>Corum Ventum,<emph.end type="italics"></emph.end> <lb></lb>the Northweſt <lb></lb>Wind, for <emph type="italics"></emph>Ventum <lb></lb>Libanotum.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Tell me, in the next place, if we, having firſt directed <lb></lb><arrow.to.target n="marg436"></arrow.to.target> <lb></lb>the <emph type="italics"></emph>Teleſcope<emph.end type="italics"></emph.end> yonder away towards the Tower of ^{*} <emph type="italics"></emph>Burano,<emph.end type="italics"></emph.end> ſix <lb></lb>miles from hence, do turn it angularly to the right hand, or to the <lb></lb>left, or elſe upwards or downwards, but a ^{*}ſtraws breadth, what ef <lb></lb><arrow.to.target n="marg437"></arrow.to.target> <lb></lb>fect ſhall it have upon us touching the finding out of the ſaid tower?</s></p><p type="margin"><s><margin.target id="marg436"></margin.target><emph type="italics"></emph>Two mutations <lb></lb>made in the Tele <lb></lb>ſcope, depending on <lb></lb>the agitation of the <lb></lb>Ship.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg437"></margin.target>* This is a Caſtle <lb></lb>ſix Italian miles <lb></lb>from <emph type="italics"></emph>Venice<emph.end type="italics"></emph.end> <lb></lb>Northwards.</s></p><p type="main"><s>SALV. </s><s>It would make us immediately loſe ſight of it, for ſuch <lb></lb>a declination, though ſmall here, may import there hundreds and <lb></lb><arrow.to.target n="marg438"></arrow.to.target> <lb></lb>thouſands of yards.</s></p><p type="margin"><s><margin.target id="marg438"></margin.target>* <emph type="italics"></emph>Vnnerod' ug <lb></lb>na,<emph.end type="italics"></emph.end> the black or <lb></lb>paring of a nail.</s></p><p type="main"><s>SAGR. </s><s>But if without changing the angle, keeping the tube <lb></lb>alwayes parallel to it ſelf, we ſhould transfer it ten or twelve <lb></lb>yards farther off to the right or left hand, upwards or downwards, <lb></lb>what alteration would it make as to the Tower?</s></p><p type="main"><s>SALV. </s><s>The change would be abſolutely undiſcernable; for <lb></lb>that the ſpaces here and there being contained between parallel <lb></lb>rayes, the mutations made here and there, ought to be equal, and <lb></lb>becauſe the ſpace which the Inſtrument diſcovers yonder, is capa <lb></lb>ble of many of thoſe Towers; therefore we ſhall not loſe ſight of it.</s></p><p type="main"><s>SAGR. </s><s>Returning now to the Ship, we may undoubtedly af <lb></lb>firm, that the <emph type="italics"></emph>Teleſcope<emph.end type="italics"></emph.end> moving to the right or left, upwards, or <pb xlink:href="040/01/245.jpg" pagenum="227"></pb>downwards, and alſo forwards or backwards ten or fifteen fathom, <lb></lb>keeping it all the while parallel to its ſelf, the viſive ray cannot <lb></lb>ſtray from the point obſerved in the object, more than thoſe fif <lb></lb>teen fathom; and becauſe in a diſtance of eight or ten miles, the <lb></lb>Inſtrument takes in a much greater ſpace than the Gally or other <lb></lb>Veſſel kenn'd; therefore that ſmall mutation ſhall not make me <lb></lb>loſe ſight of her. </s><s>The impediment therefore, and the cauſe of <lb></lb>loſing the object cannot befall us, unleſſe upon the mutation made <lb></lb>angularly; ſince that <emph type="italics"></emph>Teleſcopes<emph.end type="italics"></emph.end> tranſportation higher or lower, to <lb></lb>the right, or to the left, by the agitation of the ſhip, cannot import <lb></lb>any great number of fathomes. </s><s>Now ſuppoſe that you had two <lb></lb><emph type="italics"></emph>Teleſcopes<emph.end type="italics"></emph.end> fixed, one at the Partners cloſe by the Deck, and the o <lb></lb>ther at the round top, nay at the main top, or main top-gallant <lb></lb>top, where you hang forth the <emph type="italics"></emph>Pennon<emph.end type="italics"></emph.end> or ſtreamer, and that they <lb></lb>be both directed to the Veſſel that is ten miles off, tell me, whe <lb></lb>ther you believe that any agitation of the ſhip, & inclination of the <lb></lb>Maſt, can make greater changes, as to the angle, in the higher tube, <lb></lb>than in the lower? </s><s>One wave ariſing, the prow will make the main <lb></lb>top give back fifteen or twenty fathom more than the foot of the <lb></lb>Maſt, and it ſhall carry the upper tube along with it ſo greata ſpace, <lb></lb>& the lower it may be not a palm; but the angle ſhall change in one <lb></lb>Inſtrument aſwell as in the other; and likewiſe a ſide-billow ſhall <lb></lb>bear the higher tube an hundred times as far to the Larboard or <lb></lb>Starboard, as it will the other below; but the angles change not at <lb></lb>all, or elſe alter both alike. </s><s>But the mutation to the right hand or <lb></lb>left, forwards or backwards, upwards or downwards, bringeth no <lb></lb>ſenſible impediment in the kenning of objects remote, though the <lb></lb>alteration of the angle maketh great change therein; Therefore it <lb></lb>muſt of neceſſity be confeſſed, that the uſe of the <emph type="italics"></emph>Teleſcope<emph.end type="italics"></emph.end> on the <lb></lb>round top is no more difficult than upon the Deck at the Partners; <lb></lb>ſeeing that the angular mutations are alike in both places.</s></p><p type="main"><s>SALV. </s><s>How much circumſpection is there to be uſed in affirming <lb></lb>or denying a propoſition? </s><s>I ſay again, thar hearing it reſolutely affir <lb></lb>med, that there is a greater motion made on the Maſts top, than at <lb></lb>its partners, every one will perſwade himſelf, that the uſe of the <emph type="italics"></emph>Te <lb></lb>leſcope<emph.end type="italics"></emph.end> is much more difficult above than below. </s><s>And thus alſo I w <lb></lb>ill excuſe thoſe Philoſophers, who grow impatient and fly out into <lb></lb>paſſion againſt ſuch as will not grant them, that that Cannon bullet <lb></lb>which they cleerly ſee to fall in a right line perpendicularly, doth <lb></lb>abſolutely move in that manner; but will have its motion to be by <lb></lb>an arch, and alſo very much inclined and tranſverſal: but let us <lb></lb>leave them in theſe labyrinths, and let us hear the other objections, <lb></lb>that our Author in hand brings againſt <emph type="italics"></emph>Copernicus.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>The Author goeth on to demonſtrate that in the Do <lb></lb>ctrine of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> it is requiſite to deny the Senſes, and the <pb xlink:href="040/01/246.jpg" pagenum="228"></pb>greateſt Senſations, as for inſtance it would be, if we that feel the <lb></lb><arrow.to.target n="marg439"></arrow.to.target> <lb></lb>reſpirations of a gentle gale, ſhould not feel the impulſe of a per <lb></lb>petual winde that beateth upon us with a velocity that runs more <lb></lb>than 2529 miles an hour, for ſo much is the ſpace that the centre <lb></lb>of the Earth in its annual motion paſſeth in an hour upon the cir <lb></lb>cumference of the grand Orb, as he diligently calculates; and <lb></lb>becauſe, as he ſaith, by the judgment of <emph type="italics"></emph>Copernicus, Cum terra <lb></lb>movetur circumpoſitus aër, motus tamen ejus, velocior licet ac ra <lb></lb>pidior celerrimo quocunque vento, à nohis non ſentiretur, ſed ſum <lb></lb>ma tum tranquilitas reputaretur, niſi alius motus accederet. </s><s>Quid <lb></lb>eſt verò decipi ſenſum, niſi hæc eſſet deceptio<emph.end type="italics"></emph.end>? [<emph type="italics"></emph>Which I make to <lb></lb>ſpeak to this ſenſe.<emph.end type="italics"></emph.end>] The circumpoſed air is moved with the Earth, <lb></lb>yet its motion, although more ſpeedy and rapid than the ſwifteſt <lb></lb>wind whatſoever, would not be perceived by us, but then would <lb></lb>be thought a great tranquillity, unleſſe ſome other motion ſhould <lb></lb>happen; what then is the deception of the ſenſe, if this be <lb></lb>not?</s></p><p type="margin"><s><margin.target id="marg439"></margin.target><emph type="italics"></emph>The annual mo <lb></lb>tion of the Earth <lb></lb>muſt cauſe a per <lb></lb>petual and ſtrong <lb></lb>winde.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>It muſt needs be that this Philoſopher thinketh, that <lb></lb>that Earth which <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> maketh to turn round, together with <lb></lb>the ambient air along the circumference of the great Orb, is not that <lb></lb>whereon we inhabit, but ſome other ſeparated from this; for that this <lb></lb>of ours carrieth us alſo along with it with the ſame velocity, as al <lb></lb><arrow.to.target n="marg440"></arrow.to.target> <lb></lb>ſo the circumjacent air: And what beating of the air can we feel, <lb></lb>when we fly with equal ſpeed from that which ſhould accoſt us? <lb></lb></s><s>This Gentleman forgot, that we no leſs than the Earth and air are <lb></lb>carried about, and that conſequently we are always touch'd by <lb></lb>one and the ſame part of the air, which yet doth not make us feel <lb></lb>it.</s></p><p type="margin"><s><margin.target id="marg440"></margin.target><emph type="italics"></emph>The air alwayes <lb></lb>touching us with <lb></lb>the ſame part of it <lb></lb>cannot make us <lb></lb>feel it.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>But I rather think that he did not ſo think; hear the <lb></lb>words which immediately follow. <emph type="italics"></emph>Præterea nos quoque rotamur <lb></lb>ex circumductione terræ &c.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Now I can no longer help nor excuſe him; do you <lb></lb>plead for him and bring him off, <emph type="italics"></emph>Simplicius.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I cannot thus upon the ſudden think of an excuſe that <lb></lb>pleaſeth me.</s></p><p type="main"><s>SALV. </s><s>Go to; take this whole night to think on it, and de <lb></lb>fend him to morrow; in the mean time let us hear ſome other of <lb></lb>his objections.</s></p><p type="main"><s>SIMP. </s><s>He proſecuteth the ſame Objection, ſhewing, that in the <lb></lb><arrow.to.target n="marg441"></arrow.to.target> <lb></lb>way of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> a man muſt deny his own ſenſes. </s><s>For that <lb></lb>this principle whereby we turn round with the Earth, either is <lb></lb>intrinſick to us, or external; that is, a rapture of that Earth; and <lb></lb>if it be this ſecond, we not feeling any ſuch rapture, it muſt be <lb></lb>confeſſed that the ſenſe of feeling, doth not feel its own object <lb></lb>touching it, nor its impreſſion on the ſenſible part: but if the prin <pb xlink:href="040/01/247.jpg" pagenum="229"></pb>ciple be intrinſecal, we ſhall not perceive a local motion that is de <lb></lb>rived from our ſelves, and we ſhall never diſcover a propenſion per <lb></lb>petually annexed to our ſelves.</s></p><p type="margin"><s><margin.target id="marg441"></margin.target><emph type="italics"></emph>He that will fol <lb></lb>low<emph.end type="italics"></emph.end> Copernicus, <lb></lb><emph type="italics"></emph>must deny his ſer <lb></lb>ſes.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>So that the inſtance of this Philoſopher lays its ſtreſs up <lb></lb>on this, that whether the principle by which we move round with <lb></lb>the Earth be either extern, or intern, yet however we muſt per <lb></lb>ceive it, and not perceiving it, it is neither the one nor the other, <lb></lb>and therefore we move not, nor conſequently the Earth. </s><s>Now I <lb></lb><arrow.to.target n="marg442"></arrow.to.target> <lb></lb>ſay, that it may be both ways, and yet we not perceive the ſame. <lb></lb></s><s>And that it may be external, the experiment of the boat ſupera <lb></lb>bundantly ſatisſieth me; I ſay, ſuperabundantly, becauſe it being <lb></lb>in our power at all times to make it move, and alſo to make it <lb></lb>ſtand ſtill, and with great exactneſs to make obſervation, whether <lb></lb>by ſome diverſity that may be comprehended by the ſenſe of feel <lb></lb>ing, we can come to know whether it moveth or no, ſeeing that <lb></lb>as yet no ſuch ſcience is obtained: Will it then be any matter of <lb></lb>wonder, if the ſame accident is unknown to us on the Earth, the <lb></lb>which may have carried us about perpetually, and we, without our <lb></lb><arrow.to.target n="marg443"></arrow.to.target> <lb></lb>being ever able to experiment its reſt? </s><s>You, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> as I be <lb></lb>lieve, have gone by boat many times to <emph type="italics"></emph>Padoua,<emph.end type="italics"></emph.end> and if you will <lb></lb>confeſs the truth, you never felt in your ſelf the participation of <lb></lb>that motion, unleſs when the boat running a-ground, or encoun <lb></lb>tring ſome obſtacle, did ſtop, and that you with the other Paſſen <lb></lb>gers being taken on a ſudden, were with danger over-ſet. </s><s>It <lb></lb>would be neceſſary that the Terreſtrial Globe ſhould meet with <lb></lb>ſome rub that might arreſt it, for I aſſure you, that then you <lb></lb>would diſcern the impulſe reſiding in you, when it ſhould toſs you <lb></lb>up towards the Stars. </s><s>It's true, that by the other ſenſes, but yet <lb></lb><arrow.to.target n="marg444"></arrow.to.target> <lb></lb>aſſiſted by Reaſon, you may perceive the motion of the boat, that <lb></lb>is, with the ſight, in that you ſee the trees and buildings placed on <lb></lb>the ſhoar, which being ſeparated from the boat, ſeem to move the <lb></lb><arrow.to.target n="marg445"></arrow.to.target> <lb></lb>contrary way. </s><s>But if you would by ſuch an experiment receive <lb></lb>intire ſatisfaction in this buſineſs of the Terreſtrial motion, look <lb></lb>on the ſtars, which upon this reaſon ſeem to move the contrary <lb></lb>way. </s><s>As to the wondering that we ſhould not feel ſuch a prin <lb></lb>ciple, ſuppoſing it to be internal, is a leſs reaſonable conceit; for <lb></lb>if we do not feel ſuch a one, that cometh to us from without, <lb></lb>and that frequently goeth away, with what reaſon can we expect <lb></lb>to feel it, if it immutably and continually reſides in us? </s><s>Now let <lb></lb>us ſee what you have farther to allege on this argument.</s></p><p type="margin"><s><margin.target id="marg442"></margin.target><emph type="italics"></emph>Our motion may <lb></lb>be either interne or <lb></lb>externe, and yet <lb></lb>we never perceive <lb></lb>or feel it.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg443"></margin.target><emph type="italics"></emph>The motion of a <lb></lb>Boat inſenſible to <lb></lb>thoſe that are with <lb></lb>in it, as to the ſenſe <lb></lb>of feeling.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg444"></margin.target><emph type="italics"></emph>The boats moti <lb></lb>on is perceptible to <lb></lb>the ſight joyn'd <lb></lb>with reaſon.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg445"></margin.target><emph type="italics"></emph>The terreſtrial <lb></lb>motion collected <lb></lb>from the ſtars.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>Take this ſhort exclamation. <emph type="italics"></emph>Ex hac itaque opinione <lb></lb>neceſſe est diffidere noſtris ſenſibus, ut penitùs fall acibus vel ſtupidis <lb></lb>in ſenſilibus, etiam conjunctiſſimis, dijudicandis. </s><s>Quam ergò ve <lb></lb>ritatem ſperare poſſumus à facultate adeò fallaci ortum trabentem<emph.end type="italics"></emph.end>? <lb></lb>[Which I render thus:] From this opinion likewiſe, we muſt of <pb xlink:href="040/01/248.jpg" pagenum="230"></pb>neceſſity ſuſpect our own ſenſes, as wholly fallible, or ſtupid in <lb></lb>judging of ſenſible things even very near at hand. </s><s>What truth <lb></lb>therefore can we hope for, to be derived from ſo deceiveable a fa <lb></lb>culty?</s></p><p type="main"><s>SALV. </s><s>But I deſire not to deduce precepts more profitable, or <lb></lb>more certain, learning to be more circumſpect and leſs confident <lb></lb>about that which at firſt bluſh is repreſented to us by the ſenſes, <lb></lb>which may eaſily deceive us. </s><s>And I would not have this Author <lb></lb>trouble himſelf in attemptiug to make us comprehend by ſenſe, <lb></lb>that this motion of deſcending Graves is ſimply right, and of <lb></lb>no other kind; nor let him exclaim that a thing ſo clear, manifeſt, <lb></lb>and obvious ſhould be brought in queſtion; for in ſo doing, he <lb></lb>maketh others believe, that he thinketh thoſe that deny that mo <lb></lb>tion to be abſolutely ſtreight, but rather circular, the ſtone did <lb></lb>ſenſibly ſee it to move in an arch, ſeeing that he inviteth their ſenſes <lb></lb>more than their Reaſon, to judg of that effect: which is not true, <lb></lb><emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> for like as I, that am indifferent in all theſe opini <lb></lb>ons, and onely in the manner of a Comedian, perſonate <emph type="italics"></emph>Coperni <lb></lb>cus<emph.end type="italics"></emph.end> in theſe our repreſentations, have never ſeen, nor thought <lb></lb>that I have ſeen that ſtone fall otherwiſe than perpendicularly, <lb></lb>ſo I believe, that to the eyes of all others it ſeemed to do the <lb></lb>ſame. </s><s>Better it is therefore, that depoſing that appearance in <lb></lb>which all agree, we make uſe of our Reaſon, either to confirm the <lb></lb>reality of that, or to diſcover its fallacy.</s></p><p type="main"><s>SAGR. </s><s>If I could any time meet with this Philoſopher, who <lb></lb>yet me thinks is more ſublime than the reſt of the followers of <lb></lb>the ſame doctrines, I would in token of my affection put him in <lb></lb>mind of an accident which he hath doubtleſs very often beheld; <lb></lb>from which, with great conformity to that which we now diſcourſe <lb></lb>of, it may be collected how eaſily one may be deceived by the bare <lb></lb>appearance, or, if you will, repreſentation of the ſenſe. </s><s>And the <lb></lb>accident is, the Moons ſeeming to follow thoſe that walk the ſtreets <lb></lb>in the night, with a pace equal to theirs, whilſt they ſee it go gli <lb></lb>ding along the Roofs of houſes, upon which it ſheweth juſt like a <lb></lb>cat, that really running along the ridges of houſes, leaveth them <lb></lb>behind. </s><s>An appearance that, did not reaſon interpoſe, would but <lb></lb>too manifeſtly delude the ſight.</s></p><p type="main"><s>SIMP. </s><s>Indeed there want not experiments that render us cer <lb></lb><arrow.to.target n="marg446"></arrow.to.target> <lb></lb>tain of the fallacy of the meer ſenſes; therefore ſuſpending ſuch <lb></lb>ſenſations for the preſent, let us hear the Arguments that follow <lb></lb>which are taken, as he ſaith, <emph type="italics"></emph>ex rerum naturâ.<emph.end type="italics"></emph.end> The firſt of which <lb></lb>is, that the Earth cannot of its own nature move with three moti <lb></lb>ons very different; or otherwiſe we muſt deny many manifeſt <lb></lb><arrow.to.target n="marg447"></arrow.to.target> <lb></lb>Axioms. </s><s>The firſt whereof is, that <emph type="italics"></emph>Omnïs effectus dependeat ab <lb></lb>aliquâ cauſâ; [i. </s><s>e.]<emph.end type="italics"></emph.end> that every effect dependeth on ſome cauſe. <pb xlink:href="040/01/249.jpg" pagenum="231"></pb>The ſecond, that <emph type="italics"></emph>Nulla res ſeipſam producat; [i. </s><s>e.]<emph.end type="italics"></emph.end> that nothing <lb></lb>produceth it ſelf: from whence it follows, that it is not poſſi <lb></lb>ble that the mover and moved ſhould be totally the ſame thing: <lb></lb>And this is manifeſt, not onely in things that are moved by an ex <lb></lb>trinſick mover; but it is gathered alſo from the principles pro <lb></lb>pounded, that the ſame holdeth true in the natural motion depen <lb></lb>dent on an intrinſick principle; otherwiſe, being that the mover, <lb></lb>as a mover, is the cauſe, and the thing moved, as moved, is the <lb></lb>effect, the ſame thing would totally be both the cauſe and effect. <lb></lb></s><s>Therefore a body doth not move its whole ſelf, that is, ſo as <lb></lb>that all moveth, and all is moved; but its neceſſary in the thing <lb></lb>moved to diſtinguiſh in ſome manner the efficient principle of the <lb></lb>motion, and that which with that motion is moved. </s><s>The third <lb></lb>Axiom is, that <emph type="italics"></emph>in rebus quæ ſenſui ſubjiciuntur, unum, quatenus <lb></lb>unum, unam ſolam rem producat; i. </s><s>e.<emph.end type="italics"></emph.end> That in things ſubject to <lb></lb>the ſenſes, one, as it is one, produceth but onely one thing: That <lb></lb>is, the ſoul in animals produceth its true divers operations, as the <lb></lb>ſight, the hearing, the ſmell, generation, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> but all theſe with <lb></lb>ſeveral inſtruments. </s><s>And in ſhort, in things ſenſible, the diverſi <lb></lb>ty of operations, is obſerved to derive it ſelf from the diverſity <lb></lb>that is in the cauſe. </s><s>Now if we put all theſe Axioms together, it <lb></lb><arrow.to.target n="marg448"></arrow.to.target> <lb></lb>will be a thing very manifeſt, that one ſimple body, as is the <lb></lb>Earth, cannot of its own nature move at the ſame time with <lb></lb>three motions, very divers: For by the foregoing ſuppoſitions, <lb></lb>all moveth not its ſelf all; it is neceſfary therefore to diſtinguiſh <lb></lb>in it three principles of its three motions; otherwiſe one and the <lb></lb>ſame principle would produce many motions; but if it contein in <lb></lb>it three principles of natural motions, beſides the part moved, it <lb></lb>ſhall not be a ſimple body, but compounded of three principle <lb></lb>movers, and of the part moved. </s><s>If therefore the Earth be a ſim <lb></lb><arrow.to.target n="marg449"></arrow.to.target> <lb></lb>ple body, it ſhall not move with three motions; nay more, it will <lb></lb>not move with any of thoſe which <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> aſcribeth to it, it <lb></lb>being to move but with one alone, for that it is manifeſt, by the <lb></lb>reaſons of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> that it moveth to its centre, as its parts do <lb></lb>ſhew, which deſcend at right angles to the Earths Spherical <lb></lb>Surface.</s></p><p type="margin"><s><margin.target id="marg446"></margin.target><emph type="italics"></emph>Arguments a <lb></lb>gainſt the Earths <lb></lb>motion taken,<emph.end type="italics"></emph.end> ex <lb></lb>rerum natura.</s></p><p type="margin"><s><margin.target id="marg447"></margin.target><emph type="italics"></emph>Three Axioms <lb></lb>that are ſuppoſed <lb></lb>manifeſt.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg448"></margin.target><emph type="italics"></emph>A ſimple body <lb></lb>as the Earth, can <lb></lb>not move with <lb></lb>three ſeveral moti <lb></lb>ons.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg449"></margin.target><emph type="italics"></emph>The Earth can <lb></lb>not move with any <lb></lb>of the motions aſſi <lb></lb>gned it by<emph.end type="italics"></emph.end> Coperni <lb></lb>cus.</s></p><p type="main"><s>SALV. </s><s>Many things might be ſaid, and conſidered touching <lb></lb>the connection of this argument; but in regard that we can re <lb></lb><arrow.to.target n="marg450"></arrow.to.target> <lb></lb>ſolve it in few words, I will not at this time without need inlarge <lb></lb>upon it; and ſo much the rather, becauſe the ſame Author hath <lb></lb>furniſhed me with an anſwer, when he ſaith that from one ſole prin <lb></lb>ple in animals, there are produced divers operations; ſo that for <lb></lb>the preſent my anſwer ſhall be, that in the ſame manner the Earth <lb></lb>from one onely principle deriveth ſeveral operations.</s></p><p type="margin"><s><margin.target id="marg450"></margin.target><emph type="italics"></emph>Anſwers to the <lb></lb>arguments contra <lb></lb>ry to the Earths <lb></lb>motion, taken<emph.end type="italics"></emph.end> ex <lb></lb>rerum natura.</s></p><p type="main"><s>SIMP. </s><s>But this anſwer will not at all ſatisfie the Author who <pb xlink:href="040/01/250.jpg" pagenum="232"></pb>makes the objection, yea, it is totally overthrown by that which <lb></lb>immediately after he addeth for a greater confirmation of his argu <lb></lb>ment, as you ſhall hear. </s><s>He re-inforceth his argument, I ſay, with <lb></lb><arrow.to.target n="marg451"></arrow.to.target> <lb></lb>another Axiome, which is this; That <emph type="italics"></emph>natura in rebus neceſſari is <lb></lb>nec deficiat, nec abundat: i.e.<emph.end type="italics"></emph.end> That nature in things neceſſary is <lb></lb>neither defective, nor ſuperfluous. </s><s>This is obvious to the obſer <lb></lb><arrow.to.target n="marg452"></arrow.to.target> <lb></lb>vers of natural things, and chiefly of animals, in which, becauſe <lb></lb>they are to move with many motions, Nature hath made many <lb></lb>flexures, and hath thereunto commodiouſly knitted the parts for <lb></lb>motion, as to the knees, to the hips, for the inabling of living <lb></lb>creatures to go, and run at their pleaſure. </s><s>Moreover in man he <lb></lb>hath framed many flexions, and joynts, in the elbow, and hand, to <lb></lb>enable them to perform many motions. </s><s>From theſe things the ar <lb></lb><arrow.to.target n="marg453"></arrow.to.target> <lb></lb>gument is taken againſt the threefold motion of the Earth. [<emph type="italics"></emph>Ei <lb></lb>ther the Body, that is one, and continuate, without any manner of <lb></lb>knittings or flexions, can exerciſe divers motions, or cannot: If it <lb></lb>can without them, then in vain hath nature framed the flexures in <lb></lb>animals; which is contrary to the Axiome: but if it cannot with <lb></lb>out them, then the Earth, one body, and continuate, and deprived of <lb></lb>flexures, and joynts, cannot of its own nature move with plurali <lb></lb>ty of motions.<emph.end type="italics"></emph.end>] You ſee now how craftily he falls upon your an <lb></lb>ſwer, as if he had foreſeen it.</s></p><p type="margin"><s><margin.target id="marg451"></margin.target><emph type="italics"></emph>A fourth Ax <lb></lb>iome againſt the <lb></lb>motion of the Earth<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg452"></margin.target><emph type="italics"></emph>Flexures neceſ <lb></lb>ſary in animals for <lb></lb>the diverſity of <lb></lb>their motions.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg453"></margin.target><emph type="italics"></emph>Another argu <lb></lb>ment againſt the <lb></lb>three fold motion of <lb></lb>the Earth.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Are you ſerious, or do you jeſt?</s></p><p type="main"><s>SIMP. </s><s>I ſpeak it with the beſt judgment I have.</s></p><p type="main"><s>SALV. </s><s>You muſt therefore ſee that you have as fortunate an <lb></lb>hand in defending the reply of this Philoſopher, againſt ſome o <lb></lb>ther rejoynders made to him; therefore anſwer for him, I pray <lb></lb>you, ſeeing we cannot have him here. </s><s>You firſt admit it for true, <lb></lb>that Nature hath made the joynts, flexures, and knuckles of li <lb></lb>ving creatures, to the intent that they might move with ſnndry <lb></lb>and divers motions; and I deny this propoſition; and ſay, that <lb></lb>theſe flexions are made, that the animal may move one, or more <lb></lb><arrow.to.target n="marg454"></arrow.to.target> <lb></lb>of its parts, the reſt remaining immoved: and I ſay, that as to the <lb></lb>ſpecies and differences of motions thoſe are of one kind alone, to <lb></lb>wit, all circular, and for this cauſe you ſee all the ends of the mo <lb></lb><arrow.to.target n="marg455"></arrow.to.target> <lb></lb>veable bones to be convex or concave, and of theſe ſome are ſphe <lb></lb>rical, as are thoſe that are to move every way, as in the ſhoulder <lb></lb><arrow.to.target n="marg456"></arrow.to.target> <lb></lb>joynt, the arme of the Enſigne doth, in diſplaying the Colours, <lb></lb>and that of the Falconer in bringing his Hawk to the lure; and <lb></lb>ſuch is the flexure of the elbow, upon which the hand turns round, <lb></lb>in boring with an augure: others are circular onely one way, and <lb></lb>as it were cylindrical, which ſerve for the members that bend one <lb></lb><arrow.to.target n="marg457"></arrow.to.target> <lb></lb>ly in one faſhion, as the joynts of the fingers one above another, <lb></lb>&c. </s><s>But without more particular inductions, one only general diſ <lb></lb>courſe may make this truth underſtood; and this is, that of a ſolid <pb xlink:href="040/01/251.jpg" pagenum="233"></pb>body that moveth, one of its extreams ſtanding ſtill without chan <lb></lb>ching place, the motion muſt needs be circular, and no other: and <lb></lb><arrow.to.target n="marg458"></arrow.to.target> <lb></lb>becauſe in the living creatures moving, one of its members doth <lb></lb>not ſeparate from the other its conterminal, therefore that motion <lb></lb>is of neceſſity circular.</s></p><p type="margin"><s><margin.target id="marg454"></margin.target><emph type="italics"></emph>The Flexures in <lb></lb>animals are not <lb></lb>made for the di <lb></lb>verſity of motions.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg455"></margin.target><emph type="italics"></emph>The motions of <lb></lb>animals are of one <lb></lb>ſort.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg456"></margin.target><emph type="italics"></emph>The ends of the <lb></lb>bones are all ro <lb></lb>tund.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg457"></margin.target><emph type="italics"></emph>It is demonſtra <lb></lb>ted, that the ends <lb></lb>of the bones are of <lb></lb>neceſſity to be ro <lb></lb>tund.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg458"></margin.target><emph type="italics"></emph>The motions of <lb></lb>animals are all <lb></lb>circular.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>How can this be? </s><s>For I ſee the animal move with an <lb></lb>hundred motions that are not circular, and very different from one <lb></lb>another, as to run, to skip, to climbe, to deſcend, to ſwim, and <lb></lb>many others. <lb></lb><arrow.to.target n="marg459"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg459"></margin.target><emph type="italics"></emph>Secondary moti <lb></lb>ons of animals de <lb></lb>pendent on the firſt<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Tis well: but theſe are ſecondary motions, depending <lb></lb>on the preceding motions of the joynts and flexures. </s><s>Upon the <lb></lb>plying of the legs to the knees, and the thighs to the hips, which <lb></lb>are circular motions of the parts, is produced, as conſequents, the <lb></lb>skip, or running, which are motions of the whole body, and theſe <lb></lb>may poſſibly not be circular. </s><s>Now becauſe one part of the ter</s></p><p type="main"><s><arrow.to.target n="marg460"></arrow.to.target> <lb></lb>reſtrial Globe is not required to move upon another part immove <lb></lb>able, but that the motion is to be of the whole body, there is no <lb></lb>need in it of flexures.</s></p><p type="margin"><s><margin.target id="marg460"></margin.target><emph type="italics"></emph>The<emph.end type="italics"></emph.end> Terreſtriall <lb></lb>Globe <emph type="italics"></emph>hath noe <lb></lb>need of flexures.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>This (will the aduerſary rejoyn) might be, if the moti <lb></lb>on were but one alone, but they being three, and thoſe very dif <lb></lb>ferent from each other, it is not poſſible that they ſhould concur in <lb></lb><arrow.to.target n="marg461"></arrow.to.target> <lb></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 anſwer of the <lb></lb>Philoſopher. </s><s>Againſt which I make oppoſition another way; and <lb></lb>ask you, whether you think that by way of joynts and flexures one <lb></lb>may adapt the terreſtrial Globe to the participation of three diffe <lb></lb>rent circular motions? </s><s>Do you not anſwer me? </s><s>Seeing you are <lb></lb>ſpeechleſſe, I will undertake to anſwer for the Philoſopher, who <lb></lb>would abſolutely reply that they might; for that otherwiſe it <lb></lb>would have been ſuperfluous, and beſides the purpoſe to have pro <lb></lb>poſed to conſideration, that nature maketh the flexions, to the <lb></lb>end, the moveable may move with different motions; and that <lb></lb>therefore the terreſtrial Globe having no flexures, it cannot have <lb></lb>thoſe three motions which are aſcribed to it. </s><s>For if he had <lb></lb>thought, that neither by help of flexures, it could be rendered apt <lb></lb>for ſuch motions, he would have freely affirmed, that the Globe <lb></lb>could not move with three motions. </s><s>Now granting this, I intreat <lb></lb><arrow.to.target n="marg462"></arrow.to.target> <lb></lb>you, and by you, if it were poſſible, that Philoſopher, Au <lb></lb>thor of the Argument, to be ſo courteous as to teach me in what <lb></lb>manner thoſe flexures ſhould be accommodated, ſo that thoſe <lb></lb>three motions might commodiouſly be excerciſed; and I grant you <lb></lb>four or ſix moneths time to think of an anſwer. </s><s>As to me, it ſeem <lb></lb>eth that one principle onely may cauſe a plurality of motions in <lb></lb><arrow.to.target n="marg463"></arrow.to.target> <lb></lb>the Terreſtrial Globe, juſt in the ſame manner that, as I told you <lb></lb>before, one onely principle with the help of various inſtruments <pb xlink:href="040/01/252.jpg" pagenum="234"></pb>produceth ſundry and divers motions in living creatures. </s><s>And as <lb></lb>to the flexures there is no need of them, the motions being of the <lb></lb>whole, and not of ſome particular parts; and becauſe they are <lb></lb>to be circular, the meer ſpherical figure is the moſt perfect articu <lb></lb>lation or flection that can be deſired.</s></p><p type="margin"><s><margin.target id="marg462"></margin.target><emph type="italics"></emph>It is deſired to <lb></lb>know, by means of <lb></lb>what flexures and <lb></lb>joynts the<emph.end type="italics"></emph.end> Terre <lb></lb>ſtrial Globe <emph type="italics"></emph>might <lb></lb>move with three <lb></lb>diverſe motions.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg463"></margin.target><emph type="italics"></emph>One only princi <lb></lb>ple may cauſe a <lb></lb>plurality of moti <lb></lb>ons in the Earth.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>The moſt that ought to be granted upon this, would be, <lb></lb>that it may hold true in one ſingle motion, but in three different <lb></lb>motions, in my opinion, and that of the Author, it is impoſſi <lb></lb>ble; as he going on, proſecuting the objection, writes in the fol <lb></lb>lowing words. <emph type="italics"></emph>Let us ſuppoſe, with<emph.end type="italics"></emph.end> Copernicus, <emph type="italics"></emph>that the Earth <lb></lb>moveth of its own faculty, and upon an intrinſick principle from <lb></lb>Weſt to Eaſt in the plane of the Ecliptick; and again, that it alſo <lb></lb>by an intrinſick principle revolveth about its centre, from Eaſt to <lb></lb>Weſt; and for a third motion, that it of its own inclination defle <lb></lb>cteth from North to South, and ſo back again.<emph.end type="italics"></emph.end> It being a conti <lb></lb>nuate body, and not knit together with joints and flections, our <lb></lb>fancy and our judgment will never be able to comprehend, that <lb></lb>one and the ſame natural and indiſtinct principle, that is, that <lb></lb>one and the ſame propenſion, ſhould actuate it at the ſame inſtant <lb></lb>with different, and as it were of contrary motions. </s><s>I cannot be <lb></lb>lieve that any one would ſay ſuch a thing, unleſſe he had under <lb></lb>took to maintain this poſition 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></lb><emph type="italics"></emph>Fingamus modo cum Copernico terram aliqua ſuâ vi, & ab indito <lb></lb>principio impelli ab Occaſu ad Ortum in Eclipticæ plano; tum rur <lb></lb>ſus revolvi ab indito etiam principio, circa ſuimet centrum, ab<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg464"></arrow.to.target> <lb></lb><emph type="italics"></emph>Ortu in Occaſum; tertio deſlecti rurſus ſu opte nutu à ſeptentrio <lb></lb>ne in Auſtrum, & viciſſim.<emph.end type="italics"></emph.end> I had thought, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that <lb></lb>that you might have erred in reciting the words of the Au <lb></lb>thor, but now I ſee that he, and that very groſſely, decei <lb></lb>veth himſelf; and to my grief, I find that he hath ſet himſelf to <lb></lb>oppoſe a poſition, which he hath not well underſtood; for theſe <lb></lb>are not the motions which <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> aſſignes to the Earth. <lb></lb></s><s>Where doth he find that <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> maketh the annual motion <lb></lb>by the Ecliptick contrary to the motion about its own centre? </s><s>It <lb></lb>muſt needs be that he never read his Book, which in an hundred <lb></lb>places, and in the very firſt Chapters affirmeth thoſe motions to <lb></lb>be both towards the ſame parts, that is from Weſt to Eaſt. <lb></lb></s><s>But without others telling him, ought he not of himſelf to com <lb></lb>prehend, that attributing to the Earth the motions that are ta <lb></lb>ken, one of them from the Sun, and the other from the <emph type="italics"></emph>pri <lb></lb>mum wobile,<emph.end type="italics"></emph.end> they muſt of neceſſity both move one and the ſame <lb></lb>way. <lb></lb><arrow.to.target n="marg465"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg464"></margin.target><emph type="italics"></emph>A groſſe error <lb></lb>of the oppoſer of<emph.end type="italics"></emph.end> <lb></lb>Copernicus.</s></p><p type="margin"><s><margin.target id="marg465"></margin.target><emph type="italics"></emph>A ſubtil and <lb></lb>withal ſimple ar <lb></lb>gument againſt<emph.end type="italics"></emph.end> <lb></lb>Copernicus.</s></p><p type="main"><s>SIMP. </s><s>Take heed that you do not erre your ſelf, and <emph type="italics"></emph>Coperni <lb></lb>cus<emph.end type="italics"></emph.end> alſo. </s><s>The Diurnal motion of the <emph type="italics"></emph>primum mobile,<emph.end type="italics"></emph.end> is it not from <pb xlink:href="040/01/253.jpg" pagenum="235"></pb>Eaſt to Weſt? </s><s>And the annual motion of the Sun through the <lb></lb>Ecliptick, is it not on the contrary from Weſt to Eaſt? </s><s>How <lb></lb>then can you make theſe motions being conferred on the Earth, of <lb></lb>contraries to become conſiſtents?</s></p><p type="main"><s>SAGR. Certainly, <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> hath diſcovered to us the original <lb></lb>cauſe of error of this Philoſopher; and in all probability he <lb></lb>would have ſaid the very ſame.</s></p><p type="main"><s>SALV. </s><s>Now if it be in our power, let us at leaſt recover <lb></lb><emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> from this errour, who ſeeing the Stars in their riſing <lb></lb>to appear above the Oriental Horizon, will make it no difficult <lb></lb>thing to underſtand, that in caſe that motion ſhould not belong </s></p><p type="main"><s><arrow.to.target n="marg466"></arrow.to.target> <lb></lb>to the Stars, it would be neceſſary to confeſſe, that the Horizon, <lb></lb>with a contrary motion would go down; and that conſequently <lb></lb>the Earth would reoolve in it ſelf a contrary way to that where <lb></lb>with the Stars ſeem to move, that is from Weſt to Eaſt, which <lb></lb>is according to the order of the Signes of the Zodiack. </s><s>As, in the <lb></lb>next place, to the other motion, the Sun being fixed in the cen <lb></lb>tre of the Zodiack, and the Earth moveable about its circumfe <lb></lb>rence, to make the Sun ſeem unto us to move about the ſaid Zo <lb></lb>diack, according to the order of the Signes, it is neceſſary, that <lb></lb>the E arth move according to the ſame order, to the end that the <lb></lb>Sun may ſeem to us to poſſeſſe alwayes that degree in the Zodiack, <lb></lb>that is oppoſite to the degree in which we find the Earth; and thus <lb></lb>the Earth running, <emph type="italics"></emph>verbi gratia,<emph.end type="italics"></emph.end> through <emph type="italics"></emph>Aries,<emph.end type="italics"></emph.end> the Sun will <lb></lb>appear to run thorow <emph type="italics"></emph>Libra<emph.end type="italics"></emph.end>; and the Earth paſſing thorow the <lb></lb>ſigne <emph type="italics"></emph>Taurus,<emph.end type="italics"></emph.end> the Sun will paſſe thorow <emph type="italics"></emph>Scorpio,<emph.end type="italics"></emph.end> and ſo the <lb></lb>Earth going thorow <emph type="italics"></emph>Gemini,<emph.end type="italics"></emph.end> the Sun ſeemeth to go thorow <emph type="italics"></emph>Sa <lb></lb>gittarius<emph.end type="italics"></emph.end>; but this is moving both the ſame way, that is accord <lb></lb>ing to the order of the ſignes; as alſo was the revolution of the <lb></lb>Earth about its own centre.</s></p><p type="margin"><s><margin.target id="marg466"></margin.target><emph type="italics"></emph>The error of the <lb></lb>Antagoniſt is ma <lb></lb>nifeſt, by decla <lb></lb>ring that the an <lb></lb>nual and diurnal <lb></lb>motions belonging <lb></lb>to the Earth are <lb></lb>both one way, and <lb></lb>not contrary.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I underſtand you very well, and know not what to al <lb></lb>ledge in excuſe of ſo groſſe an error.</s></p><p type="main"><s>SALV. </s><s>And yet, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> there is one yet worſe then this; and <lb></lb>it is, that he makes the Earth move by the diurnal motion about <lb></lb>its own centre from Eaſt to Weſt; and perceives not that if this <lb></lb>were ſo, the motion of twenty four hours appropriated by him <lb></lb>to the Univerſe, would, in our ſeeming, proceed from Weſt to <lb></lb>Eaſt; the quite contrary to that which we behold.</s></p><p type="main"><s>SIMP. </s><s>Oh ſtrange! Why I, that have ſcarce ſeen the firſt <lb></lb>elements of the Sphere, would not, I am confident, have erred <lb></lb>ſo horribly.</s></p><p type="main"><s>SALV. </s><s>Judg now what pains this Antagoniſt may be thought <lb></lb>to have taken in the Books of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> if he abſolutely invert <lb></lb><arrow.to.target n="marg467"></arrow.to.target> <lb></lb>the ſenſe of this grand and principal Hypotheſis, upon which is <lb></lb>founded the whole ſumme of thoſe things wherein <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> <pb xlink:href="040/01/254.jpg" pagenum="236"></pb>diſſenteth from the doctrine of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ptolomy.<emph.end type="italics"></emph.end> As again, <lb></lb><arrow.to.target n="marg468"></arrow.to.target> <lb></lb>to this third motion, which the Author aſſignes to the Terreſtrial <lb></lb>Globe, as the judgment of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> I know not which he would <lb></lb>mean thereby: it is not that queſtionleſſe, which <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> aſ <lb></lb>cribes unto it conjunctly with the other two, annual and diurnal, <lb></lb>which hath nothing to do with declining towards the South and <lb></lb>North; but onely ſerveth to keep the axis of the diurnal revoluti <lb></lb>on continually parallel to it ſelf; ſo that it muſt be confeſt, that <lb></lb>either the Authour did not underſtand this, or that elſe he diſſem <lb></lb>bled it. </s><s>But although this great miſtake ſufficeth to free us from <lb></lb>any obligation of a farther enquiry into his objections; yet ne <lb></lb>vertheleſſe I ſhall have them in eſteem; as indeed they deſerve to <lb></lb>be valued much before the many others of impertinent Antago <lb></lb>niſts. </s><s>Returning therefore to his objection, I ſay, that the two <lb></lb>motions, annual and diurnal, are not in the leaſt contrary, nay are <lb></lb>towards the ſame way, and therefore may depend on one and the <lb></lb>ſame principle. </s><s>The third is of it ſelf, and voluntarily ſo conſequen <lb></lb>tial to the annual, that we need not trouble our ſelves (as I ſhall <lb></lb>ſhew in its place) to ſtudy for principles either internal or external, <lb></lb>from which, as from its cauſe, to make it produced.</s></p><p type="margin"><s><margin.target id="marg467"></margin.target><emph type="italics"></emph>By another groſs <lb></lb>error it is ſeen that <lb></lb>the Antagoniſt had <lb></lb>but little ſtudied<emph.end type="italics"></emph.end> <lb></lb>Copernicus.</s></p><p type="margin"><s><margin.target id="marg468"></margin.target><emph type="italics"></emph>It is queſtioned, <lb></lb>whether the oppo <lb></lb>nent underſtood <lb></lb>the third motion <lb></lb>aſſigned to the <lb></lb>Earth by<emph.end type="italics"></emph.end> Coperni <lb></lb>cus.</s></p><p type="main"><s>SAGR. </s><s>I ſhall alſo, as being induced thereto by natural reaſon, <lb></lb>ſay ſomething to this Antagoniſt. </s><s>He will condemn <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> <lb></lb>unleſſe I be able to anſwer him to all objections, and to ſatisfie <lb></lb>him in all queſtions he ſhall ask; as if my ignorance were a neceſ <lb></lb>ſary argument of the falſhood of his Doctrine. </s><s>But if this way of <lb></lb>condemning Writers be in his judgment legal, he ought not to <lb></lb>think it unreaſonable, if I ſhould not approve of <emph type="italics"></emph>Arîſtotle<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Pto <lb></lb>lomy,<emph.end type="italics"></emph.end> when he cannot reſolve, better than my ſelf, thoſe doubts <lb></lb>which I propound to him, touching their Doctrine. </s><s>He asketh me, <lb></lb>what are the principles by which the Terreſtrial Globe is moved <lb></lb><arrow.to.target n="marg469"></arrow.to.target> <lb></lb>with the Annual motion through the Zodiack, and with the Diur <lb></lb>nal through the Equinoctial about its own axis. </s><s>I anſwer, that <lb></lb>they are like to thoſe by which <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> is moved about the Zodi <lb></lb>ack in thirty years, and about its own centre in a much ſhorter <lb></lb>time along the Equinoctial, as the collateral apparition and oc <lb></lb>cultation of its Globes doth evince. </s><s>They are principles like to <lb></lb>thoſe, whereby he ſcrupleth not to grant, that the Sun runneth tho <lb></lb>row the Ecliptick in a year, and revolveth about its own centre <lb></lb>parallel to the Equinoctial in leſſe than a moneth, as its ſpots doth <lb></lb>ſenſibly demonſtrate. </s><s>They are things like to thoſe whereby the <lb></lb>Medicean Stars run through the Zodiack in twelve years, and <lb></lb>all the while revolve in ſmall circles, and ſhort periods of time a <lb></lb>bout <emph type="italics"></emph>Jupiter.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg469"></margin.target><emph type="italics"></emph>The ſame argu <lb></lb>ment anſwered by <lb></lb>examples of the <lb></lb>like motions in o <lb></lb>ther cœleſtial bo <lb></lb>dies.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>This Author will deny all theſe things, as deluſions of <lb></lb>the fight, cauſed by the cryſtals of the <emph type="italics"></emph>Teleſcope.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/255.jpg" pagenum="237"></pb><p type="main"><s>SAGR. </s><s>But this would be to draw a further inconvenience up <lb></lb>on himſelf, in that he holdeth, that the bare eye cannot be decei <lb></lb>ved in judging of the right motion of deſcending graves, and yet <lb></lb>holds that it is deceived in beholding theſe other motions at ſuch <lb></lb>time as its viſive vertue is perfected, and augmented to thirty times <lb></lb>as much as it was before. </s><s>We tell him therefore, that the Earth in <lb></lb>like manner partaketh of the plurality of motions: and it is per <lb></lb>haps the ſame, whereby the Loadſtone hath its motion down <lb></lb>wards, as grave, and two circular motions, one Horizontal, and the <lb></lb>other Vertical under the Meridian. </s><s>But what more; tell me, <emph type="italics"></emph>Sim <lb></lb>plicius,<emph.end type="italics"></emph.end> between which do you think this Author would put a <lb></lb>greater difference, 'twixt right and circular motion, or 'twixt moti <lb></lb>on and reſt?</s></p><p type="main"><s>SIMP. 'Twixt motion and reſt, certainly. </s><s>And this is mani <lb></lb><arrow.to.target n="marg470"></arrow.to.target> <lb></lb>feſt, for that circular motion is not contrary to the right, according <lb></lb>to <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end>; nay, he granteth that they may mix with each o <lb></lb>ther; which it is impoſſible for motion and reſt to do.</s></p><p type="margin"><s><margin.target id="marg470"></margin.target><emph type="italics"></emph>Motion and reſt <lb></lb>are more different <lb></lb>than right motion <lb></lb>and circular.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Therefore its a propoſition leſſe improbable to place <lb></lb>in one natural body two internal principles, one to right motion, <lb></lb>and the other to circular, than two ſuch interne principles one to <lb></lb>motion, and the other to reſt. </s><s>Now both theſe poſitions agree to <lb></lb><arrow.to.target n="marg471"></arrow.to.target> <lb></lb>the natural inclination that reſideth in the parts of the Earth to re <lb></lb>turn to their whole, when by violence they are divided from it; <lb></lb>and they onely diſſent in the operation of the whole: for the lat <lb></lb>ter of them will have it by an interne principle to ſtand ſtill, and <lb></lb>the former aſcribeth to it the circular motion. </s><s>But by your con <lb></lb>ceſſion, and the confeſſion of this Philoſopher, two principles, one <lb></lb>to motion, and the other to reſt, are incompatible together, like as <lb></lb>their effects are incompatible: but now this evenes not in the two <lb></lb>motions, right, and circular, which have no repugnance to each <lb></lb>other.</s></p><p type="margin"><s><margin.target id="marg471"></margin.target><emph type="italics"></emph>One may more <lb></lb>rationally aſcribe <lb></lb>to the Earth two <lb></lb>internal principles <lb></lb>to the right, and <lb></lb>circular motion, <lb></lb>than two to motion <lb></lb>and reſt.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Adde this more, that in all probability it may be that <lb></lb><arrow.to.target n="marg472"></arrow.to.target> <lb></lb>the motion, that the part of the Earth ſeparated doth make whilſt <lb></lb>it returneth towards its whole, is alſo circular, as hath been alrea <lb></lb>dy declared; ſo that in all reſpects, as far as concernes the preſent <lb></lb>caſe, Mobility ſeemeth more likely than Reſt. </s><s>Now proceed, <lb></lb><emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> to what remains.</s></p><p type="margin"><s><margin.target id="marg472"></margin.target><emph type="italics"></emph>The motion of <lb></lb>the parts of the <lb></lb>Earth returning to <lb></lb>their whole may be <lb></lb>circular.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>The Authour backs his Argument with producing ano <lb></lb>ther abſurdity, that is, that the ſame motions agree to Natures ex <lb></lb>treamly different; but experience ſheweth, that the operations <lb></lb><arrow.to.target n="marg473"></arrow.to.target> <lb></lb>and motions of different natures, are different; and Reaſon con <lb></lb>firmeth the ſame: for otherwiſe we ſhould have no way left to <lb></lb>know and diſtinguiſh of natures, if they ſhould not have their <lb></lb>particular motions and operations, that might guide us to the <lb></lb>knowledge of their ſubſtances.</s></p> <pb xlink:href="040/01/256.jpg" pagenum="238"></pb><p type="margin"><s><margin.target id="marg473"></margin.target><emph type="italics"></emph>The diverſity of <lb></lb>motions helpeth us <lb></lb>in knowing the di <lb></lb>verſity of natures.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I have twice or thrice obſerved in the diſcourſes of this <lb></lb>Authour, that to prove that a thing is ſo, or ſo, he ſtill alledgeth, <lb></lb>that in that manner it is conformable with our underſtanding; or <lb></lb>that otherwiſe we ſhould never be able to conceive of it; or that <lb></lb>the <emph type="italics"></emph>Criterium<emph.end type="italics"></emph.end> of Philoſophy would be overthrown. </s><s>As if that na <lb></lb><arrow.to.target n="marg474"></arrow.to.target> <lb></lb>ture had firſt made mens brains, and then diſpoſed all things in <lb></lb>conformity to the capacity of their intellects. </s><s>But I incline rather <lb></lb>to think that Nature firſt made the things themſelves, as ſhe beſt <lb></lb>liked, and afterwards framed the reaſon of men capable of con <lb></lb>ceiving (though not without great pains) ſome part of her ſe <lb></lb>crets.</s></p><p type="margin"><s><margin.target id="marg474"></margin.target><emph type="italics"></emph>Nature firſt <lb></lb>made things as ſhe <lb></lb>pleaſed, and after <lb></lb>wards capacitated <lb></lb>mens underſtand <lb></lb>ings for conceiving <lb></lb>of them.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>I am of the ſame opinion. </s><s>But tell me, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> <lb></lb>which are theſe different natures, to which, contrary to expe <lb></lb>rience and reaſon, <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> aſſignes the ſame motions and ope <lb></lb>rations.</s></p><p type="main"><s>SIMP. </s><s>They are theſe. </s><s>The Water, the Air, (which doubt <lb></lb>leſſe are Natures different from the Earth) and all things that <lb></lb>are in thoſe elements compriſed, ſhall each of them have thoſe <lb></lb>three motions, which <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> pretends to be in the Terreſtriall <lb></lb>Globe; and my Authour proceedeth to demonſtrate Geometri <lb></lb><arrow.to.target n="marg475"></arrow.to.target> <lb></lb>cally, that, according to the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Doctrine, a cloud that is <lb></lb>ſuſpended in the Air, and that hangeth a long time over our <lb></lb>heads without changing place, muſt of neceſſity have all thoſe three <lb></lb>motions that belong to the Terreſtrial Globe. </s><s>The demonſtra <lb></lb>tion is this, which you may read your ſelf, for I cannot repeat it <lb></lb>without book.</s></p><p type="margin"><s><margin.target id="marg475"></margin.target>Copernicus <emph type="italics"></emph>er <lb></lb>roneouſly aſſigneth <lb></lb>the ſame operations <lb></lb>to different natures<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>I ſhall not ſtand reading of it, nay I think it an imper <lb></lb>tinency in him to have inſerted it, for I am certain, that no <lb></lb><emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> will deny the ſame. </s><s>Therefore admitting him what he <lb></lb>would demonſtrate, let us ſpeak to the objection, which in my <lb></lb>judgment hath no great ſtrength to conclude any thing contrary <lb></lb>to the <emph type="italics"></emph>Copernican Hypotheſis,<emph.end type="italics"></emph.end> ſeeing that it derogates nothing from <lb></lb>thoſe motions, and thoſe operations, whereby we come to the <lb></lb>knowledge of the natures, &c. </s><s>Anſwer me, I pray you, <emph type="italics"></emph>Simplici <lb></lb>us:<emph.end type="italics"></emph.end> Thoſe accidents wherein ſome things exactly concur, can <lb></lb>they ſerve to inform us of the different natures of thoſe things? <lb></lb><arrow.to.target n="marg476"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg476"></margin.target><emph type="italics"></emph>From commune <lb></lb>accidents one can <lb></lb>not know different <lb></lb>natures.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>No Sir: nay rather the contrary, for from the idendity <lb></lb>of operations and of accidents nothing can be inferred, but an <lb></lb>idendity of natures.</s></p><p type="main"><s>SALV. </s><s>So that the different natures of the Water, Earth, Air, <lb></lb>and other things conteined in theſe Elements, is not by you argu <lb></lb>ed from thoſe operations, wherein all theſe Elements and their af <lb></lb>fixes agree, but from other operations; is it ſo?</s></p><p type="main"><s>SIMP. </s><s>The very ſame.</s></p><p type="main"><s>SALV. </s><s>So that he who ſhould leave in the Elements all thoſe <pb xlink:href="040/01/257.jpg" pagenum="239"></pb>motions, operations, and other accidents, by which their natures <lb></lb>are diſtinguiſhed, would not deprive us of the power of coming <lb></lb>to the knowledge of them; although he ſhould remove thoſe o <lb></lb>perations, in which they unitedly concur, and which for that reaſon <lb></lb>are of no uſe for the diſtinguiſhing of thoſe natures.</s></p><p type="main"><s>SIMP. </s><s>I think your diſſertation 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></lb>conſtituted immoveable about the centre, is it not the opinion of <lb></lb>your ſelf, <emph type="italics"></emph>Ariſtotle, Prolomy,<emph.end type="italics"></emph.end> and all their ſectators?</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 quieſ <lb></lb>cence about the centre, there is no argument drawn of the different <lb></lb>natures of theſe Elements, and things elementary, but that <lb></lb>knowledge muſt be collected from other qualities not common; <lb></lb>and therefore whoſo ſhould deprive the Elements of this common <lb></lb>reſt only, and ſhould leave unto them all their other operations, <lb></lb>would not in the leaſt block up the way that leadeth to the know <lb></lb>ledge of their eſſences. </s><s>But <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> depriveth them onely of <lb></lb>this common reſt, and changeth the ſame into a common motion, <lb></lb>leaving them gravity, levity, the motions upwards, downwards, </s></p><p type="main"><s><arrow.to.target n="marg477"></arrow.to.target> <lb></lb>ſlower, faſter, rarity, denſity, the qualities of hot, cold, dry, moiſt, <lb></lb>and in a word, all things beſides. </s><s>Therefore ſuch an abſurdity, as <lb></lb>this Authour imagineth to himſelf, is no <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> poſition; nor <lb></lb>doth the concurrence in an identity of motion import any more or <lb></lb>leſs, than the concurrence in an identity of reſt about the diverſi <lb></lb>fying, or not diverſifying of natures. </s><s>Now tell us, if there be any <lb></lb>argument to the contrary.</s></p><p type="margin"><s><margin.target id="marg477"></margin.target><emph type="italics"></emph>The concurrence <lb></lb>of the Elements in <lb></lb>a common motion <lb></lb>importeth no more <lb></lb>or leſſe, than their <lb></lb>concurrence in a <lb></lb>common reſt.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>There followeth a fourth objection, taken from a natu <lb></lb><arrow.to.target n="marg478"></arrow.to.target> <lb></lb>ral obſervation, which is, <emph type="italics"></emph>That bodies of the ſame kind, have mo <lb></lb>tions that agree in kinde, or elſe they agree in reſt. </s><s>But by the<emph.end type="italics"></emph.end> Co <lb></lb>pernican Hypotheſis, <emph type="italics"></emph>bodies that agree in kinde, and are moſt ſem-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg479"></arrow.to.target> <lb></lb><emph type="italics"></emph>blable to one another, would be very diſcrepant, yea diametrically <lb></lb>repugnant as to motion; for that Stars ſo like to one another, would <lb></lb>be nevertheleſſe ſo unlike in motion, as that ſix Planets would perpe <lb></lb>tually turn round; but the Sun and all the fixeed Stars would ſtand <lb></lb>perpetually immoveable.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg478"></margin.target><emph type="italics"></emph>A fourth argu <lb></lb>ment againſt<emph.end type="italics"></emph.end> Co <lb></lb>pernicus.</s></p><p type="margin"><s><margin.target id="marg479"></margin.target><emph type="italics"></emph>Bodies of the <lb></lb>ſame kinde have <lb></lb>motions that agree <lb></lb>in kinde.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>The forme of the argument appeareth good; but yet <lb></lb>I believe that the application or matter is defective: and if the <lb></lb>Authour will but perſiſt in his aſſumption, the conſequence ſhall <lb></lb>make directly againſt him. </s><s>The Argument runs thus; Amongſt <lb></lb>mundane bodies, ſix there are that do perpetually move, and they <lb></lb><arrow.to.target n="marg480"></arrow.to.target> <lb></lb>are the ſix Planets; of the reſt, that is, of the Earth, Sun, and <lb></lb>fixed Stars, it is diſputable which of them moveth, and which <lb></lb>ſtands ſtill, it being neceſſary, that if the Earth ſtand ſtill, the Sun <lb></lb>and ſixed Stars do move; and it being alſo poſſible, that the Sun <pb xlink:href="040/01/258.jpg" pagenum="240"></pb>and fixed Stars may ſtand immoveable, in caſe the Earth ſhould <lb></lb>move: the matter of fact in diſpute is, to which of them we may <lb></lb>with moſt convenience aſcribe motion, and to which reſt. </s><s>Natural <lb></lb>reaſon dictates, that motion ought to be aſſigned to the bodies, <lb></lb>which in kind and eſſence moſt agree with thoſe bodies which do <lb></lb>undoubtedly move, and reſt to thoſe which moſt diſſent from them; <lb></lb>and in regard that an eternal reſt and perpetual motion are moſt <lb></lb>different, it is manifeſt, that the nature of the body always move <lb></lb>able ought to be moſt different from the body alwayes ſtable. <lb></lb></s><s>Therefore, in regard that we are dubious of motion and reſt, <lb></lb>let us enquire, whether by the help of ſome other eminent affecti <lb></lb>on, we may diſcover, which moſt agreeth with the bodies certain <lb></lb>ly moveable, either the Earth, or the Sun and fixed Stars. </s><s>But ſee <lb></lb>how Nature, in favour of our neceſſity and deſire, preſents us <lb></lb>with two eminent qualities, and no leſs different than motion and <lb></lb>reſt, and they are light and darkneſs, to wit, the being by nature <lb></lb>moſt bright, and the being obſcure, and wholly deprived of light: <lb></lb>the bodies therefore adorned with an internal and eternal ſplen <lb></lb>dour, are moſt different in eſſence from thoſe deprived of light: <lb></lb>The Earth is deprived of light, the Sun is moſt ſplendid in it ſelf, <lb></lb>and ſo are the fixed Stars. </s><s>The ſix Planets do abſolutely <lb></lb>want light, as the Earth; therefore their eſſence agreeth with <lb></lb>the Earth, and differeth from the Sun and fixed Stars. </s><s>There <lb></lb>fore is the Earth moveable, immoveable the Sunne and Starry <lb></lb>Sphere.</s></p><p type="margin"><s><margin.target id="marg480"></margin.target><emph type="italics"></emph>From the Earths <lb></lb>obſcurity, and the <lb></lb>ſplendour of the <lb></lb>Sun, and fixed <lb></lb>Stars, is argued, <lb></lb>that it is movea <lb></lb>ble, and they im <lb></lb>moveable.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>But the Authour will not grant, that the ſix Planets are <lb></lb>tenebroſe, and by that negative will he abide. </s><s>Or he will argue <lb></lb>the great conformity of nature between the ſix Planets, and the <lb></lb>Sun, and Fixed Stars; and the diſparity between them and the <lb></lb>Earth from other conditions than from tenebroſity and light; yea, <lb></lb>now I remember in the fifth objection, which followeth, he layeth <lb></lb>down the vaſt difference between the Earth and the Cœleſtial <lb></lb><arrow.to.target n="marg481"></arrow.to.target> <lb></lb>Bodies, in which he writeth, <emph type="italics"></emph>That the<emph.end type="italics"></emph.end> Copernican Hypotheſis <lb></lb><emph type="italics"></emph>would make great confuſion and perturbation in the Syſteme of the <lb></lb>Vniverſe, and amongst its parts:<emph.end type="italics"></emph.end> As for inſtance, amongſt Cœ <lb></lb><arrow.to.target n="marg482"></arrow.to.target> <lb></lb>bodies that are immutable and incorruptible, according to <emph type="italics"></emph>Ariſto <lb></lb>tle, Tycho,<emph.end type="italics"></emph.end> and others; amongſt bodies, I ſay, of ſuch nobility, by <lb></lb>the confeſſion of every one, and <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> himſelf, who affirmeth <lb></lb>them to be ordinate, and diſpoſed in a perfect conſtitution, and <lb></lb>removeth from them all inconſtancy of vertue amongſt, theſe bo <lb></lb>dies, I ſay once more, ſo pure, that is to ſay, amongſt <emph type="italics"></emph>Venus, Mars, <lb></lb>&c.<emph.end type="italics"></emph.end> to place the very ſink of all corruptible matters, to wit, the <lb></lb>Earth, Water, Air, and all mixt bodies.</s></p><p type="margin"><s><margin.target id="marg481"></margin.target><emph type="italics"></emph>A fifih argu <lb></lb>ment againſt<emph.end type="italics"></emph.end> Co <lb></lb>pernicus.</s></p><p type="margin"><s><margin.target id="marg482"></margin.target><emph type="italics"></emph>Another diffe <lb></lb>rence between the <lb></lb>Earth and the Cœ <lb></lb>leſtial bodies, ta <lb></lb>ken from purity & <lb></lb>impurity.<emph.end type="italics"></emph.end></s></p><p type="main"><s>But how much properer a diſtribution, and more with nature, <lb></lb>yea with God himſelf, the Architect, is it, to ſequeſter the pure <pb xlink:href="040/01/259.jpg" pagenum="241"></pb>from the impure, the mortal from the immortal, as other Schools <lb></lb>teach; which tell us that theſe impure and frail matters are con <lb></lb>teined within the anguſt concave of the Lunar Orb, above which <lb></lb>with uninterrupted Series the things Celeſtial diſtend themſelves.</s></p><p type="main"><s>SALV. It's true that the Copernican Syſteme introduceth di <lb></lb><arrow.to.target n="marg483"></arrow.to.target> <lb></lb>ſtraction in the univerſe of <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end>; but we ſpeak of our own <lb></lb>Univerſe, that is true and real. </s><s>Again if this Author will infer <lb></lb>the diſparity of eſſence between the Earth and Celeſtial bodies <lb></lb>from the incorruptibility of them, and the corruptibility of it in <lb></lb>the method of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> from which diſparity he concludeth mo <lb></lb>tion to belong to the Sun and fixed Stars, and the immobility of <lb></lb>the Earth, he will flatter himſelf with a Paralogiſme, ſuppoſing <lb></lb><arrow.to.target n="marg484"></arrow.to.target> <lb></lb>that which is in queſtion; for <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> inferreth the incorruptibi <lb></lb>lity of Celeſtial bodies from motion, which is in diſpute, whe <lb></lb>ther it belongeth to them or to the Earth. </s><s>Of the vanity of theſe <lb></lb>Rhetorical Illations enough hath been ſpoken. </s><s>And what can be <lb></lb><arrow.to.target n="marg485"></arrow.to.target> <lb></lb>more fond, than to ſay, that the Earth and Elements are bani <lb></lb>ſhed and ſequeſtred from the Celeſtial Spheres, and confined <lb></lb>within the Lunar Orb? </s><s>Is, not then the Moons Orb one of the <lb></lb>Celeſtial Spheres, and according to conſent compriſed in the <lb></lb>middle of all the reſt? </s><s>Its a new way to ſeparate the pure from <lb></lb>the impure, and the ſick from the ſound, to aſſigne the infected <lb></lb>quarters in the heart of the City: I had thought that the ^{*} Peſt <lb></lb><arrow.to.target n="marg486"></arrow.to.target> <lb></lb>houſe ought to have been removed as far off as was poſſible. <lb></lb><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> admireth the diſpoſition of the parts of the Univerſe, <lb></lb>for that God hath conſtituted the grand Lamp, which is to give <lb></lb>light all over his Temple in the centre of it, and not on one <lb></lb>ſide. </s><s>And as to the Earths being betwixt <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Mars,<emph.end type="italics"></emph.end> <lb></lb>we will but hint the ſame; and do you, in favour of this Author, <lb></lb>trie to remove it thence. </s><s>But let us not ^{*} mix theſe Rhetorical <lb></lb><arrow.to.target n="marg487"></arrow.to.target> <lb></lb>Flowers with ſolid Demonſtrations, rather let us leave them to <lb></lb>the Orators, or if you will to the Poets, who know how in their <lb></lb>drolling way to exalt by their prayſes things moſt ſordid, yea and <lb></lb>ſometimes moſt pernicious. </s><s>And if any thing elſe remain, let us <lb></lb>diſpatch it, as we have done the reſt.</s></p><p type="margin"><s><margin.target id="marg483"></margin.target>Copernicus <emph type="italics"></emph>in <lb></lb>troduceth confuſion <lb></lb>in the Univerſe of<emph.end type="italics"></emph.end> <lb></lb>Ariſtotle.</s></p><p type="margin"><s><margin.target id="marg484"></margin.target><emph type="italics"></emph>The Paralogiſme <lb></lb>of the Author of <lb></lb>Anti-Tycho.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg485"></margin.target><emph type="italics"></emph>It ſeemeth a <lb></lb>folly to affirm the <lb></lb>Earth to be with <lb></lb>out the Heavens.<emph.end type="italics"></emph.end></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"></emph>Intrecciare,<emph.end type="italics"></emph.end> to <lb></lb>twine flowers in a <lb></lb>garland.</s></p><p type="main"><s>SIMP. </s><s>There is the ſixth and laſt argument, wherein he ma <lb></lb><arrow.to.target n="marg488"></arrow.to.target> <lb></lb>keth it a very improbale thing. [<emph type="italics"></emph>That a corruptible and diſſipable <lb></lb>body ſhould move with a perpetual and regular motion; and this <lb></lb>he confirmeth with the example of living creatures, which moving <lb></lb>with a motion natural to them, yet grow weary, and have need of <lb></lb>repoſe to reſtore their ſtrength.<emph.end type="italics"></emph.end>] But what hath this motion to do <lb></lb>with that of the Earth, that in compariſon to theirs is immenſe? <lb></lb></s><s>Beſides, to make it move with three motions that run and draw <lb></lb>ſeveral wayes: Who would ever aſſert ſuch Paradoxes, unleſſe <lb></lb>he had ſworn to be their defender? </s><s>Nor doth that avail in this <pb xlink:href="040/01/260.jpg" pagenum="242"></pb>caſe, which <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> alledgeth, that by reaſon this motion is <lb></lb>natural to the Earth and not violent, it worketh contrary effects <lb></lb>to violent motions; and that thoſe things diſſolve and cannot <lb></lb>long ſubſiſt, to which impulſe is conferred, but thoſe ſo made <lb></lb>by nature do continue in their perfect diſpoſure; this anſwer ſuf <lb></lb>ficeth not, I ſay, for it is overthrown by that of ours. </s><s>For the a <lb></lb>nimal is a natural body, and not made by art, and its motion is <lb></lb>natural, deriving it ſelf from the ſoul, that is, from an intrinſick <lb></lb>principle; and that motion is violent, whoſe beginning is with <lb></lb>out, and on which the thing moved conferreth nothing; how <lb></lb>ever, if the animal continueth its motion any long time, it grows <lb></lb>weary, and alſo dyeth, if it obſtinately ſtrive to perſiſt therein. <lb></lb></s><s>You ſee then that in nature we meet on all ſides with notions con <lb></lb>trary to the <emph type="italics"></emph>Copernican Hypotheſis,<emph.end type="italics"></emph.end> and none in favour of it. </s><s>And <lb></lb>for that I have nothing more wherein to take the part of this Op <lb></lb>ponent, hear what he produceth againſt <emph type="italics"></emph>Keplerus<emph.end type="italics"></emph.end> (with whom <lb></lb>he diſputeth) upon that argument, which the ſaid <emph type="italics"></emph>Kepler<emph.end type="italics"></emph.end> bringeth <lb></lb>againſt thoſe who think it an inconvenient, nay impoſſible thing, <lb></lb>to augment the Starry Sphere immenſely, as the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Hy <lb></lb>potheſis requireth. <emph type="italics"></emph>Kepler<emph.end type="italics"></emph.end> therefore inſtanceth, ſaying: <emph type="italics"></emph>Difficili <lb></lb>us ect, accidens præter modulum ſubjecti intendere, quàm ſub-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg489"></arrow.to.target> <lb></lb><emph type="italics"></emph>jectum ſine accidente augere. </s><s>Copernicus ergo veriſimilius facit, <lb></lb>qui auget Orbem Stellarum fixarum abſque motu, quam Ptolomæus, <lb></lb>qui auget motum fixarum immenſà velocitate.<emph.end type="italics"></emph.end> [Which makes this <lb></lb>Engliſh.] Its harder to ſtretch the accident beyond the model of the <lb></lb>ſubject than to augment the ſubject without the accident. <emph type="italics"></emph>Coperni-<emph.end type="italics"></emph.end> <lb></lb>hath more probability on his ſide, who encreaſeth the Orb of the <lb></lb>fixed Stars without motion, than <emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> who augmenteth the <lb></lb>motion of the fixed Stars to an immenſe degree of velocity. <lb></lb><arrow.to.target n="marg490"></arrow.to.target> <lb></lb>Which objection the Author anſwereth, wondering how much <lb></lb><emph type="italics"></emph>Kepler<emph.end type="italics"></emph.end> deceived himſelf, in ſaying, that in the Ptolomaick Hypothe <lb></lb>ſis the motion encreaſeth beyond the model of the ſubject, for in <lb></lb>his judgment it doth not encreaſe, ſave onely in conformity to the <lb></lb>model, and that according to its encreaſement, the velocity of <lb></lb><arrow.to.target n="marg491"></arrow.to.target> <lb></lb>the motion is augmented. </s><s>Which he proveth by ſuppoſing a ma <lb></lb>chine to be framed, that maketh one revolution in twenty four <lb></lb>hours, which motion ſhall be called moſt ſlow; afterwards ſup <lb></lb>poſing its ſemidiameter to be prolonged, as far as to the diſtance <lb></lb>of the Sun, its extreme will equal the velocity of the Sun; and <lb></lb>it being cantinued out unto the Starry Sphere, it will equal the <lb></lb>velocity of the fixed Stars, though in the circumferrnce of the <lb></lb>machine it be very ſlow. </s><s>Now applying this conſideration of the <lb></lb>machine to the Starry Sphere, let us imagine any point in its ſe <lb></lb>midiameter, as neer to the centre as is the ſemidiameter of the ma <lb></lb>chine; the ſame motion that in the Starry Sphere is exceeding <pb xlink:href="040/01/261.jpg" pagenum="243"></pb>ſwift, ſhall in that point be exceeding ſlow; But the great mag <lb></lb>nitude of the body is that which maketh it of exceeding ſlow, to <lb></lb>become exceeding ſwift, although it continueth ſtill the ſame, and <lb></lb>thus the velocity encreaſeth, not beyond the model of the ſub <lb></lb>ject, but rather according to it, and to its magnitude; very dif <lb></lb>ferently from the imagination of <emph type="italics"></emph>Kepler.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg488"></margin.target><emph type="italics"></emph>A ſixth argu <lb></lb>ment againſt<emph.end type="italics"></emph.end> Co <lb></lb>pernicus, <emph type="italics"></emph>taken <lb></lb>from animals, who <lb></lb>have need of reſt, <lb></lb>though their moli <lb></lb>on be natural.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg489"></margin.target><emph type="italics"></emph>An argument <lb></lb>from<emph.end type="italics"></emph.end> Kepler <emph type="italics"></emph>in fa <lb></lb>vour of<emph.end type="italics"></emph.end> Coperni <lb></lb>cus.</s></p><p type="margin"><s><margin.target id="marg490"></margin.target><emph type="italics"></emph>The Author of <lb></lb>the Anti Tycho op <lb></lb>poſeth<emph.end type="italics"></emph.end> Kepler.</s></p><p type="margin"><s><margin.target id="marg491"></margin.target><emph type="italics"></emph>The velocity of <lb></lb>the circular moti <lb></lb>on increaſeth, ac <lb></lb>cording to the en <lb></lb>creaſe of the dia <lb></lb>meter of the circle.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>I do not believe that this Author hath entertained ſo <lb></lb>mean and poor a conceit of <emph type="italics"></emph>Kepler,<emph.end type="italics"></emph.end> as to perſwade himſelf that <lb></lb>he did not underſtand, that the higheſt term of a line drawn from <lb></lb>the centre unro the Starry Sphere, moveth more ſwiftly than a <lb></lb>point of the ſame line taken within a yard or two of the centre. </s><s>And <lb></lb>therefore of neceſſity he muſt have conceived and comprehend <lb></lb><arrow.to.target n="marg492"></arrow.to.target> <lb></lb>ed that the mind and intention of <emph type="italics"></emph>Kepler<emph.end type="italics"></emph.end> was to have ſaid, that <lb></lb>it is leſſe inconvenient to encreaſe an immoveable body to an ex <lb></lb>traordinary magnitude, than to aſcribe an extraordinary velocity <lb></lb>to a body, though very bigge, having regard to the model, <lb></lb>that is to the gauge, and to the example of other natural bodies; <lb></lb>in which we ſee, that the diſtance from the centre encreaſing, the <lb></lb>velocity diminiſheth; that is, that the periods of their circulati <lb></lb>ons take up longer times. </s><s>But in reſt which is not capable of aug <lb></lb><arrow.to.target n="marg493"></arrow.to.target> <lb></lb>mentation or diminution, the grandure or ſmalneſſe of the body <lb></lb>maketh no differeuce. </s><s>So that if the anſwer of the Author would <lb></lb>be directed againſt the argument of <emph type="italics"></emph>Kepler,<emph.end type="italics"></emph.end> it is neceſſary, that <lb></lb>that Author doth hold, that to the movent principle its one and the <lb></lb>ſame to move in the ſame time a body very ſmall, or very im <lb></lb>menſe, in regard that the augmentation of velocity inſeparably <lb></lb>attends the augmentation of the maſſe. </s><s>But this again is contrary <lb></lb><arrow.to.target n="marg494"></arrow.to.target> <lb></lb>to the Architectonical rule of nature, which doth in the leſſer <lb></lb>Spheres, as we ſee in the Planets, and moſt ſenſibly in the Medi <lb></lb>cean Stars, obſerve to make the leſſer Orbs to circulate in ſhorter <lb></lb>times: Whence the time of <emph type="italics"></emph>Saturns<emph.end type="italics"></emph.end> revolution is longer than all <lb></lb>the times of the other leſſer Spheres, it being thirty years; now <lb></lb>the paſſing from this to a Sphere very much bigger, and to make <lb></lb>it move in 24. hours, may very well be ſaid to exceed the rules of <lb></lb>the model. </s><s>So that if we would but attentively conſider it, the <lb></lb>Authors anſwer oppoſeth not the intent and ſenſe of the argument, <lb></lb>but the expreſſing and manner of delivering of it; where again <lb></lb>the Author is injurious, and cannot deny but that he artificially <lb></lb>diſſembled his underſtanding of the words, that he might charge <lb></lb><emph type="italics"></emph>Kepler<emph.end type="italics"></emph.end> with groſſe ignorance; but the impoſture was ſo very dull <lb></lb>and obvions, that he could not with all his craft alter the opini <lb></lb>on which <emph type="italics"></emph>Kepler<emph.end type="italics"></emph.end> hath begot of his Doctrine in the minds of all <lb></lb>the Learned. </s><s>As in the next place, to the inſtance againſt the <lb></lb>perpetual motion of the Earth, taken from the impoſſibility of <lb></lb>its moving long without wearineſſe, in regard that living crea <pb xlink:href="040/01/262.jpg" pagenum="244"></pb>tures themſelves, which yet move naturally, and from an intern <lb></lb>principle, do grow weary, and have need of reſt to relax and re <lb></lb>freſh their members --------</s></p><p type="margin"><s><margin.target id="marg492"></margin.target><emph type="italics"></emph>An explanation <lb></lb>of the true ſenſe of<emph.end type="italics"></emph.end> <lb></lb>Kepler <emph type="italics"></emph>and his de <lb></lb>fence.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg493"></margin.target><emph type="italics"></emph>The greatneſſe <lb></lb>and ſmalneſſe of <lb></lb>the body make a <lb></lb>difference in moti <lb></lb>on and not in reſt.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg494"></margin.target><emph type="italics"></emph>The order of na <lb></lb>ture is to make the <lb></lb>leſſer Orbs to cir <lb></lb>culate in ſhorter <lb></lb>times, and the big <lb></lb>ger in longer times.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Methinks I hear <emph type="italics"></emph>Kepler<emph.end type="italics"></emph.end> anſwer him to that, that <lb></lb>there are ſome kinde of animals which refreſh themſelves after <lb></lb>wearineſſe, by rowling on the Earth; and that therefore there <lb></lb><arrow.to.target n="marg495"></arrow.to.target> <lb></lb>is no need to fear that the Terreſtrial Globe ſhould tire, nay it <lb></lb>may be reaſonably affirmed, that it enjoyeth a perpetual & moſt <lb></lb>tranquil repoſe, keeping it ſelf in an eternal rowling.</s></p><p type="margin"><s><margin.target id="marg495"></margin.target><emph type="italics"></emph>The feigned an <lb></lb>ſwer of<emph.end type="italics"></emph.end> Kepler <emph type="italics"></emph>co <lb></lb>vered with an ar <lb></lb>tificial Irony.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>You are too tart and Satyrical, <emph type="italics"></emph>Sagredus:<emph.end type="italics"></emph.end> but let us <lb></lb>lay aſide jeſts, whilſt we are treating of ſerious things.</s></p><p type="main"><s>SAGR. </s><s>Excuſe me, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> this that I ſay is not ſo abſo <lb></lb>lutely beſides the buſineſs, as you perhaps make it; for a motion <lb></lb>that ſerveth inſtead of reſt, and removeth wearineſs from a body <lb></lb>tired with travail, may much more eaſily ſerve to prevent the co <lb></lb><arrow.to.target n="marg496"></arrow.to.target> <lb></lb>ming of that wearineſs, like as preventive remedies are more eaſie <lb></lb>than curative. </s><s>And I hold for certain, that if the motion of ani <lb></lb>mals ſhould proceed in the ſame manner as this that is aſcribed to <lb></lb>the Earth, they would never grow weary; Seeing that the weari <lb></lb>neſs of the living creature, deriveth it ſelf, in my opinion, from <lb></lb><arrow.to.target n="marg497"></arrow.to.target> <lb></lb>the imployment of but one part alone in the moving of its ſelf, <lb></lb>and all the reſt of the body; as <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> in walking, the thighs and <lb></lb>the legs onely are imployed for carrying themſelves and all the <lb></lb>reſt: on the contrary, you ſee the motion of the heart to be as it <lb></lb>were indefatigable, becauſe it moveth it ſelf alone. </s><s>Beſides, I <lb></lb><arrow.to.target n="marg498"></arrow.to.target> <lb></lb>know not how true it may be, that the motion of the animal is na <lb></lb>tural, and not rather violent: nay, I believe that one may truly <lb></lb>ſay, that the ſoul naturally moveth the members of an animal with <lb></lb>a motion preternatural, for if the motion upwards is preternatu <lb></lb>ral to grave bodies, the lifting up of the legs, and the thighs, <lb></lb>which are grave bodies, in walking, cannot be done without vio <lb></lb>lence, and therefore not without labour to the mover. </s><s>The <lb></lb>climbing upwards by a ladder carrieth the grave body contrary to <lb></lb>its natural inclination upwards, from whence followeth wearineſs, <lb></lb>by reaſon of the bodies natural averſneſs to that motion: but in <lb></lb>moving a moveable with a motion, to which it hath no averſion, <lb></lb><arrow.to.target n="marg499"></arrow.to.target> <lb></lb>what laſſitude, what diminution of vertue and ſtrength need we <lb></lb>fear in the mover? </s><s>and how ſhould the forces waſte, where they <lb></lb>are not at all imployed?</s></p><p type="margin"><s><margin.target id="marg496"></margin.target><emph type="italics"></emph>Animals would <lb></lb>not grow weary of <lb></lb>their motion, pro <lb></lb>ceeding as that <lb></lb>which is aſſigned <lb></lb>to the terreſtrial <lb></lb>Globe.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg497"></margin.target><emph type="italics"></emph>The cauſe of the <lb></lb>wearineſſe of ani <lb></lb>mals.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg498"></margin.target><emph type="italics"></emph>The motion of <lb></lb>an animal is rather <lb></lb>to be called violent <lb></lb>than natural.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg499"></margin.target><emph type="italics"></emph>The ſtrength di <lb></lb>miniſheth not, <lb></lb>where it is not im <lb></lb>ployed.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>They are the contrary motions wherewith the Earth is <lb></lb>pretended to move, againſt which the Authour produceth his ar <lb></lb>gument.</s></p><p type="main"><s>SAGR. </s><s>It hath been ſaid already, that they are no wiſe con <lb></lb>traries, and that herein the Authour is extteamly deceived, ſo <lb></lb>that the whole ſtrength of the argument recoileth upon the Op <pb xlink:href="040/01/263.jpg" pagenum="245"></pb>ponent himſelf, whilſt he will make the <emph type="italics"></emph>Firſt Mover<emph.end type="italics"></emph.end> to hurry <lb></lb><arrow.to.target n="marg500"></arrow.to.target> <lb></lb>along with it all the inferiour Spheres, contrary to the motion <lb></lb>which they themſelves at the ſame time exerciſe. </s><s>It belongs there <lb></lb>fore to the <emph type="italics"></emph>Primum Mobile<emph.end type="italics"></emph.end> to grow weary, which beſides the <lb></lb>moving of its ſelf is made to carry ſo many other Spheres, and <lb></lb>which alſo ſtrive againſt it with a contrary motion. </s><s>So that <lb></lb>the ultimate concluſion that the Authour inferred, ſaying, that <lb></lb>diſcourſing of the effects of Nature, a man alwayes meets with <lb></lb>things that favour the opinion of <emph type="italics"></emph>Ariſtoile<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ptolomy,<emph.end type="italics"></emph.end> and ne <lb></lb>ver any one that doth not interfer with <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> ſtands in need <lb></lb>of great conſideration; and it is better to ſay, that one of theſe <lb></lb>two <emph type="italics"></emph>Hypotheſes<emph.end type="italics"></emph.end> being true, and the other neceſſarily falſe, it is <lb></lb>impoſſible that a man ſhould ever be able to finde any argu <lb></lb>ment, experience, or right reaſon, in favour of that which is <lb></lb><arrow.to.target n="marg501"></arrow.to.target> <lb></lb>falſe, like as to the truth none of theſe things can be repugnant. <lb></lb></s><s>Vaſt difference, therefore, muſt needs be found between the rea <lb></lb>ſons and arguments produced by the one and other party, for and <lb></lb>againſt theſe two opinions, the force of which I leave you your <lb></lb>ſelf to judge of, <emph type="italics"></emph>Simplicius.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg500"></margin.target><emph type="italics"></emph>The argument <lb></lb>of<emph.end type="italics"></emph.end> Claramontius <lb></lb><emph type="italics"></emph>recoileth upon him <lb></lb>ſelf.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg501"></margin.target><emph type="italics"></emph>True Propoſiti <lb></lb>ons meet with ma <lb></lb>ny concluſive ar <lb></lb>guments, ſo do not <lb></lb>the falſe.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>But you, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> being tranſported by the velocity <lb></lb>of your wit, have taken my words out of my mouth, whilſt I was <lb></lb>about to ſay ſomething, touching this laſt argument of the Author; <lb></lb>and although you have more then ſufficiently refuted him, yet <lb></lb>nevertheleſſe I will adde ſomewhat, which then ran in my minde. <lb></lb></s><s>He propoſeth it as a thing very unlikely, that a body diſſipable <lb></lb>and corruptible, as the Earth, ſhould perpetually move with a re <lb></lb>gular motion, cſpecially for that we ſee living creatures in the end <lb></lb>to grow weary, and to ſtand in need of reſt: and the improbability <lb></lb>is increaſed, in that the ſaid motion is required to be of velocity <lb></lb>incomparable and immenſe, in reſpect to that of animals. </s><s>Now, I <lb></lb>cannot ſee why the velocity of the Earth ſhould, at preſent, trou <lb></lb>ble it; ſo long as that of the ſtarry Sphere ſo very much bigger <lb></lb>doth not occaſion in it any diſturbance more conſiderable, than that <lb></lb>which the velocity of a machine, that in 24 hours maketh but one <lb></lb>ſole revolution, produceth in the ſame. </s><s>If the being of the velo <lb></lb>city of the Earths converſion, according to the model of that ma <lb></lb>chine, inferreth things of no greater moment than that, let the Au <lb></lb>thor ceaſe to fear the Earths growing weary; for that not one of <lb></lb>the moſt feeble and ſlow-pac't animals, no not a Chamæleon would <lb></lb><arrow.to.target n="marg502"></arrow.to.target> <lb></lb>tire in moving no more than ^{*} four or five yards in 24 hours; but <lb></lb>if he pleaſe to conſider the velocity to be no longer, in relation to <lb></lb><arrow.to.target n="marg503"></arrow.to.target> <lb></lb>the model of the machine, but abſolutely, and inaſmuch as the <lb></lb>moveable in 24 hours is to paſs a very great ſpace, he ought to ſhew <lb></lb>himſelf ſo much more reſerved in granting it to the ſtarry Sphere, <lb></lb>which with a velocity incomparably greater than that of the <pb xlink:href="040/01/264.jpg" pagenum="246"></pb>Earth is to carry along with it a thouſand bodies, each much big <lb></lb>ger than the Terreſtrial Globe.</s></p><p type="margin"><s><margin.target id="marg502"></margin.target>* Cinque ò ſei <lb></lb>braccia Fiorentini.</s></p><p type="margin"><s><margin.target id="marg503"></margin.target><emph type="italics"></emph>Wearineß more <lb></lb>to be feared in the <lb></lb>ſtarry Sphere than <lb></lb>in the terreſtriall <lb></lb>Globe.<emph.end type="italics"></emph.end></s></p><p type="main"><s>Here it remains for us to ſee the proofs, whereby the Authour <lb></lb>concludes the new ſtars <emph type="italics"></emph>Anno<emph.end type="italics"></emph.end> 1572. and <emph type="italics"></emph>Anno<emph.end type="italics"></emph.end> 1604. to be ſublu <lb></lb>nary, and not cœleſtial, as the <emph type="italics"></emph>Astronomers<emph.end type="italics"></emph.end> of thoſe times were <lb></lb>generally perſwaded; an enterprize very great certainly; but I <lb></lb>have conſidered, that it will be better, in regard the Book is new <lb></lb>and long, by reaſon of its many calculations, that between this e <lb></lb>vening and to morrow morning I make them as plain as I can, and <lb></lb>ſo meeting you again to morrow to continue our wonted confe <lb></lb>rences, give you a brief of what I ſhall obſerve therein; and if we <lb></lb>have time left, we will ſay ſomething of the <emph type="italics"></emph>Annual motion<emph.end type="italics"></emph.end> aſcri <lb></lb>bed to the Earth. </s><s>In the mean time, if either of you, and <emph type="italics"></emph>Simpli <lb></lb>cius<emph.end type="italics"></emph.end> in particular, hath any thing to ſay more, touching what relates <lb></lb>to the <emph type="italics"></emph>Diurnal motion,<emph.end type="italics"></emph.end> at large examined by me, we have a little <lb></lb>time ſtill left to treat thereof.</s></p><p type="main"><s>SIMP. </s><s>I have no more to ſay, unleſſe it be this, that the diſcour <lb></lb>ſes that this day have falne under our debate, have appeared to me <lb></lb>fraught with very acute and ingenious notions, alledged on <emph type="italics"></emph>Coper <lb></lb>nicus<emph.end type="italics"></emph.end> his ſide, in confirmation of the motion of the Earth, but yet <lb></lb>I find not my ſelf perſwaded to believe it; for in ſhort, the things <lb></lb>that have been ſaid conclude no more but this, that the reaſons <lb></lb>for the ſtability of the Earth are not neceſſary; but all the while <lb></lb>no demonſtration hath been produced on the other ſide, that doth <lb></lb>neceſſarily convince and prove its mobility.</s></p><p type="main"><s>SALV. </s><s>I never undertook, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> to remove you from that <lb></lb>your opinion; much leſs dare I preſume to determine definitively <lb></lb>in this controverſie: it onely was, and ſtill ſhall be in the enſuing <lb></lb>diſputations my intent, to make it appear to you, that thoſe who <lb></lb>have thought that moſt ſwift motion of 24 hours doth belong to <lb></lb>the Earth alone, and not to the Univerſe, the Earth onely exclu <lb></lb>ded, were not induced to believe, that ſo it might and ought to do <lb></lb>out of any blind perſwaſion; but that they did very well ſee, try, <lb></lb>and examine the reaſons on the contrary ſide, and alſo not ſlight <lb></lb>ly anſwer them. </s><s>With the ſame intention, if it ſtand with your <lb></lb>liking, and that of <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> we may paſſe to the conſideration of <lb></lb>that other motion; firſt, by <emph type="italics"></emph>Aristarchus Samius,<emph.end type="italics"></emph.end> and afterwards <lb></lb>by <emph type="italics"></emph>Nicholaus Copernicus<emph.end type="italics"></emph.end> aſcribed to the ſaid Terreſtrial Globe, <lb></lb>which is, as, I believe, you have heretofore heard, made under the <lb></lb>Zodiack within the ſpace of a year about the Sun, immoveably <lb></lb>placed in the centre of the ſaid Zodiack.</s></p><p type="main"><s>SIMP. </s><s>The diſquiſition is ſo great, and ſo noble, that I ſhall <lb></lb>gladly hearken to the diſcuſſion thereof, perſwading my ſelf that I <lb></lb>ſhall hear what ever can be ſaid of that matter. </s><s>And I will after <pb xlink:href="040/01/265.jpg" pagenum="247"></pb>wards by my ſelf, according to my uſual cuſtome, make more de <lb></lb>liberate reflexions upon what hath been, and is to be ſpoken; and <lb></lb>if I ſhould gain no more but this, it will be no ſmall benefit <lb></lb>that I ſhall be able to diſcourſe more Logically.</s></p><p type="main"><s>SAGR. Therefore, that we may no further weary <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> <lb></lb>we will put a period to the diſputations of this day, and re <lb></lb>aſſume our conference to morrow in the uſual manner, with hope <lb></lb>to hear very pleaſing novelties.</s></p><p type="main"><s>SIMP. </s><s>I will leave with you the Book <emph type="italics"></emph>De ſtellis novis,<emph.end type="italics"></emph.end> and car <lb></lb>ry back this of the Concluſions, to ſee what is written therein a <lb></lb>gainſt the Annual motion, which are to be the arguments of our <lb></lb>diſcourſe to morrow.</s></p><pb xlink:href="040/01/266.jpg"></pb><pb xlink:href="040/01/267.jpg"></pb><figure id="id.040.01.267.1.jpg" xlink:href="040/01/267/1.jpg"></figure><figure id="id.040.01.267.2.jpg" xlink:href="040/01/267/2.jpg"></figure><figure id="id.040.01.267.3.jpg" xlink:href="040/01/267/3.jpg"></figure><figure id="id.040.01.267.4.jpg" xlink:href="040/01/267/4.jpg"></figure><figure id="id.040.01.267.5.jpg" xlink:href="040/01/267/5.jpg"></figure><figure id="id.040.01.267.6.jpg" xlink:href="040/01/267/6.jpg"></figure><figure id="id.040.01.267.7.jpg" xlink:href="040/01/267/7.jpg"></figure><figure id="id.040.01.267.8.jpg" xlink:href="040/01/267/8.jpg"></figure><figure id="id.040.01.267.9.jpg" xlink:href="040/01/267/9.jpg"></figure><p type="caption"><s><emph type="italics"></emph>Place this Plate <lb></lb>at the end of <lb></lb>the Second<emph.end type="italics"></emph.end><lb></lb>Dialogue.</s></p> </chap><chap><pb xlink:href="040/01/268.jpg"></pb> <pb xlink:href="040/01/269.jpg" pagenum="249"></pb><p type="head"><s>GALILÆUS <lb></lb>Galilæus Lyncæus, <lb></lb>HIS <lb></lb>SYSTEME <lb></lb>OF THE <lb></lb>WORLD.</s></p><p type="head"><s>The Third Dialogue.</s></p><p type="head"><s><emph type="italics"></emph>INTERLOCVTORS.<emph.end type="italics"></emph.end></s></p><p type="head"><s>SALVIATUS, SAGREDUS, and SIMPLICIUS.</s></p><p type="main"><s>SAGR. </s><s>The great deſire wherewith I have expected <lb></lb>your coming, that I might hear the novel <lb></lb>conceits touching the annual converſi <lb></lb>on of this our Globe, hath made me <lb></lb>think the houres of the laſt night, and <lb></lb>thoſe of this morning very tedious, al <lb></lb>though I ſpent them not idly, but lying <lb></lb>awake I imployed a good part thereof in <lb></lb>ruminating upon our yeſterdayes diſcour <lb></lb>ſes, weighing the reaſons alledged by both parties, in favour of <lb></lb>the two contrary Hypotheſes, that of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ptolomy,<emph.end type="italics"></emph.end> and <lb></lb>this of <emph type="italics"></emph>Ariſtarchus,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Copernicus.<emph.end type="italics"></emph.end> And really methinks, that <lb></lb>which ever of theſe parties have been deceived, they are worthy of <lb></lb>excuſe, ſo ſpecious and valid in appearance are the reaſons that <lb></lb>may have perſwaded them either way; though nevertheleſſe we <pb xlink:href="040/01/270.jpg" pagenum="250"></pb>do for the moſt part cloſe with thoſe produced by the grave Au <lb></lb>thours firſt above mentioned. </s><s>But albeit that the <emph type="italics"></emph>Peripatetick Hy <lb></lb>potheſis,<emph.end type="italics"></emph.end> by reaſon of its antiquity, hath had many followers and <lb></lb>fautors, and the other very few; firſt, for its obſcurity, and next, <lb></lb>for its novelty, yet methinks I diſcover amongſt thoſe many, <lb></lb>and particularly amongſt the modernes ſome, who for the ſup <lb></lb>port of the opinion by them eſteemed true, have introduced <lb></lb>other reaſons ſufficiently childiſh, I could ſay ridiculous.</s></p><p type="main"><s>SALV. </s><s>I have met with the like, and ſo much worſe than <lb></lb><arrow.to.target n="marg504"></arrow.to.target> <lb></lb>yours, that I bluſh to rehearſe them, not ſo much to ſpare the fame <lb></lb>of their Authours, the names of whom might be perpetually con <lb></lb>cealed, as becauſe I am aſhamed ſo much to ſtain the honour of <lb></lb>mankinde. </s><s>In obſerving of theſe men, I have found that ſome <lb></lb>there are who prepoſterouſly reaſoning, firſt ſtabliſh the conclu <lb></lb>ſion in their fancy, and (either becauſe it is their own, or elſe be <lb></lb>longs to a perſon whom they much confide in) ſo firmly imprint <lb></lb>it in their opinions, that it is altogether impoſſible ever wholly to <lb></lb>efface it: and thoſe reaſons which they themſelves ſtumble upon, <lb></lb>or which they hear others to alledge in confirmation of the con <lb></lb>ceit entertained, though never ſo ſimple and inſipid, inſtantly find <lb></lb>credit and applauſe with them: but on the contrary, thoſe which <lb></lb>are brought againſt their opinion, though ingenuous and conclu <lb></lb>ding, they receive not only with nauſeating, but with diſdain and <lb></lb>bitter indignation, yea, you ſhall have one of theſe ſo inraged, as <lb></lb>that he will not be backward to try all wayes to ſuppreſs and ſilence <lb></lb>their adverſaries: and of this I my ſelf have had ſome experience.</s></p><p type="margin"><s><margin.target id="marg504"></margin.target><emph type="italics"></emph>Some in arguing <lb></lb>firſt fix in their <lb></lb>minds the conclu <lb></lb>ſion beleeved by <lb></lb>them, and then a <lb></lb>dapt their reaſons <lb></lb>to that.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Indeed theſe men deduce not the concluſion from the <lb></lb>premiſes, nor confirme them with reaſons, but accomodate, or to <lb></lb>ſay better, diſcommodate and diſtort the premiſes and arguments <lb></lb>to make them ſpeak in favour of their pre-aſſumed and pertinaci <lb></lb>ous concluſions. </s><s>It is not good therefore to contract familiarity <lb></lb>with theſe men; and the rather, for that their converſation is not <lb></lb>only unpleaſant, but alſo dangerous. </s><s>Yet let us continue our con <lb></lb>ference with <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> however, whom I have known this long <lb></lb>while for a man of great ingenuity, and altogether void of malice: <lb></lb>beſides he is well verſt in the Peripatetick Doctrine; ſo that I may <lb></lb>aſſure my ſelf, that what ſhall not fall within the reach of his rea <lb></lb>ſon for the ſupport of the <emph type="italics"></emph>Ariſtotelian<emph.end type="italics"></emph.end> Hypotheſis, will not eaſily <lb></lb>be found out by others. </s><s>But ſee yonder he comes, quite out of <lb></lb>winde, whoſe company we have ſo long deſired: we were juſt now <lb></lb>ſpeaking againſt the ſmall haſt you made to come to us.</s></p><p type="main"><s>SIMP. </s><s>You muſt not blame me, but <emph type="italics"></emph>Neptune,<emph.end type="italics"></emph.end> for this my long <lb></lb>ſtay; which in the ebbe of this mornings tide hath in a manner <lb></lb>drain'd away the waters, for the <emph type="italics"></emph>Gondola<emph.end type="italics"></emph.end> that brought me, being <lb></lb>entered not far from hence into a certain Channel, wanting depth, <pb xlink:href="040/01/271.jpg" pagenum="251"></pb>where I was ſtranded, and forced to ſtay there more than a full <lb></lb>hour, in expecting the return of the tide: and there waiting in <lb></lb>this manner, without being able to get out of the boat, which on a <lb></lb>ſudden ran a ground, I obſerved a certain accident, which to me <lb></lb><arrow.to.target n="marg505"></arrow.to.target> <lb></lb>ſeemed very ſtrange; and it was this, that in the waters ebbing <lb></lb>I ſaw it retreat very faſt by ſeveral ſmall rivolets, the ouze being <lb></lb>in many places diſcovered, and whilſt I ſtood looking upon this ef <lb></lb>fect, I ſaw this motion in an inſtant to ceaſe, and without a mi <lb></lb>nutes interval the ſame water to begin to return back again, and <lb></lb>the tide from ebbing to become young flood, without ſtanding <lb></lb>ſtill a moment: an effect that as long as I have dwelt in <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> <lb></lb>I never took notice of before.</s></p><p type="margin"><s><margin.target id="marg505"></margin.target><emph type="italics"></emph>The motion of <lb></lb>the water in ebbing <lb></lb>and flowing not in <lb></lb>terrupted by reſt.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>It is very much, that you ſhould be left thus on ground, <lb></lb>amongſt ſmall Channels; in which rivolets, as having very little <lb></lb>declivity, the riſing or falling of the main ſea, the thickneſs onely <lb></lb>of a paper is ſufficient to make the water to ebbe and flow for good <lb></lb>long ſpaces of time: like as in ſome creeks of the Sea, its flowing <lb></lb>four or ſix ^{*} yards onely, maketh the water to overflow the adja <lb></lb>cent Marſhes for ſome hundreds and thouſands of ^{*} acres. <lb></lb><arrow.to.target n="marg506"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg506"></margin.target>* Pertiche vene <lb></lb>tiani.</s></p><p type="main"><s>SIMP. </s><s>This I know very well, but I ſhould have thought, that <lb></lb>between the ultimate terme of ebbing, and the firſt beginnng to <lb></lb>flow, there ſhould have interpoſed ſome conſiderable interval of <lb></lb>reſt.</s></p><p type="main"><s>SAGR. </s><s>This will appear unto you, if you caſt your eye upon <lb></lb>the bank or piles, where theſe mutations are made perpendicular <lb></lb>ly, but not that there is any real time of ceſſation.</s></p><p type="main"><s>SIMP. </s><s>I did think, that becauſe theſe two motions were con <lb></lb>trary, there ought to be in the midſt between them ſome kind of <lb></lb>reſt; conformable to the Doctrine of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> which demonſtrates. <lb></lb></s><s>that <emph type="italics"></emph>in puncto regreſſus mediat quies.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I very well remember this place: but I bear in minde <lb></lb>alſo, that when I read Philoſophy, I was not thorowly ſatisfied <lb></lb>with <emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> demonſtration; but that I had many experiments <lb></lb>on the contrary, which I could ſtill rehearſe unto you, but I am <lb></lb>unwilling to ſally out into any other digreſſions, we being met <lb></lb>here to diſcourſe of the propoſed mattes, if it be poſſible, without <lb></lb>theſe excurſions wherewith we have interrupted our diſputes in <lb></lb>thoſe dayes that are paſt.</s></p><p type="main"><s>SIMP. </s><s>And yet we may with convenience, if not interrupt <lb></lb>them, at leaſt prolong them very much, for returning yeſter <lb></lb>day home, I ſet my ſelſ to read the Tractate of Concluſions, where <lb></lb>I find Demonſtrations againſt this annual motion aſcribed to the <lb></lb>Earth, very ſolid; and becauſe I would not truſt my memory with <lb></lb>the punctual relation of them, I have brought back the Book a <lb></lb>long with me.</s></p> <pb xlink:href="040/01/272.jpg" pagenum="252"></pb><p type="main"><s>SAGR. </s><s>You have done very well; but if we would re-aſſume <lb></lb>our Diſputations according to yeſterdayes appointment, it is re <lb></lb>quiſite that we firſt hear what account <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> hath to give us <lb></lb>of the Book, <emph type="italics"></emph>De ſtellis novis,<emph.end type="italics"></emph.end> and then without interruption we <lb></lb>may proceed to the Annual motion. </s><s>Now what ſay you, <emph type="italics"></emph>Salvia <lb></lb>tus<emph.end type="italics"></emph.end> touching thoſe ſtars? </s><s>Are they really pull'd down from Hea <lb></lb>ven to theſe lower regions, by vertue of that Authours calculati <lb></lb>ons, whom <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> mentioneth?</s></p><p type="main"><s>SALV. </s><s>I ſet my ſelf laſt night to peruſe his proceedings, and I <lb></lb>have this morning had another view of him, to ſee whether that <lb></lb>which he ſeemed over night to affirm, were really his ſenſe, or my <lb></lb>dreams and phantaſtical nocturnal imaginations; and in the cloſe <lb></lb>found to my great grief that thoſe things were really written and <lb></lb>printed, which for the reputation-ſake of this Philoſopher I was <lb></lb>unwilling to believe. </s><s>It is in my judgment impoſſible, but that he <lb></lb>ſhould perceive the vanity of his undertaking, aſwell becauſe it is <lb></lb>too apert, as becauſe I remember, that I have heard him mentio <lb></lb>ned with applauſe by the <emph type="italics"></emph>Academick our Friend<emph.end type="italics"></emph.end>: it ſeemeth to <lb></lb>me alſo to be a thing very unlikely, that in complacency to others, <lb></lb>he ſhould be induced to ſet ſo low a value upon his reputation, as <lb></lb>to give conſent to the publication of a work, for which he could <lb></lb>expect no other than the cenſure of the Learned.</s></p><p type="main"><s>SAGR. Yea, but you know, that thoſe will be much fewer <lb></lb>than one for an hundred, compared to thoſe that ſhall celebrate <lb></lb>and extoll him above the greateſt wits that are, or ever have been <lb></lb>in the world: He is one that hath mentioned the Peripate <lb></lb>tick inalterability of Heaven againſt a troop of <emph type="italics"></emph>Aſtronomers,<emph.end type="italics"></emph.end> and <lb></lb>that to their greater diſgrace hath foiled them at their own wea <lb></lb>pons; and what do you think four or five in a Countrey that diſ <lb></lb>cern his triflings, can do againſt the innumerable multitude, that, <lb></lb>not being able to diſcover or comprehend them, ſuffer themſelves <lb></lb>to be taken with words, and ſo much more applaud him, by how <lb></lb>much the leſſe they underſtand him? </s><s>You may adde alſo, that <lb></lb>thoſe few who underſtand, ſcorn to give an anſwer to papers ſo <lb></lb>trivial and unconcludent; and that upon very good reaſons, be <lb></lb>cauſe to the intelligent there is no need thereof, and to thoſe that <lb></lb>do not underſtand, it is but labour loſt.</s></p><p type="main"><s>SALV. </s><s>The moſt deſerved puniſhment of their demerits would <lb></lb>certainly be ſilence, if there were not other reaſons, for which it <lb></lb>is haply no leſſe than neceſſary to reſent their timerity: one of <lb></lb>which is, that we <emph type="italics"></emph>Italians<emph.end type="italics"></emph.end> thereby incur the cenſure of Illiterates, <lb></lb>and attract the laughter of Forreigners; and eſpecially to ſuch <lb></lb>who are ſeparated from our Religion; and I could ſhew you ma <lb></lb>ny of thoſe of no ſmall eminency, who ſcoff at our <emph type="italics"></emph>Academick,<emph.end type="italics"></emph.end> <lb></lb>and the many Mathematicians that are in <emph type="italics"></emph>Italie,<emph.end type="italics"></emph.end> for ſuffering the <pb xlink:href="040/01/273.jpg" pagenum="253"></pb>follies of ſuch a ^{*} Fabler againſt <emph type="italics"></emph>Aſtronomers<emph.end type="italics"></emph.end> to come into the </s></p><p type="main"><s><arrow.to.target n="marg507"></arrow.to.target> <lb></lb>light, and to be openly maintained without contradiction; but <lb></lb>this alſo might be diſpenſed with, in reſpect of the other greater <lb></lb>occaſions of laughter, wherewith we may confront them depend <lb></lb>ing on the diſſimulation of the intelligent, touching the follies of <lb></lb>theſe opponents of the Doctrines that they well enough under <lb></lb>ſtand.</s></p><p type="margin"><s><margin.target id="marg507"></margin.target>* Lorenzini.</s></p><p type="main"><s>SAGR. </s><s>I deſire not a greater proof of thoſe mens petulancy, <lb></lb>and the infelicity of a <emph type="italics"></emph>Copernican,<emph.end type="italics"></emph.end> ſubject to be oppoſed by ſuch <lb></lb>as underſtand not ſo much as the very firſt poſitions, upon which <lb></lb>he undertakes the quarrel.</s></p><p type="main"><s>SALV. </s><s>You will be no leſſe aſtoniſhed at their method in con <lb></lb>futing the <emph type="italics"></emph>Astronomers,<emph.end type="italics"></emph.end> who affirm the new Stars to be ſuperiour <lb></lb>to the Orbs of the Planets; and peradventure in the ^{†} Firmament <lb></lb><arrow.to.target n="marg508"></arrow.to.target> <lb></lb>it ſelf.</s></p><p type="margin"><s><margin.target id="marg508"></margin.target>† He taketh the <lb></lb>Firmament for the <lb></lb>Starry Sphere, and <lb></lb>as we vulgarly re <lb></lb>ceive the word.</s></p><p type="main"><s>SAGR. </s><s>But how could you in ſo ſhort a time examine all this <lb></lb>Book, which is ſo great a Volume, and muſt needs contain very <lb></lb>many demonſtrations.?</s></p><p type="main"><s>SALV. </s><s>I have confined my ſelf to theſe his firſt confutations, in <lb></lb>which with twelve demonſtrations founded upon the obſervations <lb></lb>of twelve <emph type="italics"></emph>Aſtronomers,<emph.end type="italics"></emph.end> (who all held, that the Star, <emph type="italics"></emph>Anno<emph.end type="italics"></emph.end> 1572. <lb></lb>which appeared in <emph type="italics"></emph>Caſſiopeia,<emph.end type="italics"></emph.end> was in the Firmament) he proveth it <lb></lb>on the contrary, to be beneath the Moon, conferring, two by two, <lb></lb>the meridian altitudes, proceeding in the method that you ſhall <lb></lb>underſtand by and by. </s><s>And becauſe, I think, that in the exami <lb></lb>nation of this his firſt progreſſion, I have diſcovered in this Au <lb></lb>thour a great unlikelihood of his ability to conclude any thing a <lb></lb>gainſt the <emph type="italics"></emph>Aſtronomers,<emph.end type="italics"></emph.end> in favour of the <emph type="italics"></emph>Peripatetick Philoſophers,<emph.end type="italics"></emph.end> <lb></lb>and that their opinion is more and more concludently confirmed, <lb></lb>I could not apply my ſelf with the like patience in examining his <lb></lb>other methods, but have given a very ſlight glance upon them, <lb></lb>and am certain, that the defect that is in theſe firſt impugnations, <lb></lb>is likewiſe in the reſt. </s><s>And as you ſhall ſee, by experience, very <lb></lb>few words will ſuffice to confute this whole Book, though compi <lb></lb>led with ſo great a number of laborious calculations, as here you <lb></lb><arrow.to.target n="marg509"></arrow.to.target> <lb></lb>ſee. </s><s>Therefore obſerve my proceedings. </s><s>This Authour under <lb></lb>taketh, as I ſay, to wound his adverſaries with their own weapons, <lb></lb><emph type="italics"></emph>i.e.<emph.end type="italics"></emph.end> a great number of obſervations made by themſelves, to wit, by <lb></lb>twelve or thirteen Authours in number, and upon part of them he <lb></lb>makes his ſupputations, and concludeth thoſe ſtars to have been <lb></lb>below the Moon. </s><s>Now becauſe the proceeding by interrogato <lb></lb>ries very much pleaſeth me, in regard the Authour himſelf is not <lb></lb>here, let <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> anſwer me to the queſtions that I ſhall ask <lb></lb>him, as he thinks he himſelf would, if he were preſent. </s><s>And pre <lb></lb>ſuppoſing that we ſpeak of the foreſaid Star, of <emph type="italics"></emph>Anno<emph.end type="italics"></emph.end> 1572. ap <pb xlink:href="040/01/274.jpg" pagenum="254"></pb>pearing in <emph type="italics"></emph>Caſſiopeia,<emph.end type="italics"></emph.end> tell me, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> whether you believe that <lb></lb>it might be in the ſame time placed in divers places, that is, a <lb></lb>mongſt the Elements, aud alſo amongſt the planetary Orbs, and <lb></lb>alſo above theſe amongſt the fixed Stars, and yet again infinitely <lb></lb>more high.</s></p><p type="margin"><s><margin.target id="marg509"></margin.target><emph type="italics"></emph>The method ob <lb></lb>ſerved by<emph.end type="italics"></emph.end> Clar. <emph type="italics"></emph>in <lb></lb>confuting the A <lb></lb>ſtronomers, and by<emph.end type="italics"></emph.end> <lb></lb>Salviatus <emph type="italics"></emph>in confu <lb></lb>ting him.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>There is no doubt, but that it ought to be confeſſed <lb></lb>that it is but in one only place, and at one ſole and determinate <lb></lb>diſtance from the Earth.</s></p><p type="main"><s>SALV. </s><s>Therefore if the obſervations made by the Aſtrono <lb></lb>mers were exact, and the calculations made by this Author were <lb></lb>not erroneous, it were eaſie from all thoſe and all theſe to re <lb></lb>collect the ſame diſtances alwayes to an hair, is not this true?</s></p><p type="main"><s>SIMP. </s><s>My reaſon hitherto tells me that ſo it muſt needs be; <lb></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></lb>been made, there ſhould not be ſo much as two onely that prove <lb></lb>true, what would you think of them?</s></p><p type="main"><s>SIMP. </s><s>I would think that they were all falſe, either through <lb></lb>the fault of the computiſt, or through the defect of the obſer <lb></lb>vators, and at the moſt that could be ſaid, I would ſay, that but <lb></lb>onely one of them and no more was true; but as yet I know not <lb></lb>which to chooſe.</s></p><p type="main"><s>SALV. </s><s>Would you then from falſe fundamentals deduce and <lb></lb>eſtabliſh a doubtful concluſion for ttue? </s><s>Certainly no. </s><s>Now the <lb></lb>calculations of this Author are ſuch, that no one of them agrees <lb></lb>with another, you may ſee then what credit is to be given to <lb></lb>them.</s></p><p type="main"><s>SIMP. Indeed, if it be ſo, 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"></emph>Simplicius,<emph.end type="italics"></emph.end> and <lb></lb>the Author by telling <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> that his arguments would hold <lb></lb>good if the Author had undertook to go about to find out exact <lb></lb>ly the diſtance of the Star from the Earth, which I do not think <lb></lb>to be his intention; but onely to demonſtrate that from thoſe <lb></lb>obſervations he collected that the Star was ſublunary. </s><s>So <lb></lb>that if from thoſe obſervations, and from all the computations <lb></lb>made thereon, the height of the Star be alwayes collected to be <lb></lb>leſſe than that of the Moon, it ſerves the Authors turn to con <lb></lb>vince all thoſe Aſtronomers of moſt impardonable ignorance, <lb></lb>that through the defect either of Geometry or Arithmetick, have <lb></lb>not known how to draw true concluſions from their own obſerva <lb></lb>tions themſelves.</s></p><p type="main"><s>SALV. </s><s>It will be convenient therefore that I turn my ſelf to <lb></lb>you, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> who ſo cunningly aphold the Doctrine of this <lb></lb>Author. </s><s>And to ſee whether I can make <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> though not <lb></lb>very expert in calcnlations, and demonſtrations to apprehend the <pb xlink:href="040/01/275.jpg" pagenum="255"></pb>inconcluſiveneſſe at leaſt of the demonſtrations of this Author, <lb></lb>firſt propoſed to conſideration, and how both he, and all the <lb></lb>Aſtronomers with whom he contendeth, do agree that the new <lb></lb>Star had not any motion of its own, and onely went round with <lb></lb>the diurnal motion of the <emph type="italics"></emph>primum mobile<emph.end type="italics"></emph.end>; but diſſent about the <lb></lb>placing of it, the one party putting it in the Celeſtial Region, <lb></lb>that is above the Moon, and haply above the fixed Stars, and <lb></lb>the other judging it to be neer to the Earth, that is, under the <lb></lb>concave of the Lunar Orb. </s><s>And becauſe the ſituation of the new <lb></lb>ſtar, of which we ſpeak, was towards the North, and at no very <lb></lb>great diſtance from the Pole, ſo that to us <emph type="italics"></emph>Septentrionals,<emph.end type="italics"></emph.end> it did <lb></lb>never ſet, it was an eaſie matter with Aſtronomical inſtruments <lb></lb>to have taken its ſeveral meridian altitudes, as well its ſmalleſt <lb></lb>under the Pole, as its greateſt above the ſame; from the compa <lb></lb>ring of which altitudes, made in ſeveral places of the Earth, <lb></lb>ſituate at different diſtances from the North, that is, different <lb></lb>from one another in relation to polar altitudes, the ſtars diſtance <lb></lb>might be inferred: For if it was in the Firmament amongſt the <lb></lb><arrow.to.target n="marg510"></arrow.to.target> <lb></lb>other fixed ſtars, its meridian altitudes taken in divers elevations <lb></lb>of the pole, ought neceſſarily to differ from each other with the <lb></lb>ſame variations that are found amongſt thoſe elevations them <lb></lb>ſelves; that is, for example, if the elevation of the ſtar above <lb></lb>the horizon was 30 degrees, taken in the place where the polar <lb></lb>altitude was <emph type="italics"></emph>v. </s><s>gr.<emph.end type="italics"></emph.end> 45 degrees, the elevation of the ſame ſtar <lb></lb>ought to have been encreaſed 4 or 5 degrees in thoſe more Nor <lb></lb>thernly places where the pole was higher by the ſaid 4 or 5 de <lb></lb>grees. </s><s>But if the ſtars diſtance from the Earth was but very little, <lb></lb>in compariſon of that of the Firmament; its meridian altitudes <lb></lb>ought approaching to the North to encreaſe conſiderably more <lb></lb>than the polar altitudes; and by that greater encreaſe, that is, <lb></lb>by the exceſſe of the encreaſe of the ſtars elevation, above the <lb></lb>encreaſe of the polar elevation (which is called the difference of <lb></lb>Parallaxes) is readily calculated with a cleer and ſure method, <lb></lb>the ſtars diſtance from the centre of the Earth. </s><s>Now this Author <lb></lb>taketh the obſervations made by thirteen Aſtronomers in ſundry <lb></lb>elevations of the pole, and conferring a part of them at his plea <lb></lb>ſure, he computeth by twelve collations the new ſtars height to <lb></lb>have been alwayes beneath the Moon; but this he adventures to <lb></lb>do in hopes to find ſo groſſe ignorance in all thoſe, into whoſe <lb></lb>hands his book might come, that to ſpeak the truth, it hath turn'd <lb></lb>my ſtomack; and I wait to ſee how thoſe other Aſtronomers, and <lb></lb>particularly <emph type="italics"></emph>Kepler,<emph.end type="italics"></emph.end> againſt whom this Author principally in <lb></lb>veigheth, can contein themſelves in ſilence, for he doth not uſe <lb></lb>to hold his tongue on ſuch occaſions; unleſſe he did poſſibly <lb></lb>think the enterprize too much below him. </s><s>Now to give you to <pb xlink:href="040/01/276.jpg" pagenum="256"></pb>underſtand the ſame, I have upon this paper tranſcribed the con <lb></lb>cluſions that he inferreth from his twelve indagations; the firſt of <lb></lb>which is upon the two obſervations: <lb></lb><arrow.to.target n="table1"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg510"></margin.target><emph type="italics"></emph>The greateſt and <lb></lb>leaſt elevations of <lb></lb>the new ſtar differ <lb></lb>not from each o <lb></lb>ther more than the <lb></lb>polar allitudes, the <lb></lb>ſaid ſtar being in <lb></lb>the Firmnment.<emph.end type="italics"></emph.end></s></p><table><table.target id="table1"></table.target><row><cell>Of <emph type="italics"></emph>Maurolicus<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Hainzelius,<emph.end type="italics"></emph.end> from which the Star is collected to have been diſtant from the centre leſſe than 3 ſemidiameters of the Earth, the difference of Parallaxes being 4 <emph type="italics"></emph>gr. 42 m.<emph.end type="italics"></emph.end>30 <emph type="italics"></emph>ſec.<emph.end type="italics"></emph.end></cell><cell>3 <emph type="italics"></emph>ſemid.<emph.end type="italics"></emph.end></cell></row><row><cell>2. And is calculated on the obſervations of <emph type="italics"></emph>Hain-zelius,<emph.end type="italics"></emph.end> with Parall. of 8. <emph type="italics"></emph>m. 30 ſec.<emph.end type="italics"></emph.end> and its di-ſtance from the centre is computed to be more than</cell><cell>25 <emph type="italics"></emph>ſemid.<emph.end type="italics"></emph.end></cell></row><row><cell>3. And upon the obſervations of <emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Hain-zelius,<emph.end type="italics"></emph.end> with Parall. of 10 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> and the diſtance of the centre is collected to be little leſſe than</cell><cell>19 <emph type="italics"></emph>ſemid.<emph.end type="italics"></emph.end></cell></row><row><cell>4. And upon the obſervations of <emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end> and the <emph type="italics"></emph>Landgrave,<emph.end type="italics"></emph.end> with Parall. of 14 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> the diſtance from the centre is made to be about</cell><cell>10 <emph type="italics"></emph>ſemid.<emph.end type="italics"></emph.end></cell></row><row><cell>5. And upon the obſervations of <emph type="italics"></emph>Hainzelius<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Gemma,<emph.end type="italics"></emph.end> with Parall. of 42 <emph type="italics"></emph>m. 30 ſec.<emph.end type="italics"></emph.end> whereby the diſtance is gathered to be about</cell><cell>4 <emph type="italics"></emph>ſemid.<emph.end type="italics"></emph.end></cell></row><row><cell>6. And upon the obſervations of the <emph type="italics"></emph>Landgrave<emph.end type="italics"></emph.end>and <emph type="italics"></emph>Camerarius,<emph.end type="italics"></emph.end> with Parall. of 8 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> the di-ſtance is concluded to be about</cell><cell>4 <emph type="italics"></emph>ſemid.<emph.end type="italics"></emph.end></cell></row><row><cell>7. And upon the obſervations of <emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Hage-cius,<emph.end type="italics"></emph.end> with Parall. of 6 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> and the diſtance is made</cell><cell>31 <emph type="italics"></emph>ſemid.<emph.end type="italics"></emph.end></cell></row><row><cell>8. And upon the obſervations of <emph type="italics"></emph>Hagecius<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Vr-ſinus<emph.end type="italics"></emph.end> with Parall. of 43 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> and the ſtars diſtance from the ſuperficies of the Earth is rendred</cell><cell>1/2 <emph type="italics"></emph>ſemid.<emph.end type="italics"></emph.end></cell></row><row><cell>9. And upon the obſervations of <emph type="italics"></emph>Landgravius<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Buſchius,<emph.end type="italics"></emph.end> with Parall. of 15 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> and the di-ſtance from the ſuperficies of the Earth is by ſupputation</cell><cell>1/48 <emph type="italics"></emph>ſemid.<emph.end type="italics"></emph.end></cell></row><row><cell>10. And upon the obſervations of <emph type="italics"></emph>Maurolice<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Munocius,<emph.end type="italics"></emph.end> with Parall. of 4 <emph type="italics"></emph>m. 30 ſec.<emph.end type="italics"></emph.end> and the compnted diſtance from the Earths ſurface is</cell><cell>1/5 <emph type="italics"></emph>ſemid.<emph.end type="italics"></emph.end></cell></row><row><cell>11. And upon the obſervations of <emph type="italics"></emph>Munocius<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Gemma,<emph.end type="italics"></emph.end> with Parall. of 55 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> and the diſtance from the centre is rendred</cell><cell>13 <emph type="italics"></emph>ſemid.<emph.end type="italics"></emph.end></cell></row> <pb xlink:href="040/01/277.jpg" pagenum="257"></pb><row><cell>12. And upon the obſervations of <emph type="italics"></emph>Munoſius<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Vrſinus<emph.end type="italics"></emph.end> with Parall. of 1 <emph type="italics"></emph>gr. 36 m.<emph.end type="italics"></emph.end> and the di-ſtance from the centre cometh forth leſſe than</cell><cell>7 <emph type="italics"></emph>ſemid.<emph.end type="italics"></emph.end></cell></row></table><p type="main"><s>Theſe are twelve indagations made by the Author at his electi <lb></lb>on, amongſt many which, as he ſaith, might be made by combi <lb></lb>ning the obſervations of theſe thirteen obſervators. </s><s>The which <lb></lb>twelve we may believe to be the moſt favourable to prove his <lb></lb>intention.</s></p><p type="main"><s>SAGR. </s><s>I would know whether amongſt the ſo many other in <lb></lb>dagations pretermitted by the Author, there were not ſome that <lb></lb>made againſt him, that is, from which calculating one might find <lb></lb>the new ſtar to have been above the Moon, as at the very firſt <lb></lb>ſight I think we may reaſonably queſtion; in regard I ſee theſe <lb></lb>already produced to be ſo different from one another, that ſome <lb></lb>of them give me the diſtance of the ſaid ſtar from the Earth, 4, 6, <lb></lb>10, 100, a thouſand, and an hundred thouſand times bigger one <lb></lb>than another; ſo that I may well ſuſpect that amongſt thoſe that <lb></lb>he did not calculate, there was ſome one in fauour of the adverſe <lb></lb>party. </s><s>And I gueſſe this to be the more probable, for that I can <lb></lb>not conceive that thoſe Aſtronomers the obſervators could want <lb></lb>the knowledg and practice of theſe computations, which I think <lb></lb>do not depend upon the abſtruceſt things in the World. </s><s>And in <lb></lb>deed it will ſeem to me a thing more than miraculous, if whilſt in <lb></lb>theſe twelve inveſtigations onely, there are ſome that make the <lb></lb>ſtar to be diſtant from the Earth but a few miles, and others that <lb></lb>make it to be but a very fmall matter below the Moon, there are <lb></lb>none to be found that in favour of the contrary part do make it <lb></lb>ſo much as twenty yards above the Lunar Orb. </s><s>And that which <lb></lb>ſhall be yet again more extravagant, that all thoſe Aſtronomers <lb></lb>ſhould have been ſo blind as not to have diſcovered that their ſo <lb></lb>apparent miſtake.</s></p><p type="main"><s>SALV. </s><s>Begin now to prepare your ears to hear with infinite <lb></lb>admiration to what exceſſes of confidence of ones own authority <lb></lb>and others folly, the deſire of contradicting and ſhewing ones <lb></lb>ſelf wiſer than others, tranſports a man. </s><s>Amongſt the indaga <lb></lb>tions omitted by the Author, there are ſuch to be found as make <lb></lb>the new ſtar not onely above the Moon, but above the fixed <lb></lb>ſtars alſo. </s><s>And theſe are not a few, but the greater part, as you <lb></lb>ſhall ſee in this other paper, where I have ſet them down.</s></p><p type="main"><s>SAGR. </s><s>But what ſaith the Author to theſe? </s><s>It may be he did <lb></lb>not think of them?</s></p><p type="main"><s>SALV. </s><s>He hath thought of them but too much: but ſaith, that <lb></lb>the obſervations upon which the calculations make the ſtar to be <lb></lb>infinitely remote, are erroneous, and that they cannot be com <lb></lb>bined to one another.</s></p> <pb xlink:href="040/01/278.jpg" pagenum="258"></pb><p type="main"><s>SIMP. </s><s>But this ſeemeth to me a very lame evaſion; for the ad <lb></lb>verſe party may with as much reaſon reply, that thoſe are errone <lb></lb>ous wherewith he collecteth the ſtar to have been in the Elemen <lb></lb>tary Region.</s></p><p type="main"><s>SALV. </s><s>Oh <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> if I could but make you comprehend <lb></lb>the craft, though no great craftineſſe of this Author, I ſhould <lb></lb>make you to wonder, and alſo to be angry to ſee how that he <lb></lb>palliating his ſagacity with the vail of the ſimplicity of your ſelf; <lb></lb>and the reſt of meer Philoſophers, would inſinuate himſelf into <lb></lb>your good opinion, by tickling your cars, and ſwelling your am <lb></lb>bition, pretending to have convinced and ſilenced theſe petty <lb></lb>Aſtronomers, who went about to aſſault the impregnable inalte <lb></lb>rability of the <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> Heaven, and which is more, to have <lb></lb>foild and conquered them with their own arms. </s><s>I will try with all <lb></lb>my ability to do the ſame; and in the mean time let <emph type="italics"></emph>Sagredus<emph.end type="italics"></emph.end> <lb></lb>take it in good part, if <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> and I try his patience, perhaps <lb></lb>a little too much, whilſt that with a ſuperfluous circumlocution <lb></lb>(ſuperfluous I ſay to his moſt nimble apprehenſion) I go about to <lb></lb>make out a thing, which it is not convenient ſhould be hid and <lb></lb>unknown unto him.</s></p><p type="main"><s>SAGR. </s><s>I ſhall not onely without wearineſſe, but alſo with <lb></lb>much delight hearken to your diſcourſes; and ſo ought all <emph type="italics"></emph>Peripa <lb></lb>tetick<emph.end type="italics"></emph.end> Philoſophers, to the end they may know how much they <lb></lb>are oblieged to this their Protector.</s></p><p type="main"><s>SALV. </s><s>Tell me, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> whether you do well comprehend, <lb></lb>how, the new ſtar being placed in the meridian circle yonder to <lb></lb>wards the North, the ſame to one that from the South ſhould <lb></lb>go towards the North, would ſeem to riſe higher and higher a <lb></lb>bove the Horizon, as much as the Pole, although it ſhould have <lb></lb>been ſcituate amongſt the fixed ſtars; but, that in caſe it were <lb></lb>conſiderably lower, that is nearer to the Earth, it would appear <lb></lb>to aſcend more than the ſaid pole, and ſtill more by how much <lb></lb>its vicinity was greater?</s></p><p type="main"><s>SIMP. </s><s>I think that I do very well conceive the ſame; in to <lb></lb>ken whereof I will try if I can make a mathematical Scheme of <lb></lb>it, and in this great circle <emph type="italics"></emph>[in Fig. </s><s>1. of this Dialogue.]<emph.end type="italics"></emph.end> I will <lb></lb>marke the pole P; and in theſe two lower circles I will note two <lb></lb>ſtars beheld from one place on the Earth, which let be A; and <lb></lb>let the two ſtars be theſe B and C, beheld in the ſame line A B C, <lb></lb>which line I prolong till it meet with a fixed ſtar in D. </s><s>And then <lb></lb>walking along the Earth, till I come to the term E, the two <lb></lb>ſtars will appear to me ſeparated from the fixed ſtar D, and ad <lb></lb>vanced neerer to the pole P, and the lower ſtar B more, which <lb></lb>will appear to me in G, and the ſtar C leſſe, which will ap <lb></lb>pear to me in F, but the fixed ſtar D will have kept the ſame <lb></lb>diſtance from the Pole.</s></p> <pb xlink:href="040/01/279.jpg" pagenum="259"></pb><p type="main"><s>SALV. </s><s>I ſee that you underſtand the buſineſſe very well. </s><s>I be <lb></lb>lieve that you do likewiſe comprehend, that, in regard the ſtar B <lb></lb>is lower than C, the angle which is made by the rayes of the <lb></lb>ſight, which departing from the two places A and E, meet in C, <lb></lb>to wit, this angle A C E, is more narrow, or if we will ſay more <lb></lb>acute than the angle conſtituted in B, by the rayes A B and <lb></lb>E <emph type="italics"></emph>B.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>This I likewiſe underſtand very well.</s></p><p type="main"><s>SALV. </s><s>And alſo, the Earth beine very little and almoſt inſen <lb></lb>ſible, in reſpect of the Firmament <emph type="italics"></emph>(or Starry Sphere<emph.end type="italics"></emph.end>;) and con <lb></lb>ſequently the ſpace A E, paced on the Earth, being very ſmall in <lb></lb>compariſon of the immenſe length of the lines E G and E F, paſ <lb></lb>ſing from the Earth unto the Firmament, you thereby collect that <lb></lb>the ſtar C might riſe and aſcend ſo much and ſo much above the <lb></lb>Earth, that the angle therein made by the rayes which depart <lb></lb>from the ſaid ſtationary points A and E, might become moſt a <lb></lb>cute, and as it were abſolutely null and inſenſible.</s></p><p type="main"><s>SIMP. </s><s>And this alſo is moſt manifeſt to ſenſe.</s></p><p type="main"><s>SALV. </s><s>Now you know <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> that Aſtronomers and Ma <lb></lb>thematicians have found infallible rules by way of Geometry and <lb></lb>Arithmetick, to be able by help of the quantity of theſe angles <lb></lb><emph type="italics"></emph>B<emph.end type="italics"></emph.end> and C, and of their differences, with the additional knowledg <lb></lb>of the diſtance of the two places A and E, to find to a foot the <lb></lb>remoteneſſe of ſublime bodies; provided alwayes that the afore <lb></lb>ſaid diſtance, and angles be exactly taken.</s></p><p type="main"><s>SIMP. </s><s>So that if the Rules dependent on <emph type="italics"></emph>Geometry<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Aſtro <lb></lb>nomy<emph.end type="italics"></emph.end> be true, all the fallacies and errours that might be met with <lb></lb>in attempting to inveſtigate thoſe altitudes of new Stars or Co <lb></lb>mets, or other things muſt of neceſſity depend on the diſtance A E, <lb></lb>and on the angles B and C, not well meaſured. </s><s>And thus all thoſe <lb></lb>differences which are found in theſe twelve workings depend, not <lb></lb>on the deſects of the rules of the Calculations, but on the errours <lb></lb>committed in finding out thoſe angles, and thoſe diſtances, by means <lb></lb>of the Inſtrumental Obſervations.</s></p><p type="main"><s>SALV. True; and of this there is no doubt to be made. </s><s>Now <lb></lb>it is neceſſary that you obſerve intenſely, how in removing the Star <lb></lb>from B to C, whereupon the angle alwayes grows more acute, the <lb></lb>ray E B G goeth farther and farther off from the ray A B D in <lb></lb>the part beneath the angle, as you may ſee in the line E C F, <lb></lb>whoſe inferiour part E C is more remote from the part A C, than <lb></lb>is the part E B, but it can never happen, that by any whatſoever <lb></lb>immenſe receſſion, the lines A D and E F ſhould totally ſever from <lb></lb>each other, they being finally to go and conjoyn in the Star: and <lb></lb>onely this may be ſaid, that they would ſeparate, and reduce them <lb></lb>ſelves to parallels, if ſo be the receſſion ſhould be infinite, which <pb xlink:href="040/01/280.jpg" pagenum="260"></pb>caſe is not to be ſuppoſed. </s><s>But becauſe (obſerve well) the diſtance <lb></lb>of the Firmament, in relation to the ſmallneſſe of the Earth, as <lb></lb>hath been ſaid, is to be accounted, as if it were infinite; therefore <lb></lb>the angle conteined betwixt the two rayes, that being drawn from <lb></lb>the points A and E, go to determine in a fixed Star, is eſteemed <lb></lb>nothing, and thoſe rayes held to be two parallel lines; and there <lb></lb>fore it is concluded, that then only may the New Star be affirmed <lb></lb>to have been in the Firmament, when from the collating of the <lb></lb>Obſervations made in divers places, the ſaid angle is, by calcula <lb></lb>tion, gathered to be inſenſible, and the lines, as it were, parallels. <lb></lb></s><s>But if the angle be of a conſiderable quantity, the New Star muſt <lb></lb>of neceſſity be lower than thoſe fixed; and alſo than the Moon, in <lb></lb>caſe the angle A B E ſhould be greater than that which would be <lb></lb>made in the Moons centre.</s></p><p type="main"><s>SIMP. </s><s>Then the remoteneſſe of the Moon is not ſo great, that <lb></lb>a like angle ſhould be ^{*}inſenſible in her? <lb></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 ſenſible, not onely in the Moon, but <lb></lb>in the Sun alſo.</s></p><p type="main"><s>SIMP. </s><s>But if this be ſo, it's poſſible that the ſaid angle may <lb></lb>be obſerved in the New Star, without neceſſitating it to be inferi <lb></lb>our to the Sun, aſwell as to the Moon.</s></p><p type="main"><s>SALV. </s><s>This may very well be, yea, and is in the preſent caſe, <lb></lb>as you ſhall ſee in due place; that is, when I ſhall have made plain <lb></lb>the way, in ſuch manner that you alſo, though not very perfect in <lb></lb><emph type="italics"></emph>Aſtronomical<emph.end type="italics"></emph.end> calculations, may clearly ſee, and, as it were, with <lb></lb>your hands feel how that this Authour had it more in his eye to <lb></lb>write in complacency of the <emph type="italics"></emph>Peripateticks,<emph.end type="italics"></emph.end> by palliating and diſ <lb></lb>ſembling ſundry things, than to eſtabliſh the truth, by producing <lb></lb>them with naked ſincerity: therefore let us proceed forwards. </s><s>By <lb></lb>the things hitherto ſpoken, I ſuppoſe that you comprehend very <lb></lb>well how that the diſtance of the new Star can never be <lb></lb>made ſo immenſe, that the angle ſo often named ſhall wholly diſ <lb></lb>appear, and that the two rayes of the Obſervators at the places <lb></lb>A and E, ſhall become altogether parallels: and you may conſe <lb></lb>quently comprehend to the full, that if the calculations ſhould <lb></lb>collect from the obſervations, that that angle was totally null, or <lb></lb>that the lines were truly parallels, we ſhould be certain that the <lb></lb>obſervations were at leaſt in ſome ſmall particular erroneous: <lb></lb>But, if the calculations ſhould give us the ſaid lines to be ſepara <lb></lb>ted not only to equidiſtance, that is, ſo as to be parallel, but to <lb></lb>have paſt beyond that terme, and to be dilated more above than <lb></lb>below, then muſt it be reſolutely concluded, that the obſervations <lb></lb>were made with leſſe accurateneſſe, and in a word, to be errone <lb></lb>ous; as leading us to a manifeſt impoſſibility. </s><s>In the next place, <lb></lb>you muſt believe me, and ſuppoſe it for true, that two right lines <pb xlink:href="040/01/281.jpg" pagenum="261"></pb>which depart from two points marked upon another right line, are <lb></lb>then wider above than below, when the angles included between <lb></lb>them upon that right line are greater than two right angles; and <lb></lb>if theſe angles ſhould be equal to two right angles, the lines would <lb></lb>be parallels; but if they were leſs than two right angles, the lines <lb></lb>would be concurrent, and being continued out would undoubted <lb></lb>ly interſect the triangle.</s></p><p type="main"><s>SIMP. </s><s>Without taking it upon truſt from you, I know the <lb></lb>ſame; and am not ſo very naked of <emph type="italics"></emph>Geometry,<emph.end type="italics"></emph.end> as not to know a <lb></lb>Propoſition, which I have had occaſion of reading very often in <lb></lb><emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> that is, that the three angles of all triangles are equall to <lb></lb>two right angles: ſo that if I take in my Figure the triangle ABE, <lb></lb>it being ſuppoſed that the line E A is right; I very well conceive, <lb></lb>that its three angles A, E, B, are equal to two right angles; and <lb></lb>that conſequently the two angles E and A are leſſe than two right <lb></lb>angles, ſo much as is the angle B. </s><s>Whereupon widening the lines <lb></lb>A B and E B (ſtill keeping them from moving out of the points A <lb></lb>and E) untill that the angle conteined by them towards the parts <lb></lb>B, diſappear, the two angles beneath ſhall be equal to two right <lb></lb>angles, and thoſe lines ſhall be reduced to parallels: and if one <lb></lb>ſhould proceed to enlarge them yet more, the angles at the points <lb></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"></emph>Archimedes,<emph.end type="italics"></emph.end> and have freed me from the <lb></lb>expence of more words in declaring to you, that whenſoever the <lb></lb>calculations make the two angles A and E to be greater than two <lb></lb>right angles, the obſervations without more adoe will prove erro <lb></lb>neous. </s><s>This is that which I had a deſire that you ſhould perfect <lb></lb>ly underſtand, and which I doubted that I was not able ſo to make <lb></lb>out, as that a meer <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> Philoſopher might attain to the <lb></lb>certain knowledg thereof. </s><s>Now let us go on to what remains. <lb></lb></s><s>And re-aſſuming that which even now you granted me, namely, <lb></lb>that the new ſtar could not poſſibly be in many places, but in one <lb></lb>alone, when ever the ſupputations made upon the obſervations of <lb></lb>theſe Aſtronomers do not aſſign it the ſame place, its neceſſary <lb></lb>that it be an errour in the obſervations, that is, either in taking the <lb></lb>altitudes of the pole, or in taking the elevations of the ſtar, or in <lb></lb>the one or other working. </s><s>Now for that in the many workings <lb></lb>made with the combinations two by two, there are very few of <lb></lb>the obſervations that do agree to place the ſtar in the ſame ſitua <lb></lb>tion; therefore theſe few onely may happily be the non-errone <lb></lb>ous, but the others are all abſolutely falſe.</s></p><p type="main"><s>SAGR. </s><s>It will be neceſſary then to give more credit to theſe <lb></lb>few alone, than to all the reſt together, and becauſe you ſay, <lb></lb>that theſe which accord are very few, and I amongſt theſe 12, <lb></lb>do find two that ſo accord, which both make the diſtance of the <pb xlink:href="040/01/282.jpg" pagenum="262"></pb>ſtar from the centre of the Earth 4 ſemidiameters, which are theſe, <lb></lb>the fifth and ſixth, therefore it is more probable that the new ſtar <lb></lb>was elementary, than celeſtial.</s></p><p type="main"><s>SALV. </s><s>You miſtake the point; for if you note well it was not <lb></lb>written, that the diſtance was exactly 4 ſemidiameters, but about <lb></lb>4 ſemidiameters; and yet you ſhall ſee that thoſe two diſtances <lb></lb>differed from each other many hundreds of miles. </s><s>Here they are; <lb></lb>you ſee that this fifth, which is 13389 <emph type="italics"></emph>Italian<emph.end type="italics"></emph.end> miles, exceeds the <lb></lb>ſixth, which is 13100 miles, by almoſt 300 miles.</s></p><p type="main"><s>SAGR. </s><s>Which then are thoſe few that agree in placing the ſtar <lb></lb>in the ſame ſituation?</s></p><p type="main"><s>SALV. </s><s>They are, to the diſgrace of this Author five workings, <lb></lb>which all place it in the firmament, as you ſhall ſee in this note, <lb></lb>where I have ſet down many other combinations. </s><s>But I will grant <lb></lb>the Author more than peradventure he would demand of me, which <lb></lb>is in ſum, that in each combination of the obſervations there is <lb></lb>ſome error; which I believe to be abſolutely neceſſary; for the <lb></lb>obſervations being four in number that ſerve for one working, <lb></lb>that is, two different altitudes of the Pole, and two different eleva <lb></lb>tions of the ſtar, made by different obſervers, in different pla <lb></lb>ces, with different inſtruments, who ever hath any ſmall know</s></p><p type="main"><s><arrow.to.target n="marg512"></arrow.to.target> <lb></lb>ledg of this art, will ſay, that amongſt all the four, it is impoſſible <lb></lb>but there will be ſome error; and eſpecially ſince we ſee that in <lb></lb>taking but one onely altitude of the Pole, with the ſame inſtru <lb></lb>ment, in the ſame place, by the ſame obſerver, that hath re <lb></lb>peated the obſervation a thouſand times, there will ſtill be a titu <lb></lb>bation of one, or ſometimes of many minutes, as in this ſame <lb></lb>book you may ſee in ſeveral places. </s><s>Theſe things preſuppoſed, <lb></lb>I ask you <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> whether you believe that this Authour held <lb></lb>theſe thirteen obſervators for wiſe, underſtanding and expert men <lb></lb>in uſing thoſe inſtruments, or elſe for inexpert, and bunglers?</s></p><p type="margin"><s><margin.target id="marg512"></margin.target><emph type="italics"></emph>Aſtronomical In <lb></lb>struments are very <lb></lb>ſubject to errour.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>It muſt needs be that he eſteemed them very acute and <lb></lb>intelligent; for if he had thought them unskilful in the buſineſſe, <lb></lb>he might have omitted his ſixth book as inconcluſive, as being <lb></lb>founded upon ſuppoſitions very erroneous; and might take us for <lb></lb>exceſſively ſimple, if he ſhould think he could with their inex <lb></lb>pertneſſe perſwade us to believe a falſe poſition of his for truth.</s></p><p type="main"><s>SALV. </s><s>Therefore theſe obſervators being ſuch, and that yet <lb></lb>notwithſtanding they did erre, and ſo conſequently needed cor <lb></lb>rection, that ſo one might from their obſervations infer the <lb></lb>beſt hints that may be; it is convenient that we apply unto them <lb></lb>the leaſt and neereſt emendations and corrections that may be; <lb></lb>ſo that they do but ſuffice to reduce the obſervations from impoſ <lb></lb>ſibility to poſſibility; ſo as <emph type="italics"></emph>v. </s><s>gr.<emph.end type="italics"></emph.end> if one may but correct a mani <lb></lb>feſt errour, and an apparent impoſſibility of one of their obſer <pb xlink:href="040/01/283.jpg" pagenum="263"></pb>vations by the addition or ſubſtraction of two or three minutes, and <lb></lb>with that amendment to reduce it to poſſibility, a man ought <lb></lb>not to eſſay to adjuſt it by the addition or ſubſtraction of fifteen, <lb></lb>twenty, or fifty.</s></p><p type="main"><s>SIMP. </s><s>I think the Authour would not deny this: for granting <lb></lb>that they are expert and judicious men, it ought to be thought that <lb></lb>they did rather erre little than much.</s></p><p type="main"><s>SALV. </s><s>Obſerve again; The places where the new Star is pla <lb></lb>ced, are ſome of them manifeſtly impoſſible, and others poſſible. <lb></lb></s><s>Abſolutely impoſſible it is, that it ſhould be an infinite ſpace ſupe <lb></lb>riour to the fixed Stars, for there is no ſuch place in the world; <lb></lb>and if there were, the Star there ſcituate would have been imper <lb></lb>ceptible to us: it is alſo impoſſible that it ſhould go creeping along <lb></lb>the ſuperficies of the Earth; and much leſſe that it ſhould be <lb></lb>within the ſaid Terreſtrial Globe. </s><s>Places poſſible are theſe that <lb></lb>be in controverſie, it not interferring with our underſtanding, that <lb></lb>a viſible object in the likeneſſe of a Star might be aſwell above the <lb></lb>Moon, as below it. </s><s>Now whilſt one goeth about to compute by <lb></lb>the way of Obſervations and Calculations made with the utmoſt <lb></lb>certainty that humane diligence can attain unto what its place was, <lb></lb>it is found that the greateſt part of thoſe Calculations make it <lb></lb>more than infinitely ſuperiour to the Firmament, others make it <lb></lb>very neer to the ſurface of the Earth, and ſome alſo under the <lb></lb>ſame; and of the reſt, which place it in ſituations not impoſſible, <lb></lb>none of them agree with each other; inſomuch that it muſt be <lb></lb>confeſſed, that all thoſe obſervations are neceſſarily falſe; ſo that <lb></lb>if we would nevertheleſs collect ſome fruit from ſo many laborious <lb></lb>calculations, we muſt have recourſe to the corrections, amending <lb></lb>all the obſervations.</s></p><p type="main"><s>SIMP. </s><s>But the Authour will ſay, that of the obſervations that <lb></lb>aſſign to the Star impoſſible places, there ought no account to be <lb></lb>made, as being extreamly erroneous and falſe; and thoſe onely <lb></lb>ought to be accepted, that conſtitute it in places not impoſſible: <lb></lb>and amongſt theſe a man ought to ſeek, by help of the moſt pro <lb></lb>bable, and moſt numerous concurrences, not if the particular and <lb></lb>exact ſituation, that is, its true diſtance from the centre of the <lb></lb>Earth, at leaſt, whether it was amongſt the Elements, or elſe a <lb></lb>mongſt the Cœleſtial bodies.</s></p><p type="main"><s>SALV. </s><s>The diſcourſe which you now make, is the ſelf ſame <lb></lb>that the Author made, in favour of his cauſe, but with too unrea <lb></lb>ſonable a diſadvantage to his adverſaries; and this is that princi <lb></lb>pal point that hath made me exceſſively to wonder at the too great <lb></lb>confidence that he expreſſed to have, no leſs of his own authority, <lb></lb>than of the blindneſs and inadvertency of the Aſtronomers; in <lb></lb>favour of whom I will ſpeak, and you ſhall anſwer for the Author. <pb xlink:href="040/01/284.jpg" pagenum="264"></pb>And firſt, I ask you, whether the Aſtronomers, in obſerving with <lb></lb>their Inſtruments, and ſeeking <emph type="italics"></emph>v. </s><s>gr.<emph.end type="italics"></emph.end> how great the elevation of a <lb></lb>Star is above the Horizon, may deviate from the truth, aſwell in <lb></lb>making it too great, as too little; that is, may erroneouſly com <lb></lb>pute, that it is ſometime higher than the truth, and ſometimes low <lb></lb>er; or elſe whether the errour muſt needs be alwayes of one <lb></lb>kinde, to wit, that erring they alwayes make it too much, and ne <lb></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 eaſie to commit an errour <lb></lb>the one way, as the other.</s></p><p type="main"><s>SALV. </s><s>I believe the Author would anſwer the ſame. </s><s>Now of <lb></lb>theſe two kinds of errours, which are contraries, and into which the <lb></lb>obſervators of the new ſtar may equally have fallen, applied to <lb></lb>calculations, one ſort will make the ſtar higher, and the other lower <lb></lb>than really it is. </s><s>And becauſe we have already agreed, that all <lb></lb>the obſervations are falſe; upon what ground would this Au <lb></lb>thor have us to accept thoſe for moſt congruous with the truth, <lb></lb>that ſhew the ſtar to have been near at hand, than the others that <lb></lb>ſhew it exceſſively remote?</s></p><p type="main"><s>SIMP. </s><s>By what I have, as yet, collected of the Authors mind, <lb></lb>I ſee not that he doth refuſe thoſe obſervations, and indagations <lb></lb>that might make the ſtar more remote than the Moon, and alſo <lb></lb>than the Sun, but only thoſe that make it remote (as you your ſelf <lb></lb>have ſaid) more than an infinite diſtance; the which diſtance, be <lb></lb>cauſe you alſo do refuſe it as impoſſible, he alſo paſſeth over, as <lb></lb>being convicted of infinite falſhood; as alſo thoſe obſervations <lb></lb>are of impoſſibility. </s><s>Methinks, therefore, that if you would con <lb></lb>vince the Author, you ought to produce ſupputations, more exact, <lb></lb>or more in number, or of more diligent obſervers, which conſtitute <lb></lb>the ſtar in ſuch and ſuch a diſtance above the Moon, or above the <lb></lb>Sun, and to be brief, in a place poſſible for it to be in, like as he <lb></lb>produceth theſe twelve, which all place the ſtar beneath the Moon <lb></lb>in places that have a being in the world, and where it is poſſible for <lb></lb>it to be.</s></p><p type="main"><s>SALV. </s><s>But <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> yours and the Authors Equivocation <lb></lb>lyeth in this, yours in one reſpect, and the Authors in another; I <lb></lb>diſcover by your ſpeech that you have formed a conceit to your <lb></lb>ſelf, that the exorbitancies that are commited in the eſtabliſhing <lb></lb>the diſtance of the Star do encreaſe ſucceſſively, according to the <lb></lb>proportion of the errors that are made by the Inſtrument, in tak <lb></lb>ing the obſervations, and that by converſion, from the greatneſs <lb></lb>of the exorbitancies, may be argued the greatneſſe of the error; <lb></lb>and that thereforefore hearing it to be infered from ſuch an obſer <lb></lb>vation, that the diſtance of the ſtar is infinite, it is neceſſary, that <lb></lb>the errour in obſerving was infinite, and therefore not to be amend <pb xlink:href="040/01/285.jpg" pagenum="265"></pb>ed, and as ſuch to be refuſed; but the buſineſſe doth not ſucceed <lb></lb>in that manner, my <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> and I excuſe you for not having <lb></lb>comprehended the matter as it is, in regard of your ſmall experi <lb></lb>ence in ſuch affairs; but yet cannot I under that cloak palliate the <lb></lb>error of the Author, who diſſembling the knowledge of this which <lb></lb>he did perſwade himſelf that we in good earneſt did not under <lb></lb>ſtand, hath hoped to make uſe of our ignorance, to gain the bet <lb></lb>ter credit to his Doctrine, among the multitude of illiterate men. <lb></lb></s><s>Therefore for an advertiſement to thoſe who are more credulous <lb></lb>then intelligent, and to recover you from error, know that its poſ <lb></lb>ſible (and that for the moſt part it will come to paſſe) that an <lb></lb>obſervation, that giveth you the ſtar <emph type="italics"></emph>v. </s><s>gr.<emph.end type="italics"></emph.end> at the diſtance of <emph type="italics"></emph>Sa <lb></lb>turn,<emph.end type="italics"></emph.end> by the adition or ſubſtraction of but one ſole minute from <lb></lb>the elevation taken with the inſtrument, ſhall make it to become <lb></lb>infinitely diſtant; and therefore of poſſible, impoſſible, and by <lb></lb>converſion, thoſe calculations which being grounded upon thoſe <lb></lb>obſervations, make the ſtar infinitely remote, may poſſibly often <lb></lb>times with the addition or ſubduction of one ſole minute, reduce it <lb></lb>to a poſſible ſcituation: and this which I ſay of a minute, may al <lb></lb>ſo happen in the correction of half a minute, a ſixth part, and leſs. <lb></lb></s><s>Now fix it well in your mind, that in the higheſt diſtances, that is <lb></lb><emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> the height of <emph type="italics"></emph>Saturn,<emph.end type="italics"></emph.end> or that of the fixed Stars, very ſmall <lb></lb>errors made by the Obſervator, with the inſtrument, render the <lb></lb>ſcituation determinate and poſſible, infinite & impoſſible. </s><s>This doth <lb></lb>not ſo evene in the ſublunary diſtances, and near the earth, where <lb></lb>it may happen that the obſervation by which the Star is collected to <lb></lb>be remote <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> 4. Semidiameters terreſtrial, may encreaſe or dimi <lb></lb>niſh, not onely one minute but ten, and an hundred, and many <lb></lb>more, without being rendred by the calculation either infinitely <lb></lb>remote, or ſo much as ſuperior to the Moon. </s><s>You may hence <lb></lb>comprehend that the greatneſſe of the error (to ſo ſpeak) inſtru <lb></lb>mental, are not to be valued by the event of the calculation, but <lb></lb>by the quantity it ſelf of degrees and minutes numbred upon the <lb></lb>inſtrument, and theſe obſervations are to be called more juſt or <lb></lb>leſs erroneous, which with the addition or ſubſtraction of fewer <lb></lb>minutes, reſtore the ſtar to a poſſible ſituation; and amongſt the <lb></lb>poſſible places, the true one may be believed to have been that, a <lb></lb>bout which a greater number of diſtances concurre upon calcula <lb></lb>ting the more exact obſervations.</s></p><p type="main"><s>SIMP. </s><s>I do not very well apprehend this which you ſay: nor <lb></lb>can I of my ſelf conceive how it can be, that in greater diſtances, <lb></lb>greater exorbitancies can ariſe from the errour of one minute only, <lb></lb>than in the ſmaller from ten or an hundred; and therefore would <lb></lb>gladly underſtand the ſame.</s></p><p type="main"><s>SALV. </s><s>You ſhall ſee it, if not Theorically, yet at leaſt Practi <pb xlink:href="040/01/286.jpg" pagenum="266"></pb>cally, by this ſhort aſſumption, that I have made of all the combi <lb></lb>nations, and of part of the workings pretermitted by the Author, <lb></lb>which I have calculated upon this ſame paper.</s></p><p type="main"><s>SAGR. </s><s>You muſt then from yeſterday, till now, which yet is <lb></lb>not above eighteen hours, have done nothing but compute, with <lb></lb>out taking either food or ſleep.</s></p><p type="main"><s>SALV. </s><s>I have refreſhed my ſelf both thoſe wayes; but truth is, <lb></lb>make theſe ſupputations with great brevity; and, if I may ſpeak <lb></lb>the truth, I have much admired, that this Author goeth ſo farre a <lb></lb>bout, and introduceth ſo many computations no wiſe neceſsary to <lb></lb>the queſtion in diſpute. </s><s>And for a full knowledge of this, and al <lb></lb>ſo to the end it may ſoon be ſeen, how that from the obſervations <lb></lb>of the Aſtronomers, whereof this Author makes uſe, it is more pro <lb></lb>bably gathered, that the new ſtar might have been above the <lb></lb>Moon, and alſo above all the Planets, yea amongſt the fixed ſtars, <lb></lb>and yet higher ſtill than they, I have tranſcribed upon this paper <lb></lb>all the obſervations ſet down by the ſaid Authour, which were <lb></lb>made by thirteen Aſtronomers, wherein are noted the Polar alti <lb></lb>tude, and the altitudes of the ſtar in the meridian, aſwell the <lb></lb>leſſer under the Pole, as the greater and higher, and they are <lb></lb>theſe. <lb></lb><arrow.to.target n="table2"></arrow.to.target> <lb></lb><arrow.to.target n="table3"></arrow.to.target> <pb xlink:href="040/01/287.jpg" pagenum="267"></pb><arrow.to.target n="table4"></arrow.to.target> <lb></lb><arrow.to.target n="table5"></arrow.to.target> <lb></lb><arrow.to.target n="table6"></arrow.to.target> <lb></lb><arrow.to.target n="table7"></arrow.to.target></s></p> <pb xlink:href="040/01/288.jpg" pagenum="268"></pb><table><table.target id="table2"></table.target><row><cell></cell><cell><emph type="italics"></emph>Tycho.<emph.end type="italics"></emph.end></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></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 greateſt.</cell></row><row><cell></cell><cell>27</cell><cell>57</cell><cell>the leaſt.</cell></row><row><cell>And theſe are, according to the firſt paper: but accor-ding to the ſecond, the greateſt 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"></emph>Hainzelius.<emph.end type="italics"></emph.end></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>ſec.<emph.end type="italics"></emph.end></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"></emph>Peucerus<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Sculerus.<emph.end type="italics"></emph.end></cell><cell></cell><cell></cell><cell><emph type="italics"></emph>Landgravius.<emph.end type="italics"></emph.end></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></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"></emph>Camerarius.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></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"></emph>Hagecius<emph.end type="italics"></emph.end></cell><cell></cell><cell></cell><cell><emph type="italics"></emph>Maurolycus.<emph.end type="italics"></emph.end></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></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"></emph>Munocius.<emph.end type="italics"></emph.end></cell><cell></cell><cell></cell><cell><emph type="italics"></emph>Vrſinus.<emph.end type="italics"></emph.end></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></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 ſtar</cell><cell>67</cell><cell>30</cell><cell>Altitude of the ſtar</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"></emph>Reinholdus.<emph.end type="italics"></emph.end></cell><cell></cell><cell></cell><cell><emph type="italics"></emph>Buchius.<emph.end type="italics"></emph.end></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></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 ſtar</cell><cell>79</cell><cell>30</cell><cell>Altitude of the ſtar</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"></emph>Gemma.<emph.end type="italics"></emph.end></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell></row><row><cell>Altitude of the pole</cell><cell>50</cell><cell>50</cell></row><row><cell>Altitude of the ſtar</cell><cell>79</cell><cell>45</cell></row></table><p type="main"><s>Now to ſee my whole proceeding, we may begin from theſe <lb></lb>calculations, which are four, omitted by the Author, perhaps be <lb></lb>cauſe they make againſt him, in regard they place the ſtar above <lb></lb>the moon by many ſemidiameters of the Earth. </s><s>The firſt of <lb></lb>which is this, computed upon the obſervations of the Landgrave of <lb></lb><emph type="italics"></emph>Haſſia,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end>; which are, even by the Authors conceſſion, <lb></lb>two of the moſt exact obſervers: and in this firſt, I will declare <lb></lb>the order that I hold in the working; which ſhall ſerve for all the <lb></lb>reſt, in that they are all made by the ſame rule, not varying in any <lb></lb>thing, ſave in the quantity of the given ſummes, that is, in the <lb></lb>number of the degrees of the Poles altitude, and of the new Stars <lb></lb>elevation above the Horizon, the diſtance of which from the cen <lb></lb>tre of the Earth, in proportion to the ſemidiameter of the terre <lb></lb>ſtrial Globe is ſought, touching which it nothing imports in this <lb></lb>caſe, to know how many miles that ſemidiameter conteineth; <lb></lb>whereupon the reſolving that, and the diſtance of places where <lb></lb>the obſervations were made, as this Author doth, is but time and <lb></lb>labour loſt; nor do I know why he hath made the ſame, and eſpe <lb></lb>cially why at the laſt he goeth about to reduce the miles found, in <lb></lb>to ſemidiameters of the Terreſtrial Globe.</s></p><p type="main"><s>SIMP. </s><s>Perhaps he doth this to finde with ſuch ſmall meaſures, <lb></lb>and with their fractions the diſtance of the Star terminated to three <lb></lb>or four inches; for we that do not underſtand your rules of Arith <lb></lb>metick, are ſtupified in hearing your concluſions; as for inſtance, <lb></lb>whilſt we read; Therefore the new Star or Comet was diſtant <lb></lb>from the Earths centre three hundred ſeventy and three thouſand <lb></lb>eight hundred and ſeven miles; and moreover, two hundred and <lb></lb>eleven, four chouſand ninety ſevenths 373807 211/4097, and upon theſe <lb></lb>preciſe punctualities, wherein you take notice of ſuch ſmall mat <lb></lb>ters, we do conceive it to be impoſſible, that you, who in our cal <lb></lb>culations keep an account of an inch, can at the cloſe deceive us ſo <lb></lb>much as an hundred miles.</s></p><p type="main"><s>SALV. </s><s>This your reaſon and excuſe would paſſe for currant, <lb></lb>if in a diſtance of thouſands of miles, a yard over or under were <lb></lb>of any great moment, and if the ſuppoſitions that we take for <lb></lb>true, were ſo certain, as that they could aſſure us of producing an <lb></lb>indubitable truth in the concluſion; but here you ſee in the twelve <lb></lb>workings of the Author, the diſtances of the Star, which from <lb></lb>them one may conclude to have been different from each other, <lb></lb>(and therefore wide of the truth) for many hundreds and thou <lb></lb>ſands of miles: now whilſt that I am more than certain, that that <lb></lb>which I ſeek muſt needs differ from the truth by hundreds of miles, <lb></lb>to what purppſe is it to be ſo curious in our calculations, for fear <lb></lb>of miſſing the quantity of an inch? </s><s>But let us proceed, at laſt, <lb></lb>to the working, which I reſolve in this manner. <emph type="italics"></emph>Tycho,<emph.end type="italics"></emph.end> as may be <pb xlink:href="040/01/289.jpg" pagenum="269"></pb>ſeen in that ſame note obſerved the ſtar in the polar altitude of 55 <lb></lb>degrees and 58 <emph type="italics"></emph>mi. </s><s>pri.<emph.end type="italics"></emph.end> And the polar altitude of the <emph type="italics"></emph>Landgrave<emph.end type="italics"></emph.end> <lb></lb>was 51 degrees and 18 <emph type="italics"></emph>mi. </s><s>pri.<emph.end type="italics"></emph.end> The altitude of the ſtar in the Me <lb></lb>ridian taken by <emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end> was 27 degrees 45 <emph type="italics"></emph>mi. </s><s>pri.<emph.end type="italics"></emph.end> The <emph type="italics"></emph>Land <lb></lb>grave<emph.end type="italics"></emph.end> found its altitude 23 degrees 3 <emph type="italics"></emph>mi. </s><s>pri.<emph.end type="italics"></emph.end> The which altitudes <lb></lb>are theſe noted here, as you ſee. <lb></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell></row><row><cell><emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end> Pole</cell><cell>55</cell><cell>58</cell><cell>* 27</cell><cell>45</cell></row><row><cell><emph type="italics"></emph>Landgr.<emph.end type="italics"></emph.end> Pole</cell><cell>51</cell><cell>18</cell><cell>* 23</cell><cell>3</cell></row></table><p type="main"><s>This done, ſubſtract the leſſe from the greater, and there remains <lb></lb>theſe differences here underneath. <lb></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></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"></emph>gr. </s><s>4 mi. </s><s>pr.<emph.end type="italics"></emph.end> <lb></lb>is leſſe than the difference of the altitudes of the Star 4 <emph type="italics"></emph>gr. </s><s>42 mi. <lb></lb></s><s>pr.<emph.end type="italics"></emph.end> and therefore we have the difference of parallaxes, 0 <emph type="italics"></emph>gr. </s><s>2 mi. <lb></lb></s><s>pri.<emph.end type="italics"></emph.end> Theſe things being found, take the Authours own figure <lb></lb>[<emph type="italics"></emph>Fig. </s><s>2.<emph.end type="italics"></emph.end>] in which the point B is the ſtation of the <emph type="italics"></emph>Landgrave,<emph.end type="italics"></emph.end> <lb></lb>D the ſtation of <emph type="italics"></emph>Tycho,<emph.end type="italics"></emph.end> C the place of the ſtar, A the centre <lb></lb>of the Earth, A B E the vertical line of the <emph type="italics"></emph>Landgrave,<emph.end type="italics"></emph.end> A D F <lb></lb><arrow.to.target n="table10"></arrow.to.target> <lb></lb><arrow.to.target n="table11"></arrow.to.target> <lb></lb><arrow.to.target n="table12"></arrow.to.target> <lb></lb>of <emph type="italics"></emph>Tycho,<emph.end type="italics"></emph.end> and the angle B C D the difference of Parallaxes. </s><s>And <pb xlink:href="040/01/290.jpg" pagenum="270"></pb>becauſe the angle B A D, conteined between the vertical lines, is <lb></lb>equal to the difference of the Polar altitudes, it ſhall be 4<emph type="italics"></emph>gr. </s><s>40m.<emph.end type="italics"></emph.end> <lb></lb>which I note here apart; and I finde the chord of it by the Table <lb></lb>of Arches and Chords, and ſet it down neer unto it, which is 8142 <lb></lb>parts, of which the ſemidiameter A B is 100000. Next, I finde <lb></lb>the angle B D C with eaſe, for the half of the angle B A D, which <lb></lb>is 2 <emph type="italics"></emph>gr. </s><s>20 m.<emph.end type="italics"></emph.end> added to a right angle, giveth the angle B D F 92 <emph type="italics"></emph>gr.<emph.end type="italics"></emph.end> <lb></lb>20 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> to which adding the angle C D F, which is the diſtance from <lb></lb>the vertical point of the greateſt altitude of the Star, which here is <lb></lb>62 <emph type="italics"></emph>gr. </s><s>15 m.<emph.end type="italics"></emph.end> it giveth us the quantity of the angle B D C, <lb></lb>154 <emph type="italics"></emph>grad. </s><s>45 min.<emph.end type="italics"></emph.end> the which I ſet down together with its Sine, <lb></lb>taken out of the Table, which is 42657, and under this I note <lb></lb>the angle of the Parallax B C D 0 <emph type="italics"></emph>gr. </s><s>2 m.<emph.end type="italics"></emph.end> with its Sine 58. <lb></lb>And becauſe in the Triangle B C D, the ſide D B is to the ſide <lb></lb>B C; as the ſine of the oppoſite angle B C D, to the ſine of the <lb></lb>oppoſite angle B D C: therefore, if the line B D were 58. B C <lb></lb>would be 42657. And becauſe the Chord D B is 8142. of thoſe <lb></lb>parts whereof the ſemidiameter B A is 100000. and we ſeek to <lb></lb>know how many of thoſe parts is B C; therefore we will ſay, by <lb></lb>the Golden Rule, if when B D is 58. B G is 42657. in caſe the <lb></lb>ſaid D B were 8142. how much would B C be? </s><s>I multiply the <lb></lb>ſecond term by the third, and the product is 347313294. which <lb></lb>ought to be divided by the firſt, namely, by 58. and the quotient <lb></lb>ſhall be the number of the parts of the line B C, whereof the ſe <lb></lb>midiameter A B is 100000. And to know how many ſemidiame <lb></lb>ters B A, the ſaid line B C doth contein, it will be neceſſary anew <lb></lb>to divide the ſaid quotient ſo found by 100000. and we ſhall have <lb></lb>the number oſ ſemidiameters conteined in B G. </s><s>Now the num <lb></lb>ber 347313294. divided by 58. giveth 5988160 1/4. as here you <lb></lb>may ſee. <lb></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell>Its chord 8142 of thoſe</cell></row><row><cell>Ang. B A D</cell><cell>4</cell><cell>40</cell><cell>parts, whereof the ſemid.</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></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 firſt <lb></lb>quotient found, that is, 347313294. by the product of the multi <lb></lb>plication of the two numbers 58. and 100000. that is, <pb xlink:href="040/01/291.jpg" pagenum="271"></pb><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 alſo there will come forth 59 5113294/5800000</s></p><p type="main"><s>And ſo many ſemidiameters are contained in the line B C, to <lb></lb>which one being added for the line A B, we ſhall have little leſſe <lb></lb>than 61. ſemidiameters for the two lines A B C; and therefore <lb></lb>the right diſtance from the centre A, to the Star C, ſhall be more <lb></lb>than 60. ſemidiameters, and therefore it is ſuperiour to the Moon, <lb></lb>according to <emph type="italics"></emph>Ptolomy,<emph.end type="italics"></emph.end> more than 27. ſemidiameters, and according <lb></lb>to <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> more than 8. ſuppoſing that the diſtance of the <lb></lb>Moon from the centre of the Earth by <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> his account is <lb></lb>what the Author maketh it, 52 ſemidiameters. </s><s>With this ſame <lb></lb>working, I find by the obſervations of <emph type="italics"></emph>Camerarius,<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Muno <lb></lb>ſius,<emph.end type="italics"></emph.end> that the Star was ſituate in that ſame diſtance, to wit, ſome <lb></lb>what more than 60. ſemidiameters. </s><s>Theſe are the obſervations, <lb></lb>and theſe following next after them the calculations. <lb></lb><arrow.to.target n="table16"></arrow.to.target> <lb></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell></row><row><cell>Altitude of <emph type="italics"></emph>Camerar.<emph.end type="italics"></emph.end></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"></emph>Munoſ.<emph.end type="italics"></emph.end></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></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 ſubtenſe 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"></emph>The Golden Rule.<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="table18"></arrow.to.target> <lb></lb><arrow.to.target n="table19"></arrow.to.target></s></p> <pb xlink:href="040/01/292.jpg" pagenum="272"></pb><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>Diſtance B C 59. and</cell></row><row><cell>116</cell><cell>6948</cell><cell>73380</cell><cell>almoſt 60. ſemidiameters.</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 obſervations of <emph type="italics"></emph>Tycho,<emph.end type="italics"></emph.end> and <lb></lb>of <emph type="italics"></emph>Munoſius,<emph.end type="italics"></emph.end> from which the Star is calculated to be diſtant from <lb></lb>the Centre of the Earth 478 Semidiameters and more. <lb></lb><arrow.to.target n="table20"></arrow.to.target> <lb></lb><arrow.to.target n="table21"></arrow.to.target> <lb></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell></row><row><cell>Altitudes</cell><cell><emph type="italics"></emph>Tycho.<emph.end type="italics"></emph.end></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"></emph>Munoſ.<emph.end type="italics"></emph.end></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"></emph>B A D.<emph.end type="italics"></emph.end></cell><cell>16</cell><cell>28</cell><cell>its chord</cell><cell>28640</cell></row><row><cell>Angles</cell><cell><emph type="italics"></emph>B D C.<emph.end type="italics"></emph.end></cell><cell>104</cell><cell>14</cell><cell>Sines</cell><cell>96930</cell></row><row><cell></cell><cell><emph type="italics"></emph>B C D.<emph.end type="italics"></emph.end></cell><cell>0</cell><cell>2</cell><cell></cell><cell>58</cell></row></table><p type="main"><s><emph type="italics"></emph>The Golden Rule.<emph.end type="italics"></emph.end> <lb></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>Theſe workings following make the Star remote from the Cen <lb></lb>tre, more than 358 Semidiameters. <lb></lb><arrow.to.target n="table24"></arrow.to.target> <lb></lb><arrow.to.target n="table25"></arrow.to.target></s></p> <pb xlink:href="040/01/293.jpg" pagenum="273"></pb><table><table.target id="table24"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell></row><row><cell>Altitudes</cell><cell><emph type="italics"></emph>Peucerus<emph.end type="italics"></emph.end></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"></emph>Munoſius<emph.end type="italics"></emph.end></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell></cell></row><row><cell></cell><cell><emph type="italics"></emph>B A D.<emph.end type="italics"></emph.end></cell><cell>12</cell><cell>24</cell><cell>its chord</cell><cell>21600</cell></row><row><cell>Angles</cell><cell><emph type="italics"></emph>B D C.<emph.end type="italics"></emph.end></cell><cell>106</cell><cell>16</cell><cell>Sines</cell><cell>95996</cell></row><row><cell></cell><cell><emph type="italics"></emph>B C D.<emph.end type="italics"></emph.end></cell><cell>0</cell><cell>2</cell><cell></cell><cell>58</cell></row></table><p type="main"><s>The Golden Rule. <lb></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 ſtar is found to be diſtant from the <lb></lb>centre more than 716. ſemidiameters. <lb></lb><arrow.to.target n="table27"></arrow.to.target> <lb></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>ſec.<emph.end type="italics"></emph.end></cell></row><row><cell>Altitudes</cell><cell><emph type="italics"></emph>Landgr.<emph.end type="italics"></emph.end></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"></emph>Hainzel.<emph.end type="italics"></emph.end></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>ſec.<emph.end type="italics"></emph.end></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></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>Theſe as you ſee are five workings which place the ſtar very <lb></lb>much above the Moon. </s><s>And here I deſire you to conſider upon <lb></lb>that particular, which even now I told you, namely, that in great <pb xlink:href="040/01/294.jpg" pagenum="274"></pb>diſtances, the mutations, or if you pleaſe corrections, of a ve <lb></lb>ry few minutes, removeth the ſtar a very great way farther off. <lb></lb></s><s>As for example, in the firſt of theſe workings, where the calcu <lb></lb>lation made the ſtar 60. ſemidiameters remote from the centre, <lb></lb>with the Parallax of 2. minutes; he that would maintain that it <lb></lb>was in the Firmament, is to correct in the obſervations but onely <lb></lb>two minutes, nay leſſe, for then the Parallax ceaſeth, or be <lb></lb>commeth ſo ſmall, that it removeth the ſtar to an immenſe di <lb></lb>ſtance, which by all is received to be the Firmament. </s><s>In the ſe <lb></lb>cond indagation, or working, the correction of leſſe than 4 <emph type="italics"></emph>m. <lb></lb></s><s>prim.<emph.end type="italics"></emph.end> doth the ſame. </s><s>In the third, and fourth, like as in the firſt, <lb></lb>two minutes onely mount the ſtar even above the Firmament. <lb></lb></s><s>In the laſt preceding, a quarter of a minute, that is 15. ſeconds, <lb></lb>gives us the ſame. </s><s>But it doth not ſo occur in the ſublunary alti <lb></lb>tudes; for if you fancy to your ſelf what diſtance you moſt <lb></lb>like, and go about to correct the workings made by the Au <lb></lb>thour, and adjuſt them ſo as that they all anſwer in the ſame <lb></lb>determinate diſtance, you will find how much greater correcti <lb></lb>ons they do require.</s></p><p type="main"><s>SAGR. </s><s>It cannot but help us in our fuller underſtanding of <lb></lb>things, to ſee ſome examples of this which you ſpeak of.</s></p><p type="main"><s>SALV. </s><s>Do you aſſign any whatſoever determinate ſublunary <lb></lb>diſtance at pleaſure in which to conſtitute the ſtar, for with ſmall <lb></lb>ado we may aſſertain our ſelves whether corrections like to theſe, <lb></lb>which we ſee do ſuffice to reduce it amongſt the fixed ſtars, will <lb></lb>reduce it to the place by you aſſigned.</s></p><p type="main"><s>SAGR. </s><s>To take a diſtance that may favour the Authour, we <lb></lb>will ſuppoſe it to be that which is the greateſt of all thoſe found <lb></lb>by him in his 12 workings; for whilſt it is in controverſie be <lb></lb>tween him and Aſtronomers, and that they affirm the ſtar to <lb></lb>have been ſuperiour to the Moon, and he that it was inferiour, <lb></lb>very ſmall ſpace that he proveth it to have been lower, giveth <lb></lb>him the victory.</s></p><p type="main"><s>SALV. </s><s>Let us therefore take the ſeventh working wrought <lb></lb>upon the obſervations of <emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Thaddæus Hagecius,<emph.end type="italics"></emph.end> by <lb></lb>which the Authour found the ſtar to have been diſtant from the <lb></lb>centre 32. ſemidiameters, which ſituation is moſt favourable to <lb></lb>his purpoſe; and to give him all advantages, let us moreover <lb></lb>place it in the diſtance moſt disfavouring the <emph type="italics"></emph>Aſtronomers,<emph.end type="italics"></emph.end> which <lb></lb>is to ſituate it above the Firmament. </s><s>That therefore being ſup <lb></lb>poſed, let us ſeek in the next place what corrections it would be ne <lb></lb>ceſſary to apply to his other 11 workings. </s><s>And let us begin at the <lb></lb>firſt calculated upon the obſervations of <emph type="italics"></emph>Hainzelius<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Mauroice<emph.end type="italics"></emph.end>; <lb></lb>in which the Authour findeth the diſtance from the centre about <lb></lb>3. ſemidiameters with the Parallax of 4 <emph type="italics"></emph>gr. </s><s>42 m. </s><s>30. ſec.<emph.end type="italics"></emph.end> Let <pb xlink:href="040/01/295.jpg" pagenum="275"></pb>us ſee whether by withdrawing it 20. minutes onely, it will riſe <lb></lb>to the height of 32. ſemidiameters: See the ſhort and true opera <lb></lb>tion. </s><s>Multiply the ſine of the angle B D C, by the ſine of the <lb></lb><arrow.to.target n="table30"></arrow.to.target> <lb></lb><arrow.to.target n="table31"></arrow.to.target> <lb></lb><arrow.to.target n="table32"></arrow.to.target> <lb></lb>chord B D, and divide the product, the five laſt figures being cut <lb></lb>off by the ſine of the Parallax, and the quotient will be 28. ſe <lb></lb>midiameters, and an half, ſo that though you make a correction <lb></lb>of 4 <emph type="italics"></emph>gr. </s><s>22 min. </s><s>30 ſec.<emph.end type="italics"></emph.end> taken from 4 <emph type="italics"></emph>gr. </s><s>42 min. </s><s>30 ſec.<emph.end type="italics"></emph.end> it ſhall <lb></lb>not elevate the ſtar to the altitude of 32. ſemidiameters, which <lb></lb>correction for <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> his underſtanding it, is of 262. minutes, <lb></lb>and an half.</s></p><table><table.target id="table30"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>ſec.<emph.end type="italics"></emph.end></cell></row><row><cell><emph type="italics"></emph>Hainzelius<emph.end type="italics"></emph.end></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"></emph>Maurolicus<emph.end type="italics"></emph.end></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>ſec.<emph.end type="italics"></emph.end></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 ſecond operation made upon the obſervations of <emph type="italics"></emph>Hain <lb></lb>zelius,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Sculerus,<emph.end type="italics"></emph.end> with the Parallax of 0 <emph type="italics"></emph>gr. </s><s>8 min. </s><s>30 ſec.<emph.end type="italics"></emph.end> <lb></lb>the ſtar is found in the height of 25. ſemidiameters or therea <lb></lb>bouts, as may be ſeen in the ſubſequent working. <lb></lb><arrow.to.target n="table33"></arrow.to.target> <pb xlink:href="040/01/296.jpg" pagenum="276"></pb><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"></emph>gr. </s><s>8 m. </s><s>30 ſec.<emph.end type="italics"></emph.end> to 7 <emph type="italics"></emph>gr.<emph.end type="italics"></emph.end> <lb></lb>7 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> whoſe ſine is 204, the ſtar elevateth to 30 ſemidiameters or <lb></lb>thereabouts; therefore the correction of 0 <emph type="italics"></emph>gr. </s><s>1 mi. </s><s>30 ſec.<emph.end type="italics"></emph.end> doth <lb></lb>not ſuffice. <lb></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 ſee what correction is requiſite for the third work <lb></lb>ing made upon the obſervations of <emph type="italics"></emph>Hainzelius<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Tycho,<emph.end type="italics"></emph.end> which <lb></lb>rendereth the ſtar about 19 ſemidiameters high, with the Pa <lb></lb>rallax of 10 <emph type="italics"></emph>m. </s><s>pri.<emph.end type="italics"></emph.end> The uſual angles and their ſines, and chord <lb></lb>found by the Authour, are theſe next following; and they re <lb></lb>move the ſtar (as alſo in the Authours working) 19 ſemidia <lb></lb>meters from the centre of the Earth. </s><s>It is neceſſary therefore for <lb></lb>the raiſing of it, to diminiſh the Parallax according to the Rule <lb></lb>which he likewiſe obſerveth in the ninth working. </s><s>Let us there <lb></lb>fore ſuppoſe the Parallax to be 6 <emph type="italics"></emph>m. </s><s>prim.<emph.end type="italics"></emph.end> whoſe ſine is 175, and <lb></lb>the diviſion being made, there is found likewiſe leſſe than 31 <lb></lb>ſemidiameters for the ſtars diſtance. </s><s>And therefore the correcti <lb></lb>on of 4 <emph type="italics"></emph>min. </s><s>prim.<emph.end type="italics"></emph.end> is too little to ſerve the Authours purpoſe. <lb></lb><arrow.to.target n="table36"></arrow.to.target> <pb xlink:href="040/01/297.jpg" pagenum="277"></pb><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 reſt with the ſame <lb></lb>rule, and with the chords and ſines found out by the Authour <lb></lb>himſelf; in this the Parallax is 14 <emph type="italics"></emph>m. </s><s>prim.<emph.end type="italics"></emph.end> and the height found <lb></lb>leſſe than 10 ſemidiameters, and diminiſhing the Parallax from <lb></lb>14 <emph type="italics"></emph>min.<emph.end type="italics"></emph.end> to 4 <emph type="italics"></emph>min.<emph.end type="italics"></emph.end> yet nevertheleſſe you ſee that the ſtar doth not <lb></lb>elevate full 31 ſemidiameters. </s><s>Therefore 10 <emph type="italics"></emph>min.<emph.end type="italics"></emph.end> in 14 <emph type="italics"></emph>min.<emph.end type="italics"></emph.end> doth <lb></lb>not ſuffice. <lb></lb><arrow.to.target n="table38"></arrow.to.target> <lb></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 ſines and the <lb></lb>chord as you ſee, and the Parallax is 0 <emph type="italics"></emph>gr. </s><s>42 m. </s><s>30 ſec.<emph.end type="italics"></emph.end> which <lb></lb>rendereth the height of the ſtar about 4 ſemidiameters, and cor <lb></lb>recting the Parallax, with reducing it from 0 <emph type="italics"></emph>gr. </s><s>42 m. </s><s>30 ſec.<emph.end type="italics"></emph.end> <lb></lb>to 0 <emph type="italics"></emph>gr. </s><s>5 m.<emph.end type="italics"></emph.end> onely, doth not ſuffice to raiſe it to ſo much as 28 ſe <lb></lb>midiameters, the correction therefore of 0 <emph type="italics"></emph>gr. </s><s>37 m. </s><s>30 ſec.<emph.end type="italics"></emph.end> is <lb></lb>too little. <lb></lb><arrow.to.target n="table40"></arrow.to.target> <pb xlink:href="040/01/298.jpg" pagenum="278"></pb><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 ſixth operation the chord, the ſines and Parallax are as <lb></lb>followeth, and the ſtar is found to be about 4 ſemidiameters; let <lb></lb>us ſee whether it will be reduced, abating the Parallax from 8 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> <lb></lb>to 1 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> onely; Here is the operation, and the ſtar raiſed but to <lb></lb>27. ſemidiameters or thereabout; therefore the correction of 7 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> <lb></lb>in 8 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> doth not ſuffice. <lb></lb><arrow.to.target n="table42"></arrow.to.target> <lb></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"></emph>gr.<emph.end type="italics"></emph.end></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 ſines, and the Parallax, <lb></lb>as you ſee, are theſe enſuing, and hence the Authour calculates <lb></lb>the height of the ſtar to be 1. ſemidiameter and an half, with the <lb></lb>Parallax of 43. <emph type="italics"></emph>min.<emph.end type="italics"></emph.end> which reduced to 1 <emph type="italics"></emph>min.<emph.end type="italics"></emph.end> yet notwithſtand <lb></lb>ing giveth the ſtar leſſe remote than 24. ſemidiameters, the corre <lb></lb>ction therefore of 42. <emph type="italics"></emph>min.<emph.end type="italics"></emph.end> is not enough. <lb></lb><arrow.to.target n="table44"></arrow.to.target> <pb xlink:href="040/01/299.jpg" pagenum="279"></pb><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 ſee the ninth. </s><s>Here is the chord, the ſines and <lb></lb>the Parallax which is 15 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> From whence the Authour calcu <lb></lb>lates the diſtance of the ſtar from the ſuperficies of the Earth <lb></lb>to be leſſe than a ^{*} ſeven and fortieth part of a ſemidiameter, <lb></lb><arrow.to.target n="marg513"></arrow.to.target> <lb></lb>but this is an errour in the calcultaion, for it cometh forth truly, <lb></lb>as we ſhall ſee here below, more than a ſifth: See here the quo <lb></lb>tienr is 90/436, which is more than one fifth. <lb></lb><arrow.to.target n="table46"></arrow.to.target> <lb></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></lb>tine verſion is erro <lb></lb>neous, making it <lb></lb>a fortieth part of, <lb></lb><emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></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 preſently after ſubjoyns in way of <lb></lb>amending the obſervations, that is, that it ſuſſiceth not to re <lb></lb>duce the difference of Parallax, neither to a minute, nor yet <lb></lb>to the eighth part of a minute is true. </s><s>But I ſay, that neither <lb></lb>will the tenth part of a minute reduce the height of the ſtar to <lb></lb>32. ſemidiameters; for the ſine of the tenth part of a minute, <lb></lb>that is of ſix ſeconds, is 3; by which if we according to our Rule <lb></lb>ſhould divide 90. or we may ſay, if we ſhould divide 9058672. <lb></lb>by 300000. the quotient will be 30 58672/100000, that is little more <lb></lb>than 30. ſemidiameters and an half.</s></p><p type="main"><s>The tenth giveth the altitude of the ſtar one fifth of a ſemi <lb></lb>diameter, with theſe angles, ſines, and Parallax, that is, 4 <emph type="italics"></emph>gr.<emph.end type="italics"></emph.end> <pb xlink:href="040/01/300.jpg" pagenum="280"></pb>30 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> which I ſee that being reduced from 4 <emph type="italics"></emph>gr. </s><s>30 min.<emph.end type="italics"></emph.end> to 2 <emph type="italics"></emph>min.<emph.end type="italics"></emph.end> <lb></lb>yet nevertheleſſe it elevates not the ſtar to 29. ſemidiameters. <lb></lb><arrow.to.target n="table48"></arrow.to.target> <lb></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"></emph>gr. 30 m.<emph.end type="italics"></emph.end></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 ſtar to the Authour remote about <lb></lb>13. ſemidiameters, with the Parallax of 55. <emph type="italics"></emph>min.<emph.end type="italics"></emph.end> let us ſee, re <lb></lb>ducing it to 20 <emph type="italics"></emph>min.<emph.end type="italics"></emph.end> whether it will exalt the ſtar: See here the <lb></lb>calculation elevates it to little leſſe than 33. ſemidiameters, the <lb></lb>correction therefore is little leſſe than 35. <emph type="italics"></emph>min.<emph.end type="italics"></emph.end> in 55. <emph type="italics"></emph>min.<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="table50"></arrow.to.target> <lb></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"></emph>gr. 55 m.<emph.end type="italics"></emph.end></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"></emph>gr. </s><s>36. min.<emph.end type="italics"></emph.end> maketh the <lb></lb>ſtar leſſe high than 6. ſemidiameters, reducing the Parallax to <lb></lb>20 <emph type="italics"></emph>min.<emph.end type="italics"></emph.end> it carrieth the ſtar to leſſe than 30. ſemidiameters di <lb></lb>ſtance, therefore the correction of 1 <emph type="italics"></emph>gr. </s><s>16. min.<emph.end type="italics"></emph.end> ſufficeth not. <pb xlink:href="040/01/301.jpg" pagenum="281"></pb><arrow.to.target n="table52"></arrow.to.target> <lb></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"></emph>gr. 36 m.<emph.end type="italics"></emph.end></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"></emph>Theſe are the Corrections of the Parallaxes <lb></lb>of the ten workings of the Author, to <lb></lb>reduce the Star to the altitude of<emph.end type="italics"></emph.end> <lb></lb>32 <emph type="italics"></emph>Semidiameters.<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="table54"></arrow.to.target> <lb></lb><arrow.to.target n="table55"></arrow.to.target></s></p><table><table.target id="table54"></table.target><row><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>ſec.<emph.end type="italics"></emph.end></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>ſec.<emph.end type="italics"></emph.end></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 ſee, that to reduce the Star to 32. Semidiame <lb></lb>ters in altitude, it is requiſite from the ſum of the Parallaxes 836. <lb></lb>to ſubtract 756. and to reduce them to 80. nor yet doth that <lb></lb>correction ſuffice.</s></p> <pb xlink:href="040/01/302.jpg" pagenum="282"></pb><p type="main"><s>Here we ſee alſo, (as I have noted even now) that ſhould the <lb></lb>Authour conſent to aſſign the diſtance of 32. Semidiameters for <lb></lb>the true height of the Star, the correction of thoſe his 10. workings, <lb></lb>(I ſay 10. becauſe the ſecond being very high, is reduced to the <lb></lb>height of 32. Semidiameters, with 2. minutes correction) to make <lb></lb>them all to reſtore the ſaid Star to that diſtance, would require ſuch <lb></lb>a reduction of Parallaxes, that amongſt the whole number of ſub <lb></lb>ſtractions they ſhould make more than 756 <emph type="italics"></emph>m. </s><s>pr.<emph.end type="italics"></emph.end> whereas in the <lb></lb>5. calculated by me, which do place the Star above the Moon, to <lb></lb>correct them in ſuch ſort, as to conſtitute it in the Firmament, <lb></lb>the correction onely of 10. minutes, and one fourth ſufficeth.</s></p><p type="main"><s>Now adde to theſe, other 5. workings, that place the Star pre <lb></lb>ciſely in the Firmament, without need of any correction at all, <lb></lb>and we ſhall have ten workings or indagations that agree to place <lb></lb>it in the Firmament, with the correction onely of 5. of them (as <lb></lb>hath been ſeen) but 10. <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> and 15 <emph type="italics"></emph>ſec.<emph.end type="italics"></emph.end> Whereas for the correcti <lb></lb>on of thoſe 10. of the Authour, to reduce them to the altitude of <lb></lb>32. ſemidiameters, there will need the emendations of 756 mi <lb></lb>nutes in 836. that is, there muſt from the ſumme 836 be ſubſtra <lb></lb>cted 756. if you would have the Star elevated to the altitude of <lb></lb>32. ſemidiameters, and yet that correction doth not fully ſerve.</s></p><p type="main"><s>The workings that immediately without any correction free the <lb></lb>Star from Parallaxes, and therefore place it in the Firmament, <lb></lb>and that alſo in the remoteſt parts of it, and in a word, as high <lb></lb>as the Pole it ſelf, are theſe 5. noted here. <lb></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell></row><row><cell><emph type="italics"></emph>Camerar.<emph.end type="italics"></emph.end></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"></emph>Peucerus<emph.end type="italics"></emph.end></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell></row><row><cell><emph type="italics"></emph>Landgrav.<emph.end type="italics"></emph.end></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"></emph>Hainzel.<emph.end type="italics"></emph.end></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell></row><row><cell><emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end></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"></emph>Peucerus<emph.end type="italics"></emph.end></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"></pb><row><cell></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell></row><row><cell><emph type="italics"></emph>Reinhold.<emph.end type="italics"></emph.end></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"></emph>Hainzel.<emph.end type="italics"></emph.end></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell></row><row><cell><emph type="italics"></emph>Camerar.<emph.end type="italics"></emph.end></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"></emph>Hagecius<emph.end type="italics"></emph.end></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></lb>ſervations of all theſe Aſtronomers, thoſe that make the Stars ſub <lb></lb>lime to an infinite diſtance, are many in number, namely, about <lb></lb>30. more than thoſe who give the Star, by calculation, to be be <lb></lb>low the Moon; and becauſe (as it was agreed npon between us) it <lb></lb>is to be believed that the Obſervators have erred rather little than <lb></lb>much, it is a manifeſt thing that the corrections to be applied to <lb></lb>the Obſervaations, which make the ſtar of an infinite altitude, to <lb></lb>reduce it lower, do ſooner, and with leſſer amendment place it in <lb></lb>the Firmament, than beneath the Moon; ſo that all theſe applaud <lb></lb>the opinion of thoſe who put it amongſt the fixed Stars. </s><s>You may <lb></lb>adde, that the corrections required for thoſe emendations, are <lb></lb>much leſſer than thoſe, by which the Star from an unlikely proxi <lb></lb>mity may be removed to the height more favourable for this Au <lb></lb>thour, as by the foregoing examples hath been ſeen; amongſt <lb></lb>which impoſſible proximities, there are three that ſeem to remove <lb></lb>the Star from the Earths centre, a leſſe diſtance than one Semidi <lb></lb>ameter, making it, as it were, to turn round under ground, and <lb></lb>theſe are thoſe combinations, wherein the Polar altitude of one <lb></lb>of the Obſervators being greater than the Polar altitude of the <lb></lb>other, the elevation of the Star taken by the firſt, is leſſer than the <lb></lb>elation of the Star taken by the latter.</s></p><p type="main"><s>The firſt of theſe is this of the <emph type="italics"></emph>Landgrave<emph.end type="italics"></emph.end> with <emph type="italics"></emph>Gemma,<emph.end type="italics"></emph.end> <lb></lb>where the Polar altitude of the <emph type="italics"></emph>Landgrave 51 gr. </s><s>18 min.<emph.end type="italics"></emph.end> is <lb></lb>greater than the Polar altitude of <emph type="italics"></emph>Gemma,<emph.end type="italics"></emph.end> which is 50 <emph type="italics"></emph>gr. </s><s>50 m.<emph.end type="italics"></emph.end> <lb></lb>But the altitude of the Star of the <emph type="italics"></emph>Landgrave 79 gr. </s><s>30 min.<emph.end type="italics"></emph.end> <lb></lb>is leſſer than that of the Star, of <emph type="italics"></emph>Gemma 79 gr. </s><s>45 min.<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="table57"></arrow.to.target></s></p> <pb xlink:href="040/01/304.jpg" pagenum="284"></pb><table><table.target id="table57"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell></row><row><cell><emph type="italics"></emph>Landgrave<emph.end type="italics"></emph.end></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"></emph>Gemma<emph.end type="italics"></emph.end></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 theſe below. <lb></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></cell></row><row><cell><emph type="italics"></emph>Buſchius.<emph.end type="italics"></emph.end></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"></emph>Gemma.<emph.end type="italics"></emph.end></cell><cell></cell><cell>50</cell><cell>50</cell><cell></cell><cell>79</cell><cell>45</cell></row><row><cell><emph type="italics"></emph>Reinholdus.<emph.end type="italics"></emph.end></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"></emph>Gemma.<emph.end type="italics"></emph.end></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 demonſtrated, you may gueſſe how <lb></lb>much this firſt way of finding out the diſtance of the Star, and <lb></lb>proving it ſublunary introduced by the Authour, maketh againſt <lb></lb>himſelf, and how much more probably and clearly the diſtance <lb></lb>thereof is collected to have been amongſt the more remote fixed <lb></lb>Stars.</s></p><p type="main"><s>SIMP. </s><s>As to this particular, I think that the inefficacy of the <lb></lb>Authors demonftrations is very plainly diſcovered; But I ſee that all <lb></lb>this was compriſed in but a few leaves of his Book, and it may be, <lb></lb>that ſome other of his Arguments are more concluſive then theſe <lb></lb>firſt.</s></p><p type="main"><s>SALV. </s><s>Rather they muſt needs be leſſe valid, if we will take <lb></lb>thoſe that lead the way for a proof of the reſt: For (as it is clear) <lb></lb>the uncertainty and inconcluſiveneſſe of thoſe, is manifeſtly ob <lb></lb>ſerved to derive it ſelf from the errours committed in the inſtru <lb></lb>mental obſervations, upon which the Polar Altitude, and height <lb></lb>of the Star was thought to have been juſtly taken, all in effect <lb></lb>having eaſily erred; And yet to find the Altitude of the Pole, A <lb></lb>ſtronomers have had Ages of time to apply themſelves to it, at their <lb></lb>leaſure: and the Meridian Altitudes of the Star are eaſier to be <lb></lb>obſerved, as being moſt terminate, and yielding the Obſervator <lb></lb>ſome time to continue the ſame, in regard they change not ſenſibly, <lb></lb>in a ſhort time, as thoſe do that are remote from the Meridian. </s><s>And <lb></lb>if this be ſo, as it is moſt certain, what credit ſhall we give to Calcu <lb></lb>lations founded upon Obſervations more numerous, more difficult <lb></lb>to be wrought, more momentary in variation, and we may add, <lb></lb>with Inſtruments more incommodious and erroneous? </s><s>Upon a <lb></lb>ſlight peruſal of the enſuing demonſtrations, I ſee that the Com <lb></lb>putations are made upon Altitudes of the Star taken in different <lb></lb>Vertical Circles, which are called by the Arabick name, <emph type="italics"></emph>Azimuths<emph.end type="italics"></emph.end>; in <lb></lb>which obſervations moveable inſtruments are made uſe of, not on <lb></lb>ly in the Vertical Circles, but in the Horizon alſo, at the ſame time; <lb></lb>inſomuch that it is requiſite in the ſame moment that the altitude <lb></lb>is taken, to have obſerved, in the Horizon, the diſtance of the Vir <pb xlink:href="040/01/305.jpg" pagenum="285"></pb>tical point in which the Star is, from the Meridian; Moreover, <lb></lb>after a conſiderable interval of time, the operation muſt be re <lb></lb>peated, and exact account kept of the time that paſſed, truſting <lb></lb>either to Dials, or to other obſervations of the Stars. </s><s>Such an <emph type="italics"></emph>Olio<emph.end type="italics"></emph.end> <lb></lb>of Obſervations doth he ſet before you, comparing them with <lb></lb>ſuch another made by another obſerver in another place with a <lb></lb>nother different inſtrument, and at another time; and from this <lb></lb>the Authour ſeeks to collect what would have been, the Elevations <lb></lb>of the Star, and Horizontal Latitudes happened in the time and <lb></lb>hour of the other firſt obſervations, and upon ſuch a coæquation he <lb></lb>in the end grounds his account. </s><s>Now I refer it to you, what credit <lb></lb>is to be given to that which is deduced from ſuch like workings. <lb></lb></s><s>Moreover, I doubt not in the leaſt, but that if any one would tor <lb></lb>ture himſelf with ſuch tedious computations, he would find, as in <lb></lb>thoſe aforegoing, that there were more that would favour the ad <lb></lb>verſe party, than the Authour: But I think it not worth the while <lb></lb>to take ſo much pains in a thing, which is not, amongſt thoſe prima <lb></lb>ry ones, by us underſtood.</s></p><p type="main"><s>SAGR. </s><s>I am of your Opinion in this particular: But this buſi <lb></lb>neſſe being environed with ſo many intricacies, uncertainties, and <lb></lb>errours, upon what confidence have ſo many Aſtronomers poſitive <lb></lb>ly pronounced the new Star to have been ſo high?</s></p><p type="main"><s>SALV. </s><s>Upon two ſorts of obſervations moſt plain, moſt eaſie, <lb></lb>and moſt certain; one only of which is more than ſufficient to aſſure <lb></lb>us, that it was ſcituate in the Firmament, or at leaſt by a great <lb></lb>diſtance ſuperiour to the Moon. </s><s>One of which is taken from the <lb></lb>equality, or little differing inequality of its diſtances from the <lb></lb>Pole, aſwell whilſt it was in the loweſt part of the Meridian, as <lb></lb>when it was in the uppermoſt: The other is its having perpetual <lb></lb>ly kept the ſame diſtances from certain of the fixed Stars, adjacent <lb></lb>to it, and particularly from the eleventh of <emph type="italics"></emph>Caſſiopea,<emph.end type="italics"></emph.end> no more <lb></lb>remote from it than one degree and an half; from which two par <lb></lb>ticulars is undoubtedly inferred, either the abſolute want of Paral <lb></lb>lax, or ſuch a ſmalneſſe thereof, that it doth aſſure us with very <lb></lb>expeditious Calculations of its great diſtance from the Earth.</s></p><p type="main"><s>SAGR. </s><s>But theſe things, were they not known to this Author? <lb></lb></s><s>and if he ſaw them, what doth he ſay unto them?</s></p><p type="main"><s>SALV. </s><s>We are wont to ſay, of one that having no reply that <lb></lb>is able to cover his fault, produceth frivolous excuſes, <emph type="italics"></emph>cerca di at <lb></lb>taccarſi alle funi del cielo,<emph.end type="italics"></emph.end> [He ſtrives to take hold of the Cords of <lb></lb>Heaven;] but this Authour runs, not to the Cords, but to the Spi <lb></lb>ders Web of Heaven; as you ſhall plainly ſee in our examination <lb></lb>of theſe two particulars even now hinted. </s><s>And firſt, that which <lb></lb>ſheweth us the Polar diſtances of the Obſervators one by one, I <lb></lb>have noted down in theſe brief Calculations; For a full under <pb xlink:href="040/01/306.jpg" pagenum="286"></pb>ſtanding of which, I ought firſt to advertiſe you, that when ever <lb></lb>the new Star, or other Phænomenon is near to the earth, turning <lb></lb>with a Diurnal motion about the Pole, it will ſeem to be farther <lb></lb>off from the ſaid Pole, whilſt it is in the lower part of the Meridi <lb></lb>an, then whilſt it is above, as in this Figure [<emph type="italics"></emph>being fig. </s><s>third of <lb></lb>this Dial.<emph.end type="italics"></emph.end>] may be ſeen. </s><s>In which the point T. denotes the cen <lb></lb>tre of the Earth; O the place of the Obſervator; the Arch VPC <lb></lb>the Firmament; P. the Pole. </s><s>The <emph type="italics"></emph>Phænomenon,<emph.end type="italics"></emph.end> [<emph type="italics"></emph>or appearance<emph.end type="italics"></emph.end>] <lb></lb>moving along the Circle F S. is ſeen one while under the Pole by <lb></lb>the Ray O F C. and another while above, according to the Ray <lb></lb>O S D. ſo that the places ſeen in the Firmament are D. and C. but <lb></lb>the true places in reſpect of the Centre T, are B, and A, equidi <lb></lb>ſtant from the Pole. </s><s>Where it is manifeſt that the apparent place <lb></lb>of the <emph type="italics"></emph>Phænomenon<emph.end type="italics"></emph.end> S, that is the point D, is nearer to the Pole than <lb></lb>the other apparent place C, ſeen along the Line or Ray O F C, <lb></lb>which is the firſt thing to be noted. </s><s>In the ſecond place you muſt <lb></lb>note that the exces of the apparent inferiour diſtance from the Pole, <lb></lb>over and above the apparent ſuperiour diſtance from the ſaid Pole, <lb></lb>is greater than the Inferiour Parallax of the <emph type="italics"></emph>Phænomenon,<emph.end type="italics"></emph.end> that is, I <lb></lb>ſay, that the exceſſe of the Arch C P, (the apparent inferior di <lb></lb>ſtance) over and above the Arch P D, (the apparent ſuperior di <lb></lb>ſtance) is greater then the Arch C A, (that is the inferiour Para <lb></lb>lax.) Which is eaſily proved; for the Arch C P. more exceedeth <lb></lb>P D, then P B; P B, being bigger than P D, but P B. is equal to <lb></lb>P A, and the exceſſe of C P, above P A, is the arch, C A, there <lb></lb>fore the exceſſe of the arch C P above the arch P D, is great <lb></lb>er than the arch C A, which is the parallax of the Phænomenon <lb></lb>placed in F, which was to be demonſtrated. </s><s>And to give all ad <lb></lb>vantages to the Author, let us ſuppoſe that the parallax of the ſtar <lb></lb>in F, is the whole exceſſe of the arch C P (that is of the inferiour <lb></lb>diſtance from the pole) above the arch P D (the inferiour di <lb></lb>ſtance.) I proceed in the next place to examine that which the <lb></lb>obſervations of all Aſtronomers cited by the Authour giveth us, <lb></lb>amongſt which, there is not one that maketh not againſt himſelf <lb></lb>and his purpoſe. </s><s>And let us begin with theſe of <emph type="italics"></emph>Buſchius,<emph.end type="italics"></emph.end> who <lb></lb>findeth the ſtars diſtance from the pole, when it was ſuperiour, to be <lb></lb>28 <emph type="italics"></emph>gr. </s><s>10 m.<emph.end type="italics"></emph.end> and the inferiour to be 28 <emph type="italics"></emph>gr. </s><s>30 m.<emph.end type="italics"></emph.end> ſo that the ex <lb></lb>ceſſe is 0 <emph type="italics"></emph>gr. </s><s>20 m.<emph.end type="italics"></emph.end> which let us take (in favour of the Author) as <lb></lb>if it all were the parallax of the ſtar in F, that is the angle T F O. <lb></lb></s><s>Then the diſtance from the <emph type="italics"></emph>Vertex<emph.end type="italics"></emph.end> [or Zenith] that is the arch <lb></lb>C V, is 67 <emph type="italics"></emph>gr. </s><s>20 m.<emph.end type="italics"></emph.end> Theſe two things being found, prolong the <lb></lb>line C O, and from it let fall the perpendicular T I, and let us <lb></lb>conſider the triangle T O I, of which the angle I is right angle, <lb></lb>and the angle I O T known, as being vertical to the angle V O C, <lb></lb>the diſtance of the ſtar from the <emph type="italics"></emph>Vertex,<emph.end type="italics"></emph.end> Moreover in the triangle <pb xlink:href="040/01/307.jpg" pagenum="287"></pb>T I F, which is alſo rectangular, there is known the angle F, ta <lb></lb>ken by the parallax. </s><s>Then note in ſome place apart the two an <lb></lb>gles I O T and I F T, and of them take the ſines, which are <lb></lb>here ſet down to them, as you ſeen. </s><s>And becauſe in the triangle <lb></lb>I O T, the ſine T I is 92276. of thoſe parts, whereof the whole <lb></lb>ſine TO is 100000; and moreover in the triangle I F T, the ſine T I <lb></lb>is 582. of thoſe parts, whereof the whole ſine T F is 100000, to <lb></lb>find how many T F is of thoſe parts, whereof T O is 100000; <lb></lb>we will ſay by the Rule of three: If T I be 582. T F is an <lb></lb>100000. but if T I were 92276. how much would T F be. <lb></lb></s><s>Let us multiply 92276. by 100000. and the product will be <lb></lb>9227600000. and this muſt be divided by 582. and the quotient <lb></lb>will be 15854982. and ſo many ſhall there be in T F of thoſe <lb></lb>parts, of which there are in T O an 100000. So that if it were <lb></lb>required to know how many lines T O, are in T F, we would <lb></lb>divide 15854982 by 100000. and there will come forth 158. and <lb></lb>very near an half; and ſo many diameters ſhall be the diſtance <lb></lb>of the ſtar F, from the centre T, and to abreviate the opera <lb></lb>tion, we ſeeing, that the product of the multiplication of 92276. <lb></lb>by 100000, ought to be divided firſt by 582, and then the quo <lb></lb>tient of that diviſion by 100000. we may without multiplying <lb></lb>92276. by 100000. and with one onely diviſion of the ſine <lb></lb>92276. by the ſine 582. ſoon obtain the ſame ſolution, as may <lb></lb>be ſeen there below; where 92276. divided by 582. giveth us the <lb></lb>ſaid 158 1/2, or thereabouts. </s><s>Let us bear in mind therefore, that <lb></lb>the onely diviſion of the ſine T I, as the ſine of the angle T O I <lb></lb>by the ſine T I, as the ſine of the angle I F T, giveth us the di <lb></lb>ſtance ſought T F, in ſo many diameters T O. <lb></lb><arrow.to.target n="table59"></arrow.to.target> <lb></lb><arrow.to.target n="table60"></arrow.to.target> <lb></lb><arrow.to.target n="table61"></arrow.to.target></s></p> <pb xlink:href="040/01/308.jpg" pagenum="288"></pb><table><table.target id="table59"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></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 obſervations of <emph type="italics"></emph>Peucerus<emph.end type="italics"></emph.end> giveth us, in <lb></lb>which the inferiour diſtance from the Pole is 28 <emph type="italics"></emph>gr. </s><s>21 m.<emph.end type="italics"></emph.end> and the <lb></lb>ſuperiour 28 <emph type="italics"></emph>gr. </s><s>2 m.<emph.end type="italics"></emph.end> the difference 0 <emph type="italics"></emph>gr. </s><s>19 m.<emph.end type="italics"></emph.end> and the diſtance <lb></lb>from the vertical point 66 <emph type="italics"></emph>gr. </s><s>27 m.<emph.end type="italics"></emph.end> from which particulars is ga <lb></lb>thered the ſtars diſtance from the centre almoſt 166 ſemedia <lb></lb>meters. <lb></lb><arrow.to.target n="table62"></arrow.to.target> <lb></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></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"></emph>Tycho<emph.end type="italics"></emph.end> his obſervation holdeth forth to us, in <lb></lb>terpreted with greateſt favour to the adverſary; to wit, the inferi <lb></lb>our diſtance from the pole is 28 <emph type="italics"></emph>gr. </s><s>13 m.<emph.end type="italics"></emph.end> and the ſuperiour 28 <emph type="italics"></emph>gr. <lb></lb></s><s>2 m.<emph.end type="italics"></emph.end> omitting the difference which is 0 <emph type="italics"></emph>gr. </s><s>11 m.<emph.end type="italics"></emph.end> as if all were one <lb></lb>Parallax; the diſtance from the vertical point 62 <emph type="italics"></emph>gr. </s><s>15 m.<emph.end type="italics"></emph.end> Behold <lb></lb>here below the operation, and the diſtance of the ſtar from the <lb></lb>centre found to be 976 9/16 ſemidiameters. <lb></lb><arrow.to.target n="table64"></arrow.to.target> <lb></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></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 obſervation of <emph type="italics"></emph>Reinholdus,<emph.end type="italics"></emph.end> which is the next enſuing, giv <lb></lb>eth us the diſtance of the Star from the Centre 793. Semidia <lb></lb>meters. <lb></lb><arrow.to.target n="table66"></arrow.to.target> <lb></lb><arrow.to.target n="table67"></arrow.to.target></s></p> <pb xlink:href="040/01/309.jpg" pagenum="289"></pb><table><table.target id="table66"></table.target><row><cell></cell><cell></cell><cell><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></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 obſervation of the <emph type="italics"></emph>Landgrave,<emph.end type="italics"></emph.end> the diſtance <lb></lb>of the Star from the Centre is made to be 1057, Semidiameters. <lb></lb><arrow.to.target n="table68"></arrow.to.target> <lb></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></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 moſt favourable obſervations for the Authour be <lb></lb>ing taken from <emph type="italics"></emph>Camerarius,<emph.end type="italics"></emph.end> the diſtance of the Star from the Cen <lb></lb>tre is found to be 3143 Semidiameters. <lb></lb><arrow.to.target n="table70"></arrow.to.target> <lb></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"></emph>gr.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>m.<emph.end type="italics"></emph.end></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 Obſervation of <emph type="italics"></emph>Munoſius<emph.end type="italics"></emph.end> giveth no <emph type="italics"></emph>Parallax,<emph.end type="italics"></emph.end> and there <lb></lb>fore rendreth the new Star amongſt the higheſt of the fixed. </s><s>That <lb></lb>of <emph type="italics"></emph>Hainzelius<emph.end type="italics"></emph.end> makes it infinitely remote, but with the correction <lb></lb>of an half <emph type="italics"></emph>min. </s><s>prim.<emph.end type="italics"></emph.end> placeth it amongſt the fixed Stars. </s><s>And the <lb></lb>ſame is collected from <emph type="italics"></emph>Vrſinus,<emph.end type="italics"></emph.end> with the correction of 12. <emph type="italics"></emph>min. </s><s>prim.<emph.end type="italics"></emph.end> <lb></lb>The other Aſtronomers have not given us the diſtance above and <lb></lb>below the Pole, ſo that nothing can be concluded from them. </s><s>By <lb></lb>this time you ſee, that all the obſervations of all theſe men conſpire <lb></lb>againſt the Author, in placing the Star in the Heavenly and high <lb></lb>eſt Regions.</s></p><p type="main"><s>SAGR. </s><s>But what defence hath he for himſelf againſt ſo manifeſt <lb></lb>contradictions?</s></p><p type="main"><s>SALV. </s><s>He betakes himſelf to one of thoſe weak threads which <lb></lb>I ſpeak of; ſaying that the <emph type="italics"></emph>Parallaxes<emph.end type="italics"></emph.end> come to be leſſened by means <lb></lb>of the refractions, which opperating contrarily ſublimate the <emph type="italics"></emph>Phæ <lb></lb>nomenon,<emph.end type="italics"></emph.end> whereas the <emph type="italics"></emph>Parallaxes<emph.end type="italics"></emph.end> abaſe it. </s><s>Now of what little <lb></lb>ſtead this lamentable refuge is, judge by this, that in caſe that effectof <lb></lb>the refractions were of ſuch an efficacy, as that which not long time <lb></lb>ſince ſome Aſtronomers have introduced, the moſt that they could <lb></lb>work touching the elevating a <emph type="italics"></emph>Phæuomenon<emph.end type="italics"></emph.end> above the Horizon <pb xlink:href="040/01/310.jpg" pagenum="290"></pb>more than truth, when it is before hand 23. or 24. Degrees high, <lb></lb>would be the leſſening its <emph type="italics"></emph>Parallax<emph.end type="italics"></emph.end> about 3. minutes, the which <lb></lb>abatement is too ſmall to pull down the Star below the Moon, and <lb></lb>in ſome caſes is leſſe than the advantage given him by us in admit <lb></lb>ting that the exceſſe of the inferiour diſtance from the Pole above <lb></lb>the Superiour, is all <emph type="italics"></emph>Parallax,<emph.end type="italics"></emph.end> the which advantage is far more clear <lb></lb>and palpable than the effect of Refracton, of the greatneſſe of <lb></lb>which I ſtand in doubt, and not without reaſon. </s><s>But beſides, I <lb></lb>demand of the Author, whether he thinks that thoſe Aſtronomers, <lb></lb>of whoſe obſervations he maketh uſe, had knowledge of theſe ef <lb></lb>fects of Refractions, and conſidered the ſame, or no; if they did <lb></lb>know and conſider them, it is reaſonable to think that the, kept ac <lb></lb>count of them in aſſigning the true Elevation of the Star, making <lb></lb>in thoſe degrees of Altitude diſcovered with the Inſtruments, ſuch <lb></lb>abatements as were convenient on the account of the alterations <lb></lb>made by the Refractions; inſomuch that the diſtances by them de <lb></lb>livered, were in the end thoſe corrected and exact, and not the ap <lb></lb>parent and falſe ones. </s><s>But if he think that thoſe Authors made <lb></lb>no reflection upon the ſaid Refractions, it muſt be confeſſed, that <lb></lb>they had in like manner erred in determining all thoſe things which <lb></lb>cannot be perfectly adjuſted without allowance for the Refracti <lb></lb>ons; amongſt which things one is the preciſe inveſtigation of the <lb></lb>Polar Altitudes, which are commonly taken from the two Meridi <lb></lb>an Altitudes of ſome of the fixed Stars that are conſtantly viſible, <lb></lb>which Altitudes will come to be altered by Refraction in the ſame <lb></lb>manner, juſt as thoſe of the new Star; ſo that the Polar Altitude <lb></lb>that is deduced from them, will prove to be defective, and to par <lb></lb>take of the ſelf ſame want which this Author aſſigns to the Alti <lb></lb>tudes aſcribed to the new Star, to wit, both that and theſe will <lb></lb>be with equal falſhood placed higher than really they are. </s><s>But any <lb></lb>ſuch errour, as far as concerns our preſent buſineſſe, doth no pre <lb></lb>judce at all: For we not needing to know any more, but onely <lb></lb>the difference between the two diſtances of the new Star from the <lb></lb>Pole at ſuch time as it was inferiour and ſuperiour, it is evident that <lb></lb>ſuch diſtances would be the ſame, taking the alteration of Refra <lb></lb>ction commonly for the Star and for the Pole, or for them when <lb></lb>commonly amended. </s><s>The Authors Argument would indeed have <lb></lb>had ſome ſtrength, though very ſmall, if he had aſſured us that <lb></lb>the Altitude of the Pole had been once preciſely aſſigned, and cor <lb></lb>rected from the errour depending on refraction, from which a <lb></lb>gain the Aſtronomers had not kept themſelves in aſſigning the al <lb></lb>titudes of the new Star; but he hath not aſcertained us of that, <lb></lb>nor perhaps could he have done, nor haply, (and this is more pro <lb></lb>bable) was that caution wanting in the Obſervators.</s></p><p type="main"><s>SAGR. </s><s>This argument is in my judgment ſufficiently anſwer <pb xlink:href="040/01/311.jpg" pagenum="291"></pb>ed; therefore tell me how he diſ-ingageth himſelf in the next place <lb></lb>from that particular of the Stars having conſtantly kept the ſame <lb></lb>diſtance from the fixed Stars circumjacent to it.</s></p><p type="main"><s>SALV. </s><s>He betakes himſelf, in like manner, to two threads, yet <lb></lb>more unable to uphold him than the former: one of which is like <lb></lb>wiſe faſtened to refraction, but ſo much leſs firmly, in that he <lb></lb>ſaith, that refraction operating upon the new Star, and ſublimating <lb></lb>it higher than its true ſituation, maketh the ſeeming diſtances un <lb></lb>tain to be diſtinguiſhed from the true, when compared to the cir <lb></lb>cumpoſed fixed Stars that environ it. </s><s>Nor can I ſufficiently ad <lb></lb>mire how he can diſſemble his knowing how that the ſame refra <lb></lb>ction will work alike upon the new Star, as upon the antient one <lb></lb>its neighbour, elevating both equally, ſo as that ſuch a like acci <lb></lb>dent altereth not the ſpace betwixt them. </s><s>His other ſubterfuge is <lb></lb>yet more unhappy, and carryeth with it much of ridiculous, it be <lb></lb>ing founded upon the errour that may ariſe in the inſtrumen talo <lb></lb>peration it ſelf; whilſt that the Obſervator not being able to <lb></lb>conſtitute the centre of the eyes pupil in the centre of the Sex <lb></lb>tant (an Inſtrument imployed in obſerving the diſtance between <lb></lb>two Stars) but holding it elevated above that centre, as much as <lb></lb>the ſaid pupil is diſtant from I know not what bone of the cheek, <lb></lb>againſt which the end of the Inſtrument reſteth, there is formed <lb></lb>in the eye an angle more acute than that which is made by the ſides <lb></lb>of the Inſtrument; which angle of rayes differeth alſo from it <lb></lb>ſelf, at ſuch time as a man looketh upon Stars, not much elevated <lb></lb>above the Horizon, and the ſame being afterwards placed at a <lb></lb>great height; that angle, ſaith he, is made different, while the In <lb></lb>ſtrument goeth aſcending, the head ſtanding ſtill: but if in moun <lb></lb>ting the Inſtrument, the neck ſhould bend backwards, and the <lb></lb>head go riſing, together with the Inſtrument, the angle would then <lb></lb>continue the ſame. </s><s>So that the Authours anſwer ſuppoſeth that <lb></lb>the Obſervators in uſing the Inſtrument have not raiſed the head, <lb></lb>as they ought to have done; a thing which hath nothing of likeli <lb></lb>hood in it. </s><s>But granting that ſo it had been, I leave you to judge <lb></lb>what difference can be between two acute angles of two equicru <lb></lb>ral triangles, the ſides of one of which triangles are each four <lb></lb>[<emph type="italics"></emph>Italian] Braces<emph.end type="italics"></emph.end> [<emph type="italics"></emph>i.e.<emph.end type="italics"></emph.end> about three Engliſh yards] and thoſe of the <lb></lb>other, four braces within the quantity of the diameter of a Pea; <lb></lb>for the differences cannot be abſolutely greater between the length <lb></lb>of the two viſive rayes, whilſt the line is drawn perpendicularly <lb></lb>from the centre of the pupil, upon the plain of the Rule of the <lb></lb>Sextant (which line is no bigger than the breath of the thumb) <lb></lb>and the length of the ſame rayes, whilſt elevating the Sextant, <lb></lb>without raiſing the head together with it, that ſame line no longer <lb></lb>falleth perpendicularly upon the ſaid plane, but inclineth, making <pb xlink:href="040/01/312.jpg" pagenum="292"></pb>the angle towards the circumference ſomething acute. </s><s>But wholly <lb></lb>to free this Authour from theſe unhappy lies, let him know, (in re <lb></lb>gard it appears that he is not very skilful in the uſe of Aſtronomi <lb></lb>call Inſtruments) that in the ſides of the Sextant or Quadrant <lb></lb><arrow.to.target n="marg514"></arrow.to.target> <lb></lb>there are placed two ^{*} Sights, one in the centre, and the other at <lb></lb>the other at the oppoſite end, which are raiſed an inch or more a <lb></lb>bove the plane of the Rule; and through the tops of thoſe ſights <lb></lb>the ray of the eye is made to paſſe, which eye likewiſe is held an <lb></lb>hands breadth or two, or it may be more, from the Inſtrument; ſo <lb></lb>that neither the pupil, nor any bone of the cheek, nor of the whole <lb></lb>body toucheth or ſtayeth it ſelf upon the Inſtrument, nor much <lb></lb>leſſe is the Inſtrument upheld or mounted in the armes, eſpecially <lb></lb>if it be one of thoſe great ones, as is uſual, which weighing tens, <lb></lb>hundreds, and alſo thouſands of pounds, are placed upon very <lb></lb>ſtrong feet or frames: ſo that the whole objection vaniſheth. <lb></lb></s><s>Theſe are the ſubterfuges of this Authour, which, though they were <lb></lb>all of ſteel, would not ſecure him the hundredth part of a minute; <lb></lb>and with theſe he conceits to make us believe, that he hath com <lb></lb>penſated that difference, which importeth more than an hundred <lb></lb>minutes; I mean, that of the not obſerving a notable difference <lb></lb>in the diſtances between one of the fixed ſtars, and the new ſtar in <lb></lb>in any of their circulations; which, had it been neer to the Moon, <lb></lb>it ought to have been very conſpicuous to the meer ſight, without <lb></lb>any Inſtrument, eſpecially comparing it with the eleventh of <emph type="italics"></emph>Caſ <lb></lb>ſiopeia,<emph.end type="italics"></emph.end> its neighbour, within 1 <emph type="italics"></emph>gr. </s><s>30 m.<emph.end type="italics"></emph.end> which ought to have va <lb></lb>ried from it more than two diameters of the moon, as the more <lb></lb>intelligent Aſtronomers of t' oſe 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 ſee that unfortunate Husbandman, who af <lb></lb>ter all his expected crops, have been beaten down and deſtroyed by <lb></lb>a ſtorm, goeth up and down with a languiſhing and down-caſt <lb></lb>look, gleaning up every ſmall ear that would not ſuffice to keep a <lb></lb>chicken alive one ſole day.</s></p><p type="main"><s>SALV. Truly, this Authour came out too ſlenderly provided <lb></lb>with armes againſt the aſſailants of the Heavens inalterability, and <lb></lb>with too brittle a chain attempted to pull down the new ſtar of <lb></lb><emph type="italics"></emph>Caſſiopeia<emph.end type="italics"></emph.end> from the higheſt Regions, to theſe ſo low and elementa <lb></lb>ry. </s><s>And for that I think that we have ſufficiently demonſtrated <lb></lb>the vaſt difference that is between the arguments of thoſe Aſtro <lb></lb>nomers, and of this their Antagoniſt, it will be convenient that we <lb></lb>leave this particular, and return to our principal matter; in which <lb></lb>there preſents it ſelf to our conſideration the annual motion com <lb></lb>monly aſcribed to the Sun, but by <emph type="italics"></emph>Aristarchus Samius<emph.end type="italics"></emph.end> firſt of all, <lb></lb>and after by <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> taken from the Sun, and transferred upon <lb></lb>the Earth; againſt which Hypotheſis, methinks I ſee <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> to <lb></lb>come ſtrongly provided, and particularly with the ſword and <pb xlink:href="040/01/313.jpg" pagenum="293"></pb>buckler of the little Treatiſe of <emph type="italics"></emph>Concluſions,<emph.end type="italics"></emph.end> or Diſquiſitions Ma <lb></lb>thematical, the oppugnations of which it would be good to be <lb></lb>gin to produce.</s></p><p type="main"><s>SIMP. </s><s>I will, if you ſo pleaſe, reſerve them to the laſt, as thoſe <lb></lb>that are of lateſt invention.</s></p><p type="main"><s>SALV. </s><s>It will therefore be neceſſary, that in conformity to the <lb></lb>method hitherto obſerved, you do orderly, one by one, propound <lb></lb>the arguments, on the contrary, aſwell of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> as of the o <lb></lb>ther ancients, which ſhall be my task alſo, that ſo nothing may e <lb></lb>ſcape our ſtrict conſideration and examination; and likewiſe <emph type="italics"></emph>Sa <lb></lb>gredus,<emph.end type="italics"></emph.end> with the vivacity of his wit, ſhall interpoſe his thoughts, as <lb></lb>he ſhall finde himſelf inclined.</s></p><p type="main"><s>SAGR. </s><s>I will do it with my wonted freedome; and your com <lb></lb>mands ſhall oblige you to excuſe me in ſo doing.</s></p><p type="main"><s>SALV. </s><s>The favour will challenge thanks, and not an excuſe. <lb></lb></s><s>But now let <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> begin to propoſe thoſe doubts which diſ <lb></lb>ſwade him from believing that the Earth, in like manner, as the <lb></lb>other pianets, may move round about a fixed centre.</s></p><p type="main"><s>SIMP. </s><s>The firſt and greateſt difficulty is the repugnance and <lb></lb>incompatibility that is between being in the centre, and being far <lb></lb>from it; for if the Terreſtrial Globe were to move in a year by <lb></lb>the circumference of a circle, that is, under the Zodiack, it is im <lb></lb>poſſible that it ſhould, at the ſame time, be in the centre of the Zo <lb></lb>diack; but that the Earth is in the ſaid centre <emph type="italics"></emph>Aristotle, Ptolomy,<emph.end type="italics"></emph.end> <lb></lb>and others have many wayes proved.</s></p><p type="main"><s>SALV. </s><s>You very well argue, aud there is no queſtion but that <lb></lb>one that would make the Earth to move in the circumference of a <lb></lb>circle, muſt firſt of neceſſity prove, that it is not in the centre of <lb></lb>that ſame circle; it now followeth, that we enquire, whether the <lb></lb>Earth be, or be not in that centre, about which, I ſay, that it tur <lb></lb>neth, and you ſay that it is fixed; and before we ſpeak of this, it <lb></lb>is likewiſe neceſſary that we declare our ſelves, whether you and I <lb></lb>have both the ſame conceit of this centre, or no. </s><s>Therefore tell <lb></lb>me, what and where is this your intended centre?</s></p><p type="main"><s>SIMP. </s><s>When I ſpeak of the centre, I mean that of the Uni <lb></lb>verſe, 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 diſpute, whe <lb></lb>ther there be any ſuch centre in nature, or no; being that neither <lb></lb><arrow.to.target n="marg515"></arrow.to.target> <lb></lb>you nor any one elſe hath ever proved, whether the World be fi <lb></lb>nite and figurate, or elſe infinite and interminate; yet nevertheleſs <lb></lb>granting you, for the preſent, that it is finite, and of a terminate <lb></lb>Spherical Figure, and that thereupon it hath its centre; it will be <lb></lb>requiſite to ſee how credible it is that the Earth, and not rather <lb></lb>ſome other body, doth poſſeſſe the ſaid centre.</s></p><p type="margin"><s><margin.target id="marg515"></margin.target><emph type="italics"></emph>It hath not been <lb></lb>hitherto proved by <lb></lb>any, whether the <lb></lb>World be finite or <lb></lb>infinite.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>That the world is finite, terminato, and ſpherical, <emph type="italics"></emph>Ari-<emph.end type="italics"></emph.end> <pb xlink:href="040/01/314.jpg" pagenum="294"></pb><emph type="italics"></emph>ſtotle<emph.end type="italics"></emph.end> proveth with an hundred demonſtrations. <lb></lb><arrow.to.target n="marg516"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg516"></margin.target><emph type="italics"></emph>The Demonſtra <lb></lb>tions of<emph.end type="italics"></emph.end> Ariſtotle <lb></lb><emph type="italics"></emph>to Prove that the <lb></lb>Vniverſe is finite, <lb></lb>are all nullified by <lb></lb>denying it to be <lb></lb>moveable.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>All which in the end are reduced to one alone, and that <lb></lb>one to none at all; for if I deny his aſſumption, to wit, that the <lb></lb>Univerſe is moveable, all his demonſtrations come to nothing, for <lb></lb>he onely proveth the Univerſe to be finite and terminate, for that <lb></lb>it is moveable. </s><s>But that we may not multiply diſputes, let it be <lb></lb>granted for once, that the World is finite, ſpherical, and hath <lb></lb>its centre. </s><s>And ſeeing that that centre and figure is argued from <lb></lb>its mobility, it will, without doubt, be very reaſonable, if from the <lb></lb>circular motions of mundane bodies we proceed to the particular <lb></lb>inveſtigation of that centres proper place: Nay <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> himſelf </s></p><p type="main"><s><arrow.to.target n="marg517"></arrow.to.target> <lb></lb>hath argued and determined in the ſame manner, making that <lb></lb>ſame to be the centre of the Univerſe about which all the Cœle <lb></lb>leſtial Spheres revolve, and in which he beleived the Terreſtrial <lb></lb>Globe to have been placed. </s><s>Now tell me <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> if <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg518"></arrow.to.target> <lb></lb>ſhould be conſtrained by evident experience to alter in part this <lb></lb>his diſpoſure and order of the Univerſe, and confeſſe himſelf to <lb></lb>have been deceived in one of theſe two propoſitions, namely, ei <lb></lb>ther in placing the Earth in the centre, or in ſaying, that the <lb></lb>Cœleſtial Spheres do move about that centre, which of the two <lb></lb>confeſſions think you would he chooſe?</s></p><p type="margin"><s><margin.target id="marg517"></margin.target><emph type="italics"></emph>Ariſtotle makes <lb></lb>that point to be the <lb></lb>centre of the Uni <lb></lb>verſe about which <lb></lb>all the Celeſtial <lb></lb>Spheres do revolve.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg518"></margin.target><emph type="italics"></emph>A queſtion is <lb></lb>put, in caſe that <lb></lb>if<emph.end type="italics"></emph.end> Ariſtotle <emph type="italics"></emph>were <lb></lb>forced to receive <lb></lb>one of two propoſi <lb></lb>tions that make a <lb></lb>gainſt his doctrine, <lb></lb>which he would <lb></lb>admit.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I believe, that if it ſhould ſo fall out, the <emph type="italics"></emph>Peripate <lb></lb>ticks.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>I do not ask the <emph type="italics"></emph>Peripateticks,<emph.end type="italics"></emph.end> I demand of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> <lb></lb>for as to thoſe, I know very well what they would reply; they, as <lb></lb>obſervant and humble vaſſals of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> would deny all the ex <lb></lb>periments and all the obſervations in the World, nay, would alſo <lb></lb>refuſe to ſee them, that they might not be forced to acknowledg <lb></lb>them, and would ſay that the World ſtands as <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> writeth, <lb></lb>and not as nature will have it, for depriving them of the ſhield <lb></lb>of his Authority, with what do you think they would appear in the <lb></lb>field? </s><s>Tell me therefore what you are perſwaded <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> him <lb></lb>ſelf would do in the caſe.</s></p><p type="main"><s>SIMP. </s><s>To tell you the truth, I know not how to reſolve <lb></lb>which of the two inconveniences is to be eſteemed the leſſer.</s></p><p type="main"><s>SALV. </s><s>Apply not I pray you this term of inconvenience to a <lb></lb>thing which poſſibly may of neceſſity be ſo. </s><s>It was an inconveni <lb></lb>ence to place the Earth in the centre of the Cœleſtial revolutions; <lb></lb>but ſeeing you know not to which part he would incline, I e <lb></lb>ſteeming him to be a man of great judgment, let us examine <lb></lb>which of the two choices is the more rational, and that we will <lb></lb>hold that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> would have received. </s><s>Reaſſuming therefore our <lb></lb>diſcourſe from the beginning, we ſuppoſe with the good liking of <lb></lb><emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> that the World (of the magnitude of which we have <lb></lb>no ſenſible notice beyond the fixed ſtars) as being of a ſpherical <pb xlink:href="040/01/315.jpg" pagenum="295"></pb>figure; and moveth circularly, hath neceſſarily, and in reſpect of <lb></lb>its figure a centre; and we being moreover certain, that within <lb></lb>the ſtarry Sphere there are many Orbs, the one within another, <lb></lb>with their ſtars, which likewiſe do move circulary, it is in diſpute <lb></lb>whether it is moſt reaſonable to believe and to ſay that theſe con <lb></lb>teined Orbs do move round the ſaid centre of the World, or elſe <lb></lb>about ſome other centre far remote from that? </s><s>Tell me now <emph type="italics"></emph>Sim <lb></lb>plicius<emph.end type="italics"></emph.end> what you think concerning this particular.</s></p><p type="main"><s>SIMP. </s><s>If we could ſtay upon this onely ſuppoſition, and that <lb></lb><arrow.to.target n="marg519"></arrow.to.target> <lb></lb>we were ſure that we might encounter nothing elſe that might di <lb></lb>ſturb us, I would ſay that it were much more reaſonable to af <lb></lb>firm that the Orb containing, and the parts contained, do all <lb></lb>move about one common centre, than about divers.</s></p><p type="margin"><s><margin.target id="marg519"></margin.target><emph type="italics"></emph>Its more ratio <lb></lb>nal that the Orb <lb></lb>conteining, and the <lb></lb>parts conteined, do <lb></lb>move all about one <lb></lb>centre, than uoon <lb></lb>divers.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Now if it were true that the centre of the World is the <lb></lb><arrow.to.target n="marg520"></arrow.to.target> <lb></lb>ſame about which the Orbs of mundane bodies, that is to ſay, of <lb></lb>the Planets, move, it is moſt certain that it is not the Earth, but <lb></lb>the Sun rather that is fixed in the centre of the World. </s><s>So that as <lb></lb>to this firſt ſimple and general apprehenſion, the middle place <lb></lb>belongeth to the Sun, and the Earth is as far remote from the <lb></lb>centre, as it is from that ſame Sun.</s></p><p type="margin"><s><margin.target id="marg520"></margin.target><emph type="italics"></emph>If the centre of <lb></lb>the World be the <lb></lb>ſame with that a <lb></lb>bout which the via <lb></lb>nees move the Sun <lb></lb>and not the Earth <lb></lb>is placed in it.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>But from whence do you argue that not the Earth, but <lb></lb>the Sun is in the centre of the Planetary revolutions?</s></p><p type="main"><s>SALV. </s><s>I infer the ſame from moſt evident, and therefore ne <lb></lb>ceſſarily concludent obſervations, of which the moſt palpable to <lb></lb><arrow.to.target n="marg521"></arrow.to.target> <lb></lb>exclude the Earth from the ſaid centre, and to place the Sun <lb></lb>therein, are, the ſeeing all the Planets one while neerer and ano <lb></lb>ther while farther off from the Earth with ſo great differences, that <lb></lb>for example, <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> when it is at the fartheſt, is ſix times more <lb></lb>remote from us, than when it is neereſt, and <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> riſeth almoſt <lb></lb>eight times as high at one time as at another. </s><s>See therefore whe <lb></lb>ther <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> was not ſomewhat miſtaken in thinking that it was <lb></lb>at all times couidiſtant from us.</s></p><p type="margin"><s><margin.target id="marg521"></margin.target><emph type="italics"></emph>Obſervations from <lb></lb>whence it is col <lb></lb>lected that the Sun <lb></lb>and not the Earth <lb></lb>is in the centre of <lb></lb>the Celeſtial revo <lb></lb>lutions.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>What in the next place are the tokens that their moti <lb></lb>ons are about the Sun?</s></p><p type="main"><s>SALV. </s><s>It is argued in the three ſuperiour planets <emph type="italics"></emph>Mars, Jupi <lb></lb>ter,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Saturn,<emph.end type="italics"></emph.end> in that we find them alwayes neereſt to the <lb></lb>Earth when they are in oppoſition to the Sun, and fartheſt off <lb></lb>when they are towards the conjunction, and this approximatian <lb></lb>and receſſion importeth thus much that <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> neer at hand, ap <lb></lb>peareth very neer 60 times greater than when it is remote. </s><s>As to <lb></lb><arrow.to.target n="marg522"></arrow.to.target> <lb></lb><emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> in the next place, and to <emph type="italics"></emph>Mercury,<emph.end type="italics"></emph.end> we are certain that <lb></lb>they revolve about the Sun, in that they never move far from <lb></lb>him, and in that we ſee them one while above and another while <lb></lb><arrow.to.target n="marg523"></arrow.to.target> <lb></lb>below it, as the mutations of figure in <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> neceſſarily argueth. <lb></lb></s><s>Tonchiug the Moon it is certain, that ſhe cannot in any way <pb xlink:href="040/01/316.jpg" pagenum="296"></pb>ſeperate from the Earth, for the reaſons that ſhall be more diſtinct <lb></lb>ly alledged hereafter.</s></p><p type="margin"><s><margin.target id="marg522"></margin.target><emph type="italics"></emph>The mutation <lb></lb>of figure in<emph.end type="italics"></emph.end> Venus <lb></lb><emph type="italics"></emph>argueth its motion <lb></lb>to be about the Sun.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg523"></margin.target><emph type="italics"></emph>The Moon can <lb></lb>not ſeperate from <lb></lb>the Earth.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I expect that I ſhall hear more admirable things that <lb></lb>depend upon this annual motion of the Earth, than were thoſe <lb></lb>dependant upon the diurnal revolution. <lb></lb><arrow.to.target n="marg524"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg524"></margin.target><emph type="italics"></emph>The annual mo <lb></lb>tion of the Earth <lb></lb>mixing with the <lb></lb>motions of the o <lb></lb>ther Planets pro <lb></lb>duce extravagant <lb></lb>appearances.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>You do not therein erre: For as to the operation of <lb></lb>the diurnal motion upon the Celeſtial bodies, it neither was, nor <lb></lb>can be other, than to make the Univerſe ſeem to run precipitately <lb></lb>the contrary way; but this annual motion intermixing with the <lb></lb>particular motions of all the planets, produceth very many ex <lb></lb>travagancies, which have diſarmed and non-pluſt all the greateſt <lb></lb>Scholars in the World. </s><s>But returning to our firſt general appre <lb></lb>henſions, I reply that the centre of the Celeſtial converſions of <lb></lb>the five planets <emph type="italics"></emph>Saturn, Jupiter, Mars, Venus<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Mercury,<emph.end type="italics"></emph.end> is <lb></lb>the Sun; and ſhall be likewiſe the centre of the motion of the <lb></lb>Earth, if we do but ſucceed in our attempt of placing it in Hea <lb></lb>ven. </s><s>And as for the Moon, this hath a circular motion about the <lb></lb>Earth, from which (as I ſaid before) it can by no means alienate <lb></lb>it ſelf, but yet doth it not ceaſe to go about the Sun together with <lb></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 ſtructure, but <lb></lb>it may be, that with making a few draughts thereof, one may bet <lb></lb>ter and more eaſily diſcourſe concerning the ſame.</s></p><p type="main"><s>SALV. </s><s>Tis very true: yea for your greater ſatisfaction and ad <lb></lb>miration together, I deſire you, that you would take the pains <lb></lb>to draw the ſame; and to ſee that although you think you do not <lb></lb>apprehend it, yet you very perfectly underſtand it; And onely <lb></lb>by anſwering to my interrogations you ſhall deſigne it punctually. </s></p><p type="main"><s><arrow.to.target n="marg525"></arrow.to.target> <lb></lb>Take therefore a ſheet of paper and Compaſles; And let this <lb></lb>white paper be the immenſe expanſion of the Univerſe; in which <lb></lb>you are to diſtribute and diſpoſe its parts in order, according as <lb></lb>reaſon ſhall direct you. </s><s>And firſt, in regard that without my in <lb></lb>ſtruction you verily believe that the Earth is placed in this Uni <lb></lb>verſe, therefore note a point at pleaſure, about which you in <lb></lb>tend it to to be placed, and mark it with ſome characters.</s></p><p type="margin"><s><margin.target id="marg525"></margin.target><emph type="italics"></emph>The Syſteme of <lb></lb>the Univerſe de <lb></lb>ſigned from the ap <lb></lb>pearances.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>Let this mark A be the place of the Terreſtrial Globe.</s></p><p type="main"><s>SALV. </s><s>Very well. </s><s>I know ſecondly, that you underſtand per <lb></lb>fectly that the ſaid Earth is not within the body of the Sun, nor <lb></lb>ſo much as contiguous to it, but diſtant for ſome ſpace from the <lb></lb>ſame, and therefore aſſign to the Sun what other place you beſt <lb></lb>like, as remote from the Earth as you pleaſe, and mark this in <lb></lb>like manner.</s></p><p type="main"><s>SIMP. </s><s>Here it is done: Let the place of the Solar body <lb></lb>be O.</s></p><p type="main"><s>SALV. </s><s>Theſe two being conſtituted, I deſire that we may <pb xlink:href="040/01/317.jpg" pagenum="297"></pb>think of accomodating the body of <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> in ſuch a manner that <lb></lb>its ſtate and motion may agree with what ſenſible experiments do <lb></lb>ſhew us; and therefore recall to mind that. </s><s>which either by the <lb></lb>paſt diſcourſes, or your own obſervations you have learnt to be <lb></lb>fal that ſtar, and afterwards aſſign unto it that ſtate which you <lb></lb>think agreeth with the ſame.</s></p><p type="main"><s>SIMP. </s><s>Suppoſing thoſe <emph type="italics"></emph>Phænomena<emph.end type="italics"></emph.end> expreſſed by you, and <lb></lb>which I have likewiſe read in the little treatiſe of Concluſions, to <lb></lb><figure id="id.040.01.317.1.jpg" xlink:href="040/01/317/1.jpg"></figure> <lb></lb>be true, namely, that that ſtar never recedes from the Sun beyond <lb></lb>ſuch a determinate ſpace of 40 degrees or thereabouts, ſo as that <lb></lb>it never cometh either to appoſition with the Sun, or ſo much as <lb></lb>to quadrature, or yet to the ſextile aſpect; and more than that, <lb></lb><arrow.to.target n="marg526"></arrow.to.target> <lb></lb>ſuppoſing that it ſheweth at one time almoſt 40 times greater than <lb></lb>at another; namely, very great, when being retrograde, it goeth to <lb></lb>the veſpertine conjnnction of the Sun, and very ſmall when with a <pb xlink:href="040/01/318.jpg" pagenum="298"></pb>motion ſtraight forwards, it goeth to the matutine conjunction; <lb></lb>and moreover it being true, that when it appeareth bigge it ſhews <lb></lb>with a corniculate figure, and when it appeareth little, it ſeems <lb></lb>perfectly round, theſe appearances, I ſay, being true, I do not ſee <lb></lb>how one can chooſe but affirm the ſaid ſtar to revolve in a circle a <lb></lb><arrow.to.target n="marg527"></arrow.to.target> <lb></lb>bout the Sun, for that the ſaid circle cannot in any wiſe be ſaid <lb></lb>to encompaſſe or to contain the Earth within it, nor to be inferi <lb></lb>our to the Sun, that is between it and the Earth, nor yet ſupe <lb></lb>riour to the Sun. </s><s>That circle cannot incompaſſe the Earth, be <lb></lb>cauſe <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> would then ſometimes come to oppofition with the <lb></lb>Sun; it cannot be inferiour, for then <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> in both its conjuncti <lb></lb>ons with the Sun would ſeem horned; nor can it be ſuperiour, <lb></lb>for then it would alwayes appear round, and never cornicular; <lb></lb>and therefore for receit of it I will draw the circle CH, about <lb></lb>the Sun, without encompaſſing the Earth.</s></p><p type="margin"><s><margin.target id="marg526"></margin.target>Venus <emph type="italics"></emph>very greas <lb></lb>towards the reſpe <lb></lb>ctive conjunction <lb></lb>and very ſmall to <lb></lb>wards the matu <lb></lb>tine.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg527"></margin.target>Venus <emph type="italics"></emph>neceſſa <lb></lb>rily proved to move <lb></lb>about the Sun.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Having placed <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> it is requiſite that you think of <lb></lb><emph type="italics"></emph>Mercury,<emph.end type="italics"></emph.end> which, as you know, alwayes keeping about the Sun, <lb></lb>doth recede leſſe diſtance from it than <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end>; therefore conſider <lb></lb>with your ſelf, what place is moſt convenient to aſſign it. <lb></lb><arrow.to.target n="marg528"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg528"></margin.target><emph type="italics"></emph>The revolution of<emph.end type="italics"></emph.end> <lb></lb>Mercury <emph type="italics"></emph>concluded <lb></lb>to be about the Sun, <lb></lb>within the Orb of<emph.end type="italics"></emph.end> <lb></lb>Venus.</s></p><p type="main"><s>SIMP. </s><s>It is not to be queſtioned, but that this Planet imitat <lb></lb>ing <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> the moſt commodious place for it will be, a leſſer cir <lb></lb>cle within this of <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> in like manner about the Sun, being <lb></lb>that of its greateſt vicinity to the Sun, an argument, an evidence <lb></lb>ſufficiently proving the vigour of its illumination, above that of <lb></lb><emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> and of the other Planets, we may therefore upon theſe <lb></lb>conſiderations draw its Circle, marking it with the Characters <lb></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"></emph>neceſſarily <lb></lb>includeth within its <lb></lb>Orb the Earth, and <lb></lb>alſo the Sun.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>But <emph type="italics"></emph>Mars,<emph.end type="italics"></emph.end> Where ſhall we place it?</s></p><p type="main"><s>SIMP. <emph type="italics"></emph>Mars,<emph.end type="italics"></emph.end> Becauſe it comes to an oppoſition with the Sun, <lb></lb>its Circle muſt of neceſſity encompaſs the Earth; But I ſee that it <lb></lb>muſt neceſſarily encompaſs the Sun alſo, for coming to conjuncti <lb></lb>on with the Sun, if it did not move over it, but were below it, it <lb></lb>would appear horned, as <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> and the Moon; but it ſhews al <lb></lb>wayes round, and therefore it is neceſſary, that it no leſs includ</s></p><p type="main"><s><arrow.to.target n="marg530"></arrow.to.target> <lb></lb>eth the Sun within its circle than the Earth. </s><s>And becauſe I re <lb></lb>member that you did ſay, that when it is in oppoſition with the <lb></lb>Sun, it ſeems 60 times bigger than when it is in the conjunction, <lb></lb>me thinks that a Circle about the Centre of the Sun, and that tak <lb></lb>eth in the earth, will very well agree with theſe <emph type="italics"></emph>Phænomena,<emph.end type="italics"></emph.end> <lb></lb>which I do note and mark D I, where <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> in the point D, is near <lb></lb>to the earth, and oppoſite to the Sun; but when it is in the point <lb></lb>I, it is at Conjuction with the Sun, but very far from the Earth. <lb></lb><arrow.to.target n="marg531"></arrow.to.target> <lb></lb>And becauſe the ſame appearances are obſerved in <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> and <lb></lb><emph type="italics"></emph>Saturn,<emph.end type="italics"></emph.end> although with much leſſer difference in <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> than in <lb></lb><emph type="italics"></emph>Mars,<emph.end type="italics"></emph.end> and with yet leſſe in <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> than in <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end>; me thinks I <pb xlink:href="040/01/319.jpg" pagenum="299"></pb>underſtand that we ſhould very commodiouſly ſalve all the <emph type="italics"></emph>Phæ <lb></lb>nomena<emph.end type="italics"></emph.end> of theſe two Planets, with two Circles, in like manner, <lb></lb>drawn about the Sun, and this firſt for <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> marking it E L, and <lb></lb>another above that for <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> marked F M. <lb></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"></emph>at its oppo <lb></lb>ſition to the Sun <lb></lb>ſhews to be ſixty <lb></lb>times bigger than <lb></lb>towards the con <lb></lb>junction.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg531"></margin.target>Jupiter <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Sa <lb></lb>turn <emph type="italics"></emph>do likewiſe en <lb></lb>compaſſe the Earth, <lb></lb>and the Sun.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg532"></margin.target><emph type="italics"></emph>The approxima <lb></lb>tion and receſſion of <lb></lb>the three ſuperiour <lb></lb>Planets, importeth <lb></lb>double the Suns di <lb></lb>ſtance.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>You have behaved your ſelf bravely hitherto. </s><s>And <lb></lb>becauſe (as you ſee) the approach and receſſion of the three Su <lb></lb>periour Planets is meaſured with double the diſtance between the <lb></lb>Earth and Sun, this maketh greater difference in <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> than in <emph type="italics"></emph>Ju-<emph.end type="italics"></emph.end></s></p><p type="main"><s><arrow.to.target n="marg533"></arrow.to.target> <lb></lb><emph type="italics"></emph>piter,<emph.end type="italics"></emph.end> the Circle D I, of <emph type="italics"></emph>Mars,<emph.end type="italics"></emph.end> being leſſer than the Circle E L, <lb></lb>of <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> and likewiſe becauſe this E L, is leſſe than this Circle <lb></lb>F M, of <emph type="italics"></emph>Saturn,<emph.end type="italics"></emph.end> the ſaid difference is alſo yet leſſer in <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> than <lb></lb>in <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> and that punctually anſwereth the <emph type="italics"></emph>Phænomena.<emph.end type="italics"></emph.end> <lb></lb>It remains now that you aſſign a place to the Moon.</s></p><p type="margin"><s><margin.target id="marg533"></margin.target><emph type="italics"></emph>The difference of <lb></lb>the apparent mag <lb></lb>nitude leſſe in<emph.end type="italics"></emph.end> Sa <lb></lb>turn, <emph type="italics"></emph>than in<emph.end type="italics"></emph.end> Jupi <lb></lb>ter, <emph type="italics"></emph>an dn<emph.end type="italics"></emph.end> Jupiter <lb></lb><emph type="italics"></emph>than in<emph.end type="italics"></emph.end> Mars, <emph type="italics"></emph>and <lb></lb>why.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>Following the ſame Method (which ſeems to me very <lb></lb><arrow.to.target n="marg534"></arrow.to.target> <lb></lb>concluſive) in regard we ſee that the Moon cometh to conjunction <lb></lb>and oppoſition with the Sun, it is neceſſary to ſay, that its circle <lb></lb>encompaſſeth the Earth, but yet doth it not follow, that it muſt <lb></lb>environ the Sun, for then at that time towards its conjunction, it <lb></lb>would not ſeem horned, but alwayes round and full of Light. <lb></lb></s><s>Moreover it could never make, as it often doth, the Eclipſe of the <lb></lb>Sun, by interpoſing betwixt it and us; It is neceſſary therefore <lb></lb>to aſſign it a circle about the Earth, which ſhould be this N P, ſo <lb></lb>that being conſtituted in P, it will appear from the Earth A, to be <lb></lb>in conjunction with the Sun, and placed in N, it appeareth oppoſite <lb></lb>to the Sun, and in that poſition it may fall under the Earths ſha <lb></lb>dow, and be obſcured.</s></p><p type="margin"><s><margin.target id="marg534"></margin.target><emph type="italics"></emph>The Moons Orb <lb></lb>invironeth the <lb></lb>Earth, but not the <lb></lb>Sun.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. Now, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> what ſhall we do with the fixed <lb></lb>ſtars? </s><s>Shall we ſuppoſe them ſcattered through the immenſe abiſ <lb></lb>ſes of the Univerſe, at different diſtances, from any one determi <lb></lb>nate point; or elſe placed in a ſuperficies ſpherically diſtended a <lb></lb>bout a centre of its own, ſo that each of them may be equi <lb></lb>diſtant from the ſaid centre? <lb></lb><arrow.to.target n="marg535"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg535"></margin.target><emph type="italics"></emph>The probable <lb></lb>ſituation of the <lb></lb>fixed ſtars.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I would rather take a middle way; and would aſſign <lb></lb>them an Orb deſcribed about a determinate centre and comprized <lb></lb>within two ſpherical ſuperficies, to wit, one very high, and con <lb></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></lb>conſtitute the innumerable multitude of ſtars, but yet at divers al <lb></lb>titudes, and this might be called the Sphere of the Univerſe, contein <lb></lb>ing within it the Orbs of the planets already by us deſcribed.</s></p><p type="margin"><s><margin.target id="marg536"></margin.target><emph type="italics"></emph>Which ought to <lb></lb>be accounted the <lb></lb>ſphere of the Vm <lb></lb>verſe.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>But now we have all this while, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> diſpoſed the <lb></lb>mundane bodies exactly, according to the order of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> <lb></lb>and we have done it with your hand; and moreover to each of <lb></lb>them you have aſſigned peculiar motions of their own, except to <lb></lb>the Sun, the Earth, and ſtarry Sphere; and to <emph type="italics"></emph>Mercury<emph.end type="italics"></emph.end> with <lb></lb><emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> you have aſcribed the circular motion about the Sun, <pb xlink:href="040/01/320.jpg" pagenum="300"></pb>without encompaſſing the Earth; about the ſame Sun you make <lb></lb>the three ſuperiour Planets <emph type="italics"></emph>Mars, Jupiter,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Saturn,<emph.end type="italics"></emph.end> to move, <lb></lb>comprehending the Earth within their circles. </s><s>The Moon in the <lb></lb>next place can move in no other manner than about the Earth, <lb></lb>without taking in the Sun, and in all theſe motions you agree alſo <lb></lb>with the ſame <emph type="italics"></emph>Copernicus.<emph.end type="italics"></emph.end> There remains now three things to be <lb></lb>decided between the Sun, the Earth, and fixed ſtars, namely, <lb></lb><arrow.to.target n="marg537"></arrow.to.target> <lb></lb>Reſt, which ſeemeth to belong to the Earth; the annual motion <lb></lb>under the Zodiack, which appeareth to pertain to the Sun; and the <lb></lb>diurnal motion, which ſeems to belong to the Starry Sphere, and <lb></lb>to be by that imparted to all the reſt of the Univerſe, the Earth <lb></lb>excepted, And it being true that all the Orbs of the Planets, I <lb></lb><arrow.to.target n="marg538"></arrow.to.target> <lb></lb>mean of <emph type="italics"></emph>Mercury, Venus, Mars, Jupiter,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Saturn,<emph.end type="italics"></emph.end> do move <lb></lb>about the Sun as their centre; reſt ſeemeth with ſo much more <lb></lb>reaſon to belong to the ſaid Sun, than to the Earth, in as much <lb></lb>as in a moveable Sphere, it is more reaſonable that the centre <lb></lb>ſtand ſtill, than any other place remote from the ſaid centre; to <lb></lb>the Earth therefore, which is conſtituted in the midſt of move <lb></lb>able parts of the Univerſe, I mean between <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Mars,<emph.end type="italics"></emph.end> one <lb></lb>of which maketh its revolution in nine moneths, and the other in <lb></lb>two years, may the motion of a year very commodiouſly be aſ <lb></lb><arrow.to.target n="marg539"></arrow.to.target> <lb></lb>ſigned, leaving reſt to the Sun. </s><s>And if that be ſo, it followeth <lb></lb>of neceſſary conſequence, that likewiſe the diurnal motion be <lb></lb>longeth to the Earth; for, if the Sun ſtanding ſtill, the Earth <lb></lb>ſhould not revolve about its ſelf, but have onely the annual mo <lb></lb>tion about the Sun, our year would be no other than one day and <lb></lb>one night, that is ſix moneths of day, and ſix moneths of night, <lb></lb>as hath already been ſaid. </s><s>You may conſider withal how commo <lb></lb>diouſly the precipitate motion of 24 hours is taken away from <lb></lb>the Univerſe, and the fixed ſtars that are ſo many Suns, are made <lb></lb>in conformity to our Sun to enjoy a perpetual reſt. </s><s>You ſee more <lb></lb>over what facility one meets with in this rough draught to render <lb></lb>the reaſon of ſo great appearances in the Celeſtial bodies.</s></p><p type="margin"><s><margin.target id="marg537"></margin.target><emph type="italics"></emph>Reſt, the annual <lb></lb>motion and the di <lb></lb>urnal ought to be <lb></lb>diſtributed be <lb></lb>twixt the Sun, <lb></lb>Earth, and Fir <lb></lb>mament.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg538"></margin.target><emph type="italics"></emph>In a moveable <lb></lb>ſphere, it ſeemeth <lb></lb>more veaſonable <lb></lb>that its centre be <lb></lb>ſtable, than any o <lb></lb>ther of its parts.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg539"></margin.target><emph type="italics"></emph>Granting to the <lb></lb>Earth the annual, <lb></lb>it muſt of neceſſity <lb></lb>alſo have the diur <lb></lb>nal motion aſſign <lb></lb>ed to it.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I very well perceive that facility, but as you from this <lb></lb>ſimplicity collect great probabilities for the truth of that Syſtem, <lb></lb>others haply could make thence contrary deductions; doubting, <lb></lb>not without reaſon, why that ſame being the ancient Syſteme of <lb></lb><emph type="italics"></emph>Pythagoreans,<emph.end type="italics"></emph.end> and ſo well accommodated to the <emph type="italics"></emph>Phænomena,<emph.end type="italics"></emph.end> <lb></lb>hath in the ſucceſſion of ſo many thouſand years had ſo few fol <lb></lb>lowers, and hath been even by <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> himſelf refuted, and <lb></lb>ſince that <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> himſelf hath had no better fortune.</s></p><p type="main"><s>SALV. </s><s>If you had at any time been aſſaulted, as I have been, <lb></lb>many and many a time, with the relation of ſuch kind of frivolous <lb></lb>reaſons, as ſerve to make the vulgar contumacious, and difficult to <lb></lb>be perſwaded to hearken, (I will not ſay to conſent) to this novel <pb xlink:href="040/01/321.jpg" pagenum="301"></pb>ty, I believe that you wonder at the paucity of thoſe who are fol <lb></lb>lowers of that opinion would be much diminiſhed. </s><s>But ſmall re <lb></lb><arrow.to.target n="marg540"></arrow.to.target> <lb></lb>gard in my judgement, ought to be had of ſuch thick ſculs, as think <lb></lb>it a moſt convincing proof to confirm, and ſteadfaſtly ſettle them <lb></lb>in the belief of the earths immobility, to ſee that if this day they <lb></lb>cannot Dine at <emph type="italics"></emph>Conſtantinople,<emph.end type="italics"></emph.end> nor Sup in <emph type="italics"></emph>Jappan,<emph.end type="italics"></emph.end> that then the <lb></lb>Earth as being a moſt grave body cannot clamber above the Sun, <lb></lb>and then ſlide headlong down again; Of ſuch as theſe I ſay, <lb></lb>whoſe number is infinite, we need not make any reckoning, nor <lb></lb>need we to record their foolieries, or to ſtrive to gain to our ſide <lb></lb>as our partakers in ſubtil and ſublime opinions, men in whoſe de <lb></lb>finition the kind onely is concerned, and the difference is wanting. <lb></lb></s><s>Moreover, what ground do you think you could be able to gain, <lb></lb>with all the demonſtrations of the World upon brains ſo ſtupid, <lb></lb>as are not able of themſelves to know their down right follies? </s><s>But <lb></lb>my admiration, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> is very different from yours, you won <lb></lb>der that ſo few are followers of the <emph type="italics"></emph>Pythagorean<emph.end type="italics"></emph.end> Opinion; and I <lb></lb>am amazed how there could be any yet left till now that do em <lb></lb>brace and follow it: Nor can I ſufficiently admire the eminencie of <lb></lb><arrow.to.target n="marg541"></arrow.to.target> <lb></lb>thoſe mens wits that have received and held it to be true, and with <lb></lb>the ſprightlineſſe of their judgements offered ſuch violence to their <lb></lb>own ſences, as that they have been able to prefer that which their <lb></lb>reaſon dictated to them, to that which ſenſible experiments re <lb></lb>preſented moſt manifeſtly on the contrary. </s><s>That the reaſons againſt <lb></lb>the Diurnal virtiginous revolution of the Earth by you already ex <lb></lb>amined, do carry great probability with them, we have already <lb></lb>ſeen; as alſo that the <emph type="italics"></emph>Ptolomaicks,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ariſtotelicks,<emph.end type="italics"></emph.end> with all their <lb></lb>Sectators did receive them for true, is indeed a very great argument <lb></lb>of their efficacie; but thoſe experiments which apertly contradict <lb></lb>the annual motion, are of yet ſo much more manifeſtly repugnant, <lb></lb><arrow.to.target n="marg542"></arrow.to.target> <lb></lb>that (I ſay it again) I cannot find any bounds for my admiration, <lb></lb>how that reaſon was able in <emph type="italics"></emph>Ariſtarchus<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> to com <lb></lb>mìt ſuch a rape upon their Sences, as in deſpight thereof, to make <lb></lb>her ſelf miſtreſs of their credulity.</s></p><p type="margin"><s><margin.target id="marg540"></margin.target><emph type="italics"></emph>Diſcourſes more <lb></lb>than childiſh, ſerve <lb></lb>to keep fools in the <lb></lb>opinion of the <lb></lb>Earths ſtability.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg541"></margin.target><emph type="italics"></emph>A declaration <lb></lb>of the improbabi <lb></lb>lity of<emph.end type="italics"></emph.end> Copernicus <lb></lb><emph type="italics"></emph>his opinion.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg542"></margin.target><emph type="italics"></emph>Reaſons and diſ <lb></lb>courſe in<emph.end type="italics"></emph.end> Ariſtar <lb></lb>cus <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Coperni <lb></lb>cus <emph type="italics"></emph>prevailed over <lb></lb>manifeſt ſence.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Are we then to have ſtill more of theſe ſtrong oppoſiti <lb></lb>ons againſt this annual motion?</s></p><p type="main"><s>SALV. </s><s>We are, and they be ſo evident and ſenſible, that if a <lb></lb>ſence more ſublime and excellent than thoſe common and vulgar, <lb></lb>did not take part with reaſon, I much fear, that I alſo ſhould have <lb></lb>been much more averſe to the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Syſteem than I have been <lb></lb>ſince the time that a clearer lamp than ordinary hath enlightned <lb></lb>me.</s></p><p type="main"><s>SAGR. </s><s>Now therefore <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> let us come to joyn battail <lb></lb>for every word that is ſpent on any thing elſe, I take to be caſt a <lb></lb>way.</s></p> <pb xlink:href="040/01/322.jpg" pagenum="302"></pb><p type="main"><s>SALV. </s><s>I am ready to ſerve you. </s><s>You have already ſeen me <lb></lb>draw the form of the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Syſteme; againſt the truth of <lb></lb><arrow.to.target n="marg543"></arrow.to.target> <lb></lb>which <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> himſelf, in the firſt place, makes an hot charge; who, in <lb></lb>caſe it were true, that its diſtances from the earth ſhould ſo much <lb></lb>vary, as that from the leaſt diſtance to the greateſt, there were <lb></lb>twice as much difference, as from the earth to the Sun; it would be <lb></lb>neceſſary, that when it is neareſt unto us, its <emph type="italics"></emph>diſcus<emph.end type="italics"></emph.end> would ſhew <lb></lb>more than 60. times bigger than it ſeems, when it is fartheſt from <lb></lb>us; nevertheleſs that diverſity of apparent magnitude is not to be <lb></lb>ſeen, nay in its oppoſition with the Sun, when its neareſt to the <lb></lb>Earth, it doth not ſhew ſo much as quadruple and quintuple in <lb></lb>bigneſs, to what it is, when towards the conjunction it cometh to <lb></lb>be occulted under the Suns rayes. </s><s>Another and greater difficulty <lb></lb>doth <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> exhibit; For if revolving about the Sun, as <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg544"></arrow.to.target> <lb></lb>affirmeth, it were one while above, & another while below the ſame, <lb></lb>receding and approaching to us ſo much as the Diameter of the cir <lb></lb>cle deſcribed would be, at ſuch time as it ſhould be below the Sun, <lb></lb>and neareſt to us, its <emph type="italics"></emph>diſcus<emph.end type="italics"></emph.end> would ſhew little leſs than 40 times big <lb></lb>ger than when it is above the Sun, near to its other conjunction; yet <lb></lb>nevertheleſſe, the difference is almoſt imperceptible Let us add an <lb></lb><arrow.to.target n="marg545"></arrow.to.target> <lb></lb>other difficulty, that in caſe the body of <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> be of it ſelf dark, and <lb></lb>onely ſhineth as the Moon, by the illumination of the Sun, which <lb></lb>ſeemeth moſt reaſonable; it would ſhew forked or horned at ſuch <lb></lb>time as it is under the Sun, as the Moon doth when ſhe is in like <lb></lb>manner near the Sun; an accident that is not to be diſcovered in <lb></lb>her. </s><s>Whereupon <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> affirmeth, that either ſhe is light of <lb></lb><arrow.to.target n="marg546"></arrow.to.target> <lb></lb>her ſelf, or elſe that her ſubſtance is of ſuch a nature, that it can <lb></lb>imbue the Solar light, and tranſmit the ſame through all its whole <lb></lb>depth, ſo as to be able to appear to us alwayes ſhining; and in this <lb></lb>manner <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> excuſeth the not changing figure in <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end>: but <lb></lb>of her ſmall variation of Magnitude, he maketh no mention at all; <lb></lb><arrow.to.target n="marg547"></arrow.to.target> <lb></lb>and much leſs of <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> than was needful; I believe as being una <lb></lb>ble ſo well as he deſired to ſalve a <emph type="italics"></emph>Phænomenon<emph.end type="italics"></emph.end> ſo contrary to his <lb></lb>Hypotheſis, and yet being convinced by ſo many other occurrences <lb></lb>and reaſons he maintained, and held the ſame Hypotheſis to be true. <lb></lb></s><s>Beſides theſe things, to make the Planets, together with the Earth, <lb></lb>to move above the Sun as the Centre of their converſions, and the <lb></lb><arrow.to.target n="marg548"></arrow.to.target> <lb></lb>Moon onely to break that order, and to have a motion by it ſelf <lb></lb>about the earth; and to make both her, the Earth, and the whole <lb></lb>Elementary <emph type="italics"></emph>Sphere,<emph.end type="italics"></emph.end> to move all together about the Sun in a year, <lb></lb>this ſeemeth to pervert the order of this Syſteme, which rendreth <lb></lb>it unlikely and falſe. </s><s>Theſe are thoſe difficulties that make me <lb></lb>wonder how <emph type="italics"></emph>Aristarchus<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> who muſt needs have ob <lb></lb>ſerved them, not having been able for all that to ſalve them, have <lb></lb>yet notwithſtanding by other admirable occurrences been induced <pb xlink:href="040/01/323.jpg" pagenum="303"></pb>to conſide ſo much in that which reaſon dictated to them, as that <lb></lb>they have conſidently affirmed that the ſtructure of the Univerſe <lb></lb>could have no other figure than that which they deſigned to them <lb></lb>ſelves. </s><s>There are alſo ſeveral other very ſerious and curious doubts, <lb></lb>not ſo eaſie to be reſolved by the middle ſort of wits, but yet pe <lb></lb>netrated and declared by <emph type="italics"></emph>Coperninus,<emph.end type="italics"></emph.end> which we ſhall defer till by <lb></lb>and by, after we have anſwered to other objections that ſeem to <lb></lb>make againſt this opinion. </s><s>Now coming to the declarations and <lb></lb>anſwers to thoſe three before named grand Objections, I ſay, that <lb></lb>the two firſt not onely contradict not the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Syſteme, but <lb></lb><arrow.to.target n="marg549"></arrow.to.target> <lb></lb>greatly and abſolutely favour it; For both <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> ſeems <lb></lb>unequal to themſelves, according to the proportions aſſigned; and <lb></lb><emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> under the Sun ſeemeth horned, and goeth changing figures <lb></lb>in it ſelf exactly like the Moon.</s></p><p type="margin"><s><margin.target id="marg543"></margin.target>Mars <emph type="italics"></emph>makes an <lb></lb>hot aſſault upon the<emph.end type="italics"></emph.end> <lb></lb>Copernican <emph type="italics"></emph>Sy <lb></lb>ſteme.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg544"></margin.target><emph type="italics"></emph>The<emph.end type="italics"></emph.end> Phænome <lb></lb>na <emph type="italics"></emph>of<emph.end type="italics"></emph.end> Venus <emph type="italics"></emph>appear <lb></lb>contrary to the Sy <lb></lb>ſteme of<emph.end type="italics"></emph.end> Coperni <lb></lb>cus.</s></p><p type="margin"><s><margin.target id="marg545"></margin.target><emph type="italics"></emph>Another diffi <lb></lb>culty raiſed by<emph.end type="italics"></emph.end> Ve <lb></lb>nus <emph type="italics"></emph>againſt<emph.end type="italics"></emph.end> Coper <lb></lb>nicus.</s></p><p type="margin"><s><margin.target id="marg546"></margin.target>Venus, <emph type="italics"></emph>according <lb></lb>to<emph.end type="italics"></emph.end> Copernicus, <emph type="italics"></emph>ei <lb></lb>ther lucid in it <lb></lb>ſelf, or elſe of a <lb></lb>tranſparent ſub <lb></lb>ſtance.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg547"></margin.target>Copernicus <emph type="italics"></emph>ſpeak <lb></lb>eth nothing of the <lb></lb>ſmall variation of <lb></lb>bigneſs in<emph.end type="italics"></emph.end> Venus <lb></lb><emph type="italics"></emph>and in<emph.end type="italics"></emph.end> Mars.</s></p><p type="margin"><s><margin.target id="marg548"></margin.target><emph type="italics"></emph>The moon much <lb></lb>diſturbeth the or <lb></lb>der of the other <lb></lb>Planets.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg549"></margin.target><emph type="italics"></emph>Anſwers to the <lb></lb>three first objecti <lb></lb>ons againſt the<emph.end type="italics"></emph.end> Co <lb></lb>pernican <emph type="italics"></emph>Syſteme.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>But how came this to be concealed from <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> <lb></lb>and revealed to you?</s></p><p type="main"><s>SALV. </s><s>Theſe things cannot be comprehended, ſave onely by <lb></lb>the ſenſe of ſeeing, the which by nature was not granted to man <lb></lb>ſo perfect, as that it was able to attain to the diſcovery of ſuch dif <lb></lb>ferences; nay even the very inſtrument of ſight is an impediment <lb></lb>to it ſelf: But ſince that it hath pleaſed God in our age to vouch <lb></lb>ſafe to humane ingenuity, ſo admirable an invention of perfecting <lb></lb>our ſight, by multiplying it four, ſix, ten, twenty, thirty, and four <lb></lb>ty times, infinite objects, that either by reaſon of their diſtance, or <lb></lb>for their extream ſmallneſſe were inviſible unto us, have by help <lb></lb>of the Teleſcope been rendered viſible.</s></p><p type="main"><s>SAGR. </s><s>But <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> are none of the objects inviſible <lb></lb>for their diſtance or ſmallneſſe, yea, we do diſcern them with our <lb></lb>bare natural ſight; why then do we not diſtinguiſh the differences <lb></lb>of their magnitudes and figures?</s></p><p type="main"><s>SALV. </s><s>In this, the impediment of our very eye it ſelf hath a <lb></lb><arrow.to.target n="marg550"></arrow.to.target> <lb></lb>great ſhare, as but even now I hinted, by which the reſplendent and <lb></lb>remote objects are not repreſented to us ſimple and pure; but gives <lb></lb>them us fringed with ſtrange and adventitious rayes, ſo long and <lb></lb>denſe, that their naked body ſheweth to us agrandized ten, twen <lb></lb>ty, an hundred, yea a thouſand times more than it would appear, if <lb></lb>the capillitious rayes were taken away.</s></p><p type="margin"><s><margin.target id="marg550"></margin.target><emph type="italics"></emph>Thereaſon whence <lb></lb>it happens that<emph.end type="italics"></emph.end> Ve <lb></lb>nus <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Mars <emph type="italics"></emph>do <lb></lb>not appear to vary <lb></lb>magnitude ſo much <lb></lb>as is requiſite.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Now I remember that I have read ſomething on this <lb></lb>ſubject, I know not whether in the Solar Letters, or in the <emph type="italics"></emph>Sag <lb></lb>giatore<emph.end type="italics"></emph.end> of our common Friend, but it would be very good, aſwell <lb></lb>for recalling it into my memory, as for the information of <emph type="italics"></emph>Simpli <lb></lb>cius,<emph.end type="italics"></emph.end> who it may be never ſaw thoſe writings, that you would de <lb></lb>clare unto us more diſtinctly how this buſineſſe ſtands, the know <lb></lb>ledge whereof I think to be very neceſſary for the aſſiſting of us to <lb></lb>underſtand that of which we now ſpeak.</s></p> <pb xlink:href="040/01/324.jpg" pagenum="304"></pb><p type="main"><s>SIMP. </s><s>I muſt confeſſe that all that which <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> hath ſpo <lb></lb>ken is new unto me, for truth is, I never have had the curioſity to <lb></lb>read thoſe Books, nor have I hitherto given any great credit to <lb></lb>the Teleſcope newly introduced; rather treading in the ſteps of o <lb></lb><arrow.to.target n="marg551"></arrow.to.target> <lb></lb>ther <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> Philoſophers my companions, I have thought <lb></lb>thoſe things to be fallacies and deluſions of the Chryſtals, which <lb></lb>others have ſo much admired for ſtupendious operations: and <lb></lb>therefore if I have hitherto been in an errour, I ſhall be glad to be <lb></lb>freed from it, and allured by theſe novelties already heard from <lb></lb>you, I ſhall the more attentively hearken to the reſt.</s></p><p type="margin"><s><margin.target id="marg551"></margin.target><emph type="italics"></emph>The operations of <lb></lb>the Teleſcope ac <lb></lb>counted fallacies by <lb></lb>the<emph.end type="italics"></emph.end> Peripateticks.</s></p><p type="main"><s>SALV. </s><s>The confidence that theſe men have in their own ap <lb></lb>prehenſiveneſſe, is no leſs unreaſonable than the ſmall eſteem they <lb></lb>have of the judgment of others: yet its much that they ſhould e <lb></lb>ſteem themſelves able to judge better of ſuch an inſtrument, with <lb></lb>out ever having made trial of it, than thoſe who have made, and <lb></lb>daily do make a thouſand experiments of the ſame: But I pray <lb></lb>you, let us leave this kind of pertinacious men, whom we can <lb></lb>not ſo much as tax without doing them too great honour. </s><s>And re <lb></lb><arrow.to.target n="marg552"></arrow.to.target> <lb></lb>turning to our purpoſe, I ſay, that reſplendent objects, whether <lb></lb>it is that their light doth refract on the humidity that is upon the <lb></lb>pupils, or that it doth reflect on the edges of the eye-browes, dif <lb></lb>fuſing its reflex rayes upon the ſaid pupils, or whether it is for ſome <lb></lb>other reaſon, they do appear to our eye, as if they were environ'd <lb></lb>with new rayes, and therefore much bigger than their bodies <lb></lb>would repreſent themſelves to us, were they diveſted of thoſe ir <lb></lb><arrow.to.target n="marg553"></arrow.to.target> <lb></lb>radiations. </s><s>And this aggrandizement is made with a greater and <lb></lb>greater proportion, by how much thoſe lucid objects are leſſer and <lb></lb>leſſer; in the ſame manner for all the world, as if we ſhould ſup <lb></lb>poſe that the augmentation of ſhining locks were <emph type="italics"></emph>v.g.<emph.end type="italics"></emph.end> four inches, <lb></lb>which addition being made about a circle that hath four inches di <lb></lb>ameter would increaſe its appearance to nine times its former big <lb></lb>neſſe: but---------</s></p><p type="margin"><s><margin.target id="marg552"></margin.target><emph type="italics"></emph>Shining objects <lb></lb>ſeem environed <lb></lb>with adventitious <lb></lb>rayes.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg553"></margin.target><emph type="italics"></emph>The reaſon why <lb></lb>luminous bodies ap <lb></lb>pear enlarged <lb></lb>much the more, by <lb></lb>how much they are <lb></lb>leſſer.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I believe you would have ſaid three times; for adding <lb></lb>four inches to this ſide, and four inches to that ſide of the diame <lb></lb>ter of a circle, which is like wiſe four inches, its quantity is there <lb></lb>by tripled, and not made nine times bigger.</s></p><p type="main"><s>SALV. </s><s>A little more <emph type="italics"></emph>Geometry<emph.end type="italics"></emph.end> would do well, <emph type="italics"></emph>Simplicius.<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg554"></arrow.to.target> <lb></lb>True it is, that the diameter is tripled, but the ſuperficies, which is <lb></lb>that of which we ſpeak, increaſeth nine times: for you muſt know, <lb></lb><emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that the ſuperficies of circles are to one another, as <lb></lb>the ſquares of their diameters; and a circle that hath four inches <lb></lb>diameter is to another that hath twelve, as the ſquare of four to <lb></lb>the ſquare of twelve; that is, as 16. is to 144 and therefore it ſhall <lb></lb>be increaſed nine times, and not three; this, by way of advertiſe <lb></lb>ment to <emph type="italics"></emph>Simplicius.<emph.end type="italics"></emph.end> And proceeding forwards, if we ſhould add <pb xlink:href="040/01/325.jpg" pagenum="305"></pb>the ſaid irradiation of four inches to a circle that hath but two in <lb></lb>ches of diameter onely, the diameter of the irradiation or Gar <lb></lb>land would be ten inches, and the ſuperficial content of the circle <lb></lb>would be to the <emph type="italics"></emph>area<emph.end type="italics"></emph.end> of the naked body, as 100. to 4. for thoſe <lb></lb>are the ſquares of 10. and of 2. the agrandizement would there <lb></lb>fore be 25. times ſo much; and laſtly, the four inches of hair or <lb></lb>fringe, added to a ſmall circle of an inch in diameter, the ſame <lb></lb>would be increaſed 81. times; and ſo continually the augmenta <lb></lb>tions are made with a proportion greater and greater, according <lb></lb>as the real objects that increaſe, are leſſer and leſſer.</s></p><p type="margin"><s><margin.target id="marg554"></margin.target><emph type="italics"></emph>Superficial fi <lb></lb>gures encreaſing <lb></lb>proportion double to <lb></lb>their lines.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>The doubt which puzzled <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> never troubled <lb></lb>me, but certain other things indeed there are, of which I deſire <lb></lb>a more diſtinct underſtanding; and in particular, I would know up <lb></lb>on what ground you affirm that the ſaid agrandizement is alwayes <lb></lb>equal in all viſible objects. <lb></lb><arrow.to.target n="marg555"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg555"></margin.target><emph type="italics"></emph>Objects the more <lb></lb>vigorous they are <lb></lb>in light, the more <lb></lb>they do ſeem to in <lb></lb>creaſe.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>I have already declared the ſame in part, when I ſaid, <lb></lb>that onely lucid objects ſo increaſed, and not the obſcure; now I <lb></lb>adde what remaines, that of the reſplendent objects thoſe that are <lb></lb>of a more bright light, make the reflection greater and more re <lb></lb>ſplendent upon our pupil; whereupon they ſeem to augment <lb></lb>much more than the leſſe lucid: and that I may no more inlarge <lb></lb>my ſelf upon this particular, come we to that which the true Mi <lb></lb>ſtris of <emph type="italics"></emph>Astronomy,<emph.end type="italics"></emph.end> Experience, teacheth us. </s><s>Let us this evening, <lb></lb>when the air is very obſcure, obſerve the ſtar of <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end>; we <lb></lb>ſhall ſee 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></lb>through a tube, or elſe through a ſmall trunk, which clutching the <lb></lb>hand cloſe, and accoſting it to the eye, we lean between the palm <lb></lb>of the hands and the fingers, or elſe by an hole made with a ſmall <lb></lb>needle in a paper; and we ſhall ſee the ſaid ſtar diveſted of its <lb></lb>beams, but ſo ſmall, that we ſhall judge it leſſe, even than a ſixti <lb></lb>eth part of its great glittering light ſeen with the eye at liberty: <lb></lb>we may afterwards behold the <emph type="italics"></emph>Dog-ſtars<emph.end type="italics"></emph.end> beautiful and bigger than <lb></lb><arrow.to.target n="marg557"></arrow.to.target> <lb></lb>any of the other fixed ſtars, which ſeemeth to the bare eye no <lb></lb>great matter leſſe than <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end>; but taking from it, as before, the <lb></lb>irradiation, its <emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end> will ſhew ſo little, that it will not be <lb></lb>thought the twentieth part of that of <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> nay, he that hath not <lb></lb>very good eyes, will very hardly diſcern it; from whence it may <lb></lb>be rationally inferred, that the ſaid ſtar, as having a much more <lb></lb>lively light than <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> maketh its irradiation greater than <emph type="italics"></emph>Jupi <lb></lb>ter<emph.end type="italics"></emph.end> doth his. </s><s>In the next place, as to the irradiation of the Sun <lb></lb>and Moon, it is as nothing, by means of their magnitude, which <lb></lb><arrow.to.target n="marg558"></arrow.to.target> <lb></lb>poſſeſſeth of it ſelf alone ſo great a ſpace in our eye, that it lea <lb></lb>veth no place for the adventitious rayes; ſo that their faces ſeem <lb></lb>cloſe clipt, and terminate. </s><s>We may aſſure our ſelves of the ſame <lb></lb>truth by another experiment which I have often made triall of; <pb xlink:href="040/01/326.jpg" pagenum="306"></pb><arrow.to.target n="marg559"></arrow.to.target> <lb></lb>we may aſſure our ſelves, I ſay, that bodies ſhining with moſt| live <lb></lb>ly light do irradiate, or beam forth rayes more by far than thoſe <lb></lb>that are of a more languiſhing light. </s><s>I have many times ſeen <emph type="italics"></emph>Ju <lb></lb>piter<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> together twenty or thirty degrees diſtant from the <lb></lb>Sun, and the air being very dark, <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> appeared eight or ten <lb></lb>times bigger than <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> being both beheld by the eye at liber <lb></lb>ty; but being beheld afterwards with the Teleſcope, the <emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end> <lb></lb>of <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> diſcovered it ſelf to be four or more times greater than <lb></lb>that of <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> but the vivacity of the ſplendour of <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> was in <lb></lb>comparably bigger than the languiſhing light of <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end>; which <lb></lb>was only becauſe of <emph type="italics"></emph>Jupiters<emph.end type="italics"></emph.end> being far from the Sun, and from us; <lb></lb>and <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> neer to us, and to the Sun. </s><s>Theſe things premiſed, it <lb></lb>will not be difficult to comprehend, how Mars, when it is in oppo <lb></lb>ſition to the Sun, and therefore neerer to the Earth by ſeven times, <lb></lb>and more, than it is towards the conjunction, cometh to appear <lb></lb>ſcarce four or five times bigger in that ſtate than in this, when as it <lb></lb>ſhould appear more than fifty times ſo much; of which the only <lb></lb>irradiation is the cauſe; for if we diveſt it of the adventitious <lb></lb>rayes, we ſhall find it exactly augmented with the due proportion: <lb></lb>but to take away the capillitious border, the Teleſcope is the beſt <lb></lb><arrow.to.target n="marg560"></arrow.to.target> <lb></lb>and only means, which inlarging its <emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end> nine hundred or a <lb></lb>thouſand times, makes it to be ſeen naked and terminate, as that <lb></lb>of the Moon, and different from it ſelf in the two poſitions, ac <lb></lb><arrow.to.target n="marg561"></arrow.to.target> <lb></lb>cording to its due proportions to an hair. </s><s>Again, as to <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> <lb></lb>that in its veſpertine conjunction, when it is below the Sun, ought <lb></lb>to ſhew almoſt fourty times bigger than in the other matutine con <lb></lb>junction, and yet doth not appear ſo much as doubled; it happen <lb></lb>eth, beſides the effect of the irradiation, that it is horned; and its <lb></lb>creſcents, beſides that they are ſharp, they do receive the Suns light <lb></lb>obliquely, and therefore emit but a faint ſplendour; ſo that as <lb></lb>being little and weak, its irradiation becometh the leſſe ample <lb></lb>and vivacious, than when it appeareth to us with its Hemiſphere all <lb></lb>ſhining: but now the Teleſcope manifeſtly ſhews its hornes to <lb></lb>have been as terminate and diſtinct as thoſe of the Moon, and <lb></lb>appear, as it were, with a great circle, and in a proportion thoſe <lb></lb>well neer fourty times greater than its ſame <emph type="italics"></emph>Diſcus,<emph.end type="italics"></emph.end> at ſuch time <lb></lb>as it is ſuperiour to the Sun in its ultimate matutine apparition.</s></p><p type="margin"><s><margin.target id="marg556"></margin.target><emph type="italics"></emph>An eaſie expe <lb></lb>riment that ſhew <lb></lb>eth the increaſe in <lb></lb>the ſtars, by means <lb></lb>of the adventitious <lb></lb>rays.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg557"></margin.target>Jupiter <emph type="italics"></emph>augments <lb></lb>leſſe than the<emph.end type="italics"></emph.end> Dog <lb></lb>ſtar.</s></p><p type="margin"><s><margin.target id="marg558"></margin.target><emph type="italics"></emph>The<emph.end type="italics"></emph.end> Sun <emph type="italics"></emph>and<emph.end type="italics"></emph.end> <lb></lb>Moon <emph type="italics"></emph>increaſe lis <lb></lb>tle.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg559"></margin.target><emph type="italics"></emph>It is ſeen by ma <lb></lb>nifeſt experience, <lb></lb>that the more <lb></lb>ſplendid bodies do <lb></lb>much more irradi <lb></lb>ate than the leſſe <lb></lb>lucid.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg560"></margin.target><emph type="italics"></emph>The<emph.end type="italics"></emph.end> Teleſcope <lb></lb><emph type="italics"></emph>is the beſt means to <lb></lb>take away the ir <lb></lb>radiations of the <lb></lb>Stars.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg561"></margin.target><emph type="italics"></emph>Another ſecond <lb></lb>reaſon of the ſmall <lb></lb>apparent increaſe <lb></lb>of<emph.end type="italics"></emph.end> Venus.</s></p><p type="main"><s>SAGR. Oh, <emph type="italics"></emph>Nicholas Copernicus,<emph.end type="italics"></emph.end> how great would have been <lb></lb>thy joy to have ſeen this part of thy Syſteme, confirmed with ſo <lb></lb>manifeſt experiments! <lb></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"></emph>per <lb></lb>ſwaded by reaſons <lb></lb>contrary to ſenſible <lb></lb>experiments.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Tis true. </s><s>But how much leſſe the fame of his ſublime <lb></lb>wit amongſt the intelligent? </s><s>when as it is ſeen, as I alſo ſaid before, <lb></lb>that he did conſtantly continue to affirm (being perſwaded thereto <lb></lb>by reaſon) that which ſenſible experiments ſeemed to contradict; <lb></lb>for I cannot ceaſe to wonder that he ſhould conſtantly perſiſt in <lb></lb>ſaying, that <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> revolveth about the Sun, and is more than ſix <pb xlink:href="040/01/327.jpg" pagenum="307"></pb>times farther from us at one time, than at another; and alſo ſeem <lb></lb>eth to be alwayes of an equal bigneſs, although it ought to ſhew <lb></lb>forty times bigger when neareſt to us, than when fartheſt off.</s></p><p type="main"><s>SAGR. </s><s>But in <emph type="italics"></emph>Jupiter, Saturn<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Mercury,<emph.end type="italics"></emph.end> I believe that <lb></lb>the differences of their apparent magnitudes, ſhould ſeem punctu <lb></lb>ally to anſwer to their different diſtances.</s></p><p type="main"><s>SALV. </s><s>In the two Superiour ones, I have made preciſe ob <lb></lb>ſervations yearly for this twenty two years laſt paſt: In <emph type="italics"></emph>Mercury<emph.end type="italics"></emph.end></s></p><p type="main"><s><arrow.to.target n="marg563"></arrow.to.target> <lb></lb>there can be no obſervation of moment made, by reaſon it ſuf <lb></lb>fers not it ſelf to be ſeen, ſave onely in its greateſt digrſſieons <lb></lb>from the Sun, in which its diſtances from the earth are inſenſibly <lb></lb>unequal, and thoſe differences conſequently not to be obſerved; <lb></lb>as alſo its mutations of figures which muſt abſolutely happen in <lb></lb>it, as in <emph type="italics"></emph>Venus.<emph.end type="italics"></emph.end> And if we do ſee it, it muſt of neceſſity appear <lb></lb>in form of a Semicircle, as <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> likewiſe doth in her greateſt <lb></lb>digreſſions; but its <emph type="italics"></emph>diſcus<emph.end type="italics"></emph.end> is ſo very ſmall, and its ſplendor ſo <lb></lb>very great, by reaſon of its vicinity to the Sun, that the virtue <lb></lb>of the Teleſcope doth not ſuffice to clip its treſſes or adventitious <lb></lb>rayes, ſo as to make them appear ſhaved round about. </s><s>It re <lb></lb><arrow.to.target n="marg564"></arrow.to.target> <lb></lb>mains, that we remove that which ſeemed a great inconvenience <lb></lb>in the motion of the Earth, namely that all the Planets moving <lb></lb>about the Sun, it alone, not ſolitary as the reſt, but in company <lb></lb>with the Moon, and the whole Elementary Sphear, ſhould move <lb></lb>round about the Sun in a year; and that the ſaid Moon withal <lb></lb>ſhould move every moneth about the earth. </s><s>Here it is neceſſary <lb></lb>once again to exclaim and extol the admirable perſpicacity of <emph type="italics"></emph>Co <lb></lb>pernicus,<emph.end type="italics"></emph.end> and withal to condole his misfortune, in that he is not <lb></lb>now alive in our dayes, when for removing of the ſeeming ab <lb></lb>ſurdity of the Earth and Moons motion in conſort we ſee <emph type="italics"></emph>Jupi <lb></lb>ter,<emph.end type="italics"></emph.end> as if it were another Earth, not in conſort with the Moon, <lb></lb>but accompanied by four Moons to rovolve about the Sun in 12. <lb></lb>years together, with what ever things the Orbs of the four Medi <lb></lb>cæan Stars can contain within them.</s></p><p type="margin"><s><margin.target id="marg563"></margin.target>Mercury <emph type="italics"></emph>admit <lb></lb>teth not of clear <lb></lb>obſervations.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg564"></margin.target><emph type="italics"></emph>The difficulties <lb></lb>removed that ariſe <lb></lb>from the Earths <lb></lb>moving about the <lb></lb>Sun, not ſolitarily, <lb></lb>but in conſort with <lb></lb>the Moon.<emph.end type="italics"></emph.end></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 ſeem to be to one that ſtanding in <lb></lb><arrow.to.target n="marg565"></arrow.to.target> <lb></lb><emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> ſhould behold them; for they are of themſelves dark, and <lb></lb>receive their light from the Sun, which is manifeſt from their be <lb></lb>ing eclipſed, when they enter into the cone of <emph type="italics"></emph>Jupiters<emph.end type="italics"></emph.end> ſhadow: <lb></lb>and becauſe onely thoſe their Hemiſpheres, that look towards the <lb></lb>Sun are illuminated, to us that are without their Orbs, and near <lb></lb>er to the Sun, they ſeem alwayes <emph type="italics"></emph>lucid,<emph.end type="italics"></emph.end> but to one that ſhould be <lb></lb>in <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> they would ſhew all illuminated, at ſuch time as they <lb></lb>were in the upper parts of their circles; but in the parts inferi <lb></lb>our, that is between <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> and the Sun, they would from <emph type="italics"></emph>Ju <lb></lb>piter<emph.end type="italics"></emph.end> be obſerved to be horned; and in a word they would, to <pb xlink:href="040/01/328.jpg" pagenum="308"></pb>the obſervators ſtanding in <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> make the ſelf ſame changes <lb></lb>of Figure, that to us upon the Earth, the Moon doth make. </s><s>You <lb></lb>ſee now how theſe three things, which at ſirſt ſeémed diſſonant, <lb></lb>do admirably accord with the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Syſteme. </s><s>Here alſo by <lb></lb>the way may <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> ſee, with what probability one may con <lb></lb>clude, that the Sun and not the Earth, is in the Centre of the <lb></lb><emph type="italics"></emph>Planetary<emph.end type="italics"></emph.end> converſions. </s><s>And ſince the Earth is now placed a <lb></lb>mongſt mundane Bodies, that undoubtedly move about the Sun, <lb></lb>to wit, above <emph type="italics"></emph>Mercury<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> and below <emph type="italics"></emph>Saturn, Jupiter,<emph.end type="italics"></emph.end> <lb></lb>and <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end>; ſhall it not be in like manner probable, and perhaps <lb></lb>neceſſary to grant, that it alſo moveth round?</s></p><p type="margin"><s><margin.target id="marg565"></margin.target><emph type="italics"></emph>The<emph.end type="italics"></emph.end> Medicean <lb></lb><emph type="italics"></emph>Stars areas it were <lb></lb>four Moons about<emph.end type="italics"></emph.end> <lb></lb>Jupiter.</s></p><p type="main"><s>SIMP. </s><s>Theſe accidents are ſo notable and conſpicuous, that <lb></lb>it is not poſſible, but that <emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> and others his Sectators, ſhould <lb></lb>have had knowledge of them, and having ſo, it is likewiſe neceſ <lb></lb>ſary, that they have found a way to render reaſons of ſuch, and <lb></lb>ſo ſenſible appearances that were ſufficient, and alſo congruous <lb></lb>and probable, ſeeing that they have for ſo long a time been re <lb></lb>ceived by ſuch numbers of learned men. <lb></lb><arrow.to.target n="marg566"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg566"></margin.target><emph type="italics"></emph>The Principal <lb></lb>ſcope of Aſtrono <lb></lb>mers, is to give a <lb></lb>reaſon of appear <lb></lb>ances.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>You argue very well; but you know that the principal <lb></lb>ſcope of <emph type="italics"></emph>Aſtronomers,<emph.end type="italics"></emph.end> is to render only reaſon for the appearances <lb></lb>in the Cæleſtial Bodies, and to them, and to the motions of the <lb></lb>Stars, to accomodate ſuch ſtructures and compoſitions of Circles, <lb></lb>that the motions following thoſe calculations, anſwer to the ſaid <lb></lb>appearances, little ſcrupling to admit of ſome exorbitances, that <lb></lb>indeed upon other accounts they would much ſtick at. </s><s>And <emph type="italics"></emph>Co-<emph.end type="italics"></emph.end></s></p><p type="main"><s><arrow.to.target n="marg567"></arrow.to.target> <lb></lb><emph type="italics"></emph>pernic us<emph.end type="italics"></emph.end> himſelf writes, that he had in his firſt ſtudies reſtored the <lb></lb>Science of <emph type="italics"></emph>Aſtronomy<emph.end type="italics"></emph.end> upon the very ſuppoſitions of <emph type="italics"></emph>Ptolomy,<emph.end type="italics"></emph.end> and <lb></lb>in ſuch manner corrected the motions of the Planets, that the <lb></lb>computations did very exactly agree with the <emph type="italics"></emph>Phænomena,<emph.end type="italics"></emph.end> and <lb></lb>the <emph type="italics"></emph>Phænomena<emph.end type="italics"></emph.end> with the ſupputations, in caſe that he took the <lb></lb>Planets ſeverally one by one. </s><s>But he addeth, that in going a <lb></lb>bout to put together all the ſtructures of the particular Fabricks, <lb></lb>there reſulted thence a Monſter and <emph type="italics"></emph>Chimæra,<emph.end type="italics"></emph.end> compoſed of mem <lb></lb>bers moſt diſproportionate to one another, and altogether incom <lb></lb>patible; So that although it ſatisfied an <emph type="italics"></emph>Aſtronomer<emph.end type="italics"></emph.end> meerly <emph type="italics"></emph>A <lb></lb>rithmetical,<emph.end type="italics"></emph.end> yet did it not afford ſatisfaction or content to the <lb></lb><arrow.to.target n="marg568"></arrow.to.target> <lb></lb><emph type="italics"></emph>Aſtronomer Phyloſophical.<emph.end type="italics"></emph.end> And becauſe he very well under <lb></lb>ſtood, that if one might ſalve the Cæleſtial appearances with falſe <lb></lb>aſſumptions in nature, it might with much more eaſe be done by <lb></lb>true ſuppoſitions, he ſet himſelf diligently to ſearch whether a <lb></lb>ny amongſt the antient men of fame, had aſcribed to the World <lb></lb>any other ſtructure, than that commonly received by <emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end>; <lb></lb>and finding that ſome <emph type="italics"></emph>Pythagoreans<emph.end type="italics"></emph.end> had in particular aſſigned <lb></lb>the Diurnal converſion to the Earth, and others the annual mo <lb></lb>tion alſo, he began to compare the appearances, and particulari <pb xlink:href="040/01/329.jpg" pagenum="309"></pb>ties of the Planets motions, with theſe two new ſuppoſitions, all <lb></lb>which things jumpt exactly with his purpoſe; and ſeeing the whole <lb></lb>correſpond, with admirable facility to its parts, he imbraced this <lb></lb>new Syſteme, and it took up his reſt.</s></p><p type="margin"><s><margin.target id="marg567"></margin.target>Copernicus <emph type="italics"></emph>re <lb></lb>ſtored Aſtronomy <lb></lb>upon the ſuppoſiti <lb></lb>ous of<emph.end type="italics"></emph.end> Ptolomy:</s></p><p type="margin"><s><margin.target id="marg568"></margin.target><emph type="italics"></emph>What moved<emph.end type="italics"></emph.end> Co <lb></lb>pernicus <emph type="italics"></emph>to eſta <lb></lb>bliſh his Syſteme.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>But what great exorbitancies are there in the <emph type="italics"></emph>Ptolo <lb></lb>maick<emph.end type="italics"></emph.end> Syſteme, for which there are not greater to be found in this <lb></lb>of <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end>?</s></p><p type="main"><s>SALV. </s><s>In the <emph type="italics"></emph>Ptolomaick Hypotheſis<emph.end type="italics"></emph.end> there are diſeaſes, and in <lb></lb><arrow.to.target n="marg569"></arrow.to.target> <lb></lb>the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> their cures. </s><s>And firſt will not all the Sects of <lb></lb><emph type="italics"></emph>Phyloſophers,<emph.end type="italics"></emph.end> account it a great inconvenience, that a body na <lb></lb>turally moveable in circumgyration, ſhould move irregularly upon <lb></lb>its own Centre, and regularly upon another point? </s><s>And yet <lb></lb>there are ſuch deformed motions as theſe in the <emph type="italics"></emph>Ptolomæan<emph.end type="italics"></emph.end> Hypo <lb></lb>theſis, but in the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> all move evenly about their own <lb></lb>Centres. </s><s>In the <emph type="italics"></emph>Ptolomaick,<emph.end type="italics"></emph.end> it is neceſſary to aſſign to the Cæ <lb></lb>leſtial bodies, contrary motions, and to make them all to move, <lb></lb>from Eaſt to Weſt, and at the ſame time, from Weſt to Eaſt; <lb></lb>But in the <emph type="italics"></emph>Copernican,<emph.end type="italics"></emph.end> all the Cæleſtial revolutions are towards <lb></lb>one onely way, from Weſt to Eaſt. </s><s>But what ſhall we ſay of <lb></lb>the apparent motion of the Planets, ſo irregular, that they not on <lb></lb>ly go one while ſwift, and another while ſlow, but ſometimes <lb></lb>wholly ſeace to move; and then after a long time return back a <lb></lb>gain? </s><s>To ſalve which appearances <emph type="italics"></emph>Ptolomie<emph.end type="italics"></emph.end> introduceth very great <lb></lb><emph type="italics"></emph>Epicicles,<emph.end type="italics"></emph.end> accommodating them one by one to each Planet, with <lb></lb>ſome rules of incongruous motions, which are all with one ſin <lb></lb>gle motion of the Earth taken away. </s><s>And would not you, <emph type="italics"></emph>Sim <lb></lb>plicius,<emph.end type="italics"></emph.end> call it a great abſurditie, if in the <emph type="italics"></emph>Ptolomaick<emph.end type="italics"></emph.end> Hypothe <lb></lb>ſis, in which the particular Planets, have their peculiar Orbs aſ <lb></lb>ſigned them one above another, one muſt be frequently forced <lb></lb>to ſay, that <emph type="italics"></emph>Mars,<emph.end type="italics"></emph.end> conſtituted above the Sphære of the Sun, doth <lb></lb>ſo deſcend, that breaking the Solar Orb, it goeth under it, and <lb></lb>approacheth neaer to the Earth, than to the Body of the Sun, <lb></lb>and by and by immeaſurably aſcendeth above the ſame? </s><s>And <lb></lb>yet this, and other exorbitancies are remedied by the Soul and <lb></lb>fingle annual motion of the Earth.</s></p><p type="margin"><s><margin.target id="marg569"></margin.target><emph type="italics"></emph>Inconveniencies <lb></lb>that are in the Sy <lb></lb>ſteme of<emph.end type="italics"></emph.end> Ptolomy.</s></p><p type="main"><s>SAGR. </s><s>I would gladly be bettter informed how theſe ſtations, <lb></lb>and retrograde and direct motions, which did ever ſeem to me <lb></lb>great improbalities, do accord in this <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Syſteme. <lb></lb><arrow.to.target n="marg570"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg570"></margin.target><emph type="italics"></emph>Its a great Ar <lb></lb>gument in favour <lb></lb>of<emph.end type="italics"></emph.end> Copernicus, <emph type="italics"></emph>that <lb></lb>he obviates the ſta <lb></lb>tions & retrograda <lb></lb>tions of the motions <lb></lb>of the Planets.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>You ſhall ſee them ſo to accord, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> that <lb></lb>this onely conjecture ought to be ſufficient to make one that <lb></lb>is not more than pertinacious or ſtupid, yield, aſſent to all the <lb></lb>reſt of this Doctrine. </s><s>I tell you therefore, that nothing being <lb></lb>altered in the motion of <emph type="italics"></emph>Saturn,<emph.end type="italics"></emph.end> which is 30 years, in that <lb></lb>of <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> which is 12, in that of <emph type="italics"></emph>Mars,<emph.end type="italics"></emph.end> which is 2, in that of <lb></lb><emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> which is 9. moneths, in that of <emph type="italics"></emph>Mercury,<emph.end type="italics"></emph.end> which is 80. <pb xlink:href="040/01/330.jpg" pagenum="310"></pb>dayes, or thereabouts, the ſole annual motion of the Earth be <lb></lb>tween <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> cauſeth the apparent inequalities in all </s></p><p type="main"><s><arrow.to.target n="marg571"></arrow.to.target> <lb></lb>the five ſtars before named. </s><s>And for a facile and full under <lb></lb>ſtanding of the whole, I will deſcribe this figure of it. </s><s>There <lb></lb>fore ſuppoſe the Sun to be placed in the centre O, about which <lb></lb>we will draw the Orb deſcribed by the Earth, with the an <lb></lb>nual motion B G M, and let the circle deſcribed, <emph type="italics"></emph>v. </s><s>gr.<emph.end type="italics"></emph.end> by <lb></lb><emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> about the Sun in 12. years, be this BGM, and in the <lb></lb><figure id="id.040.01.330.1.jpg" xlink:href="040/01/330/1.jpg"></figure> <lb></lb><arrow.to.target n="marg572"></arrow.to.target> <lb></lb>ſtarry ſphere let us imagine the Zodiack Y V S. Again, in the <lb></lb>annual Orb of the Earth let us take certain equal arches, B C, <lb></lb>C D, E F, F G, G H, H I, I K, K L, L M, and in the Sphere <lb></lb>of <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> let us make certain other arches, paſſed in the ſame <lb></lb>times in which the Earth paſſeth hers, which let be B C, C D, <lb></lb>D E, E F, F G, G H, H I, I K, K L, L M, which ſhall each be <lb></lb>proportionally leſſe than theſe marked in the Earths Orb, like <lb></lb>as the motion of <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> under the Zodiack is ſlower than the <lb></lb>annual. </s><s>Suppoſing now, that when the Earth is in B, <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> is <lb></lb>in B, it ſhall appear to us in the Zodiack to be in P, deſcribing <pb xlink:href="040/01/331.jpg" pagenum="311"></pb>the right line B B P. </s><s>Next ſuppoſe the Earth to be moved from <lb></lb>B to C, and <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> from B to C, in the ſame time; <emph type="italics"></emph>Iupiter<emph.end type="italics"></emph.end> <lb></lb>ſhall appear to have paſſed in the Zodiack to Q, and to have <lb></lb>moved ſtraight forwards, according to the order of the ſignes <lb></lb>P <expan abbr="q.">que</expan> In the next place, the Earth paſſing to D, and <emph type="italics"></emph>Iupiter<emph.end type="italics"></emph.end> <lb></lb>to D, it ſhall be ſeen in the Zodiack in R, and from E, <emph type="italics"></emph>Iupi <lb></lb>ter<emph.end type="italics"></emph.end> being come to E; will appear in the Zodiack in S, having <lb></lb>all this while moved right forwards. </s><s>But the Earth afterwards <lb></lb>beginning to interpoſe more directly between <emph type="italics"></emph>Iupiter<emph.end type="italics"></emph.end> and the <lb></lb>Sun, ſhe being come to F, and <emph type="italics"></emph>Iupiter<emph.end type="italics"></emph.end> to F, he will appear in <lb></lb>T, to have already begun to return apparently back again un <lb></lb>der the Zodiack, and in that time that the Earth ſhall have paſ <lb></lb>ed the arch E F, <emph type="italics"></emph>Iupiter<emph.end type="italics"></emph.end> ſhall have entertained himſelf between <lb></lb>the points S T, and ſhall have appeared to us almoſt motion <lb></lb>leſſe and ſtationary. </s><s>The Earth being afterwards come to G, <lb></lb>and <emph type="italics"></emph>Iupiter<emph.end type="italics"></emph.end> to G, in oppoſition to the Sun, it ſhall be viſible in <lb></lb>the Zodiack at V, and much returned backwards by all the arch <lb></lb>of the Zodiack T V; howbeit that all the way purſuing its even <lb></lb>courſe it hath really gone forwards not onely in its own circle, <lb></lb>but in the Zodiack alſo in reſpect to the centre of the ſaid Zodi <lb></lb>ack, and to the Sun placed in the ſame. </s><s>The Earth and <emph type="italics"></emph>Iupiter<emph.end type="italics"></emph.end> <lb></lb>again continuing their motions, when the Earth is come to H, <lb></lb>and <emph type="italics"></emph>Iupiter<emph.end type="italics"></emph.end> to H, it ſhall ſeem very much gone backward in the <lb></lb>Zodiack by all the arch V X. </s><s>The Earth being come to I, and <lb></lb><emph type="italics"></emph>Iupiter<emph.end type="italics"></emph.end> to I, it ſhall be apparently moved in the Zodiack by the lit <lb></lb>tle ſpace X Y, and there it will ſeem ſtationary. </s><s>When after <lb></lb>wards the Earth ſhall be come to K, and <emph type="italics"></emph>Iupiter<emph.end type="italics"></emph.end> to K; in the <lb></lb>Zodiack he ſhall have paſſed the arch Y N in a direct motion; <lb></lb>and the Earth purſuing its courſe to L, ſhall ſee <emph type="italics"></emph>Iupiter<emph.end type="italics"></emph.end> in L, in <lb></lb>the point Z. </s><s>And laſtly <emph type="italics"></emph>Iupiter<emph.end type="italics"></emph.end> in M ſhall be ſeen from the Earth <lb></lb>M, to have paſſed to A, with a motion ſtill right forwards; and <lb></lb>its whole apparent retrogadation in the Zodiack ſhall anſwer to <lb></lb>the arch S Y, made by <emph type="italics"></emph>Iupiter,<emph.end type="italics"></emph.end> whilſt that he in his own circle <lb></lb>paſſeth the arch E I, and the Earth in hers the arch E I. </s><s>And <lb></lb><arrow.to.target n="marg573"></arrow.to.target> <lb></lb>this which hath been ſaid, is intended of <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> <lb></lb>alſo; and in <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> thoſe retrogradations are ſomewhat more <lb></lb>frequent than in <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> by reaſon that its motion is a little <lb></lb>ſlower than that of <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> ſo that the Earth overtaketh it <lb></lb>it in a ſhorter ſpace of time; in <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> again they are more <lb></lb>rare, for that its motion is more ſwift than that of <emph type="italics"></emph>Jupiter.<emph.end type="italics"></emph.end> <lb></lb>Whereupon the Earth conſumeth more time in recovering it. </s><s>Next <lb></lb>as to <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Mercury,<emph.end type="italics"></emph.end> whoſe Circles are comprehended by that <lb></lb><arrow.to.target n="marg574"></arrow.to.target> <lb></lb>of the Earth, their ſtations and regreſſions appear to be occaſi <lb></lb>oned, not by their motions that really are ſuch, but by the anual <lb></lb>motion of the ſaid Earth, as <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> exellently demonſtrateth, <pb xlink:href="040/01/332.jpg" pagenum="312"></pb>together with <emph type="italics"></emph>Appollonius Pergæus<emph.end type="italics"></emph.end> in <emph type="italics"></emph>lib.<emph.end type="italics"></emph.end> 5. of his Revolutions, <lb></lb><emph type="italics"></emph>Chap.<emph.end type="italics"></emph.end> 35.</s></p><p type="margin"><s><margin.target id="marg571"></margin.target><emph type="italics"></emph>The ſole annual <lb></lb>motion of the <lb></lb>Earth cauſeth <lb></lb>great inequality of <lb></lb>motions in the five <lb></lb>Planets.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg572"></margin.target><emph type="italics"></emph>A demonſtration of <lb></lb>the inequalities of <lb></lb>the three ſuperiour <lb></lb>Planets dependent <lb></lb>on the annual mo <lb></lb>tion of the Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg573"></margin.target><emph type="italics"></emph>Retrogradations <lb></lb>more frequent in<emph.end type="italics"></emph.end> <lb></lb>Saturn, <emph type="italics"></emph>leſſe in<emph.end type="italics"></emph.end> Ju <lb></lb>piter, <emph type="italics"></emph>and yet leſſe <lb></lb>in<emph.end type="italics"></emph.end> Mars, <emph type="italics"></emph>and why.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg574"></margin.target><emph type="italics"></emph>The Retrograda <lb></lb>tion of<emph.end type="italics"></emph.end> Venus <emph type="italics"></emph>and<emph.end type="italics"></emph.end> <lb></lb>Mercury <emph type="italics"></emph>demon <lb></lb>ſtrated by<emph.end type="italics"></emph.end> Apollo <lb></lb>nius <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Coperni <lb></lb>cus.</s></p><p type="main"><s>You ſee, Gentlemen, with what facility and ſimplicity the annu <lb></lb><arrow.to.target n="marg575"></arrow.to.target> <lb></lb>al motion, were it appertaining to the Earth, is accommodated <lb></lb>to render a reaſon of the apparent exorbitances, that are obſerved <lb></lb>in the motions of the five Planets, <emph type="italics"></emph>Saturn, Jupiter, Mars, Ve <lb></lb>nus<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Mercury,<emph.end type="italics"></emph.end> taking them all away, and reducing them to <lb></lb><arrow.to.target n="marg576"></arrow.to.target> <lb></lb>equal and regular motions. </s><s>And of this admirable effect, <emph type="italics"></emph>Ni <lb></lb>cholas Copernicus,<emph.end type="italics"></emph.end> hath been the firſt that hath made the reaſon <lb></lb>plain unto us. </s><s>But of another effect, no leſſe admirable than <lb></lb>this, and that with a knot, perhaps more difficult to unknit, <lb></lb>bindeth the wit of man, to admit this annual converſion, and to <lb></lb>leave it to our Terreſtrial Globe; a new and unthought of con <lb></lb>jecture ariſeth from the Sun it ſelf, which ſheweth that it is unwil <lb></lb>ling to be ſingular in ſhifting, of this atteſtation of ſo eminent a <lb></lb>concluſion, rather as a teſtimony beyond all exception, it hath <lb></lb>deſired to be heard apart. </s><s>Hearken then to this great and new <lb></lb>wonder. <lb></lb><arrow.to.target n="marg577"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg575"></margin.target><emph type="italics"></emph>The annual mo <lb></lb>tion of the Earth <lb></lb>moſt apt to render <lb></lb>a reaſon of the ex <lb></lb>orbttances of the <lb></lb>five Planets.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg576"></margin.target><emph type="italics"></emph>The Sun it ſelf <lb></lb>teſtifieth the annu <lb></lb>al motion to belong <lb></lb>to the Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg577"></margin.target><emph type="italics"></emph>The Lyncæan <lb></lb>Academick the <lb></lb>firſt diſcoverer of <lb></lb>the Solar ſpots, and <lb></lb>all the other cele <lb></lb>ſtial novelties.<emph.end type="italics"></emph.end></s></p><p type="main"><s>The firſt diſcoverer and obſerver of the <emph type="italics"></emph>Solar<emph.end type="italics"></emph.end> ſpots, as alſo of <lb></lb>all the other Cœleſtial novelties, was our <emph type="italics"></emph>Academick Lincæus<emph.end type="italics"></emph.end>; and <lb></lb>he diſcovered them <emph type="italics"></emph>anno<emph.end type="italics"></emph.end> 1610. being at that time Reader of the <lb></lb><emph type="italics"></emph>Mathematicks,<emph.end type="italics"></emph.end> in the Colledge of <emph type="italics"></emph>Padua,<emph.end type="italics"></emph.end> and there, and in <emph type="italics"></emph>Ve <lb></lb>nice,<emph.end type="italics"></emph.end> he diſcourſed thereof with ſeveral perſons, of which ſome </s></p><p type="main"><s><arrow.to.target n="marg578"></arrow.to.target> <lb></lb>are yet living: And the year following, he ſhewed them in <emph type="italics"></emph>Rome<emph.end type="italics"></emph.end> <lb></lb>to many great perſonages, as he relates in the firſt of his Letters <lb></lb>to <emph type="italics"></emph>Marcus Velſerus,<emph.end type="italics"></emph.end> ^{*} Sheriffe of <emph type="italics"></emph>Auguſta.<emph.end type="italics"></emph.end> He was the <lb></lb>firſt that againſt the opinions of the too timorous and too jealous <lb></lb><arrow.to.target n="marg579"></arrow.to.target> <lb></lb>aſſertors of the Heavens inalterability, affirmed thoſe ſpots to be <lb></lb>matters, that in ſhort times were produced and diſſolved: for as <lb></lb>to place, they were contiguous to the body of the Sun, and re <lb></lb>volved about the ſame; or elſe being carried about by the ſaid <lb></lb>Solar body, which revolveth in it ſelfe about its own Centre, in <lb></lb>the ſpace almoſt of a moneth, do finiſh their courſe in that time; <lb></lb>which motion he judged at firſt to have been made by the Sun a <lb></lb>bout an Axis erected upon the plane of the Ecliptick; in regard <lb></lb>that the arches deſcribed by the ſaid ſpots upon the <emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end> of the <lb></lb>Sun appear unto our eye right lines, and parallels to the plane of <lb></lb>the Ecliptick: which therefore come to be altered, in part, with <lb></lb>ſome accidental, wandring, and irregular motions, to which they <lb></lb>are ſubject, and whereby tumultuarily, and without any order <lb></lb>they ſucceſſively change ſituations amongſt themſelves, one <lb></lb>while crouding cloſe together, another while diſſevering, and <lb></lb>ſome dividing themſelves into many and very much changing fi <lb></lb>gures, which, for the moſt part, are very unuſual. </s><s>And albeit <lb></lb>thoſe ſo inconſtant mutations did ſomewhat alter the primary pe <pb xlink:href="040/01/333.jpg" pagenum="313"></pb>riodick courſe of the ſaid ſpots, yet did they not alter the opini <lb></lb>on of our friend, ſo as to make him believe, that they were any <lb></lb>eſſential and fixed cauſe of thoſe deviations, but he continued to <lb></lb>hold, that all the apparent alterations derived themſelves from <lb></lb>thoſe accidental mutations: in like manner, juſt as it would hap <lb></lb>pen to one that ſhould from far diſtant Regions obſerve the mo <lb></lb>tion of our Clouds; which would be diſcovered to move with a <lb></lb>moſt ſwift, great, and conſtant motion, carried round by the di <lb></lb>urnal <emph type="italics"></emph>Vertigo<emph.end type="italics"></emph.end> of the Earth (if haply that motion belong to the <lb></lb>ſame) in twenty four hours, by circles parallel to the Equinocti <lb></lb>al, but yet altered, in part, by the accidental motions cauſed by <lb></lb>the winds, which drive them, at all adventures, towards different <lb></lb>quarters of the World. </s><s>While this was in agitation, it came to <lb></lb>paſs that <emph type="italics"></emph>Velſerus<emph.end type="italics"></emph.end> ſent him two Letters, written by a certain per <lb></lb><arrow.to.target n="marg580"></arrow.to.target> <lb></lb>ſon, under the feigned name of ^{*} <emph type="italics"></emph>Apelles,<emph.end type="italics"></emph.end> upon the ſubject of <lb></lb>theſe Spots, requeſting him, with importunity, to declare his <lb></lb>thoughts freely upon thoſe Letters, and withall to let him know <lb></lb>what his opinion was touching the eſſence of thoſe ſpots; which his <lb></lb>requeſt he ſatisfied in 3 Letters, ſhewing firſt of all howvain the <lb></lb>conjectures of <emph type="italics"></emph>Apelles<emph.end type="italics"></emph.end> were; & diſcovering, ſecondly, his own opi <lb></lb>nions; withal foretelling to him, that <emph type="italics"></emph>Apelles<emph.end type="italics"></emph.end> would undoubtedly <lb></lb>be better adviſed in time, and turn to his opinion, as it afterwards <lb></lb>came to paſs. </s><s>And becauſe that our Academian (as it was alſo <lb></lb>the judgment of many others that were intelligent in Natures ſe <lb></lb>crets) thought he had in thoſe three Letters inveſtigated and de <lb></lb>monſtrated, if not all that could be deſired, or required by hu <lb></lb>mane curioſity, at leaſt all that could be attained by humane <lb></lb>reaſon in ſuch a matter, he, for ſome time (being buſied in other <lb></lb>ſtudies) intermitted his continual obſervations, and onely in com <lb></lb>placency to ſome friend, joyned with him, in making now and <lb></lb>then an abrupt obſervation: till that he, and after ſome years, <lb></lb><arrow.to.target n="marg581"></arrow.to.target> <lb></lb>we, being then at my ^{*} Country-ſeat, met with one of the ſolita <lb></lb>ry Solar ſpots very big, and thick, invited withal by a clear and <lb></lb>conſtant ſerenity of the Heavens, he, at my requeſt, made obſer <lb></lb>vations of the whole progreſſe of the ſaid ſpot, carefully marking <lb></lb>upon a ſheet of paper the places that it was in every day at the <lb></lb>time of the Suns coming into the Meridian; and we having found <lb></lb>that its courſe was not in a right line, but ſomewhat incurvated, <lb></lb>we came to reſolve, at laſt, to make other obſervations from time <lb></lb>to time; to which undertaking we were ſtrongly induced by a <lb></lb>conceit, that accidentally came into the minde of my Gueſt, <lb></lb>which he imparted to me in theſe or the like words.</s></p><p type="margin"><s><margin.target id="marg578"></margin.target><emph type="italics"></emph>The hiſtory of <lb></lb>the proceedings of <lb></lb>the Academian <lb></lb>for a long time a <lb></lb>bout the obſervati <lb></lb>on of the Solar <lb></lb>ſpots.<emph.end type="italics"></emph.end></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></lb>true name is <emph type="italics"></emph>Chri <lb></lb>ſtopher Scheiner us<emph.end type="italics"></emph.end> <lb></lb>a Jeſuit, and his <lb></lb>Book here meant <lb></lb>is intituled, <emph type="italics"></emph>Apel <lb></lb>les poſt tabulam.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg581"></margin.target>* La mia villa <lb></lb>delle Selue.</s></p><p type="main"><s>In my opinion, <emph type="italics"></emph>Philip,<emph.end type="italics"></emph.end> there is a way opened to a buſineſs of <lb></lb>very great conſequence. </s><s>For if the Axis about which the Sun <lb></lb>turneth be not erect perpendicularly to the plane of the Eclip <pb xlink:href="040/01/334.jpg" pagenum="314"></pb><arrow.to.target n="marg582"></arrow.to.target> <lb></lb>tick, but is inclined upon the ſame, as its crooked courſe, but e <lb></lb>ven now obſerved, makes me believe, we ſhall be able to make <lb></lb>ſuch conjectures of the ſtates of the Sun and Earth, as neither ſo <lb></lb>ſolid or ſo rational have been hitherto deduced from any other ac <lb></lb>cident whatſoever. </s><s>I being awakened at ſo great a promiſe, im <lb></lb>portun'd him to make a free diſcovery of his conceit unto me. <lb></lb></s><s>And he continued his diſcourſe to this purpoſe. </s><s>If the Earths <lb></lb><arrow.to.target n="marg583"></arrow.to.target> <lb></lb>motion were along the Ecliptique about the Sun; and the Sun <lb></lb>were conſtituted in the centre of the ſaid Ecliptick, and therein <lb></lb>revolved in its ſelf, not about the Axis of the ſaid Ecliptique <lb></lb>(which would be the Axis of the Earths annual motion) but up <lb></lb>on one inclined, it muſt needs follow, that ſtrange changes will <lb></lb>repreſent themſelves to us in the apparent motions of the Solar <lb></lb>ſpots, although the ſaid Axis of the Sun ſhould be ſuppoſed to <lb></lb>perſiſt perpetually and immutably in the ſame inclination, and in <lb></lb>one and the ſame direction towards the ſelf-ſame point of the <lb></lb>Univerſe. </s><s>Therefore the Terreſtrial Globe in the annual motion <lb></lb>moving round it, it will firſt follow, that to us, carried about by <lb></lb>the ſame, the courſes of the ſpots ſhall ſometimes ſeem to be <lb></lb>made in right lines, but this only twice a year, and at all other <lb></lb>times ſhall appear to be made by arches inſenſibly incurvated. <lb></lb></s><s>Secondly, the curvity of thoſe arches for one half of the year, <lb></lb>will ſhew inclined the contrary way to what they will appear in <lb></lb>the other half; that is, for ſix moneths the convexity of the ar <lb></lb>ches ſhall be towards the upper part of the Solar <emph type="italics"></emph>Diſcus,<emph.end type="italics"></emph.end> and for <lb></lb>the other ſix moneths towards the inferiour. </s><s>Thirdly, the ſpots be <lb></lb>ginning to appear, and (if I may ſo ſpeak) to riſe to our eye from <lb></lb>the left ſide of the Solar <emph type="italics"></emph>Diſcus,<emph.end type="italics"></emph.end> and going to hide themſelves <lb></lb>and to ſet in the right ſide, the Oriental termes, that is, of their <lb></lb>firſt appearings for ſix moneths, ſhall be lower than the oppoſite <lb></lb>termes of their occultations; and for other ſix moneths it ſhall <lb></lb>happen contrarily, to wit, that the ſaid ſpots riſing from more e <lb></lb>levated points, and from them deſcending, they ſhall, in their <lb></lb>courſes, go and hide themſelves in lower points; and onely for <lb></lb>two dayes in all the year ſhall thoſe termes of riſings and ſet <lb></lb>tings be equilibrated: after which freely beginning by ſmall de <lb></lb>grees the inclination of the courſes of the ſpots, and day by day <lb></lb>growing bigger, in three moneths, it ſhall arrive at its greateſt <lb></lb>obliquity, and from thence beginning to diminiſh, in ſuch another <lb></lb>time it ſhall reduce it ſelf to the other <emph type="italics"></emph>Æquilibrium.<emph.end type="italics"></emph.end> It ſhall hap <lb></lb>pen, for a fourth wonder, that the courſe of the greateſt obli <lb></lb>quity ſhall be the ſame with the courſe made by the right line, <lb></lb>and in the day of the Libration the arch of the courſe ſhall ſeem <lb></lb>more than ever incurvated. </s><s>Again, in the other times, accord <lb></lb>ing as the pendency ſhall ſucceſſively diminiſh, and make its ap <pb xlink:href="040/01/335.jpg" pagenum="315"></pb>proach towards the <emph type="italics"></emph>Æquilibrium,<emph.end type="italics"></emph.end> the incurvation of the arches <lb></lb>of the courſes on the contrary ſhall, by degrees, increaſe.</s></p><p type="margin"><s><margin.target id="marg582"></margin.target><emph type="italics"></emph>A concipt that <lb></lb>came ſuddenly in <lb></lb>to the minde of <lb></lb>the Academian<emph.end type="italics"></emph.end> <lb></lb>Lyncæus <emph type="italics"></emph>concern <lb></lb>ing the great con <lb></lb>ſequence that fol <lb></lb>lowed upon the mo <lb></lb>tion of the Solar <lb></lb>ſpots.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg583"></margin.target><emph type="italics"></emph>Extravagant mu <lb></lb>tations to be obſer <lb></lb>ved in the motions <lb></lb>of the ſpots, fore <lb></lb>ſeen by the Aca <lb></lb>demick, in caſe <lb></lb>the Earth had the <lb></lb>annual motion.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I confeſſe, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> that to interrupt you in your <lb></lb>Diſcourſe is ill manners, but I eſteem it no leſſe rudeneſs to per <lb></lb>mit you to run on any farther in words, whilſt they are, as the <lb></lb>ſaying is, caſt into the air: for, to ſpeak freely, I know not how <lb></lb>to form any diſtinct conceit of ſo much as one of theſe concluſi <lb></lb>ons, that you have pronounced; but becauſe, as I thus general <lb></lb>ly and confuſedly apprehend them, they hold forth things of ad <lb></lb>mirable conſequence, I would gladly, ſome way or other, be <lb></lb>made to underſtand the ſame.</s></p><p type="main"><s>SALV. </s><s>The ſame that befalls you, befell me alſo, whilſt my <lb></lb>Gueſt tranſported me with bare words; who afterwards aſſiſted <lb></lb>my capacity, by deſcribing the buſineſſe upon a material Inſtru <lb></lb><arrow.to.target n="marg584"></arrow.to.target> <lb></lb>ment, which was no other than a ſimple Sphere, making uſe of <lb></lb>ſome of its circles, but to a different purpoſe from that, to which <lb></lb>they are commonly applied. </s><s>Now I will ſupply the defect of <lb></lb>the Sphere, by drawing the ſame upon a piece of paper, as need <lb></lb>ſhall require. </s><s>And to repreſent the firſt accident by me propoun <lb></lb>ded, which was, that the courſes or journeys of the ſpots, twice <lb></lb>a year, and no more, might be ſeen to be made in right lines, let <lb></lb>us ſuppoſe this point O [<emph type="italics"></emph>in Fig.<emph.end type="italics"></emph.end> 4.] to be the centre of the grand <lb></lb>Orb, or, if you will, of the Ecliptick, and likewiſe alſo of the <lb></lb>Globe of the Sun it ſelf; of which, by reaſon of the great di <lb></lb>ſtance that is between it and the Earth, we that live upon the <lb></lb>Earth, may ſuppoſe that we ſee the one half: we will therefore <lb></lb>deſcribe this circle A B C D about the ſaid centre O, which repre <lb></lb>ſenteth unto us the extream term that divideth and ſeparates the <lb></lb>Hemiſphere of the Sun that is apparent to us, from the other that <lb></lb>is occult. </s><s>And becauſe that our eye, no leſſe than the centre of <lb></lb>the Earth, is underſtood to be in the plane of the Ecliptick, in <lb></lb>which is likewiſe the centre of the Sun, therefore, if we ſhould <lb></lb>fancy to our ſelves the body of the Sun to be cut thorow by the <lb></lb>ſaid plane, the ſection will appear to our eye a right line, which <lb></lb>let be B O D, and upon that a perpendicular being let fall AOC, <lb></lb>it ſhall be the Axis of the ſaid Ecliptick, and of the annual mo <lb></lb>tion of the Terreſtrial Globe. </s><s>Let us next ſuppoſe the Solar body <lb></lb>(without changing centre) to revolve in it ſelf, not about the <lb></lb>Axis A O C (which is the erect Axis upon the plane of the E <lb></lb>cliptick) but about one ſomewhat inclined, which let be this <lb></lb>E O I, the which fixed and unchangeable Axis maintaineth it ſelf <lb></lb>perpetually in the ſame inclination and direction towards the <lb></lb>ſame points of the Firmament, and of the Univerſe. </s><s>And be <lb></lb>cauſe, in the revolutions of the Solar Globe, each point of its ſu <lb></lb>perficies (the Poles excepted) deſcribeth the circumference of a <pb xlink:href="040/01/336.jpg" pagenum="316"></pb>circle, either bigger or leſſer, according as it is more or leſſe re <lb></lb>mote from the ſaid Poles, let us take the point F, equally diſtant <lb></lb>from them, and draw the diameter F O G, which ſhall be perpen <lb></lb>dicular to the Axis E I, and ſhall be the diameter of the grand <lb></lb>circle deſcribed about the Poles E I. </s><s>Suppoſing not that the <lb></lb>Earth, and we with her be in ſuch a place of the Ecliptick, that <lb></lb>the Hemiſphere of the Sun to us apparent is determin'd or bound <lb></lb>ed by the circle A B C D, which paſſing (as it alwayes doth) by <lb></lb>the Poles A C, paſſeth alſo by E I. </s><s>It is manifeſt, that the grand <lb></lb>circle, whoſe diameter is FG, ſhall be erect to the circle A B C D, <lb></lb>to which the ray that from our eye falleth upon the centre O, is <lb></lb>perpendicular; ſo that the ſaid ray falleth upon the plane of <lb></lb>the circle, whoſe diameter is F G, and therefore its circumference <lb></lb>will appear to us a right line, and the ſelf ſame with F G, where <lb></lb>upon if there ſhould be in the point F, a ſpot, it comming after <lb></lb>wards to be carried about by the Solar converſion, would, upon <lb></lb>the ſurface of the Sun, trace out the circumference of that cir <lb></lb>cle, which ſeems to us a right line. </s><s>Its courſe or paſſage will <lb></lb>therefore ſeem ſtraight. </s><s>And ſtraight alſo will the motion of the <lb></lb>other ſpots appear, which in the ſaid revolution ſhall deſcribe leſ <lb></lb>ſer circles, as being all parallel to the greater, and to our eye <lb></lb>placed at an immenſe diſtance from them. </s><s>Now, if you do but <lb></lb>conſider, how that after the Earth ſhall in ſix moneths have run <lb></lb>thorow half the grand Orb, and ſhall be ſituate oppoſite to that <lb></lb>Hemiſphere of the Sun, which is now occult unto us, ſo as that <lb></lb>the boundary of the part that then ſhall be ſeen, may be the ſelf <lb></lb>ſame A B C D, which alſo ſhall paſſe by the Poles E I; you <lb></lb>ſhall underſtand that the ſame will evene in the courſes of the <lb></lb>ſpots, as before, to wit, that all will appear to be made by right <lb></lb>lines. </s><s>But becauſe that that accident takes not place, ſave one <lb></lb>ly when the terminator or boundary paſſeth by the Poles E I, <lb></lb>and the ſaid terminator from moment to moment, by meanes of <lb></lb>the Earths annual motion, continually altereth, therefore its paſ <lb></lb>ſage by the fixed Poles E I, ſhall be momentary, and conſequent <lb></lb>ly momentary ſhall be the time, in which the motions of thoſe <lb></lb>ſpots ſhall appear ſtraight. </s><s>From what hath been hitherto ſpoken <lb></lb>one may comprehend alſo how that the apparition and beginning <lb></lb>of the motion of the ſpots from the part F, proceeding towards <lb></lb>G, their paſſages or courſes are from the left hand, aſcending to <lb></lb>wards the right; but the Earth being placed in the part diame <lb></lb>trically oppoſite the appearance of the ſpots about G, ſhall ſtill <lb></lb>be to the left hand of the beholder, but the paſſage ſhall be deſ <lb></lb>cending towards the right hand F. </s><s>Let us now deſcribe the Earth <lb></lb>te be ſituate one fourth part farther diſtant from its preſent ſtate, <lb></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"></pb>[<emph type="italics"></emph>as in Fig.<emph.end type="italics"></emph.end> 5.] and the Axis, as before A C, by which the plane <lb></lb>of our Meridian would paſſe, in which plane ſhould alſo be the <lb></lb>Axis of the Suns revolution, with its Poles, one towards us, that <lb></lb>is, in the apparent Hemiſphere, which Pole we will repreſent by <lb></lb>the point E, and the other ſhall fall in the occult Hemiſphere, <lb></lb>and I mark it I. </s><s>Inclining therefore the Axis E I, with the ſupe <lb></lb>riour part E, towards us, the great circle deſcribed by the Suns <lb></lb>converſion, ſhall be this B F D G, whoſe half by us ſeen, name <lb></lb>ly B F D, ſhall no longer ſeem unto us a right line, by reaſon the <lb></lb>Poles E I are not in the circumference A B C D, but ſhall appear <lb></lb>incurvated, and with its convexity towards the inferiour part C. <lb></lb></s><s>And it is manifeſt, that the ſame will appear in all the leſſer cir <lb></lb>cles parallel to the ſame B F D. </s><s>It is to be underſtood alſo, that <lb></lb>when the Earth ſhall be diametrically oppoſite to this ſtate, ſo <lb></lb>that it ſeeth the other Hemiſphere of the Sun, which now is hid, <lb></lb>it ſhall of the ſaid great circle behold the part D G B incurved, <lb></lb>with its convexity towards the ſuperiour part A; and the cour <lb></lb>ſes of the ſpots in theſe conſtitutions ſhall be firſt, by the arch <lb></lb>B F D, and afterwards by the other D G B, and the firſt appari <lb></lb>tions and ultimate occultations made about the points B and D, <lb></lb>ſhall be equilibrated, and not thoſe that are more or leſſe eleva <lb></lb>ted than theſe. </s><s>But if we conſtitute the Earth in ſuch a place <lb></lb>of the Ecliptick, that neither the boundary A B C D, nor the <lb></lb>Meridian A C, paſſeth by the Poles of the Axis E I, as I will ſhew <lb></lb>you anon, drawing this other Figure [<emph type="italics"></emph>viz. </s><s>Fig.<emph.end type="italics"></emph.end> 6.] wherein the <lb></lb>apparent or viſible Pole E falleth between the arch of the termi <lb></lb>nator A B, and the ſection of the Meridian A C; the diameter <lb></lb>of the great circle ſhall be F O G, and the apparent ſemicircle <lb></lb>F N G, and the occult ſemicircle G S F, the one incurvated with <lb></lb>its convexity N towards the inferiour part, and the other alſo <lb></lb>bending with its convexity S towards the upper part of the Sun. <lb></lb></s><s>The ingreſſions and exitions of the ſpots, that is, the termes F <lb></lb>and G ſhall not be librated, as the two others B and D; but F <lb></lb>ſhall be lower, and G higher: but yet with leſſer difference <lb></lb>than in the firſt Figure. </s><s>The arch alſo F N G ſhall be incurva <lb></lb>ted, but not ſo much as the precedent B F D; ſo that in this po <lb></lb>ſition the paſſages or motions of the ſpots ſhall be aſcendent <lb></lb>from the left ſide F, towards the right G, and ſhall be made by <lb></lb>curved lines. </s><s>And imagining the Earth to be conſtituted in the <lb></lb>poſition diametrically oppoſite; ſo that the Hemiſphere of the <lb></lb>Sun, which was before the occult, may be the apparent, and ter <lb></lb>minated by the ſame boundary A B C D, it will be manifeſtly <lb></lb>diſcerned, that the courſe of the ſpots ſhall be by the arch G S F, <lb></lb>beginning from the upper point G, which ſhall then be likewiſe <lb></lb>from the left hand of the beholder, and going to determine, deſ <pb xlink:href="040/01/338.jpg" pagenum="318"></pb>ſcending towards the right, in the point F. </s><s>What I have hi <lb></lb>therto ſaid, being underſtood, I believe that there remains no <lb></lb>difficulty in conceiving how ſrom the paſſing of the terminator of <lb></lb>the Solar Hemiſpheres by the Poles of the Suns converſion, or <lb></lb>neer or far from the ſame, do ariſe all the differences in the appa <lb></lb>rent courſes of the ſpots; ſo that by how much the more thoſe Poles <lb></lb>ſhall be remote from the ſaid terminator, by ſo much the more ſhall <lb></lb>thoſe courſes be incurvated, and leſſe oblique; whereupon at <lb></lb>the ſame diſtance, that is, when thoſe Poles are in the ſection of <lb></lb>the Meridian, the incurvation is reduced to the greateſt, but the <lb></lb>obliquity to the leaſt, that is to <emph type="italics"></emph>Æquilibrium,<emph.end type="italics"></emph.end> as the ſecond of <lb></lb>theſe three laſt figures [<emph type="italics"></emph>viz. </s><s>Fig.<emph.end type="italics"></emph.end> 5.] demonſtrateth. </s><s>On the <lb></lb>contrary, when the Poles are in the terminator, as the firſt of <lb></lb>theſe three figures [<emph type="italics"></emph>viz. </s><s>Fig.<emph.end type="italics"></emph.end> 4.] ſheweth the inclination is at <lb></lb>the greateſt, but the incurvation at the leaſt, and reduced to <lb></lb>rectitude. </s><s>The terminator departing from the Poles, the curvity <lb></lb>begins to grow ſenſible, the obliquity all the way encreaſing, <lb></lb>and the inclination growing leſſer.</s></p><p type="margin"><s><margin.target id="marg584"></margin.target><emph type="italics"></emph>The firſt Ac <lb></lb>cident to be obſer <lb></lb>ved in the motion <lb></lb>of the Solar ſpots; <lb></lb>and conſequently <lb></lb>all the reſt explai <lb></lb>ned.<emph.end type="italics"></emph.end></s></p><p type="main"><s>Theſe are thoſe admirable and extravagant mutations, that my <lb></lb>Gueſt told me would from time to time appear in the progreſſes <lb></lb>of the Solar ſpots, if ſo be it ſhould be true that the annual mo <lb></lb>tion belonged to the Earth, and that the Sun being conſtituted <lb></lb>in the centre of the Ecliptick, were revolved in it ſelf upon an <lb></lb>Axis, not erect, but inclined to the Plane of the ſaid Eclip <lb></lb>tick.</s></p><p type="main"><s>SAGR. </s><s>I do now very well apprehend theſe conſequences, <lb></lb>and believe that they will be better imprinted in my fancy, when <lb></lb>I ſhall come to reflect upon them, accommodating a Globe to <lb></lb>thoſe inclinations, and then beholding them from ſeveral pla <lb></lb>ces. </s><s>It now remains that you tell us what followed afterwards <lb></lb>touching the event of theſe imaginary conſequences. <lb></lb><arrow.to.target n="marg585"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg585"></margin.target><emph type="italics"></emph>The events be <lb></lb>ing obſerved, were <lb></lb>anſwerable to the <lb></lb>predictions.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>It came to paſſe thereupon, that continuing many ſe <lb></lb>veral moneths to make moſt accurate obſervations, noting down <lb></lb>with great exactneſſe the courſes or tranſitions of ſundry ſpots at <lb></lb>divers times of the year, we found the events punctually to cor <lb></lb>reſpond to the predictions.</s></p><p type="main"><s>SAGR. <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> if this which <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> ſaith be true; (nor <lb></lb>can we diſtruſt him upon his word) the <emph type="italics"></emph>Ptolomeans<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Aristo <lb></lb>teleans<emph.end type="italics"></emph.end> hadneed of ſolid arguments, ſtrong conjectures, and <lb></lb>well grounded experiments to counterpoiſe an objection of ſo <lb></lb>much weight, and to ſupport their opinion from its final over <lb></lb>throw.</s></p><p type="main"><s>SIMP. </s><s>Fair and ſoftly good Sir, for haply you may not yet <lb></lb>be got ſo far as you perſwade your ſelf you are gone. </s><s>And <lb></lb>though I am not an abſolute maſter of the ſubject of that narra <pb xlink:href="040/01/339.jpg" pagenum="319"></pb>tion given us by <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end>; yet do I not find that my Logick, </s></p><p type="main"><s><arrow.to.target n="marg586"></arrow.to.target> <lb></lb>whilſt I have a regard to form, teacheth me, that that kind of ar <lb></lb>gumentation affords me any neceſſary reaſon to conclude in fa <lb></lb>vour of the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Hypotheſis, that is, of the ſtability of <lb></lb>the Sun in the centre of the Zodiack, and of the mobility of <lb></lb>the Earth under its circumference. </s><s>For although it be true, that <lb></lb>the ſaid converſion of the Sun, and cirnition of the Earth being <lb></lb>granted, there be a neceſſity of diſcerning ſuch and ſuch ſtrange <lb></lb>extravagancies as theſe in the ſpots of the Sun, yet doth it not <lb></lb>follow that arguing <emph type="italics"></emph>per converſum,<emph.end type="italics"></emph.end> from finding ſuch like un <lb></lb>uſual accidents in the Sun, one muſt of necſſity conclude the <lb></lb>Earth to move by the circumference, and the Sun to be placed <lb></lb>in the centre of the Zodiack. </s><s>For who ſhall aſſertain me that the <lb></lb>like irregularities may not as well be viſible in the Sun, it being <lb></lb>moveable by the Ecliptick, to the inhabitants of the Earth, it <lb></lb>being alſo immoveable in the centre of the ſame? </s><s>Unleſſe you <lb></lb>demonſtrate to me, that there can be no reaſon given for that ap <lb></lb>pearance, when the Sun is made moveable, and the Earth ſtable, <lb></lb>I will not alter my opinion and belief that the Sun moveth, and <lb></lb>the Earth ſtandeth ſtill.</s></p><p type="margin"><s><margin.target id="marg586"></margin.target><emph type="italics"></emph>Though the an <lb></lb>nual motion aſſign <lb></lb>ed to the Earth an <lb></lb>ſwerth to the<emph.end type="italics"></emph.end> Phæ <lb></lb>nomena <emph type="italics"></emph>of the ſo <lb></lb>lar ſpots, yet doth <lb></lb>it not follow by con <lb></lb>verſion that from <lb></lb>the<emph.end type="italics"></emph.end> Phænomena <emph type="italics"></emph>of <lb></lb>the ſpots one may <lb></lb>infor the annual <lb></lb>motion to belong to <lb></lb>the Earth.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> behaveth himſelf very bravely, and argueth <lb></lb>very ſubtilly in defence of the cauſe of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end>; <lb></lb>and if I may ſpeak the truth, mythinks that the converſation of <lb></lb><emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> though it have been but of ſmall continuance, hath <lb></lb>much farthered him in diſcourſing ſilogiſtically. </s><s>An effect which <lb></lb>I know to be wrought in others as well as him. </s><s>But as to finding <lb></lb>and judging whether competent reaſon may be rendered of the <lb></lb>apparent exorbitancies and irregularities in the motions of the <lb></lb>ſpots, ſuppoſing the Earth to be immoveable, and the Sun <lb></lb>moveable, I ſhall expect that <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> manifeſt his opinion to <lb></lb>us, for it is very probable that he he hath conſidered of the <lb></lb>ſame, and collected together whatever may be ſaid upon the <lb></lb>point.</s></p><p type="main"><s>SALV. </s><s>I have often thought thereon, and alſo diſcourſed <lb></lb>thereof with my Friend and Gueſt afore-named; and touching <lb></lb>what is to be produced by Philoſophers and Aſtronomers, in de <lb></lb>fence of the ancient Syſteme, we are on one hand certain, cer <lb></lb>tain I ſay, that the true and pure <emph type="italics"></emph>Peripateticks<emph.end type="italics"></emph.end> laughing at ſuch <lb></lb><arrow.to.target n="marg587"></arrow.to.target> <lb></lb>as employ themſelves in ſuch, to their thinking, inſipid foole <lb></lb>ries, will cenſure all theſe <emph type="italics"></emph>Phænomena<emph.end type="italics"></emph.end> to be vain illuſions of the <lb></lb>Chriſtals; and in this manner will with little trouble free them <lb></lb>ſelves from the obligation of ſtudying any more upon the ſame. <lb></lb></s><s>Again, as to the Aſtronomical Philoſophers, after we have with <lb></lb>ſome diligence weighed that which may be alledged as a mean <lb></lb>between thoſe two others, we have not been able to find out an <pb xlink:href="040/01/340.jpg" pagenum="320"></pb>anſwer that ſufficeth to ſatisſie at once the courſe of the ſpots, <lb></lb>and the diſcourſe of the Mind. </s><s>I will explain unto you ſo much <lb></lb>as I remember thereof, that ſo you may judge thereon as ſeems <lb></lb>beſt unto you.</s></p><p type="margin"><s><margin.target id="marg587"></margin.target><emph type="italics"></emph>The Pure<emph.end type="italics"></emph.end> Peri <lb></lb>patetick <emph type="italics"></emph>Philoſo <lb></lb>phers will laugh at <lb></lb>the ſpots and their<emph.end type="italics"></emph.end> <lb></lb>Phænomena, <emph type="italics"></emph>as <lb></lb>illuſions of the <lb></lb>Chryſtals in the <lb></lb>Teleſcope.<emph.end type="italics"></emph.end></s></p><p type="main"><s>Suppoſing that the apparent motions of the Solar ſpots are the <lb></lb>ſame with thoſe that have been above declared, and ſuppoſing the <lb></lb>Earth to be immoveable in the centre of the Ecliptick, in whoſe <lb></lb>circumference let the center of the Sun be placed; it is neceſſary <lb></lb>that of all the differences that are ſeen in thoſe motions, the cau <lb></lb>ſes do reſide in the motions that are in the body of the Sun: <lb></lb>Which in the firſt place muſt neceſſarily revolve in it ſelf (<emph type="italics"></emph>i. </s><s>e.<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg588"></arrow.to.target> <lb></lb>about its own axis) carrying the ſpots along therewith; which <lb></lb>ſpots have been ſuppoſed, yea and proved to adhere to the So <lb></lb>lar ſuperficies. </s><s>It muſt ſecondly be confeſt, that the Axis of the <lb></lb>Solar converſion is not parallel to the Axis of the Ecliptick, that <lb></lb>is as much as to ſay, that it is not perpendicularly erected upon <lb></lb>the Plane of the Ecliptick, becauſe if it were ſo, the courſes and <lb></lb>exitions of thoſe ſpots would ſeem to be made by right lines pa <lb></lb>rallel to the Ecliptick. </s><s>The ſaid Axis therefore is inclining, in <lb></lb>regard the ſaid courſes are for the moſt part made by curve lines. <lb></lb></s><s>It will be neceſſary in the third place to grant that the inclinati <lb></lb>on of this Axis is not fixed, and continually extended towards <lb></lb>one and the ſame point of the Univerſe, but rather that it doth <lb></lb>alwayes from moment to moment go changing its direction; for <lb></lb>if the pendency ſhould always look towards the ſelf ſame point, <lb></lb>the courſes of the ſpots would never change appearance; but <lb></lb>appearing at one time either right or curved, bending upwards <lb></lb>or downwards, aſcending or deſcending, they would appear <lb></lb>the ſame at all times. </s><s>It is therefore neceſſary to ſay, that the <lb></lb>ſaid Axis is convertible; and is ſometimes found to be in the <lb></lb>Plane of the circle that is extreme, terminate, or of the viſible <lb></lb>Hemiſphere, I mean at ſuch time as the courſes of the ſpots <lb></lb>ſeem to be made in right lines, and more than ever pendent, <lb></lb>which happeneth twice a year; and at other times found to be in <lb></lb>the Plane of the Meridian of the Obſervator, in ſuch ſort that <lb></lb>one of its Poles falleth in the viſible Hemiſphere of the Sun, and <lb></lb>the other in the occult; and both of them remote from the ex <lb></lb>treme points, or we may ſay, from the poles of another Axis of <lb></lb>the Sun, which is parallel to the Axis of the Ecliptick; (which <lb></lb>ſecond Axis muſt neceſſarily be aſſigned to the Solar Globe) re <lb></lb>mote, I ſay, as far as the inclination of the Axis of the revolution <lb></lb>of the ſpots doth import; and moreover that the Pole falling in <lb></lb>the apparent Hemiſphere, is one while in the ſuperiour, another <lb></lb>while in the inferiour part thereof; for that it muſt be ſo, the <lb></lb>courſes themſelves do manifeſtly evince at ſuch time as they are <pb xlink:href="040/01/341.jpg" pagenum="321"></pb>equilibrated, and in their greateſt curvity, one while with <lb></lb>their convexity towards the upper part, and another while <lb></lb>towards the lower part of the Solar <emph type="italics"></emph>Diſcus.<emph.end type="italics"></emph.end> And becauſe <lb></lb>thoſe poſitions are in continuall alteration, making the in <lb></lb>clinations and incurvations now greater, now leſſer, and ſome <lb></lb>times reduce themſelves, the firſt ſort to perfect libration, and <lb></lb>the ſecond to perfect perpendicularity, it is neceſſary to aſſert that <lb></lb>the ſelf ſame Axis of the monethly revolution of the ſpots hath <lb></lb>a particular revolution of its own, whereby its Poles deſcribe <lb></lb>two circles about the Poles of another Axis, which for that rea <lb></lb>ſon ought (as I have ſaid) to be aſſigned to the Sun, the ſemidi <lb></lb>ameter of which circles anſwereth to the quantity of the incli <lb></lb>nation of the ſaid Axis. </s><s>And it is neceſſary, that the time of its <lb></lb>Period be a year; for that ſuch is the time in which all the ap <lb></lb>pearances and differences in the courſes of the ſpots do return. <lb></lb></s><s>And that the revolution of this Axis, is made about the Poles of <lb></lb>the other Axis parallel to that of the Ecliptick, & not about other <lb></lb>points, the greateſt inclinations and greateſt incurvations, which <lb></lb>are always of the ſame bigneſs, do clearly prove. </s><s>So that finally, to <lb></lb>maintain the Earth fixed in the centre, it will be neceſſary to aſ <lb></lb>ſign to the Sun, two motions about its own centre, upon two ſeve <lb></lb>ral Axes, one of which finiſheth its converſion in a year, and the <lb></lb>other in leſſe than a moneth; which aſſumption ſeemeth, to my <lb></lb>underſtanding, very hard, and almoſt impoſſible; and this de <lb></lb>pendeth on the neceſſity of aſcribing to the ſaid Solar body two <lb></lb>other motions about the Earth upon different Axes, deſcribing <lb></lb>with one the Ecliptick in a year, and with the other forming ſpi <lb></lb>rals, or circles parallel to the Equinoctial one every day: <lb></lb>whereupon that third motion which ought to be aſſigned to the <lb></lb>Solar Clobe about its own centre (I mean not that almoſt <lb></lb>monethly, which carrieth the ſpots about, but I ſpeak of that o <lb></lb>ther which ought to paſſe thorow the Axis and Poles of this <lb></lb>monethly one) ought not, for any reaſon that I ſee, to finiſh its <lb></lb>Period rather in a year, as depending on the annual motion by <lb></lb>the Ecliptick, than in twenty four hours, as depending on the <lb></lb>diurnal motion upon the Poles of the Equinoctial. </s><s>I know, that <lb></lb>what I now ſpeak is very obſcure, but I ſhall make it plain unto <lb></lb>you, when we come to ſpeak of the third motion annual, aſſign <lb></lb>ed by <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> to the Earth. </s><s>Now if theſe four motions, ſo <lb></lb>incongruous with each other, (all which it would be neceſſary to <lb></lb>aſſign to the ſelf ſame body of the Sun) may be reduced to one <lb></lb>ſole and ſimple motion, aſſigned the Sun upon an Axis that never <lb></lb>changeth poſition, and that without innovating any thing in the <lb></lb>motions for ſo many other cauſes aſſigned to the Terreſtrial <lb></lb>Globe, may ſo eaſily ſalve ſo many extravagant appearances in <pb xlink:href="040/01/342.jpg" pagenum="322"></pb>the motions of the Solar ſpots, it ſeemeth really that ſuch an <lb></lb>Hypotheſis ought not to be rejected.</s></p><p type="margin"><s><margin.target id="marg588"></margin.target><emph type="italics"></emph>If the Earth be <lb></lb>immoveable in the <lb></lb>centre of the Zodi <lb></lb>ack, there muſt be <lb></lb>aſcribed to the Sun <lb></lb>four ſeveral moti <lb></lb>ons, as is declared <lb></lb>at length.<emph.end type="italics"></emph.end></s></p><p type="main"><s>This, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> is all that came into the minds of our friend, <lb></lb>and my ſelf, that could be alledged in explanation of this <emph type="italics"></emph>Phæno <lb></lb>menon<emph.end type="italics"></emph.end> by the <emph type="italics"></emph>Copernicans,<emph.end type="italics"></emph.end> and by the <emph type="italics"></emph>Ptolomæans,<emph.end type="italics"></emph.end> in defence <lb></lb>of their opinions. </s><s>Do you inferre from thence what your judg <lb></lb>ment perſwades you.</s></p><p type="main"><s>SIMP. </s><s>I acknowledge my ſelf unable to interpoſe in ſo im <lb></lb>portant a deciſion: And, as to my particular thoughts, I will <lb></lb>ſtand neutral; and yet nevertheleſſe I hope that a time will <lb></lb>come, when our minds being illumin'd by more lofty contempla <lb></lb>tions than theſe our humane reaſonings, we ſhall be awakened <lb></lb>and freed from that miſt which now is ſo great an hinderance to <lb></lb>our ſight.</s></p><p type="main"><s>SAGR. </s><s>Excellent and pious is the counſel taken by <emph type="italics"></emph>Simpli <lb></lb>cius,<emph.end type="italics"></emph.end> and worthy to be entertained and followed by all, as that <lb></lb>which being derived from the higheſt wiſdome and ſupreameſt <lb></lb>authority, may onely, with ſecurity be received. </s><s>But yet ſo far <lb></lb>as humane reaſon is permitted to penetrate, confining my ſelf <lb></lb>within the bounds of conjectures, and probable reaſons, I will <lb></lb>ſay a little more reſolutely than <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> doth, that amongſt <lb></lb>all the ingenuous ſubtilties I ever heard, I have never met with <lb></lb>any thing of greater admiration to my intellect, nor that hath <lb></lb>more abſolutely captivated my judgment, (alwayes excepting <lb></lb>pure Geometrical and Arithmetical Demonſtrations) than theſe <lb></lb>two conjectures taken, the one from the ſtations and retrograda <lb></lb>tions of the five Planets, and the other from theſe irregularities of <lb></lb>the motions of the Solar ſpots: and becauſe they ſeem to me ſo <lb></lb>eaſily and clearly to aſſign the true reaſon of ſo extravagant ap <lb></lb>pearances, ſhewing as if they were but one ſole ſimple motion, <lb></lb>mixed with ſo many others, ſimple likewiſe, but different from <lb></lb>each other, without introducing any difficulty, rather with obvi <lb></lb>ating thoſe that accompany the other Hypotheſis; I am think <lb></lb>ing that I may rationally conclude, that thoſe who contumaci <lb></lb>ouſly withſtand this Doctrine, either never heard, or never un <lb></lb>derſtood, theſe ſo convincing arguments.</s></p><p type="main"><s>SALV. </s><s>I will not aſcribe unto them the title either of con <lb></lb>vincing, or non-convincing; in regard my intention is not, as I <lb></lb>have ſeveral times told you, to reſolve any thing upon ſo high a <lb></lb>queſtion, but onely to propoſe thoſe natural and Aſtronomicall <lb></lb>reaſons, which, for the one and other Syſteme, may be produced <lb></lb>by me, leaving the determination to others; which determinati <lb></lb>on cannot at laſt, but be very manifeſt: for one of the two poſi <lb></lb>tions being of neceſſity to be true, and the other of neceſſity to <lb></lb>be falſe, it is a thing impoſſible that (alwayes confining our ſelves <pb xlink:href="040/01/343.jpg" pagenum="323"></pb>within the limits of humane doctrine) the reaſons alledged for <lb></lb>the true Hypotheſis ſhould not manifeſt themſelves as concludent <lb></lb>as thoſe 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></lb>of the little Book of^{*} <emph type="italics"></emph>Concluſions,<emph.end type="italics"></emph.end> or Diſquiſitions which <emph type="italics"></emph>Simpli-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg589"></arrow.to.target> <lb></lb><emph type="italics"></emph>cius<emph.end type="italics"></emph.end> did bring with him.</s></p><p type="margin"><s><margin.target id="marg589"></margin.target>* I ſhould have <lb></lb>told you, that the <lb></lb>true name of this <lb></lb>concealed Au <lb></lb>thour is <emph type="italics"></emph>Chriſto <lb></lb>pher Scheinerus,<emph.end type="italics"></emph.end> <lb></lb>and its title <emph type="italics"></emph>Diſ <lb></lb>quiſitiones Ma <lb></lb>thematicæ.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>Here is the Book, and this is the place where the Au <lb></lb>thor firſt briefly deſcribeth the Syſteme of the world, according <lb></lb>to the Hypotheſis of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> ſaying, <emph type="italics"></emph>Terram igitur unà cum <lb></lb>Luna, totoque hoc elementari mundo<emph.end type="italics"></emph.end> Copernicus, &c.</s></p><p type="main"><s>SALV. </s><s>Forbear a little, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> for methinks that this <lb></lb>Authour, in this firſt entrance, ſhews himſelf to be but very ill <lb></lb>verſt in the Hypotheſis which he goeth about to confute, in re <lb></lb>gard, he ſaith that <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> maketh the Earth, together with <lb></lb>the Moon, to deſcribe the ^{*} grand Orb in a year moving from <lb></lb>Eaſt to Weſt; a thing that as it is falſe and impoſſible, ſo was it <lb></lb><arrow.to.target n="marg590"></arrow.to.target> <lb></lb>never affirmed by <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> who rather maketh it to move the <lb></lb>contrary way, I mean from Weſt to Eaſt, that is, according to <lb></lb>the order of the Signes; whereupon we come to think the ſame <lb></lb>to be the annual motion of the Sun, conſtituted immoveable in <lb></lb>the centre of the Zodiack. </s><s>See the too adventurous confidence <lb></lb>of this man; to undertake the confutation of anothers Doctrine, <lb></lb>and yet to be ignorant of the primary fundamentals; upon which <lb></lb>his adverſary layeth the greateſt and moſt important part of all <lb></lb>the Fabrick. </s><s>This is a bad beginning to gain himſelf credit <lb></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 Univerſal Syſteme, he beginneth <lb></lb>to propound his objections againſt this annual motion: and <lb></lb>the firſt are theſe, which he citeth Ironically, and in deriſion of <lb></lb><arrow.to.target n="marg591"></arrow.to.target> <lb></lb><emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> and of his followers, writing that in this phantaſtical <lb></lb>Hypotheſis of the World one muſt neceſſarily maintain very <lb></lb>groſſe abſurdities; namely, that the Sun, <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Mercury<emph.end type="italics"></emph.end> <lb></lb>are below the Earth; and that grave matters go naturally up <lb></lb>wards, and the light downwards; and that <emph type="italics"></emph>Chriſt,<emph.end type="italics"></emph.end> our Lord and <lb></lb>Redeemer, aſcended into Hell, and deſcended into Heaven, when <lb></lb>he approached towards the Sun, and that when <emph type="italics"></emph>Joſhuah<emph.end type="italics"></emph.end> com <lb></lb>manded the Sun to ſtand ſtill, the Earth ſtood ſtill, or the Sun <lb></lb>moved a contrary way to that of the Earth; and that when the <lb></lb>Sun is in <emph type="italics"></emph>Cancer,<emph.end type="italics"></emph.end> the Earth runneth through <emph type="italics"></emph>Capricorn<emph.end type="italics"></emph.end>; and that <lb></lb>the <emph type="italics"></emph>Hyemal<emph.end type="italics"></emph.end> (or Winter) Signes make the Summer, and the <lb></lb><emph type="italics"></emph>Æſtival<emph.end type="italics"></emph.end> Winter; and that the Stars do not riſe and ſet to <lb></lb>the Earth, but the Earth to the Stars; and that the Eaſt begin <lb></lb>neth in the Weſt, and the Weſt in the Eaſt; and, in a word, <lb></lb>that almoſt the whole courſe of the World is inverted.</s></p><p type="margin"><s><margin.target id="marg591"></margin.target><emph type="italics"></emph>Inſtances of a <lb></lb>certain Book Iro <lb></lb>nically propounded <lb></lb>againſt<emph.end type="italics"></emph.end> Coperni <lb></lb>cus.</s></p><p type="main"><s>SALV. </s><s>Every thing pleaſeth me, except it be his having inter <pb xlink:href="040/01/344.jpg" pagenum="324"></pb>mixed places out of the ſacred Scriptures (alwayes venerable, and <lb></lb>to be rever'd) amongſt theſe, but two ſcurrilous fooleries, and <lb></lb>attempting to wound with holy Weapons, thoſe who Philoſo <lb></lb>phating in jeſt, and for divertiſement, neither affirm nor deny, <lb></lb>but, ſome preſuppoſals and poſitions being aſſumed, do famili <lb></lb>arly argue.</s></p><p type="main"><s>SIMP. </s><s>Truth is, he hath diſpleaſed me alſo, and that not a <lb></lb>little; and eſpecially, by adding preſently after that, howbeit, <lb></lb>the <emph type="italics"></emph>Copernichists<emph.end type="italics"></emph.end> anſwer, though but very impertinently to theſe <lb></lb>and ſuch like other reaſons, yet can they not reconcile nor anſwer <lb></lb>thoſe things that follow.</s></p><p type="main"><s>SALV. </s><s>This is worſe than all the reſt; for he pretendeth to <lb></lb>have things more efficacious and concludent than the Authorities <lb></lb>of the ſacred Leaves; But I pray you, let us reverence them, <lb></lb>and paſſe on to natural and humane reaſons: and yet if he give <lb></lb>us amongſt his natural arguments, things of no more ſolidity, <lb></lb>than thoſe hitherto alleadged, we may wholly decline this under <lb></lb>taking, for I as to my own parricular, do not think it fit to ſpend <lb></lb>words in anſwering ſuch trifling impertinencies. </s><s>And as to what <lb></lb>he ſaith, that the <emph type="italics"></emph>Copernicans<emph.end type="italics"></emph.end> anſwer to theſe objections, it is <lb></lb>moſt falſe, nor may it be thought, that any man ſhould ſet him <lb></lb>ſelf to waſt his time ſo unprofitably. <lb></lb><arrow.to.target n="marg592"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg592"></margin.target><emph type="italics"></emph>Suppoſing the <lb></lb>annual motion to <lb></lb>belong to the Earth, <lb></lb>it followeth, that <lb></lb>one fixed Star, is <lb></lb>bigger than the <lb></lb>whole grand Orb.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I concur with you in the ſame judgment; therefore <lb></lb>let us hear the other inſtances that he brings, as much ſtronger. <lb></lb></s><s>And obſerve here, how he with very exact computations conclud <lb></lb>eth, that if the grand Orb of the Earth, or the ecliptick, in which <lb></lb><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> maketh it to run in a year round the Sun, ſhould be <lb></lb>as it were, inſenſible, in reſpect of the immenſitie of the Starry <lb></lb>Sphære, according as the ſaid <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> ſaith it is to be ſup <lb></lb>poſed, it would be neceſſary to grant and confirm, that the fixed <lb></lb>Stars were remote from us, an unconceivable diſtance, and that <lb></lb>the leſſer of them, were bigger than the whole grand Orb afore <lb></lb>ſaid, and ſome other much bigger than the whole Sphære of <emph type="italics"></emph>Sa <lb></lb>turn<emph.end type="italics"></emph.end>; Maſſes certainly too exceſſively vaſt, unimaginable, and <lb></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"></emph>his Ar <lb></lb>gument grounded <lb></lb>upon a falſe Hypo <lb></lb>theſis.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>I have heretofore ſeen ſuch another objection brought <lb></lb>by <emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end> againſt <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> and this is not the firſt time that I <lb></lb>have diſcovered the fallacy, or, to ſay better, the fallacies of this <lb></lb>Argumemtation, founded upon a moſt falſe Hypotheſis, and upon </s></p><p type="main"><s><arrow.to.target n="marg594"></arrow.to.target> <lb></lb>a Piopoſition of the ſaid <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> underſtood by his adverſa <lb></lb>ries, with too punctual a nicity, according to the practiſe of thoſe <lb></lb>pleaders, who finding the flaw to be in the very merit of their <lb></lb>cauſe, keep to ſome one word, fallen unawares from the contra <lb></lb>ry partie, and fly out into loud and tedious deſcants upon that. <lb></lb></s><s>But for your better information; <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> having declared <pb xlink:href="040/01/345.jpg" pagenum="325"></pb>thoſe admirable conſequences which are derived from the Earths <lb></lb><arrow.to.target n="marg595"></arrow.to.target> <lb></lb>annual motion, to the other Planets, that is to ſay, of the ^{*} directi <lb></lb><arrow.to.target n="marg596"></arrow.to.target> <lb></lb>ons and retrogradations of the three uppermoſt in particular; he <lb></lb>ſubjoyneth, that this apparent mutation (which is diſcerned more <lb></lb>in <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> than in <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> by reaſon <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> is more remote, and <lb></lb>yet leſſe in <emph type="italics"></emph>Saturn,<emph.end type="italics"></emph.end> by reaſon it is more remote than <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end>) in <lb></lb>the fixed Stars, did remain imperceptible, by reaſon of their <lb></lb>immenſe remoteneſſe from us, in compariſon of the diſtances of <lb></lb><emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> or <emph type="italics"></emph>Saturn.<emph.end type="italics"></emph.end> Here the Adverſaries of this opinion riſe up, <lb></lb>and ſuppoſing that fore-named imperceptibility of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> as <lb></lb>if it had been taken by him, for a real and abſolute thing of no <lb></lb>thing, and adding, that a fixed Star of one of the leſſer magni <lb></lb>tudes, is notwithſtanding perceptible, ſeeing that it cometh un <lb></lb>der the ſence of ſeeing, they go on to calculate with the inter <lb></lb>vention of other falſe aſſumptions, and concluding that it is neceſ <lb></lb>ſary by the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Doctrine, to admit, that a fixed Star is much <lb></lb>bigger than the whole grand Orb. </s><s>Now to diſcover the vanity <lb></lb><arrow.to.target n="marg597"></arrow.to.target> <lb></lb>of this their whole proceeding, I ſhall ſhew that a fixed Star of the <lb></lb>ſixth magnitude, being ſuppoſed to be no bigger than the Sun, <lb></lb>one may thence conclude with true demonſtrations, that the di <lb></lb>ſtance of the ſaid fixed Stars from us, cometh to be ſo great, that <lb></lb>the annual motion of the Earth, which cauſeth ſo great and <lb></lb>notable variations in the Planets, appears ſcarce obſervable in <lb></lb>them; and at the ſame time, I will diſtinctly ſhew the groſs <lb></lb>fallacies, in the aſſumptions of <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> his Adverſaries.</s></p><p type="margin"><s><margin.target id="marg594"></margin.target><emph type="italics"></emph>Litigious Lawyers <lb></lb>that are entertain <lb></lb>ed in an ill cauſe, <lb></lb>keep cloſe to ſome <lb></lb>expreſſion fallen <lb></lb>from the adverſe <lb></lb>party at unawares.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg595"></margin.target>* Or progreſſions.</s></p><p type="margin"><s><margin.target id="marg596"></margin.target><emph type="italics"></emph>The apparent <lb></lb>diverſity of motion <lb></lb>in the Planets, is <lb></lb>inſenſible in the <lb></lb>fixed Start.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg597"></margin.target><emph type="italics"></emph>Suppoſing that a <lb></lb>fixed Star of the <lb></lb>ſixth magnitude is <lb></lb>no bigger than the<emph.end type="italics"></emph.end> <lb></lb>Sun, <emph type="italics"></emph>the diverſitie <lb></lb>which is ſo great <lb></lb>in the Planets, in <lb></lb>the fixed Stars is <lb></lb>almost inſenſible.<emph.end type="italics"></emph.end></s></p><p type="main"><s>And firſt of all, I ſuppoſe with the ſaid <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> and alſo <lb></lb><arrow.to.target n="marg598"></arrow.to.target> <lb></lb>with his oppoſers, that the Semidiameter of the grand Orb, which <lb></lb>is the diſtance of the Earth from the Sun, containeth 1208 Semi <lb></lb>diameters of the ſaid Earth. </s><s>Secondly, I premiſe with the allow <lb></lb>ance aforeſaid, and of truth, that the ^{*} apparent diameter of the <lb></lb><arrow.to.target n="marg599"></arrow.to.target> <lb></lb>Sun in its mean diſtance, to be about half a degree, that is, 30. <lb></lb><emph type="italics"></emph>min. </s><s>prim.<emph.end type="italics"></emph.end> which are 1800. ſeconds, that is, 108000. thirds. <lb></lb></s><s>And becauſe the apparent Diameter of a fixed Star of the firſt <lb></lb><arrow.to.target n="marg600"></arrow.to.target> <lb></lb>magnitude, is no more than 5. ſeconds, that is, 300. thirds, and <lb></lb>the Diameter of a fixed Star of the ſixth magnitude, 50. thirds, <lb></lb>(and herein is the greateſt errour of the <emph type="italics"></emph>Anti-Copernicans<emph.end type="italics"></emph.end>) There <lb></lb><arrow.to.target n="marg601"></arrow.to.target> <lb></lb>fore the Diameter of the Sun, containeth the Diameter of a <lb></lb>fixed Star of the ſixth magnitude 2160 times. </s><s>And therefore <lb></lb>if a fixed Star of the ſixth magnitude, were ſuppoſed to be really <lb></lb>equal to the Sun, and not bigger, which is the ſame as to ſay, if <lb></lb>the Sun were ſo far removed, that its Diameter ſhould ſeem to <lb></lb>be one of the 2160. parts of what it now appeareth, its diſtance <lb></lb>ought of neceſſity to be 2160. times greater than now in effect it <lb></lb>is, which is as much as to ſay, that the diſtance of the fixed Stars <lb></lb>of the ſixth magnitude, is 2160. Semidiameters of the grand <pb xlink:href="040/01/346.jpg" pagenum="326"></pb>Orb. </s><s>And becauſe the diſtance of the Sun from the Earth, con <lb></lb><arrow.to.target n="marg602"></arrow.to.target> <lb></lb>tains by common conſent 1208. Semidiameters of the ſaid Earth, <lb></lb>and the diſtance of the fixed Stars (as hath been ſaid) 2160. <lb></lb>Semediameters of the grand Orb, therefore the Semediameter of <lb></lb>the Earth is much greater (that is almoſt double) in compariſon <lb></lb>of the grand Orb, than the Semediameter of the grand Orb, in <lb></lb><arrow.to.target n="marg603"></arrow.to.target> <lb></lb>relation to the diſtance of the Starry Sphære; and therefore the <lb></lb>variation of aſpect in the fixed Stars, cauſed by the Diameter of <lb></lb>the grand Orb, can be but little more obſervable, than that which <lb></lb>is obſerved in the Sun, occaſioned by the Semediameter of the <lb></lb>Earth.</s></p><p type="margin"><s><margin.target id="marg598"></margin.target><emph type="italics"></emph>The diſtance of <lb></lb>the Sun, containeth<emph.end type="italics"></emph.end> <lb></lb>1208 <emph type="italics"></emph>Semid. </s><s>of the <lb></lb>Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg599"></margin.target>* The Diameter <lb></lb>of the Sun, half a <lb></lb>degree.</s></p><p type="margin"><s><margin.target id="marg600"></margin.target><emph type="italics"></emph>The Diameter <lb></lb>of a fixed Star, of <lb></lb>the firſt magni <lb></lb>tude, and of one of <lb></lb>the ſixth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg601"></margin.target><emph type="italics"></emph>The apparent <lb></lb>Diameter of the <lb></lb>Sun, how much it <lb></lb>is bigger than that <lb></lb>of a fixed ſtar.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg602"></margin.target><emph type="italics"></emph>The diſtance of <lb></lb>a fixed ſtar of the <lb></lb>ſixth magnitude, <lb></lb>how much it is, the <lb></lb>ſtar being ſuppoſed <lb></lb>to be equal to the <lb></lb>Sun.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg603"></margin.target><emph type="italics"></emph>In the fixed ſtars <lb></lb>the diverſitie of a <lb></lb>ſpect, cauſed by <lb></lb>the grand Orb, is <lb></lb>little more then <lb></lb>that cauſed by the <lb></lb>Earth in the Snn.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>This is a great fall for the firſt ſtep.</s></p><p type="main"><s>SALV. </s><s>It is doubtleſſe an errour; for a fixed Star of the ſixth <lb></lb><arrow.to.target n="marg604"></arrow.to.target> <lb></lb>magnitude, which by the computation of this Authour, ought, <lb></lb>for the upholding the propoſition of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> to be as big as <lb></lb>the whole grand Orb, onely by ſuppoſing it equal to the Sun, <lb></lb>which Sun is leſſe by far, than the hundred and ſix milionth part <lb></lb>of the ſaid grand Orb, maketh the ſtarry Sphære ſo great and high <lb></lb>as ſufficeth to overthrow the inſtance brought againſt the ſaid <emph type="italics"></emph>Co <lb></lb>pernicus.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg604"></margin.target><emph type="italics"></emph>A ſtar of the <lb></lb>ſixth magnitude, <lb></lb>ſuppoſed by<emph.end type="italics"></emph.end> Tycho <lb></lb><emph type="italics"></emph>and the Authour <lb></lb>of the Book of Con <lb></lb>cluſions, an hun <lb></lb>dred and ſix mili <lb></lb>ons of times bigger <lb></lb>than needs.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Favour me with this computation.</s></p><p type="main"><s>SALV. </s><s>The ſupputation is eaſie and ſhort. </s><s>The Diameter of <lb></lb>the Sun, is eleven ſemediameters of the Earth, and the Diameter <lb></lb><arrow.to.target n="marg605"></arrow.to.target> <lb></lb>of the grand Orb, contains 2416. of thoſe ſame ſemediameters, <lb></lb>by the aſcent of both parties; ſo that the Diameter of the ſaid <lb></lb>Orb, contains the Suns Diameter 220. times very near. </s><s>And <lb></lb>becauſe the Spheres are to one another, as the Cubes of their Di <lb></lb>ameters, let us make the Cube of 220. which is 106480000. and <lb></lb>we ſhall have the grand Orb, an hundred and ſix millions, four <lb></lb>hundred and eighty thouſand times bigger than the Sun, to which <lb></lb>grand Orb, a ſtar of the fixth magnitude, ought to be equal, ac <lb></lb>cording to the aſſertion of this Authour.</s></p><p type="margin"><s><margin.target id="marg605"></margin.target><emph type="italics"></emph>The computati <lb></lb>on of the magni <lb></lb>tude of the fixed <lb></lb>Stars, in reſpect to <lb></lb>the grand Orb.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>The errour then of theſe men, conſiſteth in being ex <lb></lb>treamly miſtaken, in taking the apparent Diameter of the fixed <lb></lb>Stars.</s></p><p type="main"><s>SALV. </s><s>This is one, but not the onely errour of them; and <lb></lb><arrow.to.target n="marg606"></arrow.to.target> <lb></lb>indeed, I do very much admire how ſo many <emph type="italics"></emph>Aſtronomers,<emph.end type="italics"></emph.end> and <lb></lb>thoſe very famous, as are <emph type="italics"></emph>Alfagranus, Albategnus, Tebizius,<emph.end type="italics"></emph.end> and <lb></lb>much more modernly the <emph type="italics"></emph>Tycho's<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Clavius's,<emph.end type="italics"></emph.end> and in ſumm, <lb></lb>all the predeceſſors of our <emph type="italics"></emph>Academian,<emph.end type="italics"></emph.end> ſhould have been ſo groſly <lb></lb>miſtaken, in determining the magnitudes of all the Stars, as well <lb></lb>ſixed as moveable, the two Luminaries excepted out of that num <lb></lb>ber; and that they have not taken any heed to the adventitious <lb></lb>irradiations that deceitfully repreſent them an hundred and more <lb></lb>times bigger, than when they are beheld, without thoſe capilli <pb xlink:href="040/01/347.jpg" pagenum="327"></pb>ous rayes, nor can this their inadvertency be excuſed, in regard <lb></lb>that it was in their power to have beheld them at their pleaſure <lb></lb>without thoſe treſſes, which is done, by looking upon them at <lb></lb>their firſt appearance in the evening, or their laſt occultation in <lb></lb><arrow.to.target n="marg607"></arrow.to.target> <lb></lb>the comming on of day; and if none of the reſt, yet <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> <lb></lb>which oft times is ſeen at noon day, ſo ſmall, that one muſt ſhar <lb></lb>pen the ſight in diſcerning it; and again, in the following night, <lb></lb>ſeemeth a great flake of light, might advertiſe them of their fal <lb></lb>lacy; for I will not believe that they thought the true <emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end> to <lb></lb>be that which is ſeen in the obſcureſt darkneſſes, and not that <lb></lb>which is diſcerned in the luminous <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end>: for our lights, which <lb></lb>ſeen by night afar off appear great, and neer at hand ſhew their <lb></lb>true luſtre to be terminate and ſmall, might have eaſily have <lb></lb>made them cautious; nay, if I may freely ſpeak my thoughts, I <lb></lb>abſolutely believe that none of them, no not <emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end> himſelf, ſo <lb></lb>accurate in handling Aſtronomical Inſtruments, and that ſo great <lb></lb>and accurate, without ſparing very great coſt in their conſtru <lb></lb>ction, did ever go about to take and meaſure the apparent dia <lb></lb>meter of any Star, the Sun and Moon excepted; but I think, <lb></lb>that arbitrarily, and as we ſay, with the eye, ſome one of the <lb></lb>more antient of them pronounced the thing to be ſo and ſo, and <lb></lb>that all that followed him afterwards, without more ado, kept <lb></lb>cloſe to what the firſt had ſaid; for if any one of them had ap <lb></lb>plied himſelf to have made ſome new proof of the ſame, he would <lb></lb>doubtleſſe have diſcovered the fraud.</s></p><p type="margin"><s><margin.target id="marg606"></margin.target><emph type="italics"></emph>A common er <lb></lb>rour of all the<emph.end type="italics"></emph.end> A <lb></lb>ſtronomers, <emph type="italics"></emph>touch <lb></lb>ing the magnitude <lb></lb>of the ſtars.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg607"></margin.target>Venus <emph type="italics"></emph>renders the <lb></lb>errour of Aſtrono <lb></lb>mers in determin <lb></lb>ing the magnitudes <lb></lb>of ſtars inexcuſa <lb></lb>ble.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>But if they wanted the Teleſcope, and you have al <lb></lb>ready ſaid, that our <emph type="italics"></emph>Friend<emph.end type="italics"></emph.end> with that ſame Inſtrument came to <lb></lb>the knowledge of the truth, they ought to be excuſed, and not <lb></lb>accuſed of ignorance.</s></p><p type="main"><s>SALV. </s><s>This would hold good, if without the Teleſcope the <lb></lb>buſineſſe could not be effected. </s><s>Its true, that this Inſtrument by <lb></lb>ſhewing the <emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end> of the Star naked, and magnified an hun <lb></lb>dred or a thouſand times, rendereth the operation much more ea <lb></lb>ſie, but the ſame thing may be done, although not altogether ſo <lb></lb>exactly, without the Inſtrument, and I have many times done <lb></lb>the ſame, and my method therein was this. </s><s>I have cauſed a rope <lb></lb><arrow.to.target n="marg608"></arrow.to.target> <lb></lb>to be hanged towards ſome Star, and I have made uſe of the <lb></lb>Conſtellation, called the <emph type="italics"></emph>Harp,<emph.end type="italics"></emph.end> which riſeth between the North <lb></lb>and ^{*} North-eaſt, and then by going towards, and from <lb></lb><arrow.to.target n="marg609"></arrow.to.target> <lb></lb>the ſaid rope, interpoſed between me and the Star, I have found <lb></lb>the place from whence the thickneſſe of the rope hath juſt hid <lb></lb>the Star from me: this done, I have taken the diſtance from the <lb></lb>eye to the rope, which was one of the ſides including the angle <lb></lb>that was compoſed in the eye, and ^{*} which inſiſteth upon the <lb></lb><arrow.to.target n="marg610"></arrow.to.target> <lb></lb>thickneſſe of the rope, and which is like, yea the ſame with the <pb xlink:href="040/01/348.jpg" pagenum="328"></pb>angle in the Starry Sphere, that inſiſteth upon the diameter of <lb></lb>the Star, and by the proportion of the ropes thickneſſe to the <lb></lb>diſtance from the eye to the rope, by the table of Arches and <lb></lb>Chords, I have immediately found the quantity of the angle; u <lb></lb>ſing all the while the wonted caution that is obſerved in taking <lb></lb>angles ſo acute, not to forme the concourſe of the viſive rayes <lb></lb>in the centre of the eye, where they are onely refracted, but <lb></lb>beyond the eye, where really the pupils greatneſſe maketh them <lb></lb>to concur.</s></p><p type="margin"><s><margin.target id="marg608"></margin.target><emph type="italics"></emph>A way to mea <lb></lb>ſure the apparent <lb></lb>diameter of a ſtar.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg609"></margin.target>* Rendred in <lb></lb>Latine <emph type="italics"></emph>Corum,<emph.end type="italics"></emph.end> that <lb></lb>is to ſay, North <lb></lb>weſt.</s></p><p type="margin"><s><margin.target id="marg610"></margin.target>* <emph type="italics"></emph>i.e.<emph.end type="italics"></emph.end> Is ſubten <lb></lb>ded by.</s></p><p type="main"><s>SAGR. </s><s>I apprehend this your cautelous procedure, albeit I <lb></lb>have a kind of hæſitancy touching the ſame, but that which moſt <lb></lb>puzzleth me is, that in this operation, if it be made in the dark <lb></lb>of night, methinks that you meaſure the diameter of the irradia <lb></lb>ted <emph type="italics"></emph>Diſcus,<emph.end type="italics"></emph.end> and not the true and naked face of the Star.</s></p><p type="main"><s>SALV. </s><s>Not ſo, Sir, for the rope in covering the naked body <lb></lb>of the Star, taketh away the rayes, which belong not to it, but <lb></lb>to our eye, of which it is deprived ſo ſoon as the true <emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end> <lb></lb>thereof is hid; and in making the obſervation, you ſhall ſee, how <lb></lb>unexpectedly a little cord will cover that reaſonable big body of <lb></lb>light, which ſeemed impoſſible to be hid, unleſſe it were with a <lb></lb>much broader Screene: to meaſure, in the next place, and exa <lb></lb>ctly to find out, how many of thoſe thickneſſes of the rope inter <lb></lb>poſe in the diſtance between the ſaid rope and the eye, I take not <lb></lb>onely one diameter of the rope, but laying many pieces of the <lb></lb>ſame together upon a Table, ſo that they touch, I take with a <lb></lb>pair of Compaſſes the whole ſpace occupied by fifteen, or twen <lb></lb>ty of them, and with that meaſure I commenſurate the diſtance <lb></lb>before with another ſmaller cord taken from the rope to the con <lb></lb>courſe of the viſive rayes. </s><s>And with this ſufficiently-exact ope <lb></lb>ration I finde the apparent diameter of a fixed Star of the firſt <lb></lb>magnitude, commonly eſteemed to be 2 <emph type="italics"></emph>min. </s><s>pri.<emph.end type="italics"></emph.end> and alſo 3 <emph type="italics"></emph>min. <lb></lb></s><s>prim.<emph.end type="italics"></emph.end> by <emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end> in his <emph type="italics"></emph>Aſtronomical Letters, cap.<emph.end type="italics"></emph.end> 167. to be no <lb></lb><arrow.to.target n="marg611"></arrow.to.target> <lb></lb>more than 5 <emph type="italics"></emph>ſeconds,<emph.end type="italics"></emph.end> which is one of the 24. or 36. parts of what <lb></lb>they have held it: ſee now upon what groſſe errours their Do <lb></lb>ctrines are founded.</s></p><p type="margin"><s><margin.target id="marg611"></margin.target><emph type="italics"></emph>The diameter of <lb></lb>a fixed ſtar of the <lb></lb>firſt magnitude not <lb></lb>more than five ſec. <lb></lb></s><s>min.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I ſee and comprehend this very well, but before we <lb></lb>paſſe any further, I would propound the doubt that ariſeth in <lb></lb>me in the finding the concourſe [or interſection] of the viſual <lb></lb>rayes beyond the eye, when obſervation is made of objects com <lb></lb>prehended between very acute angles; and my ſcruple proceeds <lb></lb>from thinking, that the ſaid concourſe may be ſometimes more <lb></lb>remote, and ſometimes leſſe; and this not ſo much, by meanes <lb></lb>of the greater or leſſer magnitude of the object that is beheld, as <lb></lb>becauſe that in obſerving objects of the ſame bigneſſe, it ſeems <lb></lb>to me that the concourſe of the rayes, for certain other re <pb xlink:href="040/01/349.jpg" pagenum="329"></pb>ſpects ought to be made more and leſſe remote from the eye.</s></p><p type="main"><s>SALV. </s><s>I ſee already, whither the apprehenſion of <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> <lb></lb>a moſt diligent obſerver of Natures ſecrets, tendeth; and I <lb></lb><arrow.to.target n="marg612"></arrow.to.target> <lb></lb>would lay any wager, that amongſt the thouſands that have ob <lb></lb>ſerved Cats to contract and inlarge the pupils of their eyes very <lb></lb>much, there are not two, nor haply one that hath obſerved the <lb></lb>like effect to be wrought by the pupils of men in ſeeing, whilſt <lb></lb>the <emph type="italics"></emph>medium<emph.end type="italics"></emph.end> is much or little illumin'd, and that in the open light <lb></lb>the circlet of the pupil diminiſheth conſiderably: ſo that in loo <lb></lb>king upon the face or <emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end> of the Sun, it is reduced to a ſmall <lb></lb>neſſe leſſer than a grain of ^{*} <emph type="italics"></emph>Panick,<emph.end type="italics"></emph.end> and in beholding objects <lb></lb><arrow.to.target n="marg613"></arrow.to.target> <lb></lb>that do not ſhine, and are in a leſſe luminous <emph type="italics"></emph>medium,<emph.end type="italics"></emph.end> it is inlar <lb></lb>god to the bigneſſe of a Lintel or more; and in ſumme this <lb></lb>expanſion and contraction differeth in more than decuple pro <lb></lb>portion: From whence it is manifeſt, that when the pupil is <lb></lb>much dilated, it is neceſſary that the angle of the rayes con <lb></lb>courſe be more remote from the eye; which happeneth in be <lb></lb>holding objects little luminated. </s><s>This is a Doctrine which <emph type="italics"></emph>Sa <lb></lb>gredus<emph.end type="italics"></emph.end> hath, juſt now, given me the hint of, whereby, if we <lb></lb>were to make a very exact obſervation, and of great conſe <lb></lb>quence, we are advertized to make the obſervation of that con <lb></lb>courſe in the act of the ſame, or juſt ſuch another operation; but <lb></lb>in this our caſe, wherein we are to ſhew the errour of <emph type="italics"></emph>Astrono <lb></lb>mers,<emph.end type="italics"></emph.end> this accurateneſſe is not neceſſary: for though we ſhould, <lb></lb>in favour of the contrary party, ſuppoſe the ſaid concourſe to be <lb></lb>made upon the pupil it ſelf, it would import little, their miſtake <lb></lb>being ſo great. </s><s>I am not certain, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> that this would have <lb></lb>been your objection.</s></p><p type="margin"><s><margin.target id="marg612"></margin.target><emph type="italics"></emph>The circle of the <lb></lb>pupil of the eye en <lb></lb>largeth and con <lb></lb>tracteth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg613"></margin.target>+ <emph type="italics"></emph>Panicum,<emph.end type="italics"></emph.end> a <lb></lb>ſmall grain like to <lb></lb>Mill, I take it to be <lb></lb>the ſame with that <lb></lb>called Bird Seed.</s></p><p type="main"><s>SAGR. </s><s>It is the very ſame, and I am glad that it was not al <lb></lb>together without reaſon, as your concurrence in the ſame aſſu <lb></lb>reth me; but yet upon this occaſion I would willingly hear what <lb></lb>way may be taken to finde out the diſtance of the concourſe of <lb></lb>the viſual rayes.</s></p><p type="main"><s>SALV. </s><s>The method is very eaſie, and this it is, I take two <lb></lb>long^{*} labels of paper, one black, and the other white, and make <lb></lb><arrow.to.target n="marg614"></arrow.to.target> <lb></lb>the black half as broad as the white; then I ſtick up the white a <lb></lb>gainſt a wall, and far from that I place the other upon a ſtick, or <lb></lb>other ſupport, at a diſtance of fifteen or twenty yards, and rece <lb></lb>ding from this, ſecond another ſuch a ſpace in the ſame right line, <lb></lb>it is very manifeſt, that at the ſaid diſtance the right lines will <lb></lb>concur, that departing from the termes of the breadth of the <lb></lb>white piece, ſhall paſſe cloſe by the edges of the other label pla <lb></lb>ced in the mid-way; whence it followeth, that in caſe the eye <lb></lb>were placed in the point of the ſaid concourſe or interſection, <lb></lb>the black ſlip of paper in the midſt would preciſely hide the op <pb xlink:href="040/01/350.jpg" pagenum="330"></pb>poſite blank, if the ſight were made in one onely point; but if we <lb></lb>ſhould find, that the edges of the white cartel appear diſcovered, <lb></lb>it ſhall be a neceſſary argument that the viſual rayes do not iſſue <lb></lb>from one ſole point. </s><s>And to make the white label to be hid by <lb></lb>the black, it will be requiſite to draw neerer with the eye: <lb></lb>Therefore, having approached ſo neer, that the intermediate la <lb></lb>bel covereth the other, and noted how much the required ap <lb></lb>proximation was, the quantity of that approach ſhall be the cer <lb></lb>tain meaſure, how much the true concourſe of the viſive rayes, is <lb></lb>remote from the eye in the ſaid operation, and we ſhall moreover <lb></lb>have the diameter of the pupil, or of that circlet from whence <lb></lb>the viſive rayes proceed: for it ſhall be to the breadth of the <lb></lb>black paper, as is the diſtance from the concourſe of the lines, <lb></lb>that are produced by the edges of the papers to the place where <lb></lb>the eye ſtandeth, when it firſt ſeeth the remote paper to be hid <lb></lb>by the intermediate one, as that diſtance is, I ſay, to the diſtance <lb></lb>that is between thoſe two papers. </s><s>And therefore when we <lb></lb>would, with exactneſſe, meaſure the apparent diameter of a Star, <lb></lb>having made the obſervation in manner, as aforeſaid, it would be <lb></lb>neceſſary to compare the diameter of the rope to the diameter of <lb></lb>the pupil; and having found <emph type="italics"></emph>v.g.<emph.end type="italics"></emph.end> the diameter of the rope to be <lb></lb>quadruple to that of the pupil, and the diſtance of the eye from <lb></lb>the rope to be, for example, thirty yards, we would ſay, that the <lb></lb>true concourſe of the lines produced from the ends or extremi <lb></lb>ties of the diameter of the ſtar, by the extremities of the dia <lb></lb>meter of the rope, doth fall out to be fourty yards remote from <lb></lb>the ſaid rope, for ſo we ſhall have obſerved, as we ought, the pro <lb></lb>portion between the diſtance of the rope from the concourſe of <lb></lb>the ſaid lines, and the diſtance from the ſaid concourſe to the <lb></lb>place of the eye, which ought to be the ſame that is between <lb></lb>the diameter of the rope, and diameter of the pupil.</s></p><p type="margin"><s><margin.target id="marg614"></margin.target>* Striſce. <lb></lb><emph type="italics"></emph>How to find the <lb></lb>diſtance of the rays <lb></lb>concourſe from the <lb></lb>pupil.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I have perfectly underſtood the whole buſineſſe, and <lb></lb>therefore let us hear what <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> hath to alledge in defence of <lb></lb>the <emph type="italics"></emph>Anti-Copernicans.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>Albeit that grand and altogether incredible inconve <lb></lb>nience inſiſted upon by theſe adverſaries of <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> be much <lb></lb>moderated and abated by the diſcourſe of <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> yet do I <lb></lb>not think it weakened ſo, as that it hath not ſtrength enough left <lb></lb>to foil this ſame opinion. </s><s>For, if I have rightly apprehended the <lb></lb>chief and ultimate concluſion, in caſe, the ſtars of the ſixth mag <lb></lb>nitude were ſuppoſed to be as big as the Sun, (which yet I can <lb></lb>hardly think) yet it would ſtill be true, that the grand Orb [or <lb></lb>Ecliptick] would occaſion a mutation and variation in the ſtarry <lb></lb>Sphere, like to that which the ſemidiameter of the Earth produ <lb></lb>ceth in the Sun, which yet is obſervable; ſo that neither that, no <pb xlink:href="040/01/351.jpg" pagenum="331"></pb>nor a leſſe mutation being diſcerned in the fixed Stars, methinks <lb></lb>that by this means the annual motion of the Earth is deſtroyed <lb></lb>and overthrown.</s></p><p type="main"><s>SALV. </s><s>You might very well ſo conclude, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> if we <lb></lb>had nothing elſe to ſay in behalf of <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end>: but we have <lb></lb>many things to alledge that yet have not been mentioned; and <lb></lb>as to that your reply, nothing hindereth, but that we may ſup <lb></lb>poſe the diſtance of the fixed Stars to be yet much greater than <lb></lb>that which hath been allowed them, and you your ſelf, and who <lb></lb>ever elſe will not derogate from the propoſitions admitted by <lb></lb><emph type="italics"></emph>Piolomy<emph.end type="italics"></emph.end>'s ſectators, muſt needs grant it as a thing moſt requiſite <lb></lb>to ſuppoſe the Starry Sphere to be very much bigger yet than <lb></lb>that which even now we ſaid that it ought to be eſteemed. </s><s>For <lb></lb><arrow.to.target n="marg615"></arrow.to.target> <lb></lb>all Aſtronomers agreeing in this, that the cauſe of the greater <lb></lb>tardity of the Revolutions of the Planets is, the majority of <lb></lb>their Spheres, and that therefore <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> is more flow than <emph type="italics"></emph>Ju <lb></lb>piter,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> than the Sun, for that the firſt is to deſcribe a <lb></lb>greater circle than the ſecond, and that than this later, &c. </s><s>con <lb></lb>ſidering that <emph type="italics"></emph>Saturn v.g.<emph.end type="italics"></emph.end> the altitude of whoſe Orb is nine times <lb></lb>higher than that of the Sun, and that for that cauſe the time of <lb></lb>one Revolution of <emph type="italics"></emph>Saturn,<emph.end type="italics"></emph.end> is thirty times longer than that of a <lb></lb>converſion of the Sun, in regard that according to the Doctrine <lb></lb>of <emph type="italics"></emph>Ptolomy,<emph.end type="italics"></emph.end> one converſion of the ſtarry Sphere is finiſhed in <lb></lb>36000. years, whereas that of <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> is conſummate in thirty, <lb></lb>and that of the Sun in one, arguing with a like proportion, and <lb></lb><arrow.to.target n="marg616"></arrow.to.target> <lb></lb>ſaying, if the Orb of <emph type="italics"></emph>Saturn,<emph.end type="italics"></emph.end> by reaſon it is nine times bigger <lb></lb>than that of the Sun, revolves in a time thirty times longer, by <lb></lb>converſion, how great ought that Orb to be, which revolves <lb></lb>36000. times more ſlowly? </s><s>it ſhall be found that the diſtance of <lb></lb>the ſtarry Sphere ought to be 10800 ſemidiameters of the grand <lb></lb>Orb, which ſhould be full five times bigger than that, which even <lb></lb>now we computed it to be, in caſe that a fixed Star of the ſixth <lb></lb>magnitude were equal to the Sun. </s><s>Now ſee how much leſſer yet, <lb></lb>upon this account, the variation occaſioned in the ſaid Stars, by <lb></lb>the annual motion of the Earth, ought to appear. </s><s>And if at the <lb></lb>ſame rate we would argue the diſtance of the ſtarry Sphere from <lb></lb><arrow.to.target n="marg617"></arrow.to.target> <lb></lb><emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> and from <emph type="italics"></emph>Mars,<emph.end type="italics"></emph.end> that would give it us to be 15000. and <lb></lb>this 27000 ſemidiameters of the grand Orb, to wit, the firſt <lb></lb>ſeven, and the ſecond twelve times bigger than what the mag <lb></lb>nitude of the fixed Star, ſuppoſed equal to the Sun, did make <lb></lb>it.</s></p><p type="margin"><s><margin.target id="marg615"></margin.target><emph type="italics"></emph>All Astrono <lb></lb>mers agree that <lb></lb>the greater magni <lb></lb>tudes of the Orbes <lb></lb>is the cauſe of the <lb></lb>tardity of the con <lb></lb>verſions.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg616"></margin.target><emph type="italics"></emph>By another ſup <lb></lb>poſition taken from <lb></lb>Aſtronomers, the <lb></lb>diſtance of the fix <lb></lb>ed Stars is calcu <lb></lb>lated to be 10800 <lb></lb>ſemidiameters of <lb></lb>the grand Orb.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg617"></margin.target><emph type="italics"></emph>By the proportion <lb></lb>of<emph.end type="italics"></emph.end> Jupiter <emph type="italics"></emph>and of<emph.end type="italics"></emph.end> <lb></lb>Mais, <emph type="italics"></emph>the ſtarry <lb></lb>Sphere is found to <lb></lb>be yet more remote.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>Methinks that to this might be anſwered, that the mo <lb></lb>tion of the ſtarry Sphere hath, ſince <emph type="italics"></emph>Ptolomy,<emph.end type="italics"></emph.end> been obſerved not <lb></lb>to be ſo ſlow as he accounted it; yea, if I miſtake. </s><s>not, I have <lb></lb>heard that <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> himſelf made the Obſervation.</s></p> <pb xlink:href="040/01/352.jpg" pagenum="332"></pb><p type="main"><s>SALV. </s><s>You ſay very well; but you alledge nothing in that <lb></lb>which may favour the cauſe of the <emph type="italics"></emph>Ptolomœans<emph.end type="italics"></emph.end> in the leaſt, who <lb></lb>did never yet reject the motion of 36000. years in the ſtarry <lb></lb>Sphere, for that the ſaid tardity would make it too vaſt and im <lb></lb>menſe. </s><s>For if that the ſaid immenſity was not to be ſuppoſed in <lb></lb>Nature, they ought before now to to have denied a converſion <lb></lb>ſo ſlow as that it could not with good proportion adapt it ſelf, <lb></lb>ſave onely to a Sphere of monſtrous magnitude.</s></p><p type="main"><s>SAGR. </s><s>Pray you, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> let us loſe no more time in pro <lb></lb>ceeding, by the way of theſe proportions with people that are apt <lb></lb>to admit things moſt diſ-proportionate; ſo that its impoſſible <lb></lb>to win any thing upon them this way: and what more diſpropor <lb></lb>tionate proportion can be imagined than that which theſe men <lb></lb>ſwallow down, and admit, in that writing, that there cannot be a <lb></lb>more convenient way to diſpoſe the Cœleſtial Spheres, in order, <lb></lb>than to regulate them by the differences of the times of their pe <lb></lb>riods, placing from one degree to another the more flow above <lb></lb>the more ſwift, when they have conſtituted the Starry Sphere <lb></lb>higher than the reſt, as being the ſloweſt, they frame another <lb></lb>higher ſtill than that, and conſequently greater, and make it re <lb></lb>volve in twenty four hours, whilſt the next below, it moves not <lb></lb>round under 36000. years?</s></p><p type="main"><s>SALV. </s><s>I could wiſh, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that ſuſpending for a time <lb></lb>the affection rhat you bear to the followers of your opinion, you <lb></lb>would ſincerely tell me, whether you think that they do in their <lb></lb>minds comprehend that magnitude, which they reject afterwards <lb></lb>as uncapable for its immenſity to be aſcribed to the Univerſe. <lb></lb></s><s>For I, as to my own part, think that they do not; But believe, <lb></lb><arrow.to.target n="marg618"></arrow.to.target> <lb></lb>that like as in the apprehenſion of numbers, when once a man <lb></lb>begins to paſſe thoſe millions of millions, the imagination is con <lb></lb>founded, and can no longer form a conceipt of the ſame, ſo it <lb></lb>happens alſo in comprehending immenſe magnitudes and diſtan <lb></lb>ces; ſo that there intervenes to the comprehenſion an effect like <lb></lb>to that which befalleth the ſenſe; For whileſt that in a ſerene <lb></lb>night I look towards the Stars, I judge, according to ſenſe, that <lb></lb>their diſtance is but a few miles, and that the fixed Stars are not a <lb></lb>jot more remote than <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> or <emph type="italics"></emph>Saturn,<emph.end type="italics"></emph.end> nay than the Moon. <lb></lb></s><s>But without more ado, conſider the controverſies that have paſt <lb></lb>between the Aſtronomers and Peripatetick Philoſophers, upon <lb></lb>occaſion of the new Stars of <emph type="italics"></emph>Caſſiopeia<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Sagittary,<emph.end type="italics"></emph.end> the A <lb></lb>ſtronomers placing them amongſt the fixed Stars, and the Philo <lb></lb>ſophers believing them to be below the Moon. </s><s>So unable is our <lb></lb>ſenſe to diſtinguiſh great diſtances from the greateſt, though theſe <lb></lb>be in reality many thouſand times greater than thoſe. </s><s>In a word, <lb></lb>I ask of thee, O fooliſh man! Doth thy imagination comprehend <pb xlink:href="040/01/353.jpg" pagenum="333"></pb>that vaſt magnitude of the Univerſe, which thou afterwards judg <lb></lb>eſt to be too immenſe? </s><s>If thou comprehendeſt it; wilt thou <lb></lb>hold that thy apprehenſion extendeth it ſelf farther than the Di <lb></lb>vine Power? </s><s>wilt thou ſay, that thou canſt imagine greater <lb></lb>things than thoſe which God can bring to paſſe? </s><s>But if thou <lb></lb>apprehendeſt it not, why wilt thou paſſe thy verdict upon things <lb></lb>beyond thy comprehenſion?</s></p><p type="margin"><s><margin.target id="marg618"></margin.target><emph type="italics"></emph>Immenſe mag <lb></lb>nitudes and num <lb></lb>bers are incompre <lb></lb>henſible by our un <lb></lb>derſtanding.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>All this is very well, nor can it be denied, but that <lb></lb>Heaven may in greatneſſe ſurpaſſe our imagination, as alſo that <lb></lb>God might have created it thouſands of times vaſter than now it <lb></lb>is; but we ought not to grant any thing to have been made in <lb></lb>vain, and to be idle in the Univerſe. </s><s>Now, in that we ſee this ad <lb></lb>mirable order of the Planets, diſpoſed about the Earth in diſtan <lb></lb>ces proportionate for producing their effects for our advantage, <lb></lb>to what purpoſe is it to interpoſe afterwards between the ſublime <lb></lb>Orb of <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> and the ſtarry Sphere, a vaſt vacancy, without any <lb></lb>ſtar that is ſuperfluous, and to no purpoſe? </s><s>To what end? </s><s>For <lb></lb>whoſe profit and advantage?</s></p><p type="main"><s>SALV. </s><s>Methinks we arrogate too much to our ſelves, <emph type="italics"></emph>Simpli <lb></lb>cius,<emph.end type="italics"></emph.end> whilſt we will have it, that the onely care of us, is the ad <lb></lb>æquate work, and bound, beyond which the Divine Wiſdome <lb></lb>and Power doth, or diſpoſeth of nothing. </s><s>But I will not con <lb></lb>ſent, that we ſhould ſo much ſhorten its hand, but deſire that we <lb></lb>may content our ſelves with an aſſurance that God and Nature <lb></lb><arrow.to.target n="marg619"></arrow.to.target> <lb></lb>are ſo imployed in the governing of humane affairs, that they <lb></lb>could not more apply themſelves thereto, although they had no <lb></lb>other care than onely that of mankind; and this, I think, I am <lb></lb>able to make out by a moſt pertinent and moſt noble example, <lb></lb>taken from the operation of the Suns light, which whileſt it at <lb></lb><arrow.to.target n="marg620"></arrow.to.target> <lb></lb>tracteth theſe vapours, or ſcorcheth that plant, it attracteth, it <lb></lb>ſcorcheth them, as if it had no more to do; yea, in ripening that <lb></lb>bunch of grapes, nay that one ſingle grape, it doth apply it ſelf <lb></lb>ſo, that it could not be more intenſe if the ſum of all its buſineſs <lb></lb>had been the only maturation of that grape. </s><s>Now if this grape <lb></lb>receiveth all that it is poſſible for it to receive from the Sun, not <lb></lb>ſuffering the leaſt injury by the Suns production of a thouſand <lb></lb>other effects at the ſame time; it would be either envy or folly <lb></lb>to blame that grape, if it ſhould think or wiſh that the Sun would <lb></lb>onely appropriate its rayes to its advantage. </s><s>I am confident that <lb></lb>nothing is omitted by the Divine Providence, of what concernes <lb></lb>the government of humane affairs; but that there may not be <lb></lb>other things in the Univerſe, that depend upon the ſame infinite <lb></lb>Wiſdome, I cannot, of my ſelf, by what my reaſon holds forth <lb></lb>to me, bring my ſelf to believe. </s><s>However, if it were not ſo, <lb></lb>yet ſhould I not forbear to believe the reaſons laid before me by <pb xlink:href="040/01/354.jpg" pagenum="334"></pb>ſome more ſublime intelligence. </s><s>In the mean time, if one <lb></lb>ſhould tell me, that an immenſe ſpace interpoſed between the <lb></lb>Orbs of the Planets and the Starry Sphere, deprived of ſtars and <lb></lb>idle, would be vain and uſeleſſe, as likewiſe that ſo great an <lb></lb>immenſity for receipt of the fixed ſtars, as exceeds our utmoſt <lb></lb>comprehenſion would be ſuperfluous, I would reply, that it is <lb></lb>raſhneſſe to go about to make our ſhallow reaſon judg of the <lb></lb>Works of God, and to call vain and ſuperfluous, whatſoever <lb></lb>thing in the Univerſe is not ſubſervient to us.</s></p><p type="margin"><s><margin.target id="marg619"></margin.target><emph type="italics"></emph>God & Nature <lb></lb>do imploy them <lb></lb>ſelves in caring <lb></lb>for men, as if they <lb></lb>minded nothing <lb></lb>elſe.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg620"></margin.target><emph type="italics"></emph>An example of <lb></lb>Gods care of man <lb></lb>kind taken from <lb></lb>the Sun.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Say rather, and I believe you would ſay better, that <lb></lb><arrow.to.target n="marg621"></arrow.to.target> <lb></lb>we know not what is ſubſervient to us; and I hold it one of the <lb></lb>greateſt vanities, yea follies, that can be in the World, to ſay, <lb></lb>becauſe I know not of what uſe <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> or <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> are to me, that <lb></lb>therefore theſe Planets are ſuperfluous, yea more, that there are <lb></lb>no ſuch things <emph type="italics"></emph>in rerum natura<emph.end type="italics"></emph.end>; when as, oh fooliſh man! I <lb></lb>know not ſo much as to what purpoſe the arteries, the griſtles, <lb></lb>the ſpleen, the gall do ſerve; nay I ſhould not know that I have <lb></lb>a gall, ſpleen, or kidneys, if in many deſected Corps, they were <lb></lb>not ſhewn unto me; and then onely ſhall I be able to know what <lb></lb>the ſpleen worketh in me, when it comes to be taken from me. <lb></lb></s><s>To be able to know what this or that Cœleſtial body worketh in <lb></lb><arrow.to.target n="marg622"></arrow.to.target> <lb></lb>me (ſeeing you will have it that all their influences direct them <lb></lb>ſelves to us) it would be requiſite to remove that body for ſome <lb></lb>time; and then whatſoever effect I ſhould find wanting in me, I <lb></lb>would ſay that it depended on that ſtar. </s><s>Moreover, who will pre <lb></lb>ſume to ſay that the ſpace which they call too vaſt and uſeleſſe <lb></lb>between <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> and the fixed ſtars, is void of other mundane bo <lb></lb>dies? </s><s>Muſt it be ſo, becauſe we do not ſee them? </s><s>Then the four <lb></lb><arrow.to.target n="marg623"></arrow.to.target> <lb></lb>Medicean Planets, and the companions of <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> came firſt in <lb></lb>to Heaven, when we began to ſee them, and not before? </s><s>And <lb></lb>by this rule the innumerable other fixed ſtars had no exiſtence <lb></lb>before that men did look on them? </s><s>and the cloudy conſtellati <lb></lb>ons called <emph type="italics"></emph>Nebuloſœ<emph.end type="italics"></emph.end> were at firſt only white flakes, but afterwards <lb></lb>with the Teleſcope we made them to become conſtellations of <lb></lb>many lucid and bright ſtars. </s><s>Oh preſumptious, rather oh raſh <lb></lb>ignorance of man!</s></p><p type="margin"><s><margin.target id="marg621"></margin.target><emph type="italics"></emph>It is great raſh <lb></lb>neſſe to cenſure <lb></lb>that to be ſuperflu <lb></lb>ous in the Univerſe, <lb></lb>which we do not <lb></lb>perceive to be made <lb></lb>for us.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg622"></margin.target><emph type="italics"></emph>By depriving <lb></lb>Heaven of ſome <lb></lb>ſtar, one might <lb></lb>come to know what <lb></lb>influence it hath <lb></lb>upon us.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg623"></margin.target><emph type="italics"></emph>Many things <lb></lb>may be in Heauen, <lb></lb>that are inviſible <lb></lb>to us<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. It's to no purpoſe <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> to ſally out any more into <lb></lb>theſe unprofitable exaggerations: Let us purſue our intended <lb></lb>deſigne of examining the validity of the reaſons alledged on ei <lb></lb>ther ſide, without determining any thing, remitting the judg <lb></lb>ment thereof when we have done, to ſuch as are more knowing. <lb></lb></s><s>Returning therefore to our natural and humane diſquiſitions, I <lb></lb><arrow.to.target n="marg624"></arrow.to.target> <lb></lb>ſay, that great, little, immenſe, ſmall, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> are not abſolute, <lb></lb>but relative terms, ſo that the ſelf ſame thing compared with <lb></lb>divers others, may one while be called immenſe, and another <pb xlink:href="040/01/355.jpg" pagenum="335"></pb>while imperceptible, not to ſay ſmall. </s><s>This being ſo, I demand <lb></lb>in relation to what the Starry Sphere of <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> may be cal <lb></lb>led over vaſt. </s><s>In my judgment it cannot be compared, or ſaid <lb></lb>to be ſuch, unleſſe it be in relation to ſome other thing of the <lb></lb>ſame kind; now let us take the very leaſt of the ſame kind, <lb></lb><arrow.to.target n="marg625"></arrow.to.target> <lb></lb>which ſhall be the Lunar Orb; and if the Starry Orb may be ſo <lb></lb>cenſured to be too big in reſpect to that of the Moon, every o <lb></lb>ther magnitude that with like or greater proportion exceedeth <lb></lb>another of the ſame kind, ought to be adjudged too vaſt, and <lb></lb>for the ſame reaſon to be denied that they are to be found in the <lb></lb>World; and thus an Elephant, and a Whale, ſhall without more <lb></lb>ado be condemned for <emph type="italics"></emph>Chymæra's,<emph.end type="italics"></emph.end> and Poetical fictions, be <lb></lb>cauſe that the one as being too vaſt in relation to an Ant, which <lb></lb>is a Terreſtrial animal, and the other in reſpect to the ^{*}Gudgeon, <lb></lb><arrow.to.target n="marg626"></arrow.to.target> <lb></lb>which is a Fiſh, and are certainly ſeen to be <emph type="italics"></emph>in rerum natura,<emph.end type="italics"></emph.end> <lb></lb>would be too immeaſurable; for without all diſpute, the Ele <lb></lb>phant and Whale exceed the Ant and Gudgeon in a much great <lb></lb>er proportion than the Starry Sphere doth that of the Moon, <lb></lb>although we ſhould fancy the ſaid Sphere to be as big as the <emph type="italics"></emph>Co <lb></lb>pernican<emph.end type="italics"></emph.end> Syſteme maketh it. </s><s>Moreover, how hugely big is the <lb></lb><arrow.to.target n="marg627"></arrow.to.target> <lb></lb>Sphere of <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> or that of <emph type="italics"></emph>Saturn,<emph.end type="italics"></emph.end> defigned for a receptacle <lb></lb>but for one ſingle ſtar; and that very ſmall in compariſon of one <lb></lb>of the fixed? </s><s>Certainly if we ſhould aſſign to every one of the <lb></lb>fixed ſtars for its receptacle ſo great a part of the Worlds ſpace, <lb></lb>it would be neceſſary to make the Orb wherein ſuch innumerable <lb></lb>multitudes of them reſide, very many thouſands of times big <lb></lb>ger than that which ſerveth the purpoſe of <emph type="italics"></emph>Copernicus.<emph.end type="italics"></emph.end> Beſides, <lb></lb><arrow.to.target n="marg628"></arrow.to.target> <lb></lb>do not you call a fixed ſtar very ſmall, I mean even one of the <lb></lb>moſt apparent, and not one of thoſe which ſhun our ſight; and <lb></lb>do we not call them ſo in reſpect of the vaſt ſpace circumfuſed? <lb></lb></s><s>Now if the whole Starry Sphere were one entire lucid body; who <lb></lb><arrow.to.target n="marg629"></arrow.to.target> <lb></lb>is there, that doth not know that in an infinite ſpace there might be <lb></lb>aſſigned a diſtance ſo great, as that the ſaid lucid Sphere might <lb></lb>from thence ſhew as little, yea leſſe than a fixed ſtar, now ap <lb></lb>peareth beheld from the Earth? </s><s>From thence therefore we <lb></lb>ſhould <emph type="italics"></emph>then<emph.end type="italics"></emph.end> judg that ſelf ſame thing to be little, which <emph type="italics"></emph>now<emph.end type="italics"></emph.end> from <lb></lb>hence we eſteem to be immeaſurably great.</s></p><p type="margin"><s><margin.target id="marg624"></margin.target><emph type="italics"></emph>Great, ſmall, <lb></lb>immenſe,<emph.end type="italics"></emph.end> &c. <emph type="italics"></emph>are <lb></lb>relative terms.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg625"></margin.target><emph type="italics"></emph>Vanity of thoſe <lb></lb>mens diſcour ſewho <lb></lb>judg the ſtarry <lb></lb>ſphere too vaſt in <lb></lb>the<emph.end type="italics"></emph.end> Copernican <lb></lb><emph type="italics"></emph>Hypotheſis.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg626"></margin.target>* <emph type="italics"></emph>Spilloncola,<emph.end type="italics"></emph.end> which <lb></lb>is here put for the <lb></lb>leaſt of Fiſhes.</s></p><p type="margin"><s><margin.target id="marg627"></margin.target><emph type="italics"></emph>The ſpace aſ <lb></lb>ſigned to a fixed <lb></lb>ſtar, is much ieſſe <lb></lb>than that of a Pla <lb></lb>net.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg628"></margin.target><emph type="italics"></emph>A ſtar is cal <lb></lb>led in reſpect of the <lb></lb>ſpace that environs <lb></lb>it.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg629"></margin.target><emph type="italics"></emph>The whole ſtar <lb></lb>ry ſphere beheld <lb></lb>from a great di <lb></lb>ſtance might ap <lb></lb>pear as ſmall as <lb></lb>one ſingle ſtar.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Great in my judgment, is the folly of thoſe who <lb></lb>would have had God to have made the World more proportinal <lb></lb>to the narrow capacities of their reaſon, than to his immenſe, <lb></lb>rather infinite power.</s></p><p type="main"><s>SIMP. </s><s>All this that you ſay is very true; but that upon <lb></lb>which the adverſary makes a ſcruple, is, to grant that a fixed <lb></lb>ſtar ſhould be not onely equal to, but ſo much bigger than the <lb></lb>Sun; when as they both are particular bodies ſituate within the <pb xlink:href="040/01/356.jpg" pagenum="336"></pb>Starry Orb: “And indeed in my opinion this Authour very <lb></lb>pertinently queſtioneth and asketh: To what end, and <lb></lb>for whoſe ſake are ſuch huge machines made? </s><s>Were they <lb></lb><arrow.to.target n="marg630"></arrow.to.target> <lb></lb>produced for the Earth, for an inconſiderable point? </s><s>And <lb></lb>why ſo remote? </s><s>To the end they might ſeem ſo very ſmall, <lb></lb>and might have no influence at all upon the Earth? </s><s>To <lb></lb><arrow.to.target n="marg631"></arrow.to.target> <lb></lb>what purpoſe is ſuch a needleſſe monſtrous ^{*} immenſity be <lb></lb>tween them and <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end>? </s><s>All thoſe aſſertions fall to the <lb></lb>ground that are not upheld by probable reaſons.”</s></p><p type="margin"><s><margin.target id="marg630"></margin.target><emph type="italics"></emph>Inſtances of the <lb></lb>Authour of the <lb></lb>Concluſions by way <lb></lb>of interrogation.<emph.end type="italics"></emph.end></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 queſtions which this perſon asketh, <lb></lb><arrow.to.target n="marg632"></arrow.to.target> <lb></lb>that one may collect, that in caſe the Heavens, the Stars, and <lb></lb>the quantity of their diſtances and magnitudes which he hath <lb></lb>hitherto held, be let alone, (although he never certainly fancied <lb></lb>to himſelf any conceivable magnitude thereof) he perfectly diſ <lb></lb>cerns and comprehends the benefits that flow from thence to the <lb></lb>Earth, which is no longer an inconſiderable thing; nor are they <lb></lb>any longer ſo remote as to appear ſo very ſmall, but big enough to <lb></lb>be able to operate on the Earth; and that the diſtance between <lb></lb>them and <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> is very well proportioned, and that he, for all <lb></lb>theſe things, hath very probable reaſons; of which I would glad <lb></lb>ly have heard ſome one: but being that in theſe few words he <lb></lb><arrow.to.target n="marg633"></arrow.to.target> <lb></lb>confounds and contradicts himſelf, it maketh me think that he <lb></lb>is very poor and ill furniſhed with thoſe probable reaſons, and <lb></lb>that thoſe which he calls reaſons, are rather fallacies, or dreams <lb></lb>of an over-weening fancy. </s><s>For I ask of him, whether theſe Ce <lb></lb><arrow.to.target n="marg634"></arrow.to.target> <lb></lb>leſtial bodies truly operate on the Earth, and whether for the <lb></lb>working of thoſe effects they were produced of ſuch and ſuch <lb></lb>magnitudes, and diſpoſed at ſuch and ſuch diſtances, or elſe <lb></lb>whether they have nothing at all to do with Terrene mattets. </s><s>If <lb></lb>they have nothing to do with the Earth; it is a great folly for us <lb></lb>that are Earth-born, to offer to make our ſelves arbitrators of <lb></lb>their magnitudes, and regulators of their local diſpoſitions, ſee <lb></lb>ing that we are altogether ignorant of their whole buſineſſe and <lb></lb>concerns; but if he ſhall ſay that they do operate, and that they <lb></lb>are directed to this end, he doth affirm the ſame thing which a <lb></lb>little before he denied, and praiſeth that which even now he <lb></lb>condemned, in that he ſaid, that the Celeſtial bodies ſituate ſo <lb></lb>far remote as that they appear very ſmall, cannot have any in <lb></lb>fluence at all upon the Earth. </s><s>But, good Sir, in the Starry Sphere <lb></lb>pre-eſtabliſhed at its preſent diſtance, and which you did ac <lb></lb>knowledg to be in your judgment, well proportioned to have an <lb></lb>influence upon theſe Terrene bodies, many ſtars appear very <lb></lb>ſmall, and an hundred times as many more are wholly inviſible <lb></lb>unto us (which is an appearing yet leſſe than very ſmall) <lb></lb>therefore it is neceſſary that (contradicting your ſelf) you do <pb xlink:href="040/01/357.jpg" pagenum="337"></pb>now deny their operation upon the the Earth; or elſe that (ſtill <lb></lb>contradicting your ſelf) you grant that their appearing very ſmall <lb></lb>doth not in the leaſt leſſen their influence; or elſe that (and this <lb></lb>ſhall be a more ſincere and modeſt conceſſion) you acknowledg <lb></lb>and freely confeſſe, that our paſſing judgment upon their mag <lb></lb>nitudes and diſtances is a vanity, not to ſay preſumption or <lb></lb>raſhneſſe.</s></p><p type="margin"><s><margin.target id="marg632"></margin.target><emph type="italics"></emph>Anſwers to the <lb></lb>interrogatories of <lb></lb>the ſaid Authour.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg633"></margin.target><emph type="italics"></emph>The Auihour <lb></lb>of the Concluſi <lb></lb>ons confound and <lb></lb>contradicts him <lb></lb>ſelfin his interro <lb></lb>gations.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg634"></margin.target><emph type="italics"></emph>Inter ogatories <lb></lb>put to the Au <lb></lb>thour of the Con <lb></lb>cluſions, by which <lb></lb>the weakneſſe of <lb></lb>his is made appear.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>Truth is, I my ſelf did alſo, in reading this paſſage <lb></lb>perceive the manifeſt contradiction, in ſaying, that the Stars. (if <lb></lb>one may ſo ſpeak) of <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> appearing ſo very ſmall, could <lb></lb>not operate on the Earth, and not perceiving that he had granted <lb></lb>an influence upon the Earth to thoſe of <emph type="italics"></emph>Ptolomy,<emph.end type="italics"></emph.end> and his ſecta <lb></lb>tors, which appear not only very ſmall, but are, for the moſt <lb></lb>part, very inviſible.</s></p><p type="main"><s>SALV. </s><s>But I proceed to another conſideration: What is the <lb></lb>reaſon, doth he ſay, why the ſtars appear ſo little? </s><s>Is it haply, <lb></lb>becauſe they ſeem ſo to us? </s><s>Doth not he know, that this com <lb></lb><arrow.to.target n="marg635"></arrow.to.target> <lb></lb>meth from the Inſtrument that we imploy in beholding them, to <lb></lb>wit, from our eye? </s><s>And that this is true, by changing Inſtru <lb></lb>ment, we ſhall ſee them bigger and bigger, as much as we will. <lb></lb></s><s>And who knows but that to the Earth, which beholdeth them <lb></lb>without eyes, they may not ſhew very great, and ſuch as in reali <lb></lb>ty they are? </s><s>But it's time that, omitting theſe trifles, we come <lb></lb>to things of more moment; and therefore I having already de <lb></lb>monſtrated theſe two things: Firſt, how far off the Firmament <lb></lb>ought to be placed to make, that the grand Orb cauſeth no grea <lb></lb>ter difference than that which the Terreſtrial Orb occaſioneth in <lb></lb>the remoteneſſe of the Sun; And next, how likewiſe to make <lb></lb>that a ſtar of the Firmament appear to us of the ſame bigneſſe, <lb></lb>as now we ſee it, it is not neceſſary to ſuppoſe it bigger than the <lb></lb>Sun; I would know whether <emph type="italics"></emph>Tycho,<emph.end type="italics"></emph.end> or any of his adherents hath <lb></lb>ever attempted to find out, by any means, whether any appea <lb></lb>rance be to be diſcovered in the ſtarry Sphere, upon which one <lb></lb>may the more reſolutely deny or admit the annual motion of <lb></lb>the Earth.</s></p><p type="margin"><s><margin.target id="marg635"></margin.target><emph type="italics"></emph>That remote ol <lb></lb>jects appeare ſo <lb></lb>ſmall, is the defect <lb></lb>of the eye, as is <lb></lb>demonſtrated.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I would anſwer for them, that there is not, no nor is <lb></lb><arrow.to.target n="marg636"></arrow.to.target> <lb></lb>there any need there ſhould; ſeeing that it is <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> himſelf <lb></lb>that ſaith, that no ſuch diverſity is there: and they, arguing <emph type="italics"></emph>ad <lb></lb>hominem,<emph.end type="italics"></emph.end> admit him the ſame; and upon this aſſumption they <lb></lb>demonſtrate the improbability that followeth thereupon, name <lb></lb>ly, that it would be neceſſary to make the Sphere ſo immenſe, <lb></lb>that a fixed ſtar, to appear unto us as great as it now ſeems, ought <lb></lb>of neceſſity to be of ſo immenſe a magnitude, as that it would <lb></lb>exceed the bigneſſe of the whole grand Orb, a thing, which not <lb></lb>withſtanding, as they ſay, is altogether incredible.</s></p> <pb xlink:href="040/01/358.jpg" pagenum="338"></pb><p type="margin"><s><margin.target id="marg636"></margin.target>Tycho <emph type="italics"></emph>nor his <lb></lb>followers ever at <lb></lb>tempted to ſee whe <lb></lb>ther there are any <lb></lb>appearances in the <lb></lb>Firmament for or <lb></lb>against the annual <lb></lb>motion.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>I am of the ſame judgment, and verily believe that <lb></lb>they argue <emph type="italics"></emph>contra hominem,<emph.end type="italics"></emph.end> ſtudying more to defend another <lb></lb>man, than deſiring to come to the knowledge of the truth. </s><s>And <lb></lb><arrow.to.target n="marg637"></arrow.to.target> <lb></lb>I do not only believe, that none of them ever applied themſelves <lb></lb>to make any ſuch obſervation, but I am alſo uncertain, whether <lb></lb>any of them do know what alteration the Earths annual motion <lb></lb>ought to produce in the fixed ſtars, in caſe the ſtarry Sphere were <lb></lb>not ſo far diſtant, as that in them the ſaid diverſity, by reaſon of <lb></lb>its minuity diſ-appeareth; for their ſurceaſing that inquiſition, <lb></lb>and referring themſelves to the meer aſſertion of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> <lb></lb>may very well ſerve to convict a man, but not to acquit him of <lb></lb>the fact: For its poſſible that ſuch a diverſity may be, and yet <lb></lb><arrow.to.target n="marg638"></arrow.to.target> <lb></lb>not have been ſought for; or that either by reaſon of its minui <lb></lb>ty, or for want of exact Inſtruments it was not diſcovered by <emph type="italics"></emph>Co <lb></lb>pernicus<emph.end type="italics"></emph.end>; for though it were ſo, this would not be the firſt thing, <lb></lb>that he either for want of Inſtruments, or for ſome other defect <lb></lb>hath not known; and yet he proceeding upon other ſolid and <lb></lb>rational conjectures, affirmeth that, which the things by him not <lb></lb>diſcovered do ſeem to contradict: for, as hath been ſaid already, <lb></lb>without the Teleſcope, neither could <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> be diſcerned to in <lb></lb>creaſe 60. times; nor <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> 40. more in that than in this poſiti <lb></lb>on; yea, their differences appear much leſſe than really they are: <lb></lb>and yet nevertheleſſe it is certainly diſcovered at length, that <lb></lb>thoſe mutations are the ſame, to an hair that the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Sy <lb></lb><arrow.to.target n="marg639"></arrow.to.target> <lb></lb>ſteme required. </s><s>Now it would be very well, if with the greateſt <lb></lb>accurateneſſe poſſible one ſhould enquire whether ſuch a muta <lb></lb>tion as ought to be diſcoverable in the fixed ſtars, ſuppoſing the <lb></lb>annual motion of the Earth, would be obſerved really and in <lb></lb>effect, a thing which I verily believe hath never as yet been done <lb></lb>by any; done, ſaid I? no, nor haply (as I ſaid before) by many <lb></lb>well underſtood how it ought to be done. </s><s>Nor ſpeak I this at <lb></lb>randome, for I have heretofore ſeen a certain Manuſcript of <lb></lb>one of theſe <emph type="italics"></emph>Anti-Copernicans,<emph.end type="italics"></emph.end> which ſaid, that there would ne <lb></lb>ceſſarily follow, in caſe that opinion were true, a continual ri <lb></lb>ſing and falling of the Pole from ſix moneths to ſix moneths, ac <lb></lb>cording as the Earth in ſuch a time, by ſuch a ſpace as is the dia <lb></lb>meter of the grand Orb, retireth one while towards the North, and <lb></lb>another while towards the South; and yet it ſeemed to him reaſo <lb></lb>nable, yea neceſſary, that we, following the Earth, when we were <lb></lb>towards the North ſhould have the Pole more elevated than when <lb></lb>we are towards the South. </s><s>In this very error did one fall that was <lb></lb>otherwiſe a very skilful Mathematician, & a follower of <emph type="italics"></emph>Copernic.<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg640"></arrow.to.target> <lb></lb>as <emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end> relateth in his ^{*}<emph type="italics"></emph>Progymnaſma. </s><s>pag<emph.end type="italics"></emph.end> 684. which ſaid, that he <lb></lb>had obſerved the Polar altitude to vary, and to differ in Summer <lb></lb>from what it is in Winter: and becauſe <emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end> denieth the merit <pb xlink:href="040/01/359.jpg" pagenum="339"></pb>of the cauſe, but findeth no fault with the method of it; that <lb></lb>is, denieth that there is any mutation to be ſeen in the altitude of <lb></lb>the Pole, but doth not blame the inquiſition, for not being adap <lb></lb>ted to the finding of what is ſought, he thereby ſheweth, that he <lb></lb>alſo eſtecemed the Polar altitude varied, or not varied every ſix <lb></lb>moneths, to be a good teſtimony to diſprove or inferre the annual <lb></lb>motion of the Earth.</s></p><p type="margin"><s><margin.target id="marg637"></margin.target><emph type="italics"></emph>A ſtronomeys, <lb></lb>perhaps, have not <lb></lb>known what ap <lb></lb>pearances ought to <lb></lb>follow upon the an <lb></lb>nual motion of the <lb></lb>Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg638"></margin.target>Copernicus <emph type="italics"></emph>un <lb></lb>derſtood not ſome <lb></lb>things for want of <lb></lb>Inſtruments.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg639"></margin.target>Tycho <emph type="italics"></emph>and o <lb></lb>thers argue a <lb></lb>gainſt the annual <lb></lb>motion, from the <lb></lb>invariable eleva <lb></lb>tion of the Pole.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg640"></margin.target>* Chriſiophoius <lb></lb>Rothmannus.</s></p><p type="main"><s>SIMP. </s><s>In truth, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> my opinion alſo tells me, that the <lb></lb>ſame muſt neceſſarily enſue: for I do not think that you will de <lb></lb>ny me, but that if we walk only 60. miles towards the North, <lb></lb>the Pole will riſe unto us a degree higher, and that if we move <lb></lb>60. miles farther Northwards, the Pole will be elevated to us a <lb></lb>degree more, &c. </s><s>Now if the approaching or receding 60. miles <lb></lb>onely, make ſo notable a change in the Polar altitudes, what <lb></lb>alteration would follow, if the Earth and we with it, ſhould <lb></lb>be tranſported, I will not ſay 60. miles, but 60. thouſand miles <lb></lb>that way.</s></p><p type="main"><s>SALV. </s><s>It would follow (if it ſhould proceed in the ſame <lb></lb>proportion) that the Pole ſhall be elevated a thouſand degrees. <lb></lb></s><s>See, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> what a long rooted opinion can do. </s><s>Yea, by <lb></lb>reaſon you have fixed it in your mind for ſo many years, that it <lb></lb>is Heaven, that revolveth in twenty four hours, and not the <lb></lb>Earth, and that conſequently the Poles of that Revolution are in <lb></lb>Heaven, and not in the Terreſtrial Globe, cannot now, in an <lb></lb>hours time ſhake off this habituated conceipt, and take up the <lb></lb>contrary, fancying to your ſelf, that the Earth is that which mo <lb></lb>veth, only for ſo long time as may ſuffice to conceive of what <lb></lb>would follow, thereupon ſhould that lye be a truth. </s><s>If the Earth <lb></lb><emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> be that which moveth in its ſelf in twenty four hours, <lb></lb>in it are the Poles, in it is the Axis, in it is the Equinoctial, that <lb></lb>is, the grand Circle, deſcribed by the point, equidiſtant from the <lb></lb>Poles, in it are the inſinite Parallels bigger and leſſer deſcribed by <lb></lb>the points of the ſuperficies more and leſſe diſtant from the Poles, <lb></lb>in it are all theſe things, and not in the ſtarry Sphere, which, as <lb></lb>being immoveable, wants them all, and can only by the imagina <lb></lb>tion be conceived to be therein, prolonging the Axis of the Earth <lb></lb>ſo far, till that determining, it ſhall mark out two points placed <lb></lb>right over our Poles, and the plane of the Equinoctial being ex <lb></lb>tended, it ſhall deſcribe in Heaven a circle like it ſelf. </s><s>Now if the <lb></lb>true Axis, the true Poles, the true Equinoctial, do not change <lb></lb>in the Earth ſo long as you continue in the ſame place of the <lb></lb>Earth, and though the Earth be tranſported, as you do pleaſe, <lb></lb>yet you ſhall not change your habitude either to the Poles, or to <lb></lb>the circles, or to any other Earthly thing; and this becauſe, that <lb></lb>that tranſpoſition being common to you and to all Terreſtrial <pb xlink:href="040/01/360.jpg" pagenum="340"></pb>things; and that motion where it is common, is as if it never <lb></lb><arrow.to.target n="marg641"></arrow.to.target> <lb></lb>were; and as you change not habitude to the Terreſtrial Poles <lb></lb>(habitude I ſay, whether that they riſe, or deſcend) ſo neither <lb></lb>ſhall you change poſition to the Poles imagined in Heaven; al <lb></lb>wayes provided that by Celeſtial Poles we underſtand (as hath <lb></lb>been already defined) thoſe two points that come to be marked <lb></lb>out by the prolongation of the Terreſtrial Axis unto that length. <lb></lb></s><s>Tis true thoſe points in Heaven do change, when the Earths tran <lb></lb>ſportment is made after ſuch a manner, that its Axis cometh to <lb></lb>paſſe by other and other points of the immoveable Celeſtial <lb></lb>Sphere, but our habitude thereunto changeth not, ſo as that the <lb></lb>ſecond ſhould be more elevated to us than the firſt. </s><s>If any one <lb></lb>will have one of the points of the Firmament, which do anſwer <lb></lb>to the Poles of the Earth to aſcend, and the other to deſcend, <lb></lb>he muſt walk along the Earth towards the one, receding from the <lb></lb>other, for the tranſportment of the Earth, and with it us our <lb></lb>ſelves, (as I told you before) operates nothing at all.</s></p><p type="margin"><s><margin.target id="marg641"></margin.target><emph type="italics"></emph>Motion where <lb></lb>it is common, is as <lb></lb>if it never were.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Permit me, I beſeech you <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> to make this a <lb></lb>little more clear by an example, which although groſſe, is a <lb></lb>commodated to this purpoſe. </s><s>Suppoſe your ſelf, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> to <lb></lb><arrow.to.target n="marg642"></arrow.to.target> <lb></lb>be aboard a Ship, and that ſtanding in the Poope, or Hin-deck; <lb></lb>you have directed a Quadrant, or ſome other Aſtronomical In <lb></lb>ſtrument, towards the top of the Top-gallant-Maſt, as if you <lb></lb>would take its height, which ſuppoſe it were <emph type="italics"></emph>v. </s><s>gr.<emph.end type="italics"></emph.end> 40. degrees, <lb></lb><arrow.to.target n="marg643"></arrow.to.target> <lb></lb>there is no doubt, but that if you walk along the ^{*} Hatches to <lb></lb>wards the Maſt 25. or 30. paces; and then again direct the ſaid <lb></lb>Inſtrument to the ſame Top-Gallant-Top. </s><s>You ſhall find its ele <lb></lb>vation to be greater, and to be encreaſed <emph type="italics"></emph>v. </s><s>gr.<emph.end type="italics"></emph.end> 10. degrees; but <lb></lb>if inſtead of walking thoſe 25. or 30. paces towards the Maſt, <lb></lb>you ſtand ſtill at the Sterne, and make the whole Ship to move <lb></lb>thitherwards, do you believe that by reaſon of the 25. or 30. <lb></lb>paces that it had paſt, the elevation of the Top-Gallant-Top <lb></lb>would ſhew 10. degrees encreaſed?</s></p><p type="margin"><s><margin.target id="marg642"></margin.target><emph type="italics"></emph>An example fit <lb></lb>ted to prove that <lb></lb>the altitude of the <lb></lb>Pole ought not to <lb></lb>vary by means of <lb></lb>the Earths annual <lb></lb>motion.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg643"></margin.target>* <emph type="italics"></emph>Corſia,<emph.end type="italics"></emph.end> the bank <lb></lb>or bench on which <lb></lb>ſlaves ſit in a Gal <lb></lb>ly.</s></p><p type="main"><s>SIMP. </s><s>I believe and know that it would not gain an hairs <lb></lb>breadth in the paſſing of 30. paces, nor of a thouſand, no nor of <lb></lb>an hundred thouſand miles; but yet I believe withal that look <lb></lb>ing through the ſights at the Top and Top-Gallant, if I ſhould <lb></lb>find a fixed Star that was in the ſame elevation, I believe I ſay, <lb></lb>that, holding ſtill the Quadrant, after I had ſailed towards the <lb></lb>ſtar 60. miles, the eye would meet with the top of the ſaid <lb></lb>Maſt, as before, but not with the ſtar, which would be eleva <lb></lb>ted to me one degree.</s></p><p type="main"><s>SAGR. </s><s>Then you do not think that the ſight would fall upon <lb></lb>that point of the Starry Sphere, that anſwereth to the direction <lb></lb>of the Top-Gallant Top?</s></p> <pb xlink:href="040/01/361.jpg" pagenum="341"></pb><p type="main"><s>SIMP. No: For the point would be changed, and would be <lb></lb>beneath the ſtar firſt obſerved.</s></p><p type="main"><s>SAGR. </s><s>You are in the right. </s><s>Now like as that which in this <lb></lb>example anſwereth to the elevation of the Top-Gallant-Top, is <lb></lb>not the ſtar, but the point of the Firmament that lyeth in a right <lb></lb>line with the eye, and the ſaid top of the Maſt, ſo in the caſe <lb></lb>exemplified, that which in the Firmament anſwers to the Pole <lb></lb>of the Earth, is not a ſtar, or other fixed thing in the Firma <lb></lb>ment; but is that point in which the Axis of the Earth continu <lb></lb>ed ſtreight out, till it cometh thither doth determine, which point <lb></lb>is not fixed, but obeyeth the mutations that the Pole of the <lb></lb>Earth doth make. </s><s>And therefore <emph type="italics"></emph>Tycho,<emph.end type="italics"></emph.end> or who ever elſe that <lb></lb><arrow.to.target n="marg644"></arrow.to.target> <lb></lb>did alledg this objection, ought to have ſaid that upon that <lb></lb>ſame motion of the Earth, were it true, one might obſerve ſome <lb></lb>difference in the elevation and depreſſion (not of the Pole, but) <lb></lb>of ſome fixed ſtar toward that part which anſwereth to our Pole.</s></p><p type="margin"><s><margin.target id="marg644"></margin.target><emph type="italics"></emph>Upon the annu <lb></lb>al motion of the <lb></lb>Earth, alteration <lb></lb>may enſue in <lb></lb>ſome fixed ſtar, <lb></lb>not in the Pole.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I already very well underſtand the miſtake by them <lb></lb>committed; but yet therefore (which to me ſeems very great) of <lb></lb>the argument brought on the contrary is not leſſened, ſuppo <lb></lb>ſing relation to be had to the variation of the ſtars, and not of <lb></lb>the Pole; for if the moving of the Ship but 60. miles, make a <lb></lb>fixed ſtar riſe to me one degree, ſhall I not find alike, yea and <lb></lb>very much greater mutation, if the Ship ſhould ſail towards the <lb></lb>ſaid ſtar for ſo much ſpace as is the Diameter of the Grand <lb></lb>Orb, which you affirm to be double the diſtance that is between <lb></lb>the Earth and Sun?</s></p><p type="main"><s>SAGR. </s><s>Herein <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> there is another fallacy, which, <lb></lb><arrow.to.target n="marg645"></arrow.to.target> <lb></lb>truth is, you underſtand, but do not upon the ſudden think of <lb></lb>the ſame, but I will try to bring it to your remembrance: Tell <lb></lb>me therefore; if when after you have directed the Quadrant to <lb></lb>a fixed ſtar, and found <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> its elevation to be 40. degrees, <lb></lb>you ſhould without ſtirring from the place, incline the ſide of <lb></lb>the Ouadrant, ſo as that the ſtar might remain elevated above <lb></lb>that direction, would you thereupon ſay that the ſtar had acqui <lb></lb>red greater elevation?</s></p><p type="margin"><s><margin.target id="marg645"></margin.target><emph type="italics"></emph>The equivoke of <lb></lb>thoſe who believe <lb></lb>that in the annual <lb></lb>motion great mu <lb></lb>tations are to be <lb></lb>made about the <lb></lb>elevation of a fix <lb></lb>ed ſtar, is confu <lb></lb>ted.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>Certainly no: For the mutation was made in the In <lb></lb>ſtrument and not in the Obſerver, that did change place, mo <lb></lb>ving towards the ſame.</s></p><p type="main"><s>SAGR. </s><s>But if you ſail or walk along the ſurface of the Terre <lb></lb>ſtrial Globe, will you ſay that there is no alteration made in the <lb></lb>ſaid Quadrant, but that the ſame elevarion is ſtill retained in re <lb></lb>ſpect of the Heavens, ſo long as you your ſelf do not incline it, <lb></lb>but let it ſtand at its firſt conſtitution?</s></p><p type="main"><s>SIMP. </s><s>Give me leave to think of it. </s><s>I would ſay without <lb></lb>more ado, that it would not retain the ſame, in regard the pro <pb xlink:href="040/01/362.jpg" pagenum="342"></pb>greſſe I make is not <emph type="italics"></emph>in plano,<emph.end type="italics"></emph.end> but about the circumference of the <lb></lb>Terreſtrial Globe, which at every ſtep changeth inclination in <lb></lb>reſpect to Heaven, and conſequently maketh the ſame change <lb></lb>in the Inſtrument which is erected upon the ſame.</s></p><p type="main"><s>SAGR. </s><s>You ſay very well: And you know withal, that by <lb></lb>how much the bigger that circle ſhall be upon which you move, <lb></lb>ſo many more miles you are to walk, to make the ſaid ſtar to <lb></lb>riſe that ſame degree higher; and that ſinally if the motion to <lb></lb>wards the ſtar ſhould be in a right line, you ought to move yet <lb></lb>farther, than if it were about the circumference of never ſo <lb></lb>great a circle? <lb></lb><arrow.to.target n="marg646"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg646"></margin.target><emph type="italics"></emph>The right line, <lb></lb>and circumference <lb></lb>of an infinite cir <lb></lb>cle, are the ſame <lb></lb>thing.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. True: For in ſhort the circumference of an infinite <lb></lb>circle, and a right line are the ſame thing.</s></p><p type="main"><s>SAGR. </s><s>But this I do not underſtand, nor as I believe, doth <lb></lb><emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> apprehend the ſame; and it muſt needs be concealed <lb></lb>from us under ſome miſtery, for we know that <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> never <lb></lb>ſpeaks at random, nor propoſeth any Paradox, which doth not <lb></lb>break forth into ſome conceit, not trivial in the leaſt. </s><s>Therefore <lb></lb>in due time and place I will put you in mind to demonſtrate this, <lb></lb>that the right line is the ſame with the circumference of an infi <lb></lb>nite circle, but at preſent I am unwilling that we ſhould inter <lb></lb>rupt the diſcourſe in hand. </s><s>Returning then to the caſe, I pro <lb></lb>poſe to the conſideration of <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> how the acceſſion and <lb></lb>receſſion that the Earth makes from the ſaid fixed ſtar which is <lb></lb>neer the Pole can be made as it were by a right line, for ſuch is <lb></lb>the Diameter of the Grand Orb, ſo that the attempting to re <lb></lb>gulate the elevation and depreſſion of the Polar ſtar by the mo <lb></lb>tion along the ſaid Diameter, as if it were by the motion about <lb></lb>the little circle of the Earth, is a great argument of but little <lb></lb>judgment.</s></p><p type="main"><s>SIMP. </s><s>But we continue ſtill unſatisfied, in regard that the <lb></lb>ſaid ſmall mutation that ſhould be therein, would not be diſcer <lb></lb>ned; and if this be <emph type="italics"></emph>null,<emph.end type="italics"></emph.end> then muſt the annual motion about <lb></lb>the Grand Orb aſcribed to the Earth, be <emph type="italics"></emph>null<emph.end type="italics"></emph.end> alſo.</s></p><p type="main"><s>SAGR. </s><s>Here now I give <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> leave to go on, who as I <lb></lb>believe will not overpaſſe the elevation and depreſſion of the <lb></lb>Polar ſtar or any other of thoſe that are fixed as <emph type="italics"></emph>null,<emph.end type="italics"></emph.end> although <lb></lb>not diſcovered by any one, and affirmed by <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> himſelf <lb></lb>to be, I will not ſay <emph type="italics"></emph>null,<emph.end type="italics"></emph.end> but unobſervable by reaſon of its <lb></lb>minuity.</s></p><p type="main"><s>SALV. </s><s>I have already ſaid above, that I do not think that </s></p><p type="main"><s><arrow.to.target n="marg647"></arrow.to.target> <lb></lb>any one did ever ſet himſelf to obſerve, whether in different times <lb></lb>of the year there is any mutation to be ſeen in the fixed ſtars, that <lb></lb>may have a dependance on the annual motion of the Earth, and <lb></lb>added withal, that I doubted leaſt haply ſome might never have <pb xlink:href="040/01/363.jpg" pagenum="343"></pb>underſtood what thoſe mutations are, and amongſt what ſtars <lb></lb>they ſhould be diſcerned; therefore it would be neceſſary that <lb></lb>we in the next place narrowly examine this particular. </s><s>My ha <lb></lb><arrow.to.target n="marg648"></arrow.to.target> <lb></lb>ving onely found written in general terms that the annual moti <lb></lb>on of the Earth about the Grand Orb, ought not to be admit <lb></lb>ted, becauſe it is not probable but that by means of the ſame <lb></lb>there would be diſcoverd ſome apparent mutation in the fixed <lb></lb>ſtars, and not hearing ſay what thoſe apparent mutations ought to <lb></lb>be in particular, and in what ſtars, maketh me very reaſonably <lb></lb>to infer that they who rely upon that general poſition, have not <lb></lb>underſtood, no nor poſſibly endeavoured to underſtand, how <lb></lb>the buſineſſe of theſe mutations goeth, nor what things thoſe <lb></lb>are which they ſay ought to be ſeen. </s><s>And to this judgment I am <lb></lb><arrow.to.target n="marg649"></arrow.to.target> <lb></lb>the rather induced, knowing that the annual motion aſcribed <lb></lb>by <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> to the Earth, if it ſhould appear ſenſible in the <lb></lb>Starry Sphere, is not to make apparent mutations equal in re <lb></lb>ſpect to all the ſtars, but thoſe appearances ought to be made <lb></lb>in ſome greater, in others leſſer, and in others yet leſſer; and <lb></lb>laſtly, in others abſolutely nothing at all, by reaſon of the <lb></lb>vaſt magnitude that the circle of this annual motion is ſuppoſed <lb></lb>to be of. </s><s>As for the mutations that ſhould b ſeen, they are of <lb></lb>two kinds, one is the ſaid ſtars changing apparent magnitude, <lb></lb>and the other their variation of altitudes in the Meridian. </s><s>Upon <lb></lb>which neceſſarily followeth the mutation of riſings and ſettings, <lb></lb>and of their diſtances from the Zenith, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg647"></margin.target><emph type="italics"></emph>Enquiry is made <lb></lb>what mutations, & <lb></lb>in what ſtars, are to <lb></lb>be diſcovered, by <lb></lb>means of the an <lb></lb>nual motion of the <lb></lb>Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg648"></margin.target><emph type="italics"></emph>Aſtronomers ha <lb></lb>ving omitted to in <lb></lb>ſtance what alte <lb></lb>rations thoſe are <lb></lb>that may be deri <lb></lb>ved from the an <lb></lb>nual motion of the <lb></lb>Earth, do thereby <lb></lb>teſtifie that they <lb></lb>never rightly un <lb></lb>derſtood the ſame.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg649"></margin.target><emph type="italics"></emph>The mutations <lb></lb>of the fixed ſtars <lb></lb>ought to be in ſome <lb></lb>greater, in others <lb></lb>leſſer, and in others <lb></lb>nothing at all.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Methinks I ſee preparing for me ſuch a skean of theſe <lb></lb>revolutions, that I wiſh it may never be my task to diſ-intangle <lb></lb>them, for to confeſſe my infirmity to <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> I have ſome <lb></lb>times thought thereon, but could never find the ^{*} Lay-band of <lb></lb><arrow.to.target n="marg650"></arrow.to.target> <lb></lb>it, and I ſpeak not ſo much of this which pertains to the fixed <lb></lb>ſtars, as of another more terrible labour which you bring to my <lb></lb>remembrance by maintaining theſe Meridian Altitudes, Ortive <lb></lb>Latitudes and diſtances from the Vertex, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> And that which <lb></lb><arrow.to.target n="marg651"></arrow.to.target> <lb></lb>puzzleth my brains, ariſeth from what I am now about to tell <lb></lb>you. <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> ſuppoſeth the Starry Sphere immoveable, and <lb></lb>the Sun in the centre thereof immoveable alſo. </s><s>Therefore eve <lb></lb>ry mutation which ſeemeth unto us to be made in the Sun or in <lb></lb>the fixed ſtars, muſt of neceſſity befall the Earth and be ous. <lb></lb></s><s>But the Sun riſeth and declineth in our Meridian by a very great <lb></lb>arch of almoſt 47. degrees, and by arches yet greater and <lb></lb>greatet, varieth its Ortive and Occidual Latitudes in the oblique <lb></lb><arrow.to.target n="marg652"></arrow.to.target> <lb></lb>Horizons. </s><s>Now how can the Earth ever incline and elevate ſo <lb></lb>notably to the Sun, and nothing at all to the fixed ſtars, or ſo <lb></lb>little, that it is not to be perceived? </s><s>This is that knot which <lb></lb>could never get thorow my ^{*} Loom-Combe; and if you ſhall <pb xlink:href="040/01/364.jpg" pagenum="344"></pb>untie it, I ſhall hold you for more than an <emph type="italics"></emph>Alexander.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg650"></margin.target>* <emph type="italics"></emph>Bandola<emph.end type="italics"></emph.end> that <lb></lb>end of a skeen <lb></lb>where with houſe <lb></lb>wives faſten their <lb></lb>hankes of yarn, <lb></lb>thread or ſilk.</s></p><p type="margin"><s><margin.target id="marg651"></margin.target><emph type="italics"></emph>The grand dif <lb></lb>ficulty in<emph.end type="italics"></emph.end> Coper <lb></lb>nicus <emph type="italics"></emph>his Doctrine, <lb></lb>is that which con <lb></lb>cerns the<emph.end type="italics"></emph.end> Phæno <lb></lb>mena <emph type="italics"></emph>of the Sun <lb></lb>and fixed ſtars.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg652"></margin.target>* <emph type="italics"></emph>Pettine,<emph.end type="italics"></emph.end> it is <lb></lb>the ſtay in a Wea <lb></lb>vets Loom, that <lb></lb>permitteth no knot <lb></lb>or ſnarle to paſſe <lb></lb>it, called by them <lb></lb>the Combe of the <lb></lb>Loom.</s></p><p type="main"><s>SALV. </s><s>Theſe are ſcruples worthy of the ingenuity of <emph type="italics"></emph>Sagre <lb></lb>dus,<emph.end type="italics"></emph.end> and this doubt is ſo intricate, that even <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> himſelf <lb></lb>almoſt deſpaired of being able to explain the ſame, ſo as to <lb></lb>render it intelligible, which we ſee as well by his own confeſſion <lb></lb>of its obſcurity, as alſo by his, at two ſeveral times, taking two <lb></lb>different wayes to make it out. </s><s>And, I ingenuouſly confeſſe that <lb></lb>I underſtood not his explanation, till ſuch time as another me <lb></lb>thod more plain and manifeſt, had rendred it intelligible; and <lb></lb>yet neither was that done without a long and laborious applica <lb></lb>tion of my thoughts to the ſame.</s></p><p type="main"><s>SIMP. <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſaw the ſame ſcruple, and makes uſe there <lb></lb><arrow.to.target n="marg653"></arrow.to.target> <lb></lb>of to oppoſe certain of the Ancients, who held that the Earth <lb></lb>was a Planet; againſt whom he argueth, that if it were ſo, it <lb></lb>would follow that it alſo, as the reſt of the Planets, ſhould have a <lb></lb>plurality of motions, from whence would follow theſe variati <lb></lb>ons in the riſings and ſettings of the fixed ſtars, and likewiſe in <lb></lb>the Meridian Altitudes. </s><s>And in regard that he propoundeth the <lb></lb>difficulty, and doth not anſwer it, it muſt needs be, if not im <lb></lb>poſſible, at leaſt very difficult to be reſolved.</s></p><p type="margin"><s><margin.target id="marg653"></margin.target>Ariſtotles <emph type="italics"></emph>argu <lb></lb>ment againſt the <lb></lb>Ancients, who held <lb></lb>that the Earth <lb></lb>was a Planet.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>The ſtreſſe and ſtrength of the knot rendereth the <lb></lb>ſolution thereof more commendable and admirable; but I do <lb></lb>not promiſe you the ſame at this time, and pray you to diſpenſe <lb></lb>with me therein till too morrow, and for the preſent we will go <lb></lb>conſidering and explaining thoſe mutations and differences that <lb></lb>by means of the annual motion ought to be diſcerned in the fix <lb></lb>ed ſtars, like as even now we ſaid, for the explication whereof <lb></lb>certain preparatory points offer themſelves, which may facili <lb></lb>tate the anſwer to the grand objection. </s><s>Now reaſſuming the <lb></lb>two motions aſcribed to the Earth (two I ſay, for the third is <lb></lb>no motion, as in its place I will declare) that is the annual and <lb></lb><arrow.to.target n="marg654"></arrow.to.target> <lb></lb>diurnal, the firſt is to be underſtood to be made by the centre of <lb></lb>the Earth in or about the circumference of the grand Orb, that <lb></lb>is of a very great circle deſcribed in the plain of the fixed and <lb></lb>immutable Ecliptick; the other, namely the diurnal, is made <lb></lb>by the Globe of the Earth in it ſelf about its own centre, and <lb></lb>own Axis, not erect, but inclined to the Plane of the Ecliptick, <lb></lb>with the inclination of 23. degrees and an half, or thereabouts, <lb></lb>the which inclination is maintained all the year about, and that <lb></lb>which ought eſpecially to be obſerved, is alwayes ſituate to <lb></lb>wards the ſame point of Heaven: in ſo much that the Axis of the <lb></lb><arrow.to.target n="marg655"></arrow.to.target> <lb></lb>diurnal motion doth alwayes remain parallel to it ſelf; ſo that <lb></lb>if we imagine that ſame Axis to be continued out until it reach <lb></lb>the fixed ſtars, whilſt the centre of the Earth is encircling the <lb></lb>whole Ecliptick in a year, the ſaid Axis deſcribeth the ſuper <pb xlink:href="040/01/365.jpg" pagenum="345"></pb>ficies of an oblique Cylinder, which hath for one of its baſes <lb></lb>the ſaid annual circle, and for the other a like circle imagina <lb></lb>rily deſcribed by its extremity, or, (if you will) Pole, amongſt <lb></lb>the fixed ſtars. </s><s>And this ſame cylinder is oblique to the Plane of <lb></lb>the Ecliptick, according to the inclination of the Axis that de <lb></lb>ſcribeth it, which we have ſaid to be 23 degrees and an half, <lb></lb>the which continuing perpetually the ſame (ſave onely, that in <lb></lb>many thouſands of years it maketh ſome very ſmall mutation, <lb></lb>which nothing importeth in our preſent buſineſſe) cauſeth that <lb></lb><arrow.to.target n="marg656"></arrow.to.target> <lb></lb>the Terreſtrial Globe doth never more incline or elevate, but <lb></lb>ſtill conſerveth the ſame ſtate without mutation. </s><s>From whence <lb></lb>enſueth, that as to what pertaineth to the mutations to be ob <lb></lb>ſerved in the fixed ſtars dependant on the ſole annual motion, <lb></lb>the ſame ſhall happen to any point whatſoever of the Earths <lb></lb>ſurface, as befalleth unto the centre of the Earth it ſelf; and <lb></lb>therefore in the preſent explanations we will make uſe of the <lb></lb>centre, as if it were any whatſoever point of the ſuperficies. <lb></lb></s><s>And for a more facile underſtanding of the whole, let us deſign <lb></lb><arrow.to.target n="marg657"></arrow.to.target> <lb></lb>the ſame in lineal figures: And firſt of all let us deſcribe in the <lb></lb>Plane of the Ecliptick the circle A N B O [<emph type="italics"></emph>in Fig.<emph.end type="italics"></emph.end> 7.] and let <lb></lb>us underſtand the points A and B, to be the extreams towards <lb></lb>the North and South; that is, the beginning of [<emph type="italics"></emph>or entrance into<emph.end type="italics"></emph.end>] <lb></lb><emph type="italics"></emph>Cancer<emph.end type="italics"></emph.end> or <emph type="italics"></emph>Capricorn,<emph.end type="italics"></emph.end> and let us prolong the Diameter A B, in <lb></lb>determinately by D and C towards the Starry Sphere. </s><s>I ſay <lb></lb>now in the firſt place, that none of the fixed ſtars placed in the <lb></lb>Ecliptick, ſhall ever vary elevation, by reaſon of any whatſo <lb></lb>ever mutation made by the Earth along the ſaid Plane of the <lb></lb>Ecliptick, but ſhall alwayes appear in the ſame ſuperficies, al <lb></lb>though the Earth ſhall approach and recede as great a ſpace as is <lb></lb>that of the diameter of the Grand Orb, as may plainly be <lb></lb>ſeen in the ſaid figure. </s><s>For whether the Earth be in the point <lb></lb>A or in B, the ſtar C alwayes appeareth in the ſame line A B C; <lb></lb>although the diſtance B C, be leſſe than A C, by the whole <lb></lb>diameter A B. </s><s>The moſt therefore that can be diſcovered in the <lb></lb>ſtar C, and in any other placed in the Ecliptick, is the aug <lb></lb>mented or diminiſhed apparent magnitude, by reaſon of the ap <lb></lb>proximation or receſſion of the Earth.</s></p><p type="margin"><s><margin.target id="marg654"></margin.target><emph type="italics"></emph>The annual mo <lb></lb>tion made by the <lb></lb>centre of the Earth <lb></lb>under the Eclip <lb></lb>tick and the diur <lb></lb>nal motion made <lb></lb>by the Earth about <lb></lb>its own centre.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg655"></margin.target><emph type="italics"></emph>The axis of the <lb></lb>Earth continueth <lb></lb>alwayes parallel to <lb></lb>it ſelf, and deſcri <lb></lb>beth a Cylindrai <lb></lb>cal ſuperficies, in <lb></lb>clining to the <lb></lb>grand Orb.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg656"></margin.target><emph type="italics"></emph>The Orb of the <lb></lb>Earth never incli <lb></lb>neth, but is im <lb></lb>mutably the ſame.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg657"></margin.target><emph type="italics"></emph>The fixed ſtars <lb></lb>placed in the E <lb></lb>cliptick never ele <lb></lb>vate nor deſcend, <lb></lb>on account of the <lb></lb>annual motion, but <lb></lb>yet approach and <lb></lb>recede.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Stay a while I pray you, for I meet with a certain <lb></lb>ſcruple, which much troubleth me, and it is this: That the ſtar <lb></lb>C may be ſeen by the ſame line A B C, as wel when the Earth <lb></lb>is in A, as when it is in B, I underſtand very well, as alſo fur <lb></lb>thermore I apprehend that the ſame would happen in all the <lb></lb><arrow.to.target n="marg658"></arrow.to.target> <lb></lb>points of the line A B, ſo long as the Earth ſhould paſſe from A <lb></lb>to B by the ſaid line; but it paſſing thither, as is to be ſuppoſed, <lb></lb>by the arch A N B, it is manifeſt that when it ſhall be in the <pb xlink:href="040/01/366.jpg" pagenum="346"></pb>point N, and in any other except thoſe two A and B, the ſaid <lb></lb>ſtar ſhall no longer be obſerved in the line A B; but in others. <lb></lb></s><s>So that, if the appearing under ſeveral lines ought to cauſe <lb></lb>apparent mutations, ſome difference muſt needs appear in <lb></lb>this caſe. </s><s>Nay more, I will ſpeak it with that Philoſophical <lb></lb>freedom, which ought to be allowed amongſt Philoſophick <lb></lb>friends, methinks that you, contradicting your ſelf, deny that <lb></lb>now, which but even now to our admiration, you proved to be <lb></lb>really true, and conſiderable; I mean that which happeneth in <lb></lb>the Planets, and particularly in the three ſuperiour ones, that <lb></lb>being conſtantly in the Ecliptick, or very near unto it, do not <lb></lb>onely ſhew themſelves one while near unto us, and another <lb></lb>while remote, but ſo deformed in their regular motions, that <lb></lb>they ſeem ſometimes immoveable, and ſometimes many de <lb></lb>grees retrograde; and all upon no other occaſion than the an <lb></lb>nual motion of the Earth.</s></p><p type="margin"><s><margin.target id="marg658"></margin.target><emph type="italics"></emph>Objections againſt <lb></lb>the Earths annual <lb></lb>motion taken from <lb></lb>the fixed stars <lb></lb>placed in the E <lb></lb>cliptick.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Though by a thouſand accidents I have been hereto <lb></lb>fore aſſured of the wittineſſe of <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> yet I had a deſire by <lb></lb>this one experiment more to aſcertain me of what I may expect <lb></lb>from his ingenuity, and all this for my own intereſt, for in caſe <lb></lb>my Propoſitions ſtand but proof againſt the hammer and fur <lb></lb>nace of his judgment, I ſhall be confident that they will abide <lb></lb><arrow.to.target n="marg659"></arrow.to.target> <lb></lb>the ^{*} teſt of all Touch-ſtones. </s><s>I ſay therefore that I had pur <lb></lb>poſely diſſembled this objection, but yet not with any intent to <lb></lb>deceive you, and to put any falſhood upon you, as it might <lb></lb>have happened if the objection by me diſguiſed, and by you o <lb></lb>ver-lookt, had been the ſame in effect as it ſeemed to be in ap <lb></lb>pearance, that is, really valid and concluſive; but it is not ſo; <lb></lb>nay I rather ſuſpect that to try me, you make as if you did not <lb></lb>ſee its nullity. </s><s>But I will herein be too hard for you, and force <lb></lb>from your tongue, that which you would ſo artificially conceal; <lb></lb>and therefore tell me, what that thing ſhould be, whereby you <lb></lb>come to know the ſtation and retrogradation of the Planets, <lb></lb>which is derived from the annual motion, aud which is ſo great, <lb></lb>that at leaſt ſome foot-ſteps of ſuch an effect ought to appear in <lb></lb>the ſtars of the Ecliptick?</s></p><p type="margin"><s><margin.target id="marg659"></margin.target>* Or will prove <lb></lb>of good alloy.</s></p><p type="main"><s>SAGR. </s><s>This demand of yours containeth two queſtions, to <lb></lb>which it is neceſſary that I make reply; the firſt relates to the <lb></lb>imputation which you lay upon me of a Diſſembler; the other <lb></lb>concerneth that which may appear in the ſtars, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> As to the <lb></lb>firſt, I will ſay with your permiſſion, that it is not true, that I <lb></lb>have diſſembled my knowing the nullity of that objection; and <lb></lb>to aſſure you of the ſame, I now tell you that I very well under <lb></lb>ſtand the nullity thereof.</s></p><p type="main"><s>SALV. </s><s>But yet I do not underſtand how it can be, that you <pb xlink:href="040/01/367.jpg" pagenum="347"></pb>ſpake not friendly, when you ſaid you did not know that ſame <lb></lb>fallacy which you now confeſſe that you know very well.</s></p><p type="main"><s>SAGR. </s><s>The very confeſſion of knowing it may aſſure you <lb></lb>that I did not diſſemble, when I ſaid that I did not underſtand it; <lb></lb>for if I had had a mind, and would diſſemble, who could hin <lb></lb>der me from continuing in the ſame ſimulation, and denying ſtill <lb></lb>that I underſtand the fallacy? </s><s>I ſay therefore that I underſtood <lb></lb>not the ſame, at that time, but that I do now at this preſent ap <lb></lb>prehend it, for that you have prompted my intellect, firſt by <lb></lb>telling me reſolutely that it is <emph type="italics"></emph>null,<emph.end type="italics"></emph.end> and then by beginning to <lb></lb>queſtion me ſo at large what thing that might be, whereby I <lb></lb>might come to know the ſtation and retrogradation of the Pla <lb></lb><arrow.to.target n="marg660"></arrow.to.target> <lb></lb>nets; and becauſe this is known by comparing them with the fix <lb></lb>ed ſtars, in relation to which, they are ſeen to vary their mo <lb></lb>tions, one while towards the Weſt, and another towards the <lb></lb>Eaſt, and ſometimes to abide immoveable; and becauſe there <lb></lb>is not any thing above the Starry Sphere, immenſely more remote <lb></lb>from us, and viſible unto us, wherewith we may compare our <lb></lb>fixed ſtars, therefore we cannot diſcover in the fixed ſtars any <lb></lb>foot-ſteps of what appeareth to us in the Planets. </s><s>This I believe <lb></lb>is the ſubſtance of that which you would force from me.</s></p><p type="margin"><s><margin.target id="marg660"></margin.target><emph type="italics"></emph>The ſtation, di <lb></lb>rection and retro <lb></lb>gradation of the <lb></lb>Planets is known, <lb></lb>in relation to the <lb></lb>fixed ſtars.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>It is ſo, with the addition moreover of your admi <lb></lb><arrow.to.target n="marg661"></arrow.to.target> <lb></lb>rable ingenuity; and if with half a word I did open your eyes, <lb></lb>you by the like have remembred me that it is not altogether im <lb></lb>poſſible, but that ſometime or other ſomething obſervable may <lb></lb>be found amongſt the fixed ſtars, by which it may be gathered <lb></lb>wherein the annual converſion reſides, ſo as that they alſo no <lb></lb>leſſe than the Planets and Sun it ſelf, may appear in judgment to <lb></lb>bear witneſſe of that motion, in favour of the Earth; for I do not <lb></lb>think that the ſtas are ſpread in a ſpherical ſuperficies equally re <lb></lb>mote from a common centre, but hold, that their diſtances from <lb></lb>us are ſo various, that ſome of them may be twice and thrice as <lb></lb>remote as others; ſo that if with the Teleſcope one ſhould ob <lb></lb>ſerve a very ſmall ſtar neer to one of the bigger, and which <lb></lb>therefore was very exceeding high, it might happen that ſome <lb></lb>ſenſible mutation might fall out between them, correſpondent <lb></lb>to that of the ſuperiour Planets. </s><s>And ſo much ſhall ſerve to have <lb></lb>ſpoken at this time touching the ſtars placed in the Ecliptick. <lb></lb><arrow.to.target n="marg662"></arrow.to.target> <lb></lb>Let us now come to the fixed ſtars, placed out of the Ecliptick, <lb></lb>and let us ſuppoſe a great circle erect upor [<emph type="italics"></emph>i. </s><s>e. </s><s>at right angles <lb></lb>to<emph.end type="italics"></emph.end>] the Plane of the ^{*} ſame; and let it, for example, be a cir <lb></lb>cle that in the Starry Sphere anſwers to the Solſtitial Colure, <lb></lb><arrow.to.target n="marg663"></arrow.to.target> <lb></lb>and let us mark it C E H [<emph type="italics"></emph>in Fig.<emph.end type="italics"></emph.end> 8.] which ſhall happen to be <lb></lb>withal a Meridian, and in it we will take a ſtar without the Eclip <lb></lb>tick, which let be E. </s><s>Now this ſtar will indeed vary its elevati <pb xlink:href="040/01/368.jpg" pagenum="348"></pb>on upon the Earths motion; for from the Earth in A it ſhall be <lb></lb>ſeen according to the ray A E, with the elevation of the angle <lb></lb>E A C; but from the Earth placed in B, it ſhall be ſeen ac <lb></lb>cording to the ray B E, with the elevation of the angle E B C, <lb></lb>bigger than the other E A C, that being extern, and this in <lb></lb>tern and oppoſite in the triangle E A B, the diſtance therefore <lb></lb>of the ſtar E from the Ecliptick, ſhall appear changed; and <lb></lb>likewiſe its altitude in the Meridian ſhall become greater in the <lb></lb>poſition B, than in the place A, according as the angle E B C <lb></lb>exceeds the angle E A C, which exceſſe is the quantity of the <lb></lb>angle A E B: For in the triangle E A B, the ſide A B being <lb></lb>continued to C, the exteriour angle E B C (as being equal to <lb></lb>the two interiour and oppoſite E and A) exceedeth the ſaid an <lb></lb>gle A, by the quantity of the angle <emph type="italics"></emph>E.<emph.end type="italics"></emph.end> And if we ſhould take <lb></lb>another ſtar in the ſame Meridian, more remote from the Ecli <lb></lb>ptick, as for inſtance the ſtar H, the diverſity in it ſhall be <lb></lb>greater by being obſerved from the two ſtations A and B, accor <lb></lb>ding as the angle A H B is greater than the other <emph type="italics"></emph>E<emph.end type="italics"></emph.end>; which an <lb></lb>gle ſhall encreaſe continually according as the obſerved ſtar ſhall <lb></lb>be farther and farther from the Ecliptick, till that at laſt the <lb></lb>greateſt mutation will appear in that ſtar that ſhould be placed in <lb></lb>the very Pole of the Ecliptick. </s><s>As for a full underſtanding there <lb></lb>of we thus demonſtrate. </s><s>Suppoſe the diameter of the Grand <lb></lb>Orb to be A B, whoſe centre [<emph type="italics"></emph>in the ſame Figure<emph.end type="italics"></emph.end>] is G, and <lb></lb>let it be ſuppoſed to be continued out as far as the Starry Sphere <lb></lb>in the points D and C, and from the centre G let there be erected <lb></lb>the Axis of the Ecliptick G F, prolonged till it arrive at the ſaid <lb></lb>Sphere, in which a Meridian D F C is ſuppoſed to be deſcribed, <lb></lb>that ſhall be perpendicular to the Plane of the Ecliptick; and <lb></lb>in the arch F C any points H and <emph type="italics"></emph>E,<emph.end type="italics"></emph.end> are imagined to be taken, <lb></lb>as places of fixed ſtars: Let the lines F A, F B, A H, H G, <lb></lb>H B, A <emph type="italics"></emph>E,<emph.end type="italics"></emph.end> G <emph type="italics"></emph>E,<emph.end type="italics"></emph.end> B <emph type="italics"></emph>E,<emph.end type="italics"></emph.end> be conjoyned. </s><s>And let the angle of dif <lb></lb>ference, or, if you will, the Parallax of the ſtar placed in the <lb></lb>Pole F, be A F B, and let that of the ſtar placed in H, be the <lb></lb>angle A H <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> and let that of the ſtar in <emph type="italics"></emph>E,<emph.end type="italics"></emph.end> be the angle <lb></lb>A <emph type="italics"></emph>E<emph.end type="italics"></emph.end> B. </s><s>I ſay, that the angle of difference of the Polar ſtar F, is <lb></lb>the greateſt, and that of the reſt, thoſe that are nearer to the <lb></lb>greateſt are bigger than the more remote; that is to ſay, that the <lb></lb>angle F is bigger than the angle H, and this bigger than the angle <lb></lb><emph type="italics"></emph>E.<emph.end type="italics"></emph.end> Now about the triangle F A B, let us ſuppoſe a circle to be de <lb></lb>ſcribed. </s><s>And becauſe the angle F is acute, (by reaſon that its baſe <lb></lb>AB is leſſe than the diameter DC, of the ſemicircle D F C) it ſhall <lb></lb>be placed in the greater portion of the circumſcribed circle cut <lb></lb>by the baſe A B. </s><s>And becauſe the ſaid A B is divided in the <lb></lb>midſt, and at right angles by F G, the centre of the circumſcri <pb xlink:href="040/01/369.jpg" pagenum="349"></pb>bed circle ſhall be in the line F G, which let be the point I; and <lb></lb>becauſe that of ſuch lines as are drawn from the point G, which <lb></lb>is not the centre, unto the circumference of the circumſcribed <lb></lb>circle, the biggeſt is that which paſſeth by the centre, G F ſhall <lb></lb>be bigger than any other that is drawn from the point G, to the <lb></lb>circumference of the ſaid circle; and therefore that circumfe <lb></lb>rence will cut the line G H (which is equal to the line G F) and <lb></lb>cutting G H, it will alſo cut A H. </s><s>Let it cut it in L, and con <lb></lb>joyn the line L B. </s><s>Theſe two angles, therefore, A F B and A L B <lb></lb>ſhall be equal, as being in the ſame portion of the circle cir <lb></lb>cumſcribed. </s><s>But A L B external, is bigger than the internal H; <lb></lb>therefore the angle F is bigger than the angle H. </s><s>And by the <lb></lb>ſame method we might demonſtrate the angle H to be bigger <lb></lb>than the angle E, becauſe that of the circle deſcribed about the <lb></lb>triangle A H B, the centre is in the perpendicular G F, to which <lb></lb>the line G H is nearer than the line G E, and therefore the cir <lb></lb>cumference of it cutteth G E, and alſo A E, whereupon the pro <lb></lb>poſition is manifeſt. </s><s>We will conclude from hence, that the dif <lb></lb>ference of appearance, (which with the proper term of art, we <lb></lb>might call the Parallax of the fixed ſtars) is greater, or leſſe, ac <lb></lb>cording as the Stars obſerved are more or leſſe adjacent to the <lb></lb>Pole of the Ecliptick, ſo that, in concluſion of thoſe Stars that <lb></lb>are in the Ecliptick it ſelf, the ſaid diverſity is reduced to nothing. <lb></lb></s><s>In the next place, as to the Earths acceſſion by that motion to, <lb></lb><arrow.to.target n="marg664"></arrow.to.target> <lb></lb>or receſſion from the Stars, it appeareth to, and recedeth from <lb></lb>thoſe that are in the Ecliptick, the quantity of the whole diame <lb></lb>ter of the grand Orb, as we did ſee even now, but that acceſſion <lb></lb>or receſſion to, or from the ſtars about the Pole of the Ecliptick, <lb></lb>is almoſt nothing; and in going to and from others, this diffe <lb></lb>rence groweth greater, according as they are neerer to the Eclip <lb></lb>tick. </s><s>We may, in the third place, know, that the ſaid difference <lb></lb><arrow.to.target n="marg665"></arrow.to.target> <lb></lb>of Aſpect groweth greater or leſſer, according as the Star obſer <lb></lb>ved ſhall be neerer to us, or farther from us. </s><s>For if we draw a <lb></lb>nother Meridian, leſſe diſtant from the Earth; as for example, <lb></lb>this D F I [<emph type="italics"></emph>in Fig.<emph.end type="italics"></emph.end> 7.] a Star placed in F, and ſeen by the ſame <lb></lb>ray A F E, the Earth being in A, would, in caſe it ſhould be ob <lb></lb>ſerved from the Earth in B, appear according to the ray B F, and <lb></lb>would make the angle of difference, namely, B F A, bigger <lb></lb>than the former A E B, being the exteriour angle of the trian <lb></lb>gle B F E.</s></p><p type="margin"><s><margin.target id="marg661"></margin.target><emph type="italics"></emph>An Indice in <lb></lb>the fixed ſtars like <lb></lb>to that which is <lb></lb>ſeen in the Pla <lb></lb>nets, is an argu <lb></lb>ment of the Earths <lb></lb>annual motion.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg662"></margin.target><emph type="italics"></emph>The fixed ſtars <lb></lb>without the Eclip <lb></lb>tick elevate and <lb></lb>deſcend more or <lb></lb>leſſe, according to <lb></lb>their diſtance from <lb></lb>the ſaid Ecliptick.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg663"></margin.target>* <emph type="italics"></emph>i. </s><s>e.<emph.end type="italics"></emph.end> of the E <lb></lb>cliptick.</s></p><p type="margin"><s><margin.target id="marg664"></margin.target><emph type="italics"></emph>The Earth ap <lb></lb>proacheth or rece <lb></lb>deth from the fix <lb></lb>ed ſtars of the E <lb></lb>cliptick, the quan <lb></lb>tity of the Dinme <lb></lb>ter of the Grand <lb></lb>Orb.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg665"></margin.target><emph type="italics"></emph>The ſtars near <lb></lb>er to us make <lb></lb>greater differences <lb></lb>than the more re <lb></lb>more.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>With great delight, and alſo benefit have I heard <lb></lb>your diſcourſe; and that I may be certain, whether I have right <lb></lb><arrow.to.target n="marg666"></arrow.to.target> <lb></lb>ly underſtood the ſame, I ſhall give you the ſumme of the Con <lb></lb>cluſions in a few words. </s><s>As I take it, you have explained to us <lb></lb>the different appearances, that by means of the Earths annual mo <pb xlink:href="040/01/370.jpg" pagenum="350"></pb>tion, may be by us obſerved in the fixed ſtars to be of two <lb></lb>kinds: The one is, that of their apparent magnitudes varied, ac <lb></lb>cording as we, tranſported by the Earth, approach or recede <lb></lb>from the ſame: The other (which likewiſe dependeth on the <lb></lb>ſame acceſſion and reeeſſion) their appearing unto us in the <lb></lb>ſame Meridian, one while more elevated, and another while leſſe. <lb></lb></s><s>Moreover, you tell us (and I underſtand it very well) that the <lb></lb>one and other of theſe mutations are not made alike in all the <lb></lb>ſtars, but in ſome greater, and in others leſſer, and in others not <lb></lb>at all. </s><s>The acceſſion and receſſion whereby the ſame ſtar ought <lb></lb>to appear, one while bigger, and another while leſſer, is inſenſi <lb></lb>ble, and almoſt nothing in the ſtars neer unto the pole of the E <lb></lb>cliptick, but is greateſt in the ſtars placed in the Ecliptick it ſelf, <lb></lb>and indifferent in the intermediate: the contrary happens in the <lb></lb>other difference, that is, the elevation or depreſſion of the ſtars <lb></lb>placed in the Ecliptick is nothing at all, greateſt in thoſe neereſt <lb></lb>to the Pole of the ſaid Ecliptick, and indifferent in the interme <lb></lb>diate. </s><s>Beſides, both theſe differences are more ſenſible in the <lb></lb>Stars neereſt to us, in the more remote leſſe ſenſible, and in <lb></lb>thoſe that are very far diſtant wholly diſappear. </s><s>This is, as to <lb></lb>what concerns my ſelf; it remaineth now, as I conceive, that <lb></lb>ſomething be ſaid for the ſatisfaction of <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> who, as I <lb></lb>believe, will not eaſily be made to over-paſſe thoſe differences, <lb></lb>as inſenſible that are derived from a motion of the Earth ſo vaſt, <lb></lb>and from a mutation that tranſports the Earth into places twice <lb></lb>as far diſtant from us as the Sun.</s></p><p type="margin"><s><margin.target id="marg666"></margin.target><emph type="italics"></emph>The Epilogue of <lb></lb>the<emph.end type="italics"></emph.end> Phænomena <lb></lb><emph type="italics"></emph>of the fixed ſtars <lb></lb>cauſed by the an <lb></lb>nual motion of the <lb></lb>Earth.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>Truth is, to ſpeak freely, I am very loth to confeſſe, that <lb></lb>the diſtance of the fixed Stars ought to be ſuch, that in them the <lb></lb>fore-mentioned differences ſhould be wholly imperceptible.</s></p><p type="main"><s>SALV. </s><s>Do notthrow your ſelf into abſolute deſpair, <emph type="italics"></emph>Simpli <lb></lb>cius,<emph.end type="italics"></emph.end> for there may perhaps yet ſome qualification be found for <lb></lb>your difficulties. </s><s>And firſt, that the apparent magnitude of the <lb></lb>ſtars is not ſeen to make any ſenſible alteration, ought not to be <lb></lb>judged by you a thing improbable, in regard you ſee the gueſſes <lb></lb>of men in this particular to be ſo groſſely erroneous, eſpecially in <lb></lb>looking upon ſplendid objects; and you your ſelf beholding <lb></lb><emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> a lighted Torch at the diſtance of 200 paces, if it ap <lb></lb><arrow.to.target n="marg667"></arrow.to.target> <lb></lb>proach nearer to you 3. or 4. yards, do you think that it will <lb></lb>ſhew any whit encreaſed in magnitude? </s><s>I for my part ſhould <lb></lb>not perceive it certainly, although it ſhould approach 20. or <lb></lb>30. yards nearer; nay it hath ſometimes happened that in ſeeing <lb></lb>ſuch a light at that diſtance I know not how to reſolve whether <lb></lb>it came towards me, or retreated from me, when as it did in <lb></lb>reality approach nearer to me. </s><s>But what need I ſpeak of this? <lb></lb></s><s>If the ſelf ſame acceſſion and receſſion (I ſpeak of a diſtance <pb xlink:href="040/01/371.jpg" pagenum="351"></pb>twice as great as that from the Sun to us) in the ſtar of <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> is <lb></lb>almoſt totally imperceptible, and in <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> not very obſerva <lb></lb>ble, what ſhall we think of the fixed ſtars, which I believe you <lb></lb>will not ſcruple to place twice as far off as <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end>? </s><s>In <emph type="italics"></emph>Mars,<emph.end type="italics"></emph.end> <lb></lb>which for that it is nearer to us -------</s></p><p type="margin"><s><margin.target id="marg667"></margin.target><emph type="italics"></emph>In objects far <lb></lb>remote, and lumi <lb></lb>nous, a ſmall ap <lb></lb>proach or receſſion <lb></lb>is imperceptible.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>Pray Sir, put your ſelf to no farther trouble in this <lb></lb>particular, for I already conceive that what hath been ſpoken <lb></lb>touching the unaltered apparent magnitude of the fixed ſtars may <lb></lb>very well come to paſſe, but what ſhall we ſay of the other dif <lb></lb>ficulty that proceeds from not perceiving any variation in the <lb></lb>mutation of aſpect?</s></p><p type="main"><s>SALV. </s><s>We will ſay that which peradventure may ſatisfie <lb></lb>you alſo in this particular. </s><s>And to make ſhort, would you not <lb></lb>be ſatisfied if there ſhould be diſcovered in the ſtars face muta <lb></lb>tions that you think ought to be diſcovered, in caſe the annual <lb></lb>motion belonged to the Earth?</s></p><p type="main"><s>SIMP. </s><s>I ſhould ſo doubtleſſe, as to what concerns this par <lb></lb>ticular.</s></p><p type="main"><s>SALV. </s><s>I could wiſh you would ſay that in caſe ſuch a diffe <lb></lb><arrow.to.target n="marg668"></arrow.to.target> <lb></lb>rence were diſcovered, nothing more would remain behind, that <lb></lb>might render the mobility of the Earth queſtionable. </s><s>But al <lb></lb>though yet that ſhould not ſenſibly appear, yet is not its mo <lb></lb>bility removed, nor its immobility neceſſarily proved, it being <lb></lb>poſſible, (as <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> affirmeth) that the immenſe diſtance of <lb></lb>the Starry Sphere rendereth ſuch very ſmall <emph type="italics"></emph>Phænomena<emph.end type="italics"></emph.end> unobſer <lb></lb>vable; the which as already hath been ſaid, may poſſibly not <lb></lb>have been hitherto ſo much as ſought for, or if ſought for, yet <lb></lb>not ſought for in ſuch a way as they ought, to wit, with that <lb></lb><arrow.to.target n="marg669"></arrow.to.target> <lb></lb>exactneſſe which to ſo minute a punctuality would be neceſſary; <lb></lb>which exactneſſe is very difficult to obtain, as well by reaſon of the <lb></lb>deficiency of Aſttonomical Inſtruments, ſubject to many altera <lb></lb>tions, as alſo through the fault of thoſe that manage them with leſs <lb></lb>diligence then is requiſite. </s><s>A neceſſary argument how little cre <lb></lb>dit is to be given to thoſe obſervations may be deduced from the <lb></lb>differences which we find amongſt Aſtronomers in aſſigning the <lb></lb>places, I will not ſay, of the new Stars or Comets, but of the fixed <lb></lb>ſtars themſelves, even to the altitudes of the very Poles, in <lb></lb>which, moſt an end, they are found to differ from one another <lb></lb>many minutes. </s><s>And to ſpeak the truth, who can in a Quadrant, <lb></lb>or Sextant, that at moſt ſhall have its ſide ^{*} 3. or 4. yards long, <lb></lb><arrow.to.target n="marg670"></arrow.to.target> <lb></lb>aſcertain himſelf in the incidence of the perpendicular, or in the <lb></lb>direction of the ſights, not to erre two or three minutes, which <lb></lb>in its circumference ſhall not amount to the breadth of a grain of <lb></lb>^{*}<emph type="italics"></emph>Mylet<emph.end type="italics"></emph.end>? </s><s>Beſides that, it is almoſt impoſſible, that the Inſtrument <lb></lb><arrow.to.target n="marg671"></arrow.to.target> <lb></lb>ſhould be made, and kept with abſolute exactneſſe. <emph type="italics"></emph>Ptolomey<emph.end type="italics"></emph.end> <pb xlink:href="040/01/372.jpg" pagenum="352"></pb><arrow.to.target n="marg672"></arrow.to.target> <lb></lb>ſheweth his diſtruſt of a Spherical Inſtrument compoſed by <emph type="italics"></emph>Ar <lb></lb>chimedes<emph.end type="italics"></emph.end> hiſmelf to take the Suns ingreſſion into the Æqui <lb></lb>noctial. <lb></lb><arrow.to.target n="marg673"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg668"></margin.target><emph type="italics"></emph>If in the fixed <lb></lb>ſtars one ſhould <lb></lb>diſcover any an <lb></lb>nual mutation, the <lb></lb>motion of the <lb></lb>Earth would be <lb></lb>undeniable.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg669"></margin.target><emph type="italics"></emph>It is proved what <lb></lb>ſmall credit is to be <lb></lb>given to Aſtrono <lb></lb>mical Inſtruments <lb></lb>in minute obſerva <lb></lb>tions.<emph.end type="italics"></emph.end></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"></emph>did not <lb></lb>truſt to an Inſtru <lb></lb>ment made by<emph.end type="italics"></emph.end> Ar <lb></lb>chimedes.</s></p><p type="margin"><s><margin.target id="marg673"></margin.target><emph type="italics"></emph>Inſtruments of<emph.end type="italics"></emph.end> <lb></lb>Tycho <emph type="italics"></emph>made with <lb></lb>great expence.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>But if the Inſtruments be ſo ſuſpitious, and the obſer <lb></lb>vations ſo dubious, how can we ever come to any certainty of <lb></lb>things, or free our ſelves from miſtakes? </s><s>I have heard ſtrange <lb></lb>things of the Inſtruments of <emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end> made with extraordinary coſt, <lb></lb>and of his ſingular diligence in obſervations.</s></p><p type="main"><s>SALV. </s><s>All this I grant you; but neither one nor other of <lb></lb>theſe is ſufficient to aſcertain us in a buſineſſe of this importance. </s></p><p type="main"><s><arrow.to.target n="marg674"></arrow.to.target> <lb></lb>I deſire that we may make uſe of Inſtruments greater by far, and <lb></lb>by far certainer than thoſe of <emph type="italics"></emph>Tycho,<emph.end type="italics"></emph.end> made with a very ſmall <lb></lb>charge; the ſides of which are of 4. 6. 20. 30. and 50. miles, ſo <lb></lb><arrow.to.target n="marg675"></arrow.to.target> <lb></lb>as that a degree is a mile broad, a minute prim. </s><s>50 ^{*} yards, a <lb></lb>ſecond but little leſſe than a yard, and in ſhort we may without <lb></lb>a farthing expence procure them of what bigneſſe we pleaſe. </s><s>I <lb></lb><arrow.to.target n="marg676"></arrow.to.target> <lb></lb>being in a Countrey Seat of mine near to <emph type="italics"></emph>Florence,<emph.end type="italics"></emph.end> did plainly <lb></lb>obſerve the Suns arrival at, and departure from the Summer <lb></lb>Solſtice, whilſt one Evening at the time of its going down it ap <lb></lb>peared upon the top of a Rock on the Mountains of <emph type="italics"></emph>Pictrapana,<emph.end type="italics"></emph.end> <lb></lb>about 60. miles from thence, leaving diſcovered of it a ſmall <lb></lb>ſtreak or filament towards the North, whoſe breadth was not <lb></lb>the hundredth part of its Diameter; and the following Evening <lb></lb>at the like ſetting, it ſhew'd ſuch another part of it, but notably <lb></lb>more ſmall, a neceſſary argument, that it had begun to recede <lb></lb>from the Tropick; and the regreſſion of the Sun from the firſt to <lb></lb>the ſecond obſervation, doth not import doubtleſſe a ſecond mi <lb></lb><arrow.to.target n="marg677"></arrow.to.target> <lb></lb>nute in the Eaſt. </s><s>The obſervation made afterwards with an ex <lb></lb>quiſite Teleſcope, and that multiplyeth the <emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end> of the Sun <lb></lb>more than a thouſand times, would prove eaſie, and with all <lb></lb>delightful. </s><s>Now with ſuch an Inſtrument as this, I would have <lb></lb>obſervations to be made in the fixed ſtars, making uſe of ſome <lb></lb>of thoſe wherein the mutation ought to appear more conſpicu <lb></lb>ous, ſuch as are (as hath already been declared) the more re <lb></lb>mote from the Ecliptick, amongſt which the Harp a very great <lb></lb>ſtar, and near to the Pole of the Ecliptick, would be very pro <lb></lb>per in Countries far North, proceeding according to the man <lb></lb>ner that I ſhall ſhew by and by, but in the uſe of another ſtar; <lb></lb>and I have already fancied to my ſelf a place very well adapted <lb></lb>for ſuch an obſervation. </s><s>The place is an open Plane, upon <lb></lb>which towards the North there riſeth a very eminent Mountain, <lb></lb>in the apex or top whereof is built a little Chappel, ſituate Eaſt <lb></lb>and Weſt, ſo as that the ridg of its Roof may interſect at right <lb></lb>angles, the meridian of ſome building ſtanding in the Plane. </s><s>I <lb></lb>will place a beam parallel to the ſaid ridg, or top of the Roof, <pb xlink:href="040/01/373.jpg" pagenum="353"></pb>and diſtant from it a yard or thereabouts. </s><s>This being placed, I <lb></lb>will ſeek in the Plain the place from whence one of the ſtars of <lb></lb><emph type="italics"></emph>Charls's<emph.end type="italics"></emph.end> Waine, in paſſing by the Meridian, cometh to hide it <lb></lb>ſelf behind the beam ſo placed, or in caſe the beam ſhould not <lb></lb>be ſo big as to hide the ſtar, I will finde a ſtation where one <lb></lb>may ſee the ſaid beam to cut the ſaid ſtar into two equal parts; <lb></lb>an effect that with an ^{*} exquiſite Teleſcope may be perfectly <lb></lb>diſcerned. </s><s>And if in the place where the ſaid accident is diſcover <lb></lb>ed, there were ſome building, it will be the more commodious; <lb></lb>but if not, I will cauſe a Pole to be ſtuck very faſt in the <lb></lb>ground, with ſome ſtanding mark to direct where to place the <lb></lb>eye anew, when ever I have a mind to repeat the obſervation. <lb></lb></s><s>The firſt of which obſervations I will make about the Summer <lb></lb>Solſtice, to continue afterwards from Moneth to Moneth, or <lb></lb>when I ſhall ſo pleaſe, to the other Solſtice; with which obſer <lb></lb>vation one may diſcover the elevation and depreſſion of the ſtar, <lb></lb>though it be very ſmall. </s><s>And if in that operation it ſhall hap <lb></lb>pen, that any mutation ſhall diſcover it ſelf, what and how great <lb></lb>benefit will it bring to Aſtronomy? </s><s>Seeing that thereby, beſides <lb></lb>our being aſſured of the annual motion, we may come to know <lb></lb>the grandure and diſtance of the ſame ſtar.</s></p><p type="margin"><s><margin.target id="marg674"></margin.target><emph type="italics"></emph>What Inſtru <lb></lb>ments are apt for <lb></lb>moſt exact obſer <lb></lb>vation.<emph.end type="italics"></emph.end></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"></emph>An exquiſite <lb></lb>obſervation of the <lb></lb>approach and de <lb></lb>parture of the Sun <lb></lb>from the Summer <lb></lb>Solſtice.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg677"></margin.target><emph type="italics"></emph>A place aecom <lb></lb>modated for the <lb></lb>obſervation of the <lb></lb>fixed ſtars, as to <lb></lb>what concers the <lb></lb>annual motion of <lb></lb>the Earth.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I very well comprehend your whole proceedings; <lb></lb>and the operation ſeems to me ſo eaſie, and ſo commodious for <lb></lb>the purpoſe, that it may very rationally be thought, that either <lb></lb><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> himſelf, or ſome other Aſtronomer had made trial <lb></lb>of it.</s></p><p type="main"><s>SALV. </s><s>But I judg the quite contrary, for it is not probable, <lb></lb>that if any one had experimented it, he would not have men <lb></lb>tioned the event, whether it fell out in favour of this, or that <lb></lb>opinion; beſides that, no man that I can find, either for this, <lb></lb>or any other end, did ever go about to make ſuch an Obſervati <lb></lb>on; which alſo without an exact Teleſcope could but badly be <lb></lb>effected.</s></p><p type="main"><s>SIMP. </s><s>I am fully ſatisfied with what you ſay. </s><s>But ſeeing <lb></lb>that it is a great while to night, if you defire that I ſhall paſſe <lb></lb>the ſame quietly, let it not be a trouble to you to explain unto <lb></lb>us thoſe Problems, the declaration whereof you did even now <lb></lb>requeſt might be deferred until too morrow. </s><s>Be pleaſed to grant <lb></lb>us your promiſed indulgence, and, laying aſide all other diſcour <lb></lb>ſes, proceed to ſhew us, that the motions which <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> aſſigns <lb></lb>to the Earth being taken for granted, and ſuppoſing the Sun <lb></lb>and fixed ſtars immoveable, there may follow the ſame acci <lb></lb>dents touching the elevations and depreſſions of the Sun, touch <lb></lb>ing the mutations of the Seaſons, and the inequality of dayes <lb></lb>and nights, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> in the ſelf ſame manner, juſt as they are with <pb xlink:href="040/01/374.jpg" pagenum="345[354]"></pb>facility apprehended in the <emph type="italics"></emph>Prolomaick<emph.end type="italics"></emph.end> Syſteme.</s></p><p type="main"><s>SALV. </s><s>I neither ought, nor can deny any thing that <emph type="italics"></emph>Sagredus<emph.end type="italics"></emph.end> <lb></lb>ſhall requeſt: And the delay by me deſired was to no other end, <lb></lb>ſave only that I might have time once again to methodize thoſe <lb></lb>prefatory points, in my fancy, that ſerve for a large and plain de <lb></lb>claration of the manner how the forenamed accidents follow, as <lb></lb>well in the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> poſition, as in the <emph type="italics"></emph>Ptolomaick<emph.end type="italics"></emph.end>: nay, with <lb></lb><arrow.to.target n="marg678"></arrow.to.target> <lb></lb>much greater facility and ſimplicity in that than in this. </s><s>Whence <lb></lb>one may manifeſtly conceive that Hypotheſis to be as eaſie to be <lb></lb>effected by nature, as difficult to be apprehended by the under <lb></lb>ſtanding: yet nevertheleſſe, I hope by making uſe of another <lb></lb><arrow.to.target n="marg679"></arrow.to.target> <lb></lb>kind of explanation, than that uſed by <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> to render like <lb></lb>wiſe the apprehending of it ſomewhat leſſe obſcure. </s><s>Which <lb></lb>that I may do, I will propoſe certain ſuppoſitions of themſelves <lb></lb>known and manifeſt, and they ſhall be theſe that follow.</s></p><p type="margin"><s><margin.target id="marg678"></margin.target><emph type="italics"></emph>The<emph.end type="italics"></emph.end> Coperni <lb></lb>can <emph type="italics"></emph>Syſteme diffi <lb></lb>cult to be under <lb></lb>ſtood, but eaſie to <lb></lb>be effected.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg679"></margin.target><emph type="italics"></emph>Neceſſary pre <lb></lb>poſitions for the <lb></lb>better conceiving <lb></lb>of the conſequences <lb></lb>of the Earths mo <lb></lb>tion.<emph.end type="italics"></emph.end></s></p><p type="main"><s>Firſt, I ſuppoſe that the Earth is a ſpherical body, turning <lb></lb>round upon its own Axis and Poles, and that each point aſſigned <lb></lb>in its ſuperficies, deſcribeth the circumference of a circle, great <lb></lb>er or leſſer, according as the point aſſigned ſhall be neerer or <lb></lb>farther from the Poles: And that of theſe circles the greateſt is <lb></lb>that which is deſcribed by a point equidiſtant from the ſaid Poles; <lb></lb>and all theſe circles are parallel to each other; and <emph type="italics"></emph>Parallels<emph.end type="italics"></emph.end> we <lb></lb>will call them.</s></p><p type="main"><s>Secondly, The Earth being of a Spherical Figure, and of an o <lb></lb>pacous ſubſtance, it is continually illuminated by the Sun, accor <lb></lb>ding to the half of its ſurface, the other half remaining obſcure, <lb></lb>and the boundary that diſtinguiſheth the illuminated part from <lb></lb>the dark being a grand circle, we will call that circle the <emph type="italics"></emph>termi <lb></lb>nator of the light.<emph.end type="italics"></emph.end></s></p><p type="main"><s>Thirdly, If the Circle that is terminator of the light ſhould <lb></lb>paſſe by the Poles of the Earth, it would cut (being a grand <lb></lb>and principal circle) all the parallels into equal parts; but not <lb></lb>paſſing by the Poles, it would cut them all in parts unequal, ex <lb></lb>cept only the circle in the middle, which, as being a grand circle <lb></lb>will be cut into equal parts.</s></p><p type="main"><s>Fourthly, The Earth turning round upon its own Poles, the <lb></lb>quantities of dayes and nights are termined by the arches of the <lb></lb>Parallels, interſected by the circle, that is, the terminator of the <lb></lb>light, and the arch that is ſcituate in the illuminated Hemiſphere <lb></lb>preſcribeth the length of the day, and the remainer is the quan <lb></lb>tity of the night.</s></p><p type="main"><s>Theſe things being preſuppoſed, for the more clear under <lb></lb><arrow.to.target n="marg680"></arrow.to.target> <lb></lb>ſtanding of that which remaines to be ſaid, we will lay it down <lb></lb>in a Figure. </s><s>And firſt, we will draw the circumference of a <lb></lb>circle, that ſhall repreſent unto us that of the grand Orb deſcri <pb xlink:href="040/01/375.jpg" pagenum="355"></pb>bed in the plain of the Ecliptick, and this we will divide into <lb></lb>four equal parts with the two diameters <emph type="italics"></emph>Capricorn Cancer,<emph.end type="italics"></emph.end> and <lb></lb><emph type="italics"></emph>Libra Aries,<emph.end type="italics"></emph.end> which, at the ſame time, ſhall repreſent unto us the <lb></lb>four Cardinal points, that is, the two Solſtices, and the two E <lb></lb>quinoctials; and in the centre of that circle we will place the <lb></lb>Sun O, fixed and immoveable.</s></p><p type="margin"><s><margin.target id="marg680"></margin.target><emph type="italics"></emph>A plain Scheme <lb></lb>repreſenting the<emph.end type="italics"></emph.end> <lb></lb>Copernican <emph type="italics"></emph>Hypo <lb></lb>theſis, and its con <lb></lb>ſequences.<emph.end type="italics"></emph.end></s></p><figure id="id.040.01.375.1.jpg" xlink:href="040/01/375/1.jpg"></figure><p type="main"><s>Let us next draw about the four points, Capricorn, Cancer, <lb></lb>Libra and Aries, as centres, four equal circles, which repreſent <lb></lb>unto us the Earth placed in them at four ſeveral times of the <lb></lb>year. </s><s>The which, with its centre, in the ſpace of a year, paſſeth <lb></lb>through the whole circumference, Capricorn, Aries, Cancer, Li <lb></lb>bra, moving from Eaſt to Weſt, that is, according to the order <lb></lb>of the Signes. </s><s>It is already manifeſt, that whilſt the Earth is in <lb></lb>Capricorn, the Sun will appear in Cancer, and the Earth moving <lb></lb><arrow.to.target n="marg681"></arrow.to.target> <lb></lb>along the arch Capricorn Aries, the Sun will ſeem to move along <lb></lb>the arch Cancer Libra, and in ſhort, will run thorow the Zodiack <lb></lb>according to the order of the Signes, in the ſpace of a year; and <lb></lb>by this firſt aſſumption, without all queſtion, full ſatisfaction is <lb></lb>given for the Suns apparent annual motion under the Ecliptick. <lb></lb></s><s>Now, coming to the other, that is, the diurnal motion of the <lb></lb>Earth in it ſelf, it is neceſſary to eſtabliſh its Poles and its Axis, <lb></lb>the which muſt be underſtood not to be erect perpendicularly <lb></lb>upon the plain of the Ecliptick, that is, not to be parallel to the <lb></lb>Axis of the grand Orb, but declining from a right angle 23 de <lb></lb>grees and an half, or thereabouts, with its North Pole towards <pb xlink:href="040/01/376.jpg" pagenum="356"></pb>the Axis of the grand Orb, the Earths centre being in the Solſti <lb></lb>tial point of Capricorn. </s><s>Suppoſing therefore the Terreſtrial <lb></lb>Globe to have its centre in the point Capricorn, we will deſcribe <lb></lb>its Poles and Axis A B, inclined upon the diameter Capricorn <lb></lb>Cancer 23 degrees and an half; ſo that the angle A Capricorn <lb></lb>Cancer cometh to be the complement of a Quadrant or Radius, <lb></lb>that is, 66 degrees and an half; and this inclination muſt be un <lb></lb>derſtood to be immutable, and we will ſuppoſe the ſuperiour <lb></lb>Pole A to be Boreal, or North, and the other Auſtral, or South. <lb></lb></s><s>Now imagining the Earth to revolve in it ſelf about the Axis A B <lb></lb>in twenty four hours, from Weſt to Eaſt, there ſhall by all the <lb></lb>points aſſigned in its ſuperſicies, be circles deſcribed parallel to <lb></lb>each other. </s><s>We will draw, in this firſt poſition of the Earth, <lb></lb>the greateſt C D, and thoſe two diſtant from it <emph type="italics"></emph>gr.<emph.end type="italics"></emph.end> 23. and an <lb></lb>half, E F above, and G M beneath, and the other two extream <lb></lb>ones I K and L M remote, by thoſe intervals from the Poles A <lb></lb>and B; and as we have marked theſe five, ſo we may imagine in <lb></lb>numerable others, parallel to theſe, deſcribed by the innumera <lb></lb>ble points of the Terreſtrial ſurface. </s><s>Next let us ſuppoſe the <lb></lb>Earth, with the annual motion of its centre, to transferre it ſelf <lb></lb>into the other places already marked; but to paſſe thither in ſuch <lb></lb>a manner, that its own Axis A B ſhall not only not change incli <lb></lb>nation upon the plain of the Ecliptick, but ſhall alſo never vary <lb></lb>direction; ſo that alwayes keeping parallel to it ſelf, it may <lb></lb>continually tend towards the ſame part of the Univerſe, or, if <lb></lb>you will, of the Firmament, whereas, if we do but ſuppoſe it <lb></lb>prolonged, it will, with its extream termes, deſigne a Circle pa <lb></lb>rallel and equal to the grand Orb, Libra Capricorn Aries Cancer, <lb></lb>as the ſuperiour baſe of a Cylinder deſcribed by it ſelf in the an <lb></lb>nual motion above the inferiour baſe, Libra Capricorn Aries <lb></lb>Cancer. </s><s>And therefore this immutability of inclination conti <lb></lb>nuing, we will deſign theſe other three figures about the centres <lb></lb>Aries, Cancer, and Libra, alike in every thing to that firſt de <lb></lb>ſcribed about the centre Capricorn. </s><s>Now we will conſider the <lb></lb>firſt figure of the Earth, in which, in regard the Axis A B is de <lb></lb>clined from perpendicularity upon the diameter Capricorn Can <lb></lb>cer 23 degrees and an half towards the Sun O, and the arch A I <lb></lb>being alſo 23 degrees and an half, the illumination of the Sun <lb></lb>will illuſtrate the Hemiſphere of the Terreſtrial Globe expoſed <lb></lb>towards the Sun (of which, in this place, half is to be ſeen) di <lb></lb>vided from the obſcure part by the Terminator of the light <lb></lb>I M, by which the parallel C D, as being a grand circle, ſhall <lb></lb>come to be divided into equal parts, but all the reſt into parts un <lb></lb>equal; being that the terminator of the light I M paſſeth not <lb></lb>by their Poles A B, and the parallel I K, together with all the reſt <pb xlink:href="040/01/377.jpg" pagenum="357"></pb>deſcribed within the ſame, and neerer to the pole A, ſhall wholly <lb></lb>be included in the illuminated part; as on the contrary, the op <lb></lb>poſite ones towards the Pole B, contained within the paral <lb></lb>lel L M, ſhall remain in the dark. </s><s>Moreover, the arch A I be <lb></lb>ing equal to the arch F D, and the arch A F, common to them <lb></lb>both, the two arches I K F and A F D ſhall be equal, and each <lb></lb>a quadrant or 90 degrees. </s><s>And becauſe the whole arch I F M <lb></lb>is a ſemicircle, the arch F M ſhall be a quadrant, and equal to <lb></lb>the other F K I; and therefore the Sun O ſhall be in this ſtate <lb></lb>of the Earth vertical to one that ſtands in the point F. </s><s>But by <lb></lb>the revolution diurnal about the ſtanding Axis A B, all the points <lb></lb>of the parallel E F paſſe by the ſame point F: and therefore in <lb></lb>that ſame day the Sun, at noon, ſhall be vertical to all the inha <lb></lb>bitants of the Parallel E F, and will ſeem to them to deſcribe in its <lb></lb>apparent motion the circle which we call the Tropick of Cancer. <lb></lb></s><s>But to the inhabitants of all the Parallels that are above the pa <lb></lb>rallel E F, towards the North pole A, the Sun declineth from <lb></lb>their <emph type="italics"></emph>Vertex<emph.end type="italics"></emph.end> or Zenith towards the South; and on the contrary, <lb></lb>to all the inhabitants of the Parallels that are beneath E F, to <lb></lb>wards the Equinoctial C D, and the South Pole B, the Meridian <lb></lb>Sun is elevated beyond their <emph type="italics"></emph>Vertex<emph.end type="italics"></emph.end> towards the North Pole A. <lb></lb>Next, it is viſible that of all the Parallels, only the greateſt C D <lb></lb>is cut in equal parts by the Terminator of the light I M. </s><s>But <lb></lb>the reſt, that are beneath and above the ſaid grand circle, are all <lb></lb>interſected in parts unequal: and of the ſuperiour ones, the ſe <lb></lb>midiurnal arches, namely thoſe of the part of the Terreſtrial ſur <lb></lb>face, illuſtrated by the Sun, are bigger than the ſeminocturnal <lb></lb>ones that remain in the dark: and the contrary befalls in the <lb></lb>remainder, that are under the great one C D, towards the pole B, <lb></lb>of which the ſemidiurnal arches are leſſer than the ſeminocturnal, <lb></lb>It is likewiſe apparently manifeſt, that the differences of the ſaid <lb></lb>arches go augmenting, according as the Parallels are neerer to <lb></lb>the Poles, till ſuch time as the parallel I K comes to be wholly in <lb></lb>the part illuminated, and the inhabitants thereof have a day of <lb></lb>twenty four hours long, without any night; and on the contrary, <lb></lb>the Parallel L M, remaining all in obſcurity, hath a night of <lb></lb>twenty four hours, without any day. </s><s>Come we next to the <lb></lb>third Figure of the Earth, placed with its centre in the point <lb></lb>Cancer, where the Sun ſeemeth to be in the firſt point of Ca <lb></lb>pricorn. </s><s>We have already ſeen very manifeſtly, that by reaſon <lb></lb>the Axis A B doth not change inclination, but continueth paral <lb></lb>lel to it ſelf, the aſpect and ſituation of the Earth is the ſame to <lb></lb>an hair with that in the firſt Figure; ſave onely that that Hemi <lb></lb>ſphere which in the firſt was illuminated by the Sun, in this re <lb></lb>maineth obtenebrated, and that cometh to be luminous, which in <pb xlink:href="040/01/378.jpg" pagenum="358"></pb>the firſt was tenebrous: whereupon that which happened before <lb></lb>concerning the differences of dayes and nights, touching the <lb></lb>dayes being greater or leſſer than the nights, now falls out quite <lb></lb>contrary. </s><s>And firſt, we ſee, that whereas in the firſt Figure the <lb></lb>circle I K was wholly in the light, it is now wholly in the dark; <lb></lb>and the oppoſite arch L M is now wholly in the light, which <lb></lb>was before wholly in the dark. </s><s>Of the parallels between the <lb></lb>grand circle C D, and the Pole A, the ſemidiurnal arches are now <lb></lb>leſſer than the ſeminocturnal, which before were the contrary. <lb></lb></s><s>Of the others likewiſe towards the Pole B, the ſemidiurnal arch <lb></lb>es are now bigger than the ſeminocturnal, the contrary to what <lb></lb>happened in the other poſition of the Earth. </s><s>We now ſee the <lb></lb>Sun made vertical to the inhabitants of the Tropick G N, and to <lb></lb>be depreſſed towards the South, with thoſe of the Parallel E F, <lb></lb>by all the arch E C G, that is, 47 degrees; and in ſumme, to have <lb></lb>paſſed from one to the other Tropick, traverſing the Equinoctial, <lb></lb>elevating and declining in the Meridians the ſaid ſpace of 47 de <lb></lb>grees. </s><s>And all this mutation is derived not from the inclination <lb></lb>or elevation of the Earth, but on the contrary, from its not in <lb></lb>clining or elevating at all; and in a word, by continuing always <lb></lb>in the ſame poſition, in reſpect of the Univerſe, onely with turn <lb></lb>ing about the Sun ſituate iu the midſt of the ſaid plane, in which <lb></lb>it moveth it ſelf about circularly with its annual motion. </s><s>And <lb></lb><arrow.to.target n="marg682"></arrow.to.target> <lb></lb>here is to be noted an admirable accident, which is, that like as <lb></lb>the Axis of the Earth conſerving the ſame direction towards the <lb></lb>Univerſe, or we may ſay, towards the higheſt Sphere of the fixed <lb></lb>ſtars, cauſeth the Sun to appear to elevate and incline ſo great a <lb></lb>ſpace, namely, for 47 degrees, and the fixed Stars to incline or e <lb></lb>levate nothing at all; ſo, on the contrary, if the ſame Axis of <lb></lb>the Earth ſhould maintain it ſelf continually in the ſame inclina <lb></lb>tion towards the Sun, or, if you will, towards the Axis of the <lb></lb>Zodiack, no mutation would appear to be made in the Sun about <lb></lb>its elevating or declining, whereupon the inhabitants of one and <lb></lb>the ſame place would alwayes have one and the ſame difference <lb></lb>of dayes and nights, and one and the ſame conſtitution of Sea <lb></lb>ſons, that is, ſome alwayes Winter, others alwayes Summer, <lb></lb>others Spring, &c. </s><s>but, on the contrary, the alterations in the <lb></lb>fixed Stars would appear very great, as touching their elevation, <lb></lb>and inclination to us, which would amount to the ſame 47 de <lb></lb>grees. </s><s>For the underſtanding of which let us return to conſider <lb></lb>the poſition of the Earth, in its firſt Figure, where we ſee the <lb></lb>Axis A B, with the ſuperiour Pole A, to incline towards the Sun; <lb></lb>but in its third Figure, the ſame Axis having kept the ſame dire <lb></lb>ction towards the higheſt Sphere, by keeping parallel to it ſelf, <lb></lb>inclines no longer towards the Sun with its ſuperiour Pole A, but <pb xlink:href="040/01/379.jpg" pagenum="359"></pb>on the contrary reclines from its former poſition <emph type="italics"></emph>gr.<emph.end type="italics"></emph.end> 47. and in <lb></lb>clineth towards the oppoſite part, ſo that to reſtore the ſame in <lb></lb>clination of the ſaid Pole A towards the Sun, it would be requi <lb></lb>ſite by turning round the Terreſtrial Globe, according to the <lb></lb>circumference A C B D, to tranſport it towards E thoſe ſame <lb></lb><emph type="italics"></emph>gr.<emph.end type="italics"></emph.end> 47. and for ſo many degrees, any whatſoever fixed ſtar ob <lb></lb>ſerved in the Meridian, would appear to be elevated, or inclined. <lb></lb></s><s>Let us come now to the explanation of that which remains, and <lb></lb>let us conſider the Earth placed in the fourth Figure, that is, <lb></lb>with its centre in the firſt point of Libra; upon which the Sun <lb></lb>will appear in the beginning of Aries. </s><s>And becauſe the Axis of <lb></lb><figure id="id.040.01.379.1.jpg" xlink:href="040/01/379/1.jpg"></figure> <lb></lb>the Earth, which in the firſt Figure is ſuppoſed to be inclined up <lb></lb>on the diameter Capricorn Cancer, and therefore to be in that <lb></lb>ſame plane, which cutting the plane of the grand Orb, accor <lb></lb>ding to the line Capricorn Cancer, was erected perpendicularly <lb></lb>upon the ſame, tranſpoſed into the fourth Figure, and maintai <lb></lb>ned, as hath alwayes been ſaid, parallel to it ſelf, it ſhall come <lb></lb>to be in a plane in like manner erected to the ſuperficies of <lb></lb>the Grand Orbe, and parallel to the plane, which at right <lb></lb>angles cuts the ſame ſuperficies, according to the diameter Ca <lb></lb>pricorn Cancer. </s><s>And therefore the line which goeth from <lb></lb>the centre of the Sunne to the centre of the Earth, that is, <lb></lb>O Libra, ſhall be perpendicular to the Axis BA: but the <lb></lb>ſame line which goeth from the centre of the Sunne to the <lb></lb>centre of the Earth, is alſo alwayes perpendicular to the <pb xlink:href="040/01/380.jpg" pagenum="360"></pb>circle that is the Terminator of the light; therefore this ſame <lb></lb>circle ſhall paſſe by the Poles A B in the fourth figure, and <lb></lb>in its plain the Axis A B ſhall fall, but the greateſt circle paſſing <lb></lb>by the Poles of the Parallels, divideth them all in equal parts; <lb></lb>therefore the arches I K, E F, C D, G N, L M, ſhall be all <lb></lb>ſemicircles, and the illumin'd Hemiſphere ſhall be this which <lb></lb>looketh towards us, and the Sun, and the Terminator of the <lb></lb>light ſhall be one and the ſame circle A C B D, and the Earth <lb></lb>being in this place ſhall make it Equinoctial to all its Inhabitants. <lb></lb></s><s>And the ſame happeneth in the ſecond figure, where the Earth <lb></lb>having its illuminated Hemiſphere towards the Sun, ſheweth us <lb></lb>the other that is obſcure, with its nocturnal arches, which in <lb></lb>like manner are all ſemicircles, and conſequently, here alſo it <lb></lb>maketh the Equinoctial. </s><s>And laſtly in regard that the line pro <lb></lb>duced from the centre of the Sun to the centre of the Earth, is <lb></lb>perpendicular to the Axis A B, to which the greateſt circle of <lb></lb>the parallels C D, is likewiſe erect, the ſaid line O <emph type="italics"></emph>Libra<emph.end type="italics"></emph.end> ſhall <lb></lb>paſſe of neceſſity by the ſame Plain of the parallel C D, cutting <lb></lb>its circumference in the midſt of the diurnal arch C D; and <lb></lb>therefore the Snn ſhall be vertical to any one that ſhall ſtand <lb></lb>where that interſection is made; but all the Inhabitants of that <lb></lb>Parallel ſhall paſſe the ſame, as being carried about by the <lb></lb>Earths diurnal converſion; therefore all theſ upon that day <lb></lb>ſhall have the Meridian Sun in their vertex. </s><s>And the Sun at the <lb></lb>ſame time to all the Inhabitants of the Earth ſhall ſeem to de <lb></lb>ſcribe the Grand Parallel called the Equinoctial. </s><s>Furthermore, <lb></lb>foraſmuch as the Earth being in both the Solſtitial points of the <lb></lb>Polar circles I K and L M, the one is wholly in the light, and <lb></lb>the other wholly in the dark; but when the Earth is in the Equi <lb></lb>noctial points, the halves of thoſe ſame polar circles are in the <lb></lb>light, the remainder of them being in the dark; it ſhould not <lb></lb>be hard to underſtand, how that the Earth <emph type="italics"></emph>v. </s><s>gr.<emph.end type="italics"></emph.end> from <emph type="italics"></emph>Cancer<emph.end type="italics"></emph.end> <lb></lb>(where the parallel I K is wholly in the dark) to <emph type="italics"></emph>Leo,<emph.end type="italics"></emph.end> one part of <lb></lb>the parallel towards the point I, beginneth to enter into the light, <lb></lb>and that the Terminator of the light I M beginneth to retreat to <lb></lb>wards the Pole AB, interſecting the circle ACBD nolonger in IM, <lb></lb>but in two other points falling between the terms I A and MB, of <lb></lb>the arches IA and M B; whereupon the Inhabitants of the circle <lb></lb>begin to enjoy the light, and the other Inhabitants of the circle <lb></lb>L M to partake of night. </s><s>And thus you ſee that by two ſimple <lb></lb>motions made in times proportionate to their bigneſſes, and not <lb></lb>contrary to one another, but performed, as all others that be <lb></lb>long to moveable mundane bodies, from Weſt to Eaſt aſſigned <lb></lb>to the Terreſtrial Globe, adequate reaſons are rendred of all <lb></lb>thoſe <emph type="italics"></emph>Phænomena<emph.end type="italics"></emph.end> or appearances, for the accommodating of <pb xlink:href="040/01/381.jpg" pagenum="361"></pb>which to the ſtability of the Earth it is neceſſary (forſaking that <lb></lb>Symetry which is obſerved to be between the velocities and mag <lb></lb>nitudes of moveables) to aſcribe to a Sphere, vaſt above all <lb></lb>others, an unconceiveable celerity, whilſt the other leſſer <lb></lb>Spheres move extream ſlowly; and which is more, to make that <lb></lb>motion contrary to all their motions; and, yet again to adde to <lb></lb>the improbability, to make that ſuperiour Sphere forcibly to <lb></lb>tranſport all the inferionr ones along with it contrary to their <lb></lb>proper inclination. </s><s>And here I refer it to your judgment to de <lb></lb>termine which of the two is the moſt probable.</s></p><p type="margin"><s><margin.target id="marg681"></margin.target><emph type="italics"></emph>The Suns an <lb></lb>nual motion, how <lb></lb>it comes to paſſe, <lb></lb>according to<emph.end type="italics"></emph.end> Co <lb></lb>pernicus.</s></p><p type="margin"><s><margin.target id="marg682"></margin.target><emph type="italics"></emph>An admirable <lb></lb>accident depending <lb></lb>on the not inclining <lb></lb>of the Earths axis<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>To me, as far as concerneth ſenſe, there appeareth <lb></lb>no ſmall difference betwixt the ſimplicity and facility of opera <lb></lb>ting effects by the means aſſigned in this new conſtitution, and <lb></lb>the multiplicity, conſufion, and difficulty, that is found in the <lb></lb>ancient and commonly received Hypotheſis. </s><s>For if the Univerſe <lb></lb>were diſpoſed according to this multiplicity, it would be ne <lb></lb>ceſſary to renounce many Maximes in Philoſophy commonly re <lb></lb><arrow.to.target n="marg683"></arrow.to.target> <lb></lb>ceived by Philoſophers, as for inſtance, That Nature doth <lb></lb>not multiply things without neceſſity; and, That She makes uſe <lb></lb>of the moſt facile and ſimple means in producing her effects; <lb></lb>and, That She doth nothing in vain, and the like. </s><s>I do confeſſe <lb></lb>that I never heard any thing more admirable than this, nor can I <lb></lb>believe that Humane Underſtanding ever penetrated a more <lb></lb>ſublime ſpeculation. </s><s>I know not what <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> may think <lb></lb>of it.</s></p><p type="margin"><s><margin.target id="marg683"></margin.target><emph type="italics"></emph>Axiomes com <lb></lb>monly admitted by <lb></lb>all Philoſophers.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>Theſe (if I may ſpeak my judgment freely) do ſeem <lb></lb><arrow.to.target n="marg684"></arrow.to.target> <lb></lb>to me ſome of thoſe Geometrical ſubtilties which <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> finds <lb></lb>fault with in <emph type="italics"></emph>Plato,<emph.end type="italics"></emph.end> when he accuſeth him that by his too <lb></lb>much ſtudying of Geometry he forſook ſolid Philoſophy; and I <lb></lb>have known and heard very great <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> Philoſophers to <lb></lb>diſſwade their Scholars from the Study of the Mathematicks, as <lb></lb>thoſe that render the wit cavilous, and unable to philoſophate <lb></lb>well; an Inſtitute diametrically contrary to that of <emph type="italics"></emph>Plato,<emph.end type="italics"></emph.end> who <lb></lb>admitted uone to Philoſophy, unleſſe he was firſt well entered in <lb></lb>Geometry.</s></p><p type="margin"><s><margin.target id="marg684"></margin.target>Ariſtotle <emph type="italics"></emph>tax <lb></lb>eth<emph.end type="italics"></emph.end> Plato <emph type="italics"></emph>for being <lb></lb>too ſtudious of Ge <lb></lb>ometry.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>I commend the policy of theſe your <emph type="italics"></emph>Peripateticks,<emph.end type="italics"></emph.end> in <lb></lb><arrow.to.target n="marg685"></arrow.to.target> <lb></lb>dehorting their Diſciples from the Study of Geometry, for that <lb></lb>there is no art more commodious for detecting their fallacies; but <lb></lb>ſee how they differ from the Mathematical Philoſophers, who <lb></lb>much more willingly converſe with thoſe that are well verſt in <lb></lb>the commune Peripatetick Philoſophy, than with thoſe that are <lb></lb>deſtitute of that knowledg, who for want thereof cannot di <lb></lb>ſtinguiſh between doctrine and doctrine. </s><s>But paſſing by this, tell <lb></lb>me I beſeech you, what are thoſe extravagancies and thoſe too <lb></lb>affected ſubtilties that make you think this <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Syſteme <lb></lb>the leſſe plauſible?</s></p> <pb xlink:href="040/01/382.jpg" pagenum="362"></pb><p type="margin"><s><margin.target id="marg685"></margin.target>Peripatetick <emph type="italics"></emph>Phi <lb></lb>loſophers condemn <lb></lb>the Study of Geo <lb></lb>metry, and why.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>To tell you true, I do not very well know; perhaps, <lb></lb>becauſe I have not ſo much as learnt the reaſons that are by <emph type="italics"></emph>Ftolo <lb></lb>my<emph.end type="italics"></emph.end> produced, of thoſe effects, I mean of thoſe ſtations, retrogra <lb></lb>dations, acceſſions, receſſions of the Planets; lengthenings and <lb></lb>ſhortnings of dayes, changes of ſeaſons, &c. </s><s>But omitting the <lb></lb>conſequences that depend on the firſt ſuppoſitions, I find in the <lb></lb>ſuppoſitions themſelves no ſmall difficulties; which ſuppoſitions, <lb></lb>if once they be overthrown, they draw along with them the ruine <lb></lb>of the whole fabrick. </s><s>Now foraſmuch as becauſe the whole <lb></lb>module of <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> ſeemeth in my opinion to be built upon in <lb></lb>firm foundations, in that it relyeth upon the mobility of the earth, <lb></lb>if this ſhould happen to be diſproved, there would be no need of <lb></lb>farther diſpute. </s><s>And to diſprove this, the Axiom of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> <lb></lb>is in my judgment moſt ſufficient, That of one ſimple body, <lb></lb>one ſole ſimple motion can be natural: but here in this caſe, to <lb></lb><arrow.to.target n="marg686"></arrow.to.target> <lb></lb>the Earth, a ſimple body, there are aſſigned 3. if not 4. motions, <lb></lb>and all very different from each other. </s><s>For beſides the light <lb></lb>motion, as a grave body towards its centre, which cannot be de <lb></lb>nied it, there is aſſigned to it a circular motion in a great circle <lb></lb>about the Sun in a year, and a vertiginous converſion about its <lb></lb>own centre in twenty four hours. </s><s>And that in the next place <lb></lb>which is more exorbitant, & which happly for that reaſon you paſs <lb></lb>over in ſilence, there is aſcribed to it another revolution about <lb></lb>its own centre, contrary to the former of twenty four hours, <lb></lb>and which finiſheth its period in a year. </s><s>In this my underſtand <lb></lb>ing apprehendeth a very great contradiction. <lb></lb><arrow.to.target n="marg687"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg686"></margin.target><emph type="italics"></emph>Four ſeveral <lb></lb>motions aſſigned to <lb></lb>the Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg687"></margin.target><emph type="italics"></emph>The motion of <lb></lb>deſcent belongs not <lb></lb>to the terreſtrial <lb></lb>Globe, but to its <lb></lb>parts.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>As to the motion of deſcent, it hath already been con <lb></lb>cluded not to belong to the Terreſtrial Globe which did never <lb></lb>move with any ſuch motion, nor never ſhall do; but is (if there be <lb></lb>ſuch a thing) that propenſion of its parts to reunite themſelves <lb></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></lb>and the Diurnal, theſe being both made towards one way, are <lb></lb>very compatible, in the ſame manner juſt as if we ſhould let a <lb></lb>Ball trundle downwards upon a declining ſuperficies, it would in <lb></lb>its deſcent along the ſame ſpontaneouſly revolve in it ſelf. </s><s>As <lb></lb>to the third motion aſſigned it by <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> namely about it <lb></lb>ſelf in a year, onely to keep its Axis inclined and directed <lb></lb>towards the ſame part of the Firmament, I will tell you a thing <lb></lb>worthy of great conſideration: namely <emph type="italics"></emph>ut tantum abeſt<emph.end type="italics"></emph.end> (although <lb></lb>it be made contrary to the other annual) it is ſo far from having <lb></lb>any repugnance or difficulty in it, that naturally and without any <lb></lb><arrow.to.target n="marg689"></arrow.to.target> <lb></lb>moving cauſe, it agreeth to any whatſoever ſuſpended and libra <lb></lb>ted body, which if it ſhall be carried round in the circumference <lb></lb>of a circle, immediate of it ſelf, it acquireth a converſion about <lb></lb>its own centre, contrary to that which carrieth it about, and of <pb xlink:href="040/01/383.jpg" pagenum="363"></pb>ſuch velocity, that they both finiſh one revolution in the ſame <lb></lb>time preciſely. </s><s>You may ſee this admirable, and to our pur <lb></lb><arrow.to.target n="marg690"></arrow.to.target> <lb></lb>poſe accommodate experience, if putting in a Baſon of water a <lb></lb>Ball that will ſwim; and holding the Baſon in your hand, you <lb></lb>turn round upon your toe, for you ſhall immediatly ſee the Ball <lb></lb>begin to revolve in it ſelf with a motion, contrary to that of the <lb></lb>Baſon, and it ſhall finiſh its revolution, when that of the Baſon it <lb></lb>ſhall finiſh. </s><s>Now what other is the Earth than a penſil Globe <lb></lb>librated in tenuous and yielding aire, which being carried a <lb></lb>bout in a year along the circumference of a great circle, muſt <lb></lb><arrow.to.target n="marg691"></arrow.to.target> <lb></lb>needs acquire, without any other mover, a revolution about its <lb></lb>own centre, annual, and yet contrary to the other motion in like <lb></lb>manner annual? </s><s>You ſhall ſee this effect I ſay, but if afterwards <lb></lb>you more narrowly conſider it, you ſhall find this to be no real <lb></lb>thing, but a meer appearance; and that which you think to be <lb></lb>a revolution in it ſelf, you will find to be a not moving at all, <lb></lb>but a continuing altogether immoveable in reſpect of all that <lb></lb>which without you, and without the veſſel is immoveable: for if in <lb></lb>that Ball you ſhall make ſome mark, and conſider to what part of <lb></lb>the Room where you are, or of the Field, or of Heaven it is <lb></lb>ſituate, you ſhall ſee that mark in yours, and the veſſels revolu <lb></lb>tion to look alwayes towards that ſame part; but comparing it to <lb></lb>the veſſel and to your ſelf that are moveable, it will appear to go <lb></lb>altering its direction, and with a motion contrary to yours, and <lb></lb>that of the veſſel, to go ſeeking all the points of its circumgyra <lb></lb>tion; ſo that with more reaſon you and the baſon may be ſaid <lb></lb>to turn round the immoveable Ball, than that it moveth round <lb></lb>in the baſon. </s><s>In the ſame manner the Earth ſuſpended and li <lb></lb>brated in the circumference of the Grand Orbe, and ſcituate in <lb></lb>ſuch ſort that one of its notes, as for example, its North Pole, loo <lb></lb>keth towards ſuch a Star or other part of the Firmament, it always <lb></lb>keepeth directed towards the ſame, although carried round by <lb></lb>the annual motion about the circumference of the ſaid Grand <lb></lb>Orbe. </s><s>This alone is ſufficient to make the Wonder ceaſe, and <lb></lb>to remove all difficulties. </s><s>But what will <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> ſay, if to <lb></lb>this non-indigence of the co-operating cauſe we ſhould adde <lb></lb>an admirable intrinſick vertue of the Terreſtrial Globe, of look <lb></lb><arrow.to.target n="marg692"></arrow.to.target> <lb></lb>ing with its determinate parts towards determinate parts of the <lb></lb>Firmament, I ſpeak of the Magnetick vertue conſtantly partici <lb></lb>pated by any whatſoever piece of Loade-ſtone. </s><s>And if every <lb></lb>minute particle of that S one have in it ſuch a vertue, who will <lb></lb><arrow.to.target n="marg693"></arrow.to.target> <lb></lb>queſtion but that the ſame more powerfully reſides in this whole <lb></lb>Terreſtrial Globe, abounding in that Magnetick matter, and <lb></lb>which happily it ſelf, as to its internal and primary ſubſtance, is <lb></lb>nothing elſe but a huge maſſe of Loade-ſtone.</s></p> <pb xlink:href="040/01/384.jpg" pagenum="364"></pb><p type="margin"><s><margin.target id="marg688"></margin.target><emph type="italics"></emph>The annual and <lb></lb>diurnal motion are <lb></lb>compatible in the <lb></lb>Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg689"></margin.target><emph type="italics"></emph>Every penſil and <lb></lb>librated, body car <lb></lb>ryed round in the <lb></lb>circumference of a <lb></lb>circle, acquireth of <lb></lb>it ſelf a motion in <lb></lb>it ſelf contrary to <lb></lb>that.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg690"></margin.target><emph type="italics"></emph>An Experiment <lb></lb>which ſenſibly <lb></lb>ſhews that two con <lb></lb>trary motions may <lb></lb>naturally agree in <lb></lb>the ſame move <lb></lb>able.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg691"></margin.target><emph type="italics"></emph>The third motion <lb></lb>aſcribed to the <lb></lb>Earth is rather <lb></lb>reſting immove <lb></lb>able.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg692"></margin.target><emph type="italics"></emph>An admirable <lb></lb>intern vertœe of the <lb></lb>terreſtrial Globe of <lb></lb>alwayes beholding <lb></lb>the ſame part of <lb></lb>Heaven.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg693"></margin.target><emph type="italics"></emph>The terreſtriæl <lb></lb>Globe made of <lb></lb>Loade-ſtone.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>Then you are one of thoſe it ſeems that hold the Mag <lb></lb><arrow.to.target n="marg694"></arrow.to.target> <lb></lb>netick Phyloſophy <emph type="italics"></emph>William<emph.end type="italics"></emph.end> ^{*} <emph type="italics"></emph>Gilbert.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg694"></margin.target>An eminent <lb></lb>Doctor of Phyſick, <lb></lb>our Countreyman, <lb></lb>born at <emph type="italics"></emph>Coloheſter,<emph.end type="italics"></emph.end> <lb></lb>and famous for this <lb></lb>his learned Trea <lb></lb>tiſe, publiſhed a <lb></lb>bout 60 years ſince <lb></lb>at <emph type="italics"></emph>London, The <lb></lb>Magnetick Phi <lb></lb>loſophy of<emph.end type="italics"></emph.end> William <lb></lb>Gilbert.</s></p><p type="main"><s>SALV. </s><s>I am for certain, and think that all thoſe that have <lb></lb>ſeriouſly read his Book, and tried his experiments, will bear me <lb></lb>company therein; nor ſhould I deſpair, that what hath befallen <lb></lb>me in this caſe, might poſſibly happen to you alſo, if ſo be a cu <lb></lb>rioſity, like to mine, and a notice that infinite things in Nature <lb></lb>are ſtill conceal'd from the wits of mankind, by delivering you <lb></lb>from being captivated by this or that particular writer in natural <lb></lb>things, ſhould but ſlacken the reines of your Reaſon, and mol <lb></lb>lifie the contumacy and tenaceouſneſſe of your ſenſe; ſo as that <lb></lb>they would not refuſe to hearken ſometimes to novelties never <lb></lb><arrow.to.target n="marg695"></arrow.to.target> <lb></lb>before ſpoken of. </s><s>But (permit me to uſe this phraſe) the puſilla <lb></lb>nimity of vulgar Wits is come to that paſſe, that not only like <lb></lb>blind men, they make a gift, nay tribute of their own aſſent to <lb></lb>whatſoever they find written by thoſe Authours, which in the <lb></lb>infancy of their Studies were laid before them, as authentick by <lb></lb>their Tutors, but refuſe to hear (not to ſay examine) any new <lb></lb>Propoſition or Probleme, although it not only never hath been <lb></lb>confuted, but not ſo much as examined or conſidered by their <lb></lb>Authours. </s><s>Amongſt which, one is this, of inveſtigating what is <lb></lb>the true, proper, primary, interne, and general matter and ſub <lb></lb>ſtance of this our Terreſtrial Globe; For although it never came <lb></lb>into the mind either of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> or of any one elſe, before <emph type="italics"></emph>Wil <lb></lb>liam Gilbert<emph.end type="italics"></emph.end> to think that it might be a Magnet, ſo far are <emph type="italics"></emph>Ari <lb></lb>ſtotle<emph.end type="italics"></emph.end> and the reſt from confuting this opinion, yet nevertheleſſe <lb></lb>I have met with many, that at the very firſt mention of it, as a <lb></lb>Horſe at his own ſhadow, have ſtart back, and refuſed to diſ <lb></lb>courſe thereof, and cenſured the conceipt for a vain <emph type="italics"></emph>Chymæra,<emph.end type="italics"></emph.end> <lb></lb>yea, for a ſolemn madneſſe: and its poſſible the Book of <emph type="italics"></emph>Gilbert<emph.end type="italics"></emph.end> <lb></lb>had never come to my hands, if a Peripatetick Philoſopher, of great <lb></lb>fame, as I believe, to free his Library from its contagion, had not <lb></lb>given it me.</s></p><p type="margin"><s><margin.target id="marg695"></margin.target><emph type="italics"></emph>The Puſillani <lb></lb>mity of Popular <lb></lb>Wits.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. I, who ingenuouſly confeſſe my ſelf to be one of <lb></lb>thoſe vulgar Wits, and never till within theſe few dayes that I <lb></lb>have been admitted to a ſhare in your conferences, could I pre <lb></lb>tend to have in the leaſt withdrawn from thoſe trite and popu <lb></lb>lar paths, yet, for all that, I think I have advantaged my ſelf ſo <lb></lb>much, as that I could without much trouble or difficulty, maſter <lb></lb>the roughneſſes of theſe novel and fantaſtical opinions.</s></p><p type="main"><s>SALV. </s><s>If that which <emph type="italics"></emph>Gilbert<emph.end type="italics"></emph.end> writeth be true, then is it no o <lb></lb>pinion, but the ſubject of Science; nor is it new, but as antient <lb></lb>as the Earth it ſelf; nor can it (being true) be rugged or diffi <lb></lb>cult, but plain and eaſie; and when you pleaſe I ſhall make you <lb></lb>feel the ſame in your hand, for that you of your ſelf fancy it to <pb xlink:href="040/01/385.jpg" pagenum="365"></pb>be a Ghoſt, and ſtand in fear of that which hath nothing in it of <lb></lb>dreadfull, like as a little child doth fear the Hobgoblin, without <lb></lb>knowing any more of it, ſave the name; as that which beſides <lb></lb>the name is nothing.</s></p><p type="main"><s>SIMP. </s><s>I ſhould be glad to be informed, and reclaimed from <lb></lb>an errour.</s></p><p type="main"><s>SALV. </s><s>Anſwer me then to the queſtions that I ſhall ask you. <lb></lb></s><s>And firſt of all, Tell me whether you believe, that this our Globe, <lb></lb>which we inhabit and call Earth, conſiſteth of one ſole and ſim <lb></lb>ple matter, or elſe that it is an aggregate of matters different <lb></lb>from each other.</s></p><p type="main"><s>SIMP. </s><s>I ſee it to be compoſed of ſubſtances and bodies very <lb></lb><arrow.to.target n="marg696"></arrow.to.target> <lb></lb>different; and firſt, for the greateſt parts of the compoſition, <lb></lb>I ſee the Water and the Earth, which extreamly differ from one <lb></lb>another.</s></p><p type="margin"><s><margin.target id="marg696"></margin.target><emph type="italics"></emph>The<emph.end type="italics"></emph.end> Terreſtrial <lb></lb>Globe <emph type="italics"></emph>compoſed of <lb></lb>ſundry matters.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAIV. </s><s>Let us, for this once, lay aſide the Seas and other Wa <lb></lb>ters, and let us conſider the ſolid parts, and tell me, if you think <lb></lb>them one and the ſame thing, or elſe different.</s></p><p type="main"><s>SIMP. </s><s>As to appearance, I ſee that they are different things, <lb></lb>there being very great heaps of unfruitful ſands, and others of <lb></lb>fruitful ſoiles; There are infinite ſharp and ſteril mountains, full <lb></lb>of hard ſtones and quarries of ſeveral kinds, as Porphyre, Ala <lb></lb>blaſter, Jaſper, and a thouſand other kinds of Marbles: There <lb></lb>are vaſt Minerals of ſo many kinds of metals; and in a word, <lb></lb>ſuch varieties of matters, that a whole day would not ſuffice on <lb></lb>ly to enumerate them.</s></p><p type="main"><s>SALV. </s><s>Now of all theſe different matters, do you think, <lb></lb>that in the compoſition of this grand maſſe, there do concur por <lb></lb>tions, or elſe that amongſt them all there is one part that far ex <lb></lb>ceeds the reſt, and is as it were the matter and ſubſtance of the <lb></lb>immenſe lump?</s></p><p type="main"><s>SIMP. </s><s>I believe that the Stones, Marbles, Metals, Gems, and <lb></lb>the ſo many other ſeveral matters are as it were Jewels, and ex <lb></lb>teriour and ſuperficial Ornaments of the primary Globe, which <lb></lb>in groſſe, as I believe, doth without compare exceed all theſe <lb></lb>things put together.</s></p><p type="main"><s>SALV. </s><s>And this principal and vaſt maſſe, of which thoſe <lb></lb>things above named are as it were excreſſences and ornaments, of <lb></lb>what matter do you think that it is compoſed?</s></p><p type="main"><s>SIMP. </s><s>I think that it is the ſimple, or leſſe impure element of <lb></lb>Earth.</s></p><p type="main"><s>SALV. </s><s>But what do you underſtand by Earth? </s><s>Is it haply <lb></lb>that which is diſperſed all over the fields, which is broke up with <lb></lb>Mattocks and Ploughs, wherein we ſowe corne, and plant fruits, <lb></lb>and in which great boſcages grow up, without the help of cul <pb xlink:href="040/01/386.jpg" pagenum="366"></pb>ture, and which is, in a word, the habitation of all animals, and <lb></lb>the womb of all vegetables?</s></p><p type="main"><s>SIMP. </s><s>Tis this that I would affirm to be the ſubſtance of this <lb></lb>our Globe.</s></p><p type="main"><s>SALV. </s><s>But in this you do, in my judgment, affirm that which <lb></lb>is not right: for this Earth which is broke up, is ſowed, and is <lb></lb>fertile, is but one part, and that very ſmall of the ſurface of the <lb></lb>Globe, which doth not go very deep, yea, its depth is very ſmall, <lb></lb>in compariſon of the diſtance to the centre: and experience <lb></lb>ſheweth us, that one ſhall not dig very low, but one ſhall finde <lb></lb>matters very different from this exteriour ſcurf, more ſolid, and <lb></lb>not good for the production of vegetables. </s><s>Beſides the interne <lb></lb>parts, as being compreſſed by very huge weights that lie upon <lb></lb>them, are, in all probability, ſlived, and made as hard as any <lb></lb>hard rock. </s><s>One may adde to this, that fecundity would be in <lb></lb>vain conferred upon thoſe matters which never were deſigned to <lb></lb>bear fruit, but to reſt eternally buried in the profound and dark <lb></lb>abyſſes of the Earth.</s></p><p type="main"><s>SIMP. </s><s>But who ſhall aſſure us, that the parts more inward <lb></lb>and near to the centre are unfruitful? </s><s>They alſo may, perhaps, <lb></lb>have their productions of things unknown to us?</s></p><p type="main"><s>SALV. </s><s>You may aſwell be aſſured thereof, as any man elſe, <lb></lb>as being very capable to comprehend, that if the integral bodies <lb></lb>of the Univerſe be produced onely for the benefit of Mankind, <lb></lb>this above all the reſt ought to be deſtin d to the ſole convenien <lb></lb>ces of us its inhabitants. </s><s>But what beneſit can we draw from <lb></lb>matters ſo hid and remote from us, as that we ſhall never be a <lb></lb><arrow.to.target n="marg697"></arrow.to.target> <lb></lb>ble to make uſe of them? </s><s>Therefore the interne ſubſtance of <lb></lb>this our Globe cannot be a matter frangible, diſſipable, and non <lb></lb>coherent, like this ſuperficial part which we call ^{*} EARTH: but <lb></lb><arrow.to.target n="marg698"></arrow.to.target> <lb></lb>it muſt, of neceſſity, be a moſt denſe and ſolid body, and in a <lb></lb>word, a moſt hard ſtone. </s><s>And, if it ought to be ſo, what reaſon <lb></lb>is there that ſhould make you more ſcrupulous to believe that it <lb></lb>is a Loadſtone than a Porphiry, a Jaſper, or other hard Mar <lb></lb>ble? </s><s>Happily if <emph type="italics"></emph>Gilbert<emph.end type="italics"></emph.end> had written, that this Globe is all com <lb></lb><arrow.to.target n="marg699"></arrow.to.target> <lb></lb>pounded within of ^{*} <emph type="italics"></emph>Pietra Serena,<emph.end type="italics"></emph.end> or of <emph type="italics"></emph>Chalcedon,<emph.end type="italics"></emph.end> the paradox <lb></lb>would have ſeemed to you leſſe exorbitant?</s></p><p type="margin"><s><margin.target id="marg697"></margin.target><emph type="italics"></emph>The interne parts <lb></lb>of the terreſtrial <lb></lb>Globe muſt of ne <lb></lb>ceſſity be ſolid.<emph.end type="italics"></emph.end></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></lb>the Latin tranſla <lb></lb>tour, I muſt once <lb></lb>more profeſſe my <lb></lb>ſelf ignorant.</s></p><p type="main"><s>SIMP. </s><s>That the parts of this Globe more intern are more <lb></lb>compreſſed, and ſo more ſlived together and ſolid, and more <lb></lb>and more ſo, according as they lie lower, I do grant, and ſo <lb></lb>likewiſe doth <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> but that they degenerate and become <lb></lb>other than Earth, of the ſame ſort with this of the ſuperficial <lb></lb>parts, I ſee nothing that obliege h me to believe.</s></p><p type="main"><s>SALV. </s><s>I undertook not this diſcourſe with an intent to prove <lb></lb>demonſtratively that the primary and real ſubſtance of this our <pb xlink:href="040/01/387.jpg" pagenum="367"></pb>Globe is Load-ſtone; but onely to ſhew that no reaſon could be <lb></lb>given why one ſhould be more unwilling to grant that it is of <lb></lb>Load-ſtone, than of ſome other matter. </s><s>And if you will but <lb></lb><arrow.to.target n="marg700"></arrow.to.target> <lb></lb>ſeriouſly conſider, you ſhall find that it is not improbable, that <lb></lb>one ſole, pure, and arbitrary name, hath moved men to think <lb></lb>that it conſiſts of Earth; and that is their having made uſe com <lb></lb>monly from the beginning of this word Earth, as well to ſigni <lb></lb>ſie that matter which is plowed and ſowed, as to name this our <lb></lb>Globe. </s><s>The denomination of which if it had been taken from <lb></lb>ſtone, as that it might as well have been taken from that as <lb></lb>from the Earth; the ſaying that its primary ſubſtance was ſtone, <lb></lb>would doubtleſſe have found no ſcruple or oppoſition in any <lb></lb>man. </s><s>And is ſo much the more probable, in that I verily be <lb></lb>lieve, that if one could but pare off the ſcurf of this great Globe, <lb></lb>taking away but one full thouſand or two thouſand yards; and <lb></lb>afterwards ſeperate the Stones from the Earth, the accumulati <lb></lb>on of the ſtones would be very much biger than that of the fer <lb></lb>tile Mould. </s><s>But as for the reaſons which concludently prove <emph type="italics"></emph>de <lb></lb>facto,<emph.end type="italics"></emph.end> that is our Globe is a Magnet, I have mentioned none of <lb></lb>them, nor is this a time to alledg them, and the rather, for that <lb></lb>to your benefit you may read them in <emph type="italics"></emph>Gilbert<emph.end type="italics"></emph.end>; onely to encou <lb></lb>rage you to the peruſal of them, I will ſet before you, in a ſimi <lb></lb><arrow.to.target n="marg701"></arrow.to.target> <lb></lb>litude of my own, the method that he obſerved in his Philoſo <lb></lb>phy. </s><s>I know you underſtand very well how much the know <lb></lb>ledg of the accidents is ſubſervient to the inveſtigation of the <lb></lb>ſubſtance and eſſence of things; therefore I deſire that you <lb></lb>would take pains to informe your ſelf well of many accidents and <lb></lb>properties that are found in the Magnet, and in no other ſtone, <lb></lb><arrow.to.target n="marg702"></arrow.to.target> <lb></lb>or body; as for inſtance of attracting Iron, of conferring up <lb></lb>on it by its ſole preſence the ſame virtue, of communicating <lb></lb>likewiſe to it the property of looking towards the Poles, as it <lb></lb>alſo doth it ſelf; and moreover endeavour to know by trial, <lb></lb>that it containeth in it a virtue of conferring upon the magnetick <lb></lb>needle not onely the direction under a Meridian towards the <lb></lb>Poles, with an Horizontal motion, (a property a long time ago <lb></lb>known) but a new found accident, of declining (being ballanced <lb></lb>under the Meridian before marked upon a little ſpherical Mag <lb></lb>net) of declining I ſay to determinate marks more or leſſe, ac <lb></lb>cording as that needle is held nearer or farther from the Pole, <lb></lb>till that upon the Pole it ſelf it erecteth perpendicularly, where <lb></lb>as in the middle parts it is parallel to the Axis. </s><s>Furthermore pro <lb></lb>cure a proof to be made, whether the virtue of attracting Iron, <lb></lb>reſiding much more vigorouſly about the Poles, than about the <lb></lb>middle parts, this force be not notably more vigorous in one <lb></lb>Pole than in the other, and that in all pieces of Magnet; the <pb xlink:href="040/01/388.jpg" pagenum="368"></pb>ſtronger of which Poles is that which looketh towards the South. <lb></lb></s><s>Obſerve, in the next place, that in a little Magnet this South and <lb></lb>more vigorous Pole, becometh weaker, when ever it is to take <lb></lb>up an iron in preſence of the North Pole, of another much big <lb></lb>ger Magnet: and not to make any tedious diſcourſe of it, aſſer <lb></lb>tain your ſelf, by experience, of theſe and many other properties <lb></lb>deſcribed by <emph type="italics"></emph>Gilbert,<emph.end type="italics"></emph.end> which are all ſo peculiar to the Magnet, as <lb></lb><arrow.to.target n="marg703"></arrow.to.target> <lb></lb>that none of them agree with any other matter. </s><s>Tell me now, <lb></lb><emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> if there were laid before you a thouſand pieces of <lb></lb>ſeveral matters, but all covered and concealed in a cloth, under <lb></lb>which it is hid, and you were required, without uncovering them, <lb></lb>to make a gueſſe, by external ſignes, at the matter of each of <lb></lb>them, and that in making trial, you ſhould hit upon one that <lb></lb>ſhould openly ſhew it ſelf to have all the properties by you alrea <lb></lb>dy acknowledged to reſide onely in the Magnet, and in no other <lb></lb>matter, what judgment would you make of the eſſence of ſuch a <lb></lb>body? </s><s>Would you ſay, that it might be a piece of Ebony, or <lb></lb>Alablaſter, or Tin.</s></p><p type="margin"><s><margin.target id="marg700"></margin.target><emph type="italics"></emph>Our Globe would <lb></lb>have been called <lb></lb>ſtone, in ſtead of <lb></lb>Earth, if that <lb></lb>name had been gi <lb></lb>uen it in the be <lb></lb>ginning.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg701"></margin.target><emph type="italics"></emph>The method of<emph.end type="italics"></emph.end> <lb></lb>Gilbert <emph type="italics"></emph>in his Phi <lb></lb>loſophy.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg702"></margin.target><emph type="italics"></emph>Many proper <lb></lb>ties in the Mag <lb></lb>net.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg703"></margin.target><emph type="italics"></emph>An Argument <lb></lb>proving the terre <lb></lb>ſtrial Globe to be <lb></lb>a<emph.end type="italics"></emph.end> Magnet.</s></p><p type="main"><s>SIMP. </s><s>I would ſay, without the leaſt hæſitation, that it was a <lb></lb>piece of Load-ſtone.</s></p><p type="main"><s>SALV. </s><s>If it be ſo, ſay reſolutely, that under this cover and <lb></lb>ſcurf of Earth, ſtones, metals, water, &c. </s><s>there is hid a great <lb></lb>Magnet, foraſmuch as about the ſame there may be ſeen by any <lb></lb>one that will heedfully obſerve the ſame, all thoſe very accidents <lb></lb>that agree with a true and viſible Globe of Magnet; but if no <lb></lb>more were to be ſeen than that of the Declinatory Needle, which <lb></lb>being carried about the Earth, more and more inclineth, as it ap <lb></lb>proacheth to the North Pole, and declineth leſſe towards the E <lb></lb>quinoctial, under which it finally is brought to an <emph type="italics"></emph>Æquilibrium,<emph.end type="italics"></emph.end> <lb></lb>it might ſerve to perſwade even the moſt ſcrupulous judgment. </s><s>I <lb></lb>forbear to mention that other admirable effect, which is ſenſibly <lb></lb>obſerved in every piece of Magnet, of which, to us inhabitants <lb></lb>of the Northern Hemiſphere, the Meridional Pole of the ſaid Mag <lb></lb>net is more vigorous than the other; and the difference is found <lb></lb>greater, by how much one recedeth from the Equinoctial; and <lb></lb>under the Equinoctial both the parts are of equal ſtrength, but <lb></lb>notably weaker. </s><s>But, in the Meridional Regions, far diſtant <lb></lb>from the Equinoctial, it changeth nature, and that part which to <lb></lb>us was more weak, acquireth more ſtrength than the other: and <lb></lb>all this I confer with that which we ſee to be done by a ſmall <lb></lb>piece of Magnet, in the preſence of a great one, the vertue of <lb></lb>which ſuperating the leſſer, maketh it to become obedient to it, <lb></lb>and according as it is held, either on this or on that ſide the Equi <lb></lb>noctial of the great one, maketh the ſelf ſame mutations, <lb></lb>which I have ſaid are made by every Magnet, carried on this <pb xlink:href="040/01/389.jpg" pagenum="369"></pb>ſide, or that ſide of the Equinoctiall of the Earth.</s></p><p type="main"><s>SAGR. </s><s>I was perſwaded, at the very firſt reading of the Book <lb></lb>of <emph type="italics"></emph>Gilbertus<emph.end type="italics"></emph.end>; and having met with a moſt excellent piece of <lb></lb><arrow.to.target n="marg704"></arrow.to.target> <lb></lb>Magnet, I, for a long time, made many Obſervations, and all <lb></lb>worthy of extream wonder; but above all, that ſeemeth to me <lb></lb>very ſtupendious of increaſing the faculty of taking up Iron ſo <lb></lb>much by arming it, like as the ſaid Authour teacheth; and with <lb></lb>arming that piece of mine, I multiplied its force in octuple propor <lb></lb>tion; and whereas unarmed it ſcarce took up nine ounces of <lb></lb>Iron, it being armed did take up above ſix pounds: And, it <lb></lb>may be, you have ſeen this Loadſtone in the ^{*} Gallery of your <lb></lb><arrow.to.target n="marg705"></arrow.to.target> <lb></lb><emph type="italics"></emph>Moſt Serene Grand Duke<emph.end type="italics"></emph.end> (to whom I preſented it) upholding <lb></lb>two little Anchors of Iron.</s></p><p type="margin"><s><margin.target id="marg704"></margin.target><emph type="italics"></emph>|The Magnet <lb></lb>armed takes up <lb></lb>much more Iron, <lb></lb>than when unar <lb></lb>med.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg705"></margin.target>+ Or Cloſet of <lb></lb>rarities.</s></p><p type="main"><s>SALV. </s><s>I ſaw it many times, and with great admiration, till <lb></lb>that a little piece of the like ſtone gave me greater cauſe of won <lb></lb>der, that is in the keeping of our Academick, which being no <lb></lb>more than of ſix ounces weight, and ſuſtaining, when unarmed, <lb></lb>hardly two ounces, doth, when armed, take up 160. ounces, ſo <lb></lb>as that it is of 80. times more force armed than unarmed, and <lb></lb>takes up a weight 26. times greater than its own; a much greater <lb></lb>wonder than <emph type="italics"></emph>Gilbert<emph.end type="italics"></emph.end> could ever meet with, who writeth, that he <lb></lb>could never get any Loadſtone that could reach to take up four <lb></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></lb>large Field to Phyloſophate in; and I have many times thought <lb></lb>with my ſelf, how it can be that it conferreth on that Iron, which <lb></lb>armeth it, a ſtrength ſo ſuperiour to its own; and finally, I finde <lb></lb>nothing that giveth me ſatisfaction herein; nor do I find any <lb></lb>thing extraordinary in that which <emph type="italics"></emph>Gilbert<emph.end type="italics"></emph.end> writes about this parti <lb></lb>cular; I know not whether the ſame may have befallen <lb></lb>you.</s></p><p type="main"><s>SALV. </s><s>I extreamly praiſe, admire, and envy this Authour, <lb></lb>for that a conceit ſo ſtupendious ſhould come into his minde, <lb></lb>touching a thing handled by infinite ſublime wits, and hit upon <lb></lb>by none of them: I think him moreover worthy of extraordi <lb></lb>nary applauſe for the many new and true Obſervations that he <lb></lb>made, to the diſgrace of ſo many fabulous Authours, that write <lb></lb>not only what they do not know, but what ever they hear ſpo <lb></lb>ken by the fooliſh vulgar, never ſeeking to aſſure themſelves of <lb></lb>the ſame by experience, perhaps, becauſe they are unwilling to <lb></lb>diminiſh the bulk of their Books. </s><s>That which I could have de <lb></lb>ſired in <emph type="italics"></emph>Gilbert,<emph.end type="italics"></emph.end> is, that he had been a little greater Mathematici <lb></lb>an, and particularly well grounded in <emph type="italics"></emph>Geometry,<emph.end type="italics"></emph.end> the practice <lb></lb>whereof would have rendered him leſs reſolute in accepting thoſe <lb></lb>reaſons for true Demonſtrations, which he produceth for true <pb xlink:href="040/01/390.jpg" pagenum="370"></pb>cauſes of the true concluſions obſerved by himſelf. </s><s>Which rea <lb></lb>ſons (freely ſpeaking) do not knit and bind ſo faſt, as thoſe un <lb></lb>doubtedly ought to do, in that of natural, neceſſary, and laſting <lb></lb>concluſions may be alledged. </s><s>And I doubt not, but that in pro <lb></lb>ceſſe of time this new Science will be perfected with new obſer <lb></lb>vations, and, which is more, with true and neceſſary Demonſtra <lb></lb><arrow.to.target n="marg706"></arrow.to.target> <lb></lb>tions. </s><s>Nor ought the glory of the firſt Inventor to be thereby <lb></lb>diminiſhed, nor do I leſſe eſteem, but rather more admire, the <lb></lb>Inventor of the Harp (although it may be ſuppoſed that the In <lb></lb>ſtrument at firſt was but rudely framed, and more rudely finger <lb></lb>ed) than an hundred other Artiſts, that in the inſuing Ages redu <lb></lb>ced that profeſſion to great perfection. </s><s>And methinks, that An <lb></lb>tiquity had very good reaſon to enumerate the firſt Inventors of <lb></lb>the Noble Arts amongſt the Gods; ſeeing that the common wits <lb></lb>have ſo little curioſity, and are ſo little regardful of rare and ele <lb></lb>gant things, that though they ſee and hear them exercirated by <lb></lb>the exquifite profeſſors of them, yet are they not thereby per <lb></lb>ſwaded to a deſire of learning them. </s><s>Now judge, whether Capa <lb></lb>cities of this kind would ever have attempted to have found out <lb></lb>the making of the Harp, or the invention of Muſick, upon the <lb></lb>hint of the whiſtling noiſe of the dry ſinews of a Tortois, or <lb></lb>from the ſtriking of four Hammers. </s><s>The application to great <lb></lb>inventions moved by ſmall hints, and the thinking that under a <lb></lb>primary and childiſh appearance admirable Arts may lie hid, is <lb></lb>not the part of a trivial, but of a ſuper-humane ſpirit. </s><s>Now an <lb></lb>ſwering to your demands, I ſay, that I alſo have long thought <lb></lb>upon what might poſſibly be the cauſe of this ſo tenacious and <lb></lb>potent union, that we ſee to be made between the one Iron that <lb></lb>armeth the Magnet, and the other that conjoyns it ſelf unto it. <lb></lb><arrow.to.target n="marg707"></arrow.to.target> <lb></lb>And firſt, we are certain, that the vertue and ſtrength of the ſtone <lb></lb>doth not augment by being armed, for it neither attracts at <lb></lb>greater diſtance, nor doth it hold an Iron the faſter, if between it, <lb></lb>and the arming or cap, a very fine paper, or a leaf of beaten gold, <lb></lb>be interpoſed; nay, with that interpoſition, the naked ſtone <lb></lb>takes up more Iron than the armed. </s><s>There is therefore no alte <lb></lb>ration in the vertue, and yet there is an innovation in the effect. <lb></lb><arrow.to.target n="marg708"></arrow.to.target> <lb></lb>And becauſe its neceſſary, that a new effect have a new cauſe, if <lb></lb>it be inquired what novelty is introduced in the act of taking up <lb></lb>with the cap or arming, there is no mutation to be diſcovered, but <lb></lb>in the different contact; for whereas before Iron toucht Load <lb></lb>ſtone, now Iron toucheth Iron. </s><s>Therefore it is neceſſary to con <lb></lb>clude, that the diverſity of contacts is the cauſe of the diverſity <lb></lb><arrow.to.target n="marg709"></arrow.to.target> <lb></lb>of effects. </s><s>And for the difference of contacts it cannot, as I ſee, <lb></lb>be derived from any thing elſe, ſave from that the ſubſtance of <lb></lb>the Iron is of parts more ſubtil, more pure, and more compact <pb xlink:href="040/01/391.jpg" pagenum="371"></pb>ed than thoſe of the Magnet, which are more groſſe, impure, and <lb></lb>rare. </s><s>From whence it followeth, that the ſuperficies of two I <lb></lb>rons that are to touch, by being exquiſitely plained, filed, and <lb></lb>burniſhed, do ſo exactly conjoyn, that all the infinite points of <lb></lb>the one meet with the infinite points of the other; ſo that the <lb></lb>filaments, if I may ſo ſay, that collegate the two Irons, are many <lb></lb>more than thoſe that collegate the Magnet to the Iron, by reaſon <lb></lb>that the ſubſtance of the Magnet is more porous, and leſſe com <lb></lb>pact, which maketh that all the points and filaments of the Load <lb></lb>ſtone do not cloſe with that which it unites unto. </s><s>In the next <lb></lb>place, that the ſubſtance of Iron (eſpecially the well refined, as <lb></lb>namely, the pureſt ſteel) is of parts much more denſe, ſubtil, <lb></lb>and pure than the matter of the Loadſtone, is ſeen, in that one <lb></lb>may bring its edge to an extraordinary ſharpneſſe, ſuch as is that <lb></lb>of the Raſor, which can never be in any great meaſure effected in <lb></lb>a piece of Magnet. </s><s>Then, as for the impurity of the Magnet, and <lb></lb><arrow.to.target n="marg710"></arrow.to.target> <lb></lb>its being mixed with other qualities of ſtone, it is firſt ſenſibly <lb></lb>diſcovered by the colour of ſome little ſpots, for the moſt part <lb></lb>white; and next by preſenting a needle to it, hanging in a <lb></lb>thread, which upon thoſe ſtonyneſſes cannot find repoſe, but <lb></lb>being attracted by the parts circumfuſed, ſeemeth to fly from <lb></lb><arrow.to.target n="marg711"></arrow.to.target> <lb></lb>^{*} <emph type="italics"></emph>thoſe,<emph.end type="italics"></emph.end> and to leap upon the Magnet contiguous to <emph type="italics"></emph>them:<emph.end type="italics"></emph.end> and <lb></lb>as ſome of thoſe Heterogeneal parts are for their magnitude ve <lb></lb>ry viſible, ſo we may believe, that there are others, in great a <lb></lb>bundance, which, for their ſmallneſſe, are imperceptible, that are <lb></lb>diſſeminated throughout the whole maſſe. </s><s>That which I ſay, <lb></lb>(namely, that the multitude of contacts that are made between <lb></lb>Iron and Iron, is the cauſe of the ſo ſolid conjunction) is con <lb></lb>firmed by an experiment, which is this, that if we preſent the <lb></lb>ſharpned point of a needle to the cap of a Magnet, it will ſtick <lb></lb>no faſter to it, than to the ſame ſtone unarmed: which can <lb></lb>proceed from no other cauſe, than from the equality of the con <lb></lb>tacts that are both of one ſole point. </s><s>But what then? </s><s>Let a <lb></lb>^{*} Needle be taken and placed upon a Magnet, ſo that one of its <lb></lb><arrow.to.target n="marg712"></arrow.to.target> <lb></lb>extremities hang ſomewhat over, and to that preſent a Nail; to <lb></lb>which the Needle will inſtantly cleave, inſomuch that withdraw <lb></lb>ing the Nail, the Needle will ſtand in ſuſpenſe, and with its two <lb></lb>ends touching the Magnet and the Iron; and withdrawing the <lb></lb>Nail yet a little further, the Needle will forſake the Magnet; <lb></lb>provided that the eye of the Needle be towards the Nail, and <lb></lb>the point towards the Magnet; but if the eye be towards the <lb></lb>Loadſtone, in withdrawing the Nail the Needle will cleave to <lb></lb>the Magnet; and this, in my judgment, for no other reaſon, <lb></lb>ſave onely that the Needle, by reaſon it is bigger towards the <lb></lb>eye, toucheth in much more points than its ſharp point doth.</s></p> <pb xlink:href="040/01/392.jpg" pagenum="372"></pb><p type="margin"><s><margin.target id="marg706"></margin.target><emph type="italics"></emph>The firſt obſer <lb></lb>vers and inventers <lb></lb>of things ought to <lb></lb>be admired.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg707"></margin.target><emph type="italics"></emph>The true cauſe <lb></lb>of the multiplica <lb></lb>tion of vertue in <lb></lb>the Magnet, by <lb></lb>means of the ar <lb></lb>ming.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg708"></margin.target><emph type="italics"></emph>Of a new effect <lb></lb>its neceſſary that <lb></lb>the cauſe be like <lb></lb>wiſe new.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg709"></margin.target><emph type="italics"></emph>It is proved, <lb></lb>that Iron conſists <lb></lb>of parts more ſub <lb></lb>til, pure, and com <lb></lb>pact than the mag <lb></lb>net.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg710"></margin.target><emph type="italics"></emph>A ſenſible proof <lb></lb>of the impurity of <lb></lb>the Magnet.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg711"></margin.target>* The Author <lb></lb>hereby meaneth <lb></lb>that the ſtone <lb></lb>doth not all con <lb></lb>ſiſt of magnetick <lb></lb>matter, but that <lb></lb>the whiter ſpecks <lb></lb>being weak, thoſe <lb></lb>other parts of the <lb></lb>Loadſtone of a <lb></lb>more dark & con <lb></lb>ſtant colour, con <lb></lb>tain all that vertue <lb></lb>wherewith bodies <lb></lb>are attracted.</s></p><p type="margin"><s><margin.target id="marg712"></margin.target>* A common <lb></lb>ſewing needle.</s></p><p type="main"><s>SAGR. </s><s>Your whole diſcourſe hath been in my judgment very <lb></lb>concluding, and this experiment of the Needle hath made me <lb></lb>think it little inferiour to a Mathematical Demonſtration; and <lb></lb>I ingenuouſly confeſſe, that in all the Magnetick Philoſophy, I <lb></lb>never heard or read any thing, that with ſuch ſtrong reaſons <lb></lb>gave account of its ſo many admirable accidents, of which, if the <lb></lb>cauſes were with the ſame perſpicuity laid open, I know not <lb></lb>what ſweeter food our Intellects could deſire.</s></p><p type="main"><s>SALV. </s><s>In ſeeking the reaſons of concluſions unknown unto <lb></lb>us, it is requiſite to have the good fortune to direct the diſ <lb></lb>courſe from the very beginning towards the way of truth; in <lb></lb>which if any one walk, it will eaſily happen, that one ſhall meet <lb></lb>with ſeveral other Propoſitions known to be true, either by diſ <lb></lb>putes or experiments, from the certainty of which the truth of <lb></lb>ours acquireth ſtrength and evidence; as it did in every reſpect <lb></lb>happen to me in the preſent Probleme, for being deſirous to aſ <lb></lb>ſure my ſelf, by ſome other accident, whether the reaſon of the <lb></lb>Propoſition, by me found, were true; namely, whether the ſub <lb></lb>ſtance of the Magnet were really much leſſe continuate than that <lb></lb>of Iron or of Steel, I made the Artiſts that work in the Gallery <lb></lb>of my Lord the Grand Duke, to ſmooth one ſide of that piece <lb></lb>of Magnet, which formerly was yours, and then to poliſh and <lb></lb>burniſh it; upon which to my ſatisfaction I found what I deſired. <lb></lb></s><s>For I diſcovered many ſpecks of colour different from the reſt, <lb></lb>but as ſplendid and bright, as any of the harder ſort of ſtones; <lb></lb>the reſt of the Magnet was polite, but to the tact onely, not <lb></lb>being in the leaſt ſplendid; but rather as if it were ſmeered over <lb></lb>with ſoot; and this was the ſubſtance of the Load ſtone, and <lb></lb>the ſhining part was the fragments of other ſtones intermixt <lb></lb>therewith, as was ſenſibly made known by preſenting the face <lb></lb>thereof to filings of Iron, the which in great number leapt to <lb></lb>the Load-ſtone, but not ſo much as one grain did ſtick to the <lb></lb>ſaid ſpots, which were many, ſome as big as the fourth part of <lb></lb>the nail of a mans finger, others ſomewhat leſſer, the leaſt of <lb></lb>all very many, and thoſe that were ſcarce viſible almoſt innu <lb></lb>merable. </s><s>So that I did aſſure my ſelf, that my conjecture was <lb></lb>true, when I firſt thought that the ſubſtance of the Magnet <lb></lb>was not cloſe and compact, but porous, or to ſay better, ſpon <lb></lb>gy; but with this difference, that whereas the ſponge in its <lb></lb>cavities and little cels conteineth Air or Water, the Magnet hath <lb></lb>its pores full of hard and heavy ſtone, as appears by the exqui <lb></lb>ſite luſtre which thoſe ſpecks receive. </s><s>Whereupon, as I have ſaid <lb></lb>from the beginning, applying the ſurface of the Iron to the ſu <lb></lb>perficies of the Magnet the minute particles of the Iron, though <lb></lb>perhaps more continuate than theſe of any other body (as its <pb xlink:href="040/01/393.jpg" pagenum="373"></pb>ſhining more than any other matter doth ſhew) do not all, nay <lb></lb>but very few of them incounter pure Magnet; and the contacts <lb></lb>being few, the union is but weak. </s><s>But becauſe the cap of the <lb></lb>Load-ſtone, beſides the contact of a great part of its ſuperficies, <lb></lb>inveſts its ſelf alſo with the virtue of the parts adjoyning, al <lb></lb>though they touch not; that ſide of it being exactly ſmoothed <lb></lb>to which the other face, in like manner well poliſht of the Iron to <lb></lb>be attracted, is applyed, the contact is made by innumera <lb></lb>ble minute particles, if not haply by the infinite points of both <lb></lb>the ſuperficies, whereupon the union becometh very ſtrong. <lb></lb></s><s>This obſervation of ſmoothing the ſurfaces of the Irons that are <lb></lb>to touch, came not into the thoughts of <emph type="italics"></emph>Gilbert,<emph.end type="italics"></emph.end> for he makes <lb></lb>the Irons convex, ſo that their contact is very ſmall; and there <lb></lb>upon it cometh to paſſe that the tenacity, wherewith thoſe Irons <lb></lb>conjoyn, is much leſſer.</s></p><p type="main"><s>SAGR. </s><s>I am, as I told you before, little leſſe ſatisfied with <lb></lb>this reaſon, that if it were a pure Geometrical Demonſtration; <lb></lb>and becauſe we ſpeak of a Phyſical Problem, I believe that alſo <lb></lb><emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> will find himſelf ſatisfied as far as natural ſcience ad <lb></lb>mits, in which he knows that Geometrical evidence is not to be <lb></lb>required.</s></p><p type="main"><s>SIMP. </s><s>I think indeed, that <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> with a fine circumlo <lb></lb><arrow.to.target n="marg713"></arrow.to.target> <lb></lb>cution hath ſo manifeſtly diſplayed the cauſe of this effect, that <lb></lb>any indifferent wit, though not verſt in the Sciences, may ap <lb></lb>prehend the ſame; but we, confining our ſelves to the terms of <lb></lb>Art, reduce the cauſe of theſe and other the like natural effects <lb></lb>to <emph type="italics"></emph>Sympathy,<emph.end type="italics"></emph.end> which is a certain agreement and mutual appetite <lb></lb>which ariſeth between things that are ſemblable to one another <lb></lb>in qualities; as likewiſe on the contrary that hatred & enmity for <lb></lb>which other things ſhun & abhor one another we call <emph type="italics"></emph>Antipathy.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg713"></margin.target>Sympathy <emph type="italics"></emph>and<emph.end type="italics"></emph.end> <lb></lb>Antipathy, <emph type="italics"></emph>terms <lb></lb>uſed by Philoſo <lb></lb>phers to give a rea <lb></lb>ſon eaſily of ma <lb></lb>ny narural effests.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>And thus with theſe two words men come to render <lb></lb>reaſons of a great number of accidents and effects which we ſee <lb></lb>not without admiration to be produced in nature. </s><s>But this kind <lb></lb>of philoſophating ſeems to me to have great ſympathy with a <lb></lb><arrow.to.target n="marg714"></arrow.to.target> <lb></lb>certain way of Painting that a Friend of mine uſed, who writ <lb></lb>upon the <emph type="italics"></emph>Tele<emph.end type="italics"></emph.end> or Canvaſſe in chalk, here I will have the Foun <lb></lb>tain with <emph type="italics"></emph>Diana<emph.end type="italics"></emph.end> and her Nimphs, there certain Hariers, in this <lb></lb>corner I will have a Huntſ-man with the Head of a Stag, the reſt <lb></lb>ſhall be Lanes, Woods, and Hills; and left the remainder for <lb></lb>the Painter to ſet forth with Colours; and thus he perſwaded <lb></lb>himſelf that he had painted the Story of <emph type="italics"></emph>Acteon,<emph.end type="italics"></emph.end> when as he had <lb></lb>contributed thereto nothing of his own more than the names. <lb></lb></s><s>But whether are we wandred with ſo long a digreſſion, contrary <lb></lb>to our former reſolutions? </s><s>I have almoſt forgot what the point <lb></lb>was that we were upon when we fell into this magnetick diſ <pb xlink:href="040/01/394.jpg" pagenum="374"></pb>courſe; and yet I had ſomething in my mind that I intended to <lb></lb>have ſpoken upon that ſubject.</s></p><p type="margin"><s><margin.target id="marg714"></margin.target><emph type="italics"></emph>A pleaſant ex <lb></lb>ampleaeclaring the <lb></lb>invalidity of ſome <lb></lb>Phyloſophical ar <lb></lb>gumentations.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>We were about to demonſtrate that third motion a <lb></lb>ſcribed by <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> to the Earth to be no motion but a quie <lb></lb>ſcence and maintaining of it ſelf immutably directed with its de <lb></lb>terminate parts towards the ſame & determinate parts of the Uni <lb></lb>verſe, that is a perpetual conſervation of the Axis of its diurnal <lb></lb>revolution parallel to it ſelf, and looking towards ſuch and ſuch <lb></lb>fixed ſtars; which moſt conſtant poſition we ſaid did naturally <lb></lb>agree with every librated body ſuſpended in a fluid and yielding <lb></lb><emph type="italics"></emph>medium,<emph.end type="italics"></emph.end> which although carried about, yet did it not change di <lb></lb>rectionin reſpect of things external, but onely ſeemed to revolve in <lb></lb>its ſelf, in reſpect of that which carryed it round, and to the <lb></lb>veſſel in which it was tranſported. </s><s>And then we added to this <lb></lb>ſimple and natural accident the magnetick virtue, whereby the <lb></lb>ſelf Terreſtrial Globe might ſo much the more conſtantly keep it <lb></lb>immutable, -----</s></p><p type="main"><s>SAGR. </s><s>Now I remember the whole buſineſſe; and that which <lb></lb>then came into my minde, & which I would have intimated, was a <lb></lb>certain conſideration touching the ſcruple and objection of <emph type="italics"></emph>Sim <lb></lb>plicius,<emph.end type="italics"></emph.end> which he propounded againſt the mobility of the Earth, <lb></lb><arrow.to.target n="marg715"></arrow.to.target> <lb></lb>taken from the multiplicity of motions, impoſſible to be aſſigned <lb></lb>to a ſimple body, of which but one ſole and ſimple motion, ac <lb></lb>cording to the doctrine of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> can be natural; and that <lb></lb>which I would have propoſed to conſideration, was the Magnet, <lb></lb>to which we manifeſtly ſee three motions naturally to agree: <lb></lb>one towards the centre of the Earth, as a <emph type="italics"></emph>Grave<emph.end type="italics"></emph.end>; the ſecond is <lb></lb>the circular Horizontal Motion, whereby it reſtores and con <lb></lb>ſerves its Axis towards determinate parts of the Univerſe; and <lb></lb>the third is this, newly diſcovered by <emph type="italics"></emph>Gilbert,<emph.end type="italics"></emph.end> of inclining its <lb></lb>Axis, being in the plane of a Meridian towards the ſurface of the <lb></lb>Earth, and this more and leſſe, according as it ſhall be diſtant <lb></lb>from the Equinoctial, under which it is parallel to the Axis of <lb></lb>the Earth. </s><s>Beſides theſe three, it is not perhaps improbable, <lb></lb>but that it may have a fourth, of revolving upon its own Axis, in <lb></lb>caſe it were librated and ſuſpended in the air or other fluid and <lb></lb>yielding <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> ſo that all external and accidental impediments <lb></lb>were removed, and this opinion <emph type="italics"></emph>Gilbert<emph.end type="italics"></emph.end> himſelf ſeemeth alſo to <lb></lb>applaud. </s><s>So that, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> you ſee how tottering the Axiome <lb></lb>of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> is.</s></p><p type="margin"><s><margin.target id="marg715"></margin.target><emph type="italics"></emph>The ſeveral na <lb></lb>tural motions of <lb></lb>the Magnet.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>This doth uot only not make againſt the Maxime, but <lb></lb>not ſo much as look towards it: for that he ſpeaketh of a fimple <lb></lb>body, and of that which may naturally conſiſt therewith; but <lb></lb>you propoſe that which befalleth a mixt body; nor do you tell <lb></lb>us of any thing that is new to the doctrine of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> for that <pb xlink:href="040/01/395.jpg" pagenum="375"></pb>he likewiſe granteth to mixt bodies compound motions by -----</s></p><p type="main"><s>SAGR. </s><s>Stay a little, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> & anſwer me to the queſtions <lb></lb>I ſhall ask you. </s><s>You ſay that the Load-ſtone is no ſimple body, <lb></lb><arrow.to.target n="marg716"></arrow.to.target> <lb></lb>now I defire you to tell me what thoſe ſimple bodies are, that <lb></lb>mingle in compoſing the Load-ſtone.</s></p><p type="margin"><s><margin.target id="marg716"></margin.target>Ariſtole <emph type="italics"></emph>grants <lb></lb>a compound motion <lb></lb>to mixt bodies.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I know not how to tell you th'ingredients nor ſimples <lb></lb>preciſely, but it ſufficeth that they are things elementary.</s></p><p type="main"><s>SALV. </s><s>So much ſufficeth me alſo. </s><s>And of theſe ſimple ele <lb></lb>mentary bodies, what are the natural motions?</s></p><p type="main"><s>SIMP. </s><s>They are the two right and ſimple motions, <emph type="italics"></emph>ſurſum<emph.end type="italics"></emph.end> <lb></lb>and <emph type="italics"></emph>deorſum.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Tell me in the next place? </s><s>Do you believe that the <lb></lb>motion, that ſhall remain natural to that ſame mixed body, ſhould <lb></lb>be one that may reſult from the compoſition of the two ſimple <lb></lb>natural motions of the ſimple bodies compounding, or that it <lb></lb>may be a motion impoſſible to be compoſed of them. <lb></lb><arrow.to.target n="marg717"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg717"></margin.target><emph type="italics"></emph>The motion of <lb></lb>mixt bodies ought <lb></lb>to be ſuch as may <lb></lb>reſult from the <lb></lb>compoſition of the <lb></lb>motions of the ſim <lb></lb>ple bodies com <lb></lb>pounding.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I believe that it ſhall move with the motion reſulting <lb></lb>from the compoſition of the motions of the ſimple bodies com <lb></lb>pounding, and that with a motion impoſſible to be compoſed of <lb></lb>theſe, it is impoſſible that it ſhould move.</s></p><p type="main"><s>SAGR. But, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> with two right and ſimple motions, you <lb></lb>ſhall never be able to compoſe a circular motion, ſuch as are the </s></p><p type="main"><s><arrow.to.target n="marg718"></arrow.to.target> <lb></lb>two, or three circular motions that the magnet hath: you ſee <lb></lb>then into what abſurdities evil grounded Principles, or, to ſay <lb></lb><arrow.to.target n="marg719"></arrow.to.target> <lb></lb>better, the ill-inferred conſequences of good Principles carry a <lb></lb>man; for you are now forced to ſay, that the Magnet is a mix <lb></lb>ture compounded of ſubſtances elementary and cœleſtial, if you <lb></lb>will maintain that the ſtraight motion is a peculiar to the Ele <lb></lb>ments, and the circular to the cœleſtial bodies. </s><s>Therefore if <lb></lb>you will more ſafely argue, you muſt ſay, that of the integral <lb></lb>bodies of the Univerſe, thoſe that are by nature moveable, do all <lb></lb>move circularly, and that therefore the Magnet, as a part of the <lb></lb><arrow.to.target n="marg720"></arrow.to.target> <lb></lb>true primary, and integral ſubſtance of our Globe, pertaketh of <lb></lb>the ſame qualities with it. </s><s>And take notice of this your fallacy, <lb></lb>in calling the Magnet a mixt body, and the Terreſtrial Globe a <lb></lb>ſimple body, which is ſenſibly perceived to be a thouſand times <lb></lb>more compound: for, beſides that it containeth an hundred an <lb></lb>hundred matters, exceeding different from one another, it con <lb></lb>taineth great abundance of this which you call mixt, I mean <lb></lb>of the Load-ſtone. </s><s>This ſeems to me juſt as if one ſhould call <lb></lb><arrow.to.target n="marg721"></arrow.to.target> <lb></lb>bread a mixt body, and ^{*} <emph type="italics"></emph>Pannada<emph.end type="italics"></emph.end> a ſimple body, in which there <lb></lb>is put no ſmall quantity of bread, beſides many other things edi <lb></lb>ble. </s><s>This ſeemeth to me a very admirable thing, amongſt others <pb xlink:href="040/01/396.jpg" pagenum="376"></pb><arrow.to.target n="marg722"></arrow.to.target> <lb></lb>of the Peripateticks, who grant (nor can it be denied) that our <lb></lb>Terreſtrial Globe is, <emph type="italics"></emph>de facto,<emph.end type="italics"></emph.end> a compound of infinite different <lb></lb>matters; and grant farther that of compound bodies the motion <lb></lb>ought to be compound: now the motions that admit of compo <lb></lb>ſition are the right and circular: For the two right motions, as <lb></lb>being contrary, are incompatible together, they affirm, that the <lb></lb>pure Element of Earth is no where to be found; they confeſſe, <lb></lb>that it never hath been moved with a local motion; and yet they <lb></lb>will introduce in Nature that body which is not to be found, and <lb></lb>make it move with that motion which it never exerciſed, nor ne <lb></lb>ver ſhall do, and to that body which hath, and ever had a being, <lb></lb>they deny that motion, which before they granted, ought natu <lb></lb>rally to agree therewith.</s></p><p type="margin"><s><margin.target id="marg718"></margin.target><emph type="italics"></emph>With two right <lb></lb>motions one cannot <lb></lb>compoſe circular <lb></lb>motions.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg719"></margin.target><emph type="italics"></emph>Philoſophers are <lb></lb>forced to confeſſe <lb></lb>that the Magnet <lb></lb>is compounded of <lb></lb>cœleſtial ſubſtan <lb></lb>ces, and of elemen <lb></lb>tary.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg720"></margin.target><emph type="italics"></emph>The errour of <lb></lb>thoſe who call the <lb></lb>Magnet a mixt <lb></lb>body, and the ter <lb></lb>reſtrial Globe <lb></lb>ſimble body.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg721"></margin.target>* Ogliopotrida <lb></lb><emph type="italics"></emph>a Spaniſh diſh of <lb></lb>many ingredients <lb></lb>boild together.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg722"></margin.target><emph type="italics"></emph>The Diſcourſes <lb></lb>of Peripateticks, <lb></lb>full of errours and <lb></lb>contradictions.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>I beſeech you, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> let us not weary our ſelves <lb></lb>any more about theſe particulars, and the rather, becauſe you <lb></lb>know that our purpoſe was not to determine reſolutely, or to <lb></lb>accept for true, this or that opinion, but only to propoſe for our <lb></lb>divertiſement ſuch reaſons, and anſwers as may be alledged on <lb></lb>the one ſide, or on the other; and <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> maketh this an <lb></lb>ſwer, in defence of his Peripateticks, therefore let us leave the <lb></lb>judgment in ſuſpenſe, and remit the determination into the <lb></lb>hands of ſuch as are more known than we. </s><s>And becauſe I think <lb></lb>that we have, with ſufficient prolixity, in theſe three dayes, diſ <lb></lb>courſed upon the Syſteme of the Univerſe, it will now be ſeaſo <lb></lb>nable, that we proceed to the grand accident, from whence our <lb></lb>Diſputations took beginning, I mean, of the ebbing and flowing <lb></lb>of the Sea, the cauſe whereof may, in all probability, be referred <lb></lb>to the motion of the Earth. </s><s>But that, if you ſo pleaſe, we will <lb></lb>reſerve till to morrow. </s><s>In the mean time, that I may not forget <lb></lb>it, I will ſpeak to one particular, to which I could have wiſhed, <lb></lb>that <emph type="italics"></emph>Gilbert<emph.end type="italics"></emph.end> had not lent an ear; I mean that of admitting, that <lb></lb><arrow.to.target n="marg723"></arrow.to.target> <lb></lb>in caſe a little Sphere of Loadſtone might be exactly librated, it <lb></lb>would revolve in it ſelf; becauſe there is no reaſon why it ſhould <lb></lb>do ſo; For if the whole Terreſtrial Globe hath a natural facul <lb></lb>ty of revolving about its own centre in twenty four hours, and <lb></lb>that all its parts ought to have the ſame, I mean, that faculty of <lb></lb>turning round together with their <emph type="italics"></emph>whole,<emph.end type="italics"></emph.end> about its centre in twen <lb></lb>ty four hours; they already have the ſame in effect, whilſt that, <lb></lb>being upon the Earth, they turn round along with it: And the <lb></lb>aſſigning them a revolution about their particular centres, would <lb></lb>be to aſcribe unto them a ſecond motion much different from the <lb></lb>firſt; for ſo they would have two, namely, the revolving in twen <lb></lb>ty four hours about the centre of their <emph type="italics"></emph>whole<emph.end type="italics"></emph.end>; and the turning <lb></lb>about their own: now this ſecond is arbitrary, nor is there any <pb xlink:href="040/01/397.jpg" pagenum="377"></pb>reaſon for the introducing of it: If by pluoking away a piece <lb></lb>of Loadſtone from the whole natural maſſd, it were deprived of <lb></lb>the faculty of following it, as it did, whilſt it was unitedy thereto, <lb></lb>ſo that it is thereby deprived of the revodution about the univer <lb></lb>ſal centre of the Terreſtrial Globe, it might Chaply, with ſome <lb></lb>what greater probability be thought by ſome, that the ſaid Mag <lb></lb>net was to appropriate to it ſelf a new converſion about its parti <lb></lb>cular centre; but if it do no leſſe, when ſeparated, than when <lb></lb>conjoyned, continue always to purſue its firſt, eternal, and natu <lb></lb>ral courſe, to what purpoſe ſhould we go about to obtrude upon <lb></lb>it another new one?</s></p><p type="margin"><s><margin.target id="marg723"></margin.target><emph type="italics"></emph>An improba <lb></lb>ble effect admired <lb></lb>by<emph.end type="italics"></emph.end> Gilbertus <emph type="italics"></emph>in the <lb></lb>Loadſtone.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I underſtand you very well, and this puts me in mind <lb></lb>of a Diſcourſe very like to this for the vanity of it, falling from <lb></lb><arrow.to.target n="marg724"></arrow.to.target> <lb></lb>certain Writers upon the Sphere, and I think, if I well remem <lb></lb>ber, amongſt others from <emph type="italics"></emph>Sacroboſco,<emph.end type="italics"></emph.end> who, to ſhew how the E <lb></lb>lement of Water, doth, together with the Earth, make a com <lb></lb>pleat Spherical Figure, and ſo between them both compoſe this <lb></lb>our Globe, writeth, that the ſeeing the ſmall ^{*} particles of water <lb></lb>ſhape themſelves into rotundity, as in the drops, and in the dew <lb></lb>daily apparent upon the leaves of ſeveral herbs, is a ſtrong ar <lb></lb>gument; and becauſe, according to the trite Axiome, there is <lb></lb>the ſame reaſon for the whole, as for the parts, the parts affecting <lb></lb>that ſame figure, it is neceſſary that the ſame is proper to the <lb></lb>whole Element: and truth is, methinks it is a great overſight <lb></lb>that theſe men ſhould not perceive ſo apparent a vanity, and con <lb></lb>ſider that if their argument had run right, it would have follow <lb></lb>ed, that not only the ſmall drops, but that any whatſoever greater <lb></lb>quantity of water ſeparated from the whole Element, ſhould be re <lb></lb>duced into a Globe: Which is not ſeen to happen; though indeed <lb></lb>the Senſes may ſee, and the Underſtanding perceive that the E <lb></lb>lement of Water loving to form it ſelf into a Spherical Figure <lb></lb>about the common centre of gravity, to which all grave bo <lb></lb>dies tend (that is, the centre of the Terreſtrial Globe) it <lb></lb>therein is followed by all its parts, according to the Axiome; <lb></lb>ſo that all the ſurfaces of Seas, Lakes, Pools, and in a word, <lb></lb>of all the parts of Waters conteined in veſſels, diſtend <lb></lb>themſelves into a Spherical Figure, but that Figure is an arch <lb></lb>of that Sphere that hath for its centre the centre of the Ter <lb></lb>reſtrial Globe, and do not make particular Spheres of them <lb></lb>ſelves.</s></p><p type="margin"><s><margin.target id="marg724"></margin.target><emph type="italics"></emph>The vain argu <lb></lb>mentation of ſome <lb></lb>to prove the Ele <lb></lb>ment of Water to <lb></lb>be of a Spherical <lb></lb>ſuper ficies.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>The errour indeed is childiſh; and if it had <lb></lb>been onely the ſingle miſtake of <emph type="italics"></emph>Sacroboſco,<emph.end type="italics"></emph.end> I would eaſily <lb></lb>have allowed him in it; but to pardon it alſo to his Com <lb></lb>mentators, and to other famous men, and even to <emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> <pb xlink:href="040/01/398.jpg" pagenum="378"></pb>himſelfe; this I cannot do, without bluſhing for their repu <lb></lb>tation. </s><s>But it is high time to take leave, it row being <lb></lb>very late, and we being to meet again to morrow, <lb></lb>at the uſual hour, to bring all the foregoing <lb></lb>Diſcourſes to a final concluſion. <lb></lb></s></p><pb xlink:href="040/01/399.jpg"></pb><figure id="id.040.01.399.1.jpg" xlink:href="040/01/399/1.jpg"></figure><figure id="id.040.01.399.2.jpg" xlink:href="040/01/399/2.jpg"></figure><figure id="id.040.01.399.3.jpg" xlink:href="040/01/399/3.jpg"></figure><figure id="id.040.01.399.4.jpg" xlink:href="040/01/399/4.jpg"></figure><figure id="id.040.01.399.5.jpg" xlink:href="040/01/399/5.jpg"></figure><figure id="id.040.01.399.6.jpg" xlink:href="040/01/399/6.jpg"></figure><figure id="id.040.01.399.7.jpg" xlink:href="040/01/399/7.jpg"></figure><figure id="id.040.01.399.8.jpg" xlink:href="040/01/399/8.jpg"></figure><p type="caption"><s><emph type="italics"></emph>Place this Plate <lb></lb>at the end of <lb></lb>the third<emph.end type="italics"></emph.end>Dialogue</s></p><pb xlink:href="040/01/400.jpg"></pb></chap><chap> <pb xlink:href="040/01/401.jpg" pagenum="379"></pb><p type="head"><s>GALILÆUS <lb></lb>Gailæus Lyncæus, <lb></lb>HIS <lb></lb>SYSTEME <lb></lb>OF THE <lb></lb>WORLD.</s></p><p type="head"><s>The Fourth Dialogue.</s></p><p type="head"><s><emph type="italics"></emph>INTERLOCVTORS.<emph.end type="italics"></emph.end></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></lb>accuſtomed conferences hath really been <lb></lb>later than uſual, or whether the deſire <lb></lb>of hearing the thoughts of <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> <lb></lb>touching a matter ſo curious, hath <lb></lb>made me think it ſo: But I have tar <lb></lb>ried a long hour at this window, expe <lb></lb>cting every moment when the <emph type="italics"></emph>Gondola<emph.end type="italics"></emph.end> <lb></lb>would appear that I ſent to fetch you.</s></p><p type="main"><s>SALV. </s><s>I verily believe that your imagination more than our <lb></lb>tarriance hath prolonged the time: and to make no longer de <lb></lb><arrow.to.target n="marg725"></arrow.to.target> <lb></lb>murre, it would be well, if without interpoſing more words, we <lb></lb>came to the matter it ſelf; and did ſhew, that nature hath per <lb></lb>mitted (whether the buſineſs <emph type="italics"></emph>in rei veritate<emph.end type="italics"></emph.end> be ſo, or elſe to play <pb xlink:href="040/01/402.jpg" pagenum="380"></pb>and ſport with our Fancies) hath, I ſay, hath permitted that the <lb></lb><arrow.to.target n="marg726"></arrow.to.target> <lb></lb>motions for every other reſpect, except to reſolve the ebbing and <lb></lb>flowing of the Sea, aſſigned long ſince to the earth, ſhould be found <lb></lb>now at laſt to anſwer exactly to the cauſe thereof; and, as it <lb></lb><arrow.to.target n="marg727"></arrow.to.target> <lb></lb>were, with mutual a emulation, the ſaid ebbing and flowing <lb></lb>to appear in confirmation of the Terreſtrial motion: the <emph type="italics"></emph>judices<emph.end type="italics"></emph.end> <lb></lb>whereof have hitherto been taken from the cœleſtial Phænomena, <lb></lb>in regard that of thoſe things that happen on Earth, not any one <lb></lb>was of force to prove one opinion more than another, as we al <lb></lb>ready have at large proved, by ſhewing that all the terrene occur <lb></lb>rences upon which the ſtability of the Earth and mobility of the <lb></lb>Sun and Firmament is commonly inferred, are to ſeem to us per <lb></lb>formed in the ſame manner, though we ſuppoſed the mobility of <lb></lb>the Earth, and the immobility of them. </s><s>The Element of Wa <lb></lb>ter onely, as being moſt vaſt, and which is not annexed and con <lb></lb>catenated to the Terreſtrial Globe as all its other ſolid parts are; <lb></lb>yea, rather which by reaſon of its fluidity remaineth apart <emph type="italics"></emph>ſui <lb></lb>juris,<emph.end type="italics"></emph.end> and free, is to be ranked amongſt thoſe ſublunary things, <lb></lb>from which we may collect ſome hinte and intimation of what the <lb></lb>Earth doth in relation to motion and reſt. </s><s>After I had many <lb></lb>and many a time examined with my ſelf the effects and accidents, <lb></lb>partly ſeen and partly underſtood from others, thar are to be ob <lb></lb>ſerved in the motions of waters: and moreover read and heard <lb></lb>the great vanities produced by many, as the cauſes of thoſe acci <lb></lb>dents, I have been induced upon no ſlight reaſons to omit theſe <lb></lb><arrow.to.target n="marg728"></arrow.to.target> <lb></lb>two concluſions (having made withal the neceſſary preſuppo <lb></lb>ſals) that in caſe the terreſtrial Globe be immoveable, the flux <lb></lb>and reflux of the Sea cannot be natural; and that, in caſe thoſe <lb></lb>motions be conferred upon the ſaid Globe, which have been long <lb></lb>ſince aſſigned to it, it is neceſſary that the Sea be ſubject to eb <lb></lb>bing and flowing, according to all that which we obſerve to hap <lb></lb>pen in the ſame.</s></p><p type="margin"><s><margin.target id="marg725"></margin.target><emph type="italics"></emph>Nature in ſport <lb></lb>maketh the ebbing <lb></lb>and flowing of the <lb></lb>Sea, to approve the <lb></lb>Earths mobility.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg726"></margin.target><emph type="italics"></emph>The tide, and <lb></lb>mobility of the <lb></lb>Earth mutually <lb></lb>confirm each other<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg727"></margin.target><emph type="italics"></emph>All terrene ef <lb></lb>fects, indifferently <lb></lb>confirm the motion <lb></lb>or reſt of the <lb></lb>Earth, except the <lb></lb>ebbing and flowing <lb></lb>of the Sea.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg728"></margin.target><emph type="italics"></emph>The firſt gene <lb></lb>ral concluſion of <lb></lb>the impoſſibility of <lb></lb>the ebbing and <lb></lb>flowing the immo <lb></lb>bility of the terre <lb></lb>ſtrial Globe being <lb></lb>granted.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>The Propoſition is very conſiderable, as well for it <lb></lb>ſelf as for what followeth upon the ſame by way of conſequence, <lb></lb>ſo that I ſhall the more intenſly hearken to the explanation and <lb></lb>confirmation of it. <lb></lb><arrow.to.target n="marg729"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg729"></margin.target><emph type="italics"></emph>The knowledge <lb></lb>of the offests con <lb></lb>tributes to the in <lb></lb>veſtigation of the <lb></lb>cauſes.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>Becauſe in natural queſtions, of which number this <lb></lb>which we have in hand is one, the knowledge of the effects is a <lb></lb>means to guide us to the inveſtigation and diſcovery of the cau <lb></lb>ſes, and without which we ſhould walk in the dark, nay with <lb></lb>more uncertainty, for that we know not whither we would go, <lb></lb>whereas the blind, at leaſt, know where they deſire to arrive; there <lb></lb>fore firſt of all it is neceſſary to know the effects whereof we en <lb></lb>quire the cauſes: of which effects you, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> ought more <lb></lb>abundantly and more certainly to be informed than I am, <pb xlink:href="040/01/403.jpg" pagenum="381"></pb>as one, that beſides your being born, and having, for a long <lb></lb>time, dwelt in <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> where the Tides are very notable for their <lb></lb>greatneſſe, have alſo ſailed into <emph type="italics"></emph>Syria,<emph.end type="italics"></emph.end> and, as an ingenuous and <lb></lb>apprehenſive wit, muſt needs have made many Obſervations up <lb></lb>on this ſubject: whereas I, that could onely for a time, and that <lb></lb>very ſhort, obſerve what happened in theſe extream parts of the <lb></lb><emph type="italics"></emph>Adriatick<emph.end type="italics"></emph.end> Gulph, and in our Seas below about the <emph type="italics"></emph>Tyrrhene<emph.end type="italics"></emph.end> <lb></lb>ſhores, muſt needs take many things upon the relation of o <lb></lb>thers, who, for the moſt part, not very well agreeing, and con <lb></lb>ſequently being very uncertain, contribute more of confuſion <lb></lb>than confirmation to our ſpeculations. </s><s>Nevertheleſſe, from thoſe <lb></lb>that we are ſure of, and which are the principal, I think I am a <lb></lb>ble to attain to the true and primary cauſes; not that I pretend <lb></lb>to be able to produce all the proper and adequate reaſons of <lb></lb>thoſe effects that are new unto me, and which conſequently I <lb></lb>could never have thought upon. </s><s>And that which I have to ſay, <lb></lb>I propoſe only, as a key that openeth the door to a path never <lb></lb>yet trodden by any, in certain hope, that ſome wits more ſpecu <lb></lb>lative than mine, will make a further progreſſe herin, and pene <lb></lb>trate much farther than I ſhall have done in this my firſt Diſco <lb></lb>very: And although that in other Seas, remote from us, there may <lb></lb>happen ſeveral accidents, which do not happen in our Mediter <lb></lb>ranean Sea, yet doth not this invalidate the reaſon and cauſe that <lb></lb>I ſhall produce, if ſo be that it veriſie and fully reſolve the ac <lb></lb>cidents which evene in our Sea: for that in concluſion there can <lb></lb>be but one true and primary cauſe of the effects that are of the <lb></lb>ſame kind. </s><s>I will relate unto you, therefore, the effects that I <lb></lb>know to be true, and aſſigne the cauſes thereof that I think <lb></lb>to be true, and you alſo, Gentlemen, ſhall produce ſuch <lb></lb>others as are known to you, beſides mine, and then we will <lb></lb>try whether the cauſe, by me alledged, may ſatisfie them <lb></lb>alſo.</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"></emph>Three Periods <lb></lb>of ebbings and <lb></lb>flowings, diurnal, <lb></lb>monethly, and an <lb></lb>nual.<emph.end type="italics"></emph.end></s></p><p type="main"><s>I therefore affirm the periods that are obſerved in the fluxes <lb></lb>and refluxes of the Sea-waters to be three: the firſt and princi <lb></lb>pal is this great and moſt obvious one; namely, the diurnal, accor <lb></lb>ding to which the intervals of ſome hours with the waters flow and <lb></lb>ebbe; and theſe intervals are, for the moſt part, in the Mediter <lb></lb>rane from ſix hours to ſix hours, or thereabouts, that is, they for <lb></lb>ſix hours flow, and for ſix hours ebbe. </s><s>The ſecond period is <lb></lb>monethly, and it ſeemes to take its origen from the motion of <lb></lb>the Moon, not that it introduceth other motions, but only al <lb></lb>tereth the greatneſſe of thoſe before mentioned, with a notable <lb></lb>difference, according as it ſhall wax or wane, or come to the <lb></lb>Quadrature with the Sun. </s><s>The third Period is annual, and is <lb></lb>ſeen to depend on the Sunne, and onely altereth the diurnal <pb xlink:href="040/01/404.jpg" pagenum="382"></pb>motions, by making them different in the times of the Sol <lb></lb>ſtices, as to greatneſſe, from what they are in the Equinoxes.</s></p><p type="main"><s>We will ſpeak (in the firſt place, of the diurnal motion, as <lb></lb>being the principal, and upon which the Moon and Sun ſeem to <lb></lb>exerciſe their power ſecondarily, in their monethly and annual </s></p><p type="main"><s><arrow.to.target n="marg731"></arrow.to.target> <lb></lb>alterations. </s><s>Three differences are obſervable in theſe horary <lb></lb>mutations; for in ſome places the waters riſe and fall, without <lb></lb>making any progreſſive motion; in others, without riſing or fal <lb></lb>ling they run one while towards the Eaſt, and recur another <lb></lb>while towards the Weſt; and in others they vary the heights <lb></lb>and courſe alſo, as happeneth here in <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> where the Tides in <lb></lb>coming in riſe, and in going out fall; and this they do in the ex <lb></lb>termities of the lengths of Gulphs that diſtend from Weſt to <lb></lb>Eaſt, and terminate in open ſhores, up along which ſhores the <lb></lb>Tide at time of flood hath room to extend it ſelf: but if the <lb></lb>courfe of the Tide were iutercepted by Cliffes and Banks of <lb></lb>great height and ſteepneſſe, there it will flow and ebbe without <lb></lb>any progreſſive motion. </s><s>Again, it runs to and again, without <lb></lb>changing height in the middle parts of the Mediterrane, as nota <lb></lb><arrow.to.target n="marg732"></arrow.to.target> <lb></lb>bly happeneth in the ^{*} <emph type="italics"></emph>Faro de Meſſina,<emph.end type="italics"></emph.end> between <emph type="italics"></emph>Scylla<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ca <lb></lb>rybdis,<emph.end type="italics"></emph.end> where the Currents, by reaſon of the narrowneſſe of <lb></lb>the Channel, are very ſwift; but in the more open Seas, and <lb></lb>about the Iſles that ſtand farther into the Mediterranean Sea, as <lb></lb><arrow.to.target n="marg733"></arrow.to.target> <lb></lb>the <emph type="italics"></emph>Baleares, Corſica, Sardignia, ^{*} Elba, Sicily<emph.end type="italics"></emph.end> towards the <emph type="italics"></emph>Affrican<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg734"></arrow.to.target> <lb></lb>Coaſts, <emph type="italics"></emph>Malta, ^{*} Candia, &c.<emph.end type="italics"></emph.end> the changes of watermark are <lb></lb>very ſmall; but the currents indeed are very notable, and eſpe <lb></lb>cially when the Sea is pent between Iſlands, or between them <lb></lb>and the Continent.</s></p><p type="margin"><s><margin.target id="marg731"></margin.target><emph type="italics"></emph>Varieties that <lb></lb>happen in the diur <lb></lb>nal period.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg732"></margin.target>* A Strait, ſo <lb></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 theſe onely true and certain effects, were there no more <lb></lb>to be obſerved, do, in my judgment, very probably perſwade <lb></lb>any man, that will contain himſelf within the bounds of natu <lb></lb>ral cauſes, to grant the mobility of the Earth: for to make the <lb></lb>veſſel (as it may be called) of the Mediterrane ſtand ſtill, and to <lb></lb>make the water contained therein to do, as it doth, exceeds my <lb></lb>imagination, and perhaps every mans elſe, who will but pierce <lb></lb>beyond the rinde in theſe kind of inquiries.</s></p><p type="main"><s>SIMP. </s><s>Theſe accidents, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> begin not now, they are <lb></lb>moſt ancient, and have been obſerved by very many, and ſeveral <lb></lb>have attempted to aſſigne, ſome one, ſome another cauſe for the <lb></lb>ſame: and there dwelleth not many miles from hence a famous <lb></lb>Peripatetick, that alledgeth a cauſe for the ſame newly fiſhed out <lb></lb><arrow.to.target n="marg735"></arrow.to.target> <lb></lb>of a certain Text of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> not well underſtood by his Ex <lb></lb>poſitors, from which Text he collecteth, that the true cauſe of <lb></lb>theſe motions doth only proceed from the different profundities <lb></lb>of Seas: for that the waters of greateſt depth being greater in <pb xlink:href="040/01/405.jpg" pagenum="383"></pb>abundance, and therefore more grave, drive back the Waters <lb></lb>of leſſe depth, which being afterwards raiſed, deſire to de <lb></lb>ſcend, and from this continual colluctation or conteſt proceeds <lb></lb><arrow.to.target n="marg736"></arrow.to.target> <lb></lb>the ebbing and flowing. </s><s>Again thoſe that referre the ſame to the <lb></lb>Moon are many, ſaying that ſhe hath particular Dominion over <lb></lb>the Water; and at laſt a certain Prelate hath publiſhed a little <lb></lb>Treatiſe, wher in he ſaith that the Moon wandering too and <lb></lb>fro in the Heavens attracteth and draweth towards it a Maſſe of <lb></lb>Water, which goeth continually following it, ſo that it is full Sea <lb></lb>alwayes in that part which lyeth under the Moon; and becauſe, <lb></lb>that though ſhe be under the Horizon, yet nevertheleſſe the Tide <lb></lb>returneth, he ſaith that no more can be ſaid for the ſalving of that <lb></lb>particular, ſave onely, that the Moon doth not onely naturally <lb></lb>retain this faculty in her ſelf; but in this caſe hath power to con <lb></lb>fer it upon that degree of the Zodiack that is oppoſite unto it. <lb></lb></s><s>Others, as I believe you know, do ſay that the Moon is able <lb></lb><arrow.to.target n="marg737"></arrow.to.target> <lb></lb>with her temperate heat to rarefie the Water, which being ra <lb></lb>refied, doth thereupon flow. </s><s>Nor hath there been wanting ſome <lb></lb>that ----</s></p><p type="margin"><s><margin.target id="marg735"></margin.target><emph type="italics"></emph>The cauſe of the <lb></lb>abbing and flowing <lb></lb>alledged by a cer <lb></lb>tain modern Phi <lb></lb>loſopher.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg736"></margin.target><emph type="italics"></emph>The cauſe of <lb></lb>the ebbing and <lb></lb>flowing aſcribed to <lb></lb>the Moon by a <lb></lb>certain Prelate.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg737"></margin.target>Hieronymus Bor <lb></lb>rius <emph type="italics"></emph>and other<emph.end type="italics"></emph.end> Pe <lb></lb>ripateticks <emph type="italics"></emph>refer it <lb></lb>to the temperate <lb></lb>heat of the Moon.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I pray you <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> let us hear no more of them, <lb></lb>for I do not think it is worth the while to waſt time in relating <lb></lb>them, or to ſpend our breath in confuting them; and for your <lb></lb>part, if you gave your aſſent to any of theſe or the like foole <lb></lb>ries, you did a great injury to your judgment, which neverthe <lb></lb>leſſe 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"></emph>Sagre-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg738"></arrow.to.target> <lb></lb><emph type="italics"></emph>dus,<emph.end type="italics"></emph.end> will ſpend a few words in favour of <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> if haply <lb></lb>he thinks that any probability is to be found in thoſe things that <lb></lb>he hath related. </s><s>I ſay therefore: The Waters, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that <lb></lb>have their exteriour ſuperficies higher, repel thoſe that are infe <lb></lb>riour to them, and lower; but ſo do not thoſe Waters that are <lb></lb>of greateſt profundity; and the higher having once driven back <lb></lb>the lower, they in a ſhort time grow quiet and ^{*} level. </s><s>This <lb></lb><arrow.to.target n="marg739"></arrow.to.target> <lb></lb>your <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> muſt needs be of an opinion, that all the Lakes <lb></lb>in the World that are in a calme, and that all the Seas where <lb></lb>the ebbing and flowing is inſenſible, are level in their bottoms; <lb></lb>but I was ſo ſimple, that I perſwaded my ſelf that had we no o <lb></lb><arrow.to.target n="marg740"></arrow.to.target> <lb></lb>ther plummet to ſound with, the Iſles that advance ſo high a <lb></lb>bove Water, had been a ſufficient evidence of the unevenneſſe <lb></lb>of their bottomes. </s><s>To that Prelate I could ſay that the Moon <lb></lb>runneth every day along the whole Mediterrane, and yet its <lb></lb>Waters do not riſe thereupon ſave onely in the very extream <lb></lb>bounds of it Eaſtward, and here to us at <emph type="italics"></emph>Venice.<emph.end type="italics"></emph.end> And for thoſe <lb></lb>that make the Moons temperate heat able to make the Water <lb></lb>ſwell, bid them put fire under a Kettle full of Water, and hold <pb xlink:href="040/01/406.jpg" pagenum="384"></pb>their right hand therein till that the Water by reaſon of the heat <lb></lb>do riſe but one ſole inch, and then let them take it out, and <lb></lb>write off the tumefaction of the Sea. </s><s>Or at leaſt deſire them to <lb></lb>ſhew you how the Moon doth to rarefie a certain part of the <lb></lb>Waters, and not the remainder; as for inſtance, theſe here of <lb></lb><emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> and not thoſe of <emph type="italics"></emph>Ancona, Naples, Genova<emph.end type="italics"></emph.end>: the truth is <lb></lb><arrow.to.target n="marg741"></arrow.to.target> <lb></lb>Poetick Wits are of two kinds, ſome are ready and apt to <lb></lb>invent Fables, and others diſpoſed and inclined to believe them.</s></p><p type="margin"><s><margin.target id="marg738"></margin.target><emph type="italics"></emph>Anſwers to the <lb></lb>vanities alledged <lb></lb>as cauſes of the eb <lb></lb>bing and flowing.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg739"></margin.target>+ Or rather <lb></lb>ſmooth.</s></p><p type="margin"><s><margin.target id="marg740"></margin.target><emph type="italics"></emph>The Iſles are to <lb></lb>kens of the une <lb></lb>venneſſe of the <lb></lb>bottomes of Seas.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg741"></margin.target><emph type="italics"></emph>Poetick wits of <lb></lb>two kinds.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I believe that no man believeth Fables, ſo long as he <lb></lb>knows them to be ſo; and of the opinions concerning the cauſes <lb></lb>of ebbing and flowing, which are many, becauſe I know that of <lb></lb>one ſingle effect there is but one ſingle cauſe that is true and pri <lb></lb>mary, I underſtand very well, and am certain that but one alone <lb></lb>at the moſt can be true, and for all the reſt I am ſure that they are <lb></lb>fabulous, and falſe; and its poſſible that the true one may not be <lb></lb>among thoſe that have been hitherto produced; nay I verily be <lb></lb>lieve that it is not, for it would be very ſtrange that the truth <lb></lb><arrow.to.target n="marg742"></arrow.to.target> <lb></lb>ſhould have ſo little light, as that it ſhould not be viſible amongſt <lb></lb>the umbrages of ſo many falſhoods. </s><s>But this I ſhall ſay with the <lb></lb>liberty that is permitted amongſt us, that the introduction of the <lb></lb>Earths motion, and the making it the cauſe of the ebbing and <lb></lb>flowing of Tides, ſeemeth to me as yet a conjecture no leſſe fa <lb></lb>bulous than the reſt of thoſe that I have heard; and if there <lb></lb>ſhould not be propoſed to me reaſons more conformable to natu <lb></lb>ral matters, I would without any more ado proceed to believe <lb></lb>this to be a ſupernatural effect, and therefore miraculous, and <lb></lb>unſearchable to the underſtandings of men, as infinite others there <lb></lb>are, that immediately depend on the Omnipotent hand of God. <lb></lb><arrow.to.target n="marg743"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg742"></margin.target><emph type="italics"></emph>Truth hath not <lb></lb>ſo little light as <lb></lb>not to be diſcover <lb></lb>ed amidſt the um <lb></lb>brages of fal <lb></lb>ſhoods.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg743"></margin.target>Ariſtotle <emph type="italics"></emph>holdeth <lb></lb>thoſe effects to be <lb></lb>miraculous, of <lb></lb>which the cauſes <lb></lb>are unknown.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>You argue very prudently, and according to the <lb></lb>Doctrine of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> who you know in the beginning of his <lb></lb>mechanical queſtions referreth thoſe things to a Miracle, the <lb></lb>cauſes whereof are occult. </s><s>But that the cauſe of the ebbing and <lb></lb>flowing is one of thoſe that are not to be found out, I believe <lb></lb>you have no greater proof than onely that you ſee, that amongſt <lb></lb>all thoſe that have hitherto been produced for true cauſes there <lb></lb>of, there is not one wherewith, working by what artifice you <lb></lb>will, we are able to repreſent ſuch an effect; in regard that nei <lb></lb>ther with the light of the Moon nor of the Sun, nor with <lb></lb>temperate heats, nor with different profundities, ſhall one ever <lb></lb>artificially make the Water conteined in an immoveable Veſſel <lb></lb>to run one way or another, and to ebbe and flow in one place, <lb></lb>and not in another. </s><s>But if without any other artifice, but with <lb></lb>the onely moving of the Veſſel, I am able punctually to repre <lb></lb>ſent all thoſe mutations that are obſerved in the Sea Water, why <lb></lb>will you refuſe this reaſon and run to a Miracle?</s></p> <pb xlink:href="040/01/407.jpg" pagenum="385"></pb><p type="main"><s>SIMP. </s><s>I will run to a Miracle ſtill, if you do not with ſome <lb></lb>other natural cauſes, beſides that of the motion of the Veſſels of <lb></lb>the Sea-water diſſwade me from it; for I know that thoſe Veſſels <lb></lb>move not, in regard that all the entire Terreſtrial Globe is natu <lb></lb>rally immoveable.</s></p><p type="main"><s>SALV. </s><s>But do not you think, that the Terreſtrial Globe might <lb></lb>ſupernaturally, that is, by the abſolute power of God, be made <lb></lb>moveable? </s><s>SIMP. </s><s>Who doubts it?</s></p><p type="main"><s>SALV. </s><s>Then <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> ſeeing that to make the flux and <lb></lb>reflux of the Sea, it is neceſſary to introduce a Miracle, let us <lb></lb>ſuppoſe the Earth to move miraculouſly, upon the motion of <lb></lb>which the Sea moveth naturally: and this effect ſhall be alſo the <lb></lb>more ſimple, and I may ſay natural, amongſt the miraculous o <lb></lb>perations, in that the making a Globe to move round, of which <lb></lb>kind we ſee many others to move, is leſſe difficult than to make <lb></lb>an immenſe maſſe of water go forwards and backwards, in one <lb></lb>place more ſwiftly, and in another leſſe, and to riſe and fall in <lb></lb>ſome places more; in ſome leſſe, and in ſome not at all: and to <lb></lb>work all theſe different effects in one and the ſame Veſſel that <lb></lb>containeth it: beſides, that theſe are ſeveral Miracles, and that <lb></lb>is but one onely. </s><s>And here it may be added, that the Miracle <lb></lb>of making the water to move is accompanied with another, <lb></lb>namely, the holding of the Earth ſtedfaſt againſt impetuosities <lb></lb>of the water, able to make it ſwage ſometimes one way, and <lb></lb>ſometimes another, if it were not miraculouſly kept to rights.</s></p><p type="main"><s>SAGR. </s><s>Good <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> let us for the preſent ſuſpend our <lb></lb>judgement about ſentencing the new opinion to be vain that <emph type="italics"></emph>Sal <lb></lb>viatus<emph.end type="italics"></emph.end> is about to explicate unto us, nor let us ſo haſtily flye out <lb></lb>into paſſion like the ſcolding overgrown Haggs: and as for the <lb></lb>Miracle, we may as well recurre to it when we have done hea <lb></lb>ring the Diſcourſes contained within the bounds of natural cau <lb></lb>ſes: though to ſpeak freely, all the Works of nature, or rather <lb></lb>of God, are in my judgement miraculous.</s></p><p type="main"><s>SALV. </s><s>And I am of the ſame opinion; nor doth my ſaying, <lb></lb>that the motion of the Earth is the Natural cauſe of the ebbing <lb></lb>and flowing, hinder, but that the ſaid motion of the Earth may <lb></lb>be miraculous. </s><s>Now reaſſuming our Argument, I apply, and <lb></lb>once again affirm, that it hath been hitherto unknown how it <lb></lb>might be that the Waters contained in our Mediterranean <lb></lb>Straights ſhould make thoſe motions, as we ſee it doth, if ſo be <lb></lb>the ſaid Straight, or containing Veſſel were immoveable. </s><s>And <lb></lb>that which makes the difficulty, and rendreth this matter inextri <lb></lb>cable, are the things which I am about to ſpeak of, and which <lb></lb>are daily obſerved. </s><s>Therefore lend me your attention.</s></p><p type="main"><s>We are here in <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> where at this time the Waters are low, </s></p> <pb xlink:href="040/01/408.jpg" pagenum="386"></pb><p type="main"><s><arrow.to.target n="marg744"></arrow.to.target> <lb></lb>the Sea calm, the Air tranquil; ſuppoſe it to be young flood, <lb></lb>and that in the term of five or ſix hours the water do riſe ten <lb></lb>^{*} hand breadths and more; that riſe is not made by the firſt <lb></lb>water, which was ſaid to be rarefied, but it is done by the acceſ <lb></lb>ſion of new Water: Water of the ſame ſort with the former, <lb></lb><arrow.to.target n="marg745"></arrow.to.target> <lb></lb>of the ſame brackiſhneſs, of the ſame denſity, of the ſame <lb></lb>weight: Ships, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> float therein as in the former, with <lb></lb>out drawing an hairs breadth more water; a Barrel of this ſecond <lb></lb>doth not weigh one ſingle grain more or leſs than ſuch another <lb></lb>quantity of the other, and retaineth the ſame coldneſs without <lb></lb>the leaſt alteration: And it is, in a word, Water newly and viſi <lb></lb><arrow.to.target n="marg746"></arrow.to.target> <lb></lb>bly entred by the Channels and Mouth of the ^{*} <emph type="italics"></emph>Lio.<emph.end type="italics"></emph.end> Conſider <lb></lb>now, how and from whence it came thither. </s><s>Are there happly <lb></lb>hereabouts any Gulphs or Whirle pools in the bottom of the <lb></lb>Sea, by which the Earth drinketh in and ſpueth out the Water, <lb></lb>breathing as it were a great and monſtruous Whale? </s><s>But if this <lb></lb>be ſo, how comes it that the Water doth not flow in the ſpace of <lb></lb>ſix hours in <emph type="italics"></emph>Ancona,<emph.end type="italics"></emph.end> in ^{*} <emph type="italics"></emph>Raguſa,<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Corfu,<emph.end type="italics"></emph.end> where the Tide is ve <lb></lb>ry ſmall, and happly unobſervable? </s><s>Who will invent a way to <lb></lb>pour new Water into an immoveable Veſſel, and to make that <lb></lb>it riſe onely in one determinate part of it, and in other places <lb></lb>not? </s><s>Will you ſay, that this new Water is borrowed from the <lb></lb>Ocean, being brought in by the Straight of <emph type="italics"></emph>Gibraltar<emph.end type="italics"></emph.end>? </s><s>This <lb></lb>will not remove the doubt aforeſaid, but will beget a greater. <lb></lb></s><s>And firſt tell me what ought to be the current of that Water, <lb></lb>that entering at the Straights mouth, is carried in ſix hours to <lb></lb>the remoteſt Creeks of the Mediterrane, at a diſtance of two <lb></lb>or three thouſand Miles, and that returneth the ſame ſpace again <lb></lb>in a like time at its going back? </s><s>What would Ships do that lye out <lb></lb>at Sea? </s><s>What would become of thoſe that ſhould be in the <lb></lb>Straights-mouth in a continual precipice of a vaſt accumulation of <lb></lb>Waters, that entering in at a Channel but eight Mile, broad, is to <lb></lb>give admittance to ſo much Water as in ſix hours over-floweth a <lb></lb>tract of many hundred Miles broad, & thouſands in length? </s><s>What <lb></lb>Tygre, what Falcon runneth or flyeth with ſo much ſwiftneſs? <lb></lb></s><s>With the ſwiftneſs, I ſay, of above 400 Miles an hour. </s><s>The cur <lb></lb>rents run (nor can it be denied) the long-wayes of the Gulph, but <lb></lb>ſo ſlowly, as that a Boat with Oars will out-go them, though in <lb></lb>deed not without defalking for their wanderings. </s><s>Moreover, if this <lb></lb>Water come in at the Straight, the other doubt yet remaineth, <lb></lb>namely, how it cometh to flow here ſo high in a place ſo remote, <lb></lb>without firſt riſing a like or greater height in the parts more adja <lb></lb>cent? </s><s>In a word, I cannot think that either obſtinacy, or ſharpneſs <lb></lb>of wit can ever find an anſwer to theſe Objections, nor conſe <lb></lb>quently to maintain the ſtability of the Earth againſt them, keep <lb></lb>ing within the bounds of Nature.</s></p> <pb xlink:href="040/01/409.jpg" pagenum="387"></pb><p type="margin"><s><margin.target id="marg744"></margin.target><emph type="italics"></emph>It is proved <lb></lb>impoſſible that <lb></lb>there ſhould natu <lb></lb>rally be any ebbing <lb></lb>and flowing, the <lb></lb>Earth being im <lb></lb>moveable.<emph.end type="italics"></emph.end></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"></emph>Lio<emph.end type="italics"></emph.end> is a fair <lb></lb>Port in the Vene <lb></lb>tian Gulph, lying <lb></lb>N. E. from the <lb></lb>City.</s></p><p type="main"><s>SAGR. </s><s>I have all the while perfectly apprehended you in this; <lb></lb>and I ſtand greedily attending to hear in what manner theſe won <lb></lb>ders may occur without obſtruction from the motion already aſ <lb></lb>ſigned to the Earth.</s></p><p type="main"><s>SALV. </s><s>Theſe effects being to enſue in conſequence of the mo <lb></lb>tions that naturally agree with the Earth, it is neceſſary that they <lb></lb>not onely meet with no impediment or obſtacle, but that they do <lb></lb>follow eaſily, & not onely that they follow with facility, but with <lb></lb>neceſſity, ſo as that it is impoſſible that it ſhould ſucceed otherwiſe, <lb></lb>for ſuch is the property & condition of things natural & true. </s><s>Ha <lb></lb><arrow.to.target n="marg747"></arrow.to.target> <lb></lb>ving therefore ſhewen the impoſſibility of rendring a reaſon of the <lb></lb>motions diſcerned in the Waters, & at the ſame time to maintain <lb></lb>the immobility of the veſſel that containeth them: we may proceed <lb></lb>to enquire, whether the mobility of the Container may produce <lb></lb>the required effect, in the manner that it is obſerved to evene.</s></p><p type="margin"><s><margin.target id="marg747"></margin.target><emph type="italics"></emph>True and natu <lb></lb>ral effects follow <lb></lb>without difficulty.<emph.end type="italics"></emph.end></s></p><p type="main"><s>Two kinds of motions may be conferred upon a Veſſel, where <lb></lb><arrow.to.target n="marg748"></arrow.to.target> <lb></lb>by the Water therein contained, may acquire a faculty of flu <lb></lb>ctuating in it, one while towards one ſide, and another while <lb></lb>towards another; and there one while to ebbe, and another <lb></lb>while to flow. </s><s>The firſt is, when firſt one, and then another of <lb></lb>thoſe ſides is declined, for then the Water running towards the <lb></lb>inclining ſide, will alternately be higher and lower, ſometimes <lb></lb>on one ſide, and ſometimes on another. </s><s>But becauſe that this <lb></lb>riſing and abating is no other than a receſſion and acceſſion to the <lb></lb>centre of the Earth, ſuch a motion cannot be aſcribed to the Cavi <lb></lb>ties of the ſaid Earth, that are the Veſſels which contain the Wa <lb></lb>ters; the parts of which Veſſel cannot by any whatſoever motion <lb></lb>aſſigned to the Earth, be made to approach or recede from the <lb></lb><arrow.to.target n="marg749"></arrow.to.target> <lb></lb>centre of the ſame: The other ſort of motion is, when the <lb></lb>Veſſel moveth (without inclining in the leaſt) with a progreſſive <lb></lb>motion, not uniform, but that changeth velocity, by ſometimes <lb></lb>accellerating, and other times retarding: from which diſparity <lb></lb><arrow.to.target n="marg750"></arrow.to.target> <lb></lb>it would follow, that the Water contained in the Veſſel its true, <lb></lb>but not fixed faſt to it, as its other ſolid parts, but by reaſon of <lb></lb>its fluidity, as if it were ſeparated and at liberty, and not obli <lb></lb>ged to follow all the mutations of its Container, in the retardation <lb></lb>of the Veſſel, it keeping part of the <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> before conceived, <lb></lb>would run towards the the preceding part, whereupon it would <lb></lb>of neceſſity come to riſe; and on the contrary, if new velocity <lb></lb>ſhould be added to the Veſſel, with retaining parts of its tardity, <lb></lb>ſtaying ſomewhat behind, before it could habituate it ſelf to the <lb></lb>new <emph type="italics"></emph>impetus,<emph.end type="italics"></emph.end> it would hang back towards the following part, <lb></lb>where it would come to riſe ſomething. </s><s>The which effects we <lb></lb>may plainly declare and make out to the Senſe by the example of <lb></lb>one of thoſe ſame Barks yonder, which continually come from <pb xlink:href="040/01/410.jpg" pagenum="388"></pb><arrow.to.target n="marg751"></arrow.to.target> <lb></lb>^{*} <emph type="italics"></emph>Lizza-Fuſina,<emph.end type="italics"></emph.end> laden with freſh water, for the ſervice of the City. <lb></lb></s><s>Let us therefore fancy one of thoſe Barks, to come from thence <lb></lb>with moderate velocity along the Lake, carrying the water gently, <lb></lb>of which it is full: and then either by running a ground, or by <lb></lb>ſome other impediment that it ſhall meet with, let it be notably <lb></lb>retarded. </s><s>The water therein contained ſhall not, by that means, <lb></lb>loſe, as the Bark doth, its pre-conceived <emph type="italics"></emph>impetus,<emph.end type="italics"></emph.end> but retaining <lb></lb>the ſame, ſhall run forwards towards the prow, where it ſhall <lb></lb>riſe notably, falling as much a ſtern. </s><s>But if, on the contrary, <lb></lb>the ſaid Bark, in the midſt of its ſmooth courſe, ſhall have a new <lb></lb>velocity, with notable augmentation added to it, the water con <lb></lb>tained before it can habituate it ſelf thereto, continuing in its <lb></lb>tardity, ſhall ſtay behinde, namely a ſtern, where of conſe <lb></lb>quence it ſhall mount, and abate for the ſame at the prow. </s><s>This <lb></lb>effect is undoubted and manifeſt, and may hourly be experimen <lb></lb>ted; in which I deſire that for the preſent three particulars may <lb></lb>be noted. </s><s>The flrſt is, that to make the water to riſe on one <lb></lb>ſide of the veſſel, there is no need of new water, nor that it run <lb></lb>thither, forſaking the other ſide. </s><s>The ſecond is, that the water <lb></lb>in the middle doth not riſe or fall notably, unleſſe the courſe of <lb></lb>the Bark were not before that very ſwift, and the ſhock or other <lb></lb>arreſt that held it exceeding ſtrong and ſudden, in which caſe its <lb></lb>poſſible, that not only all the water might run forwards, but <lb></lb>that the greater part thereof might iſſue forth of the Bark: and <lb></lb>the ſame alſo would enſue, whilſt that being under ſail in a <lb></lb>ſmooth courſe, a moſt violent <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> ſhould, upon an inſtant, <lb></lb>overtake it: But when to its calme motion there is added a mo <lb></lb>derate retardation or incitation, the middle parts (as I ſaid) un <lb></lb>obſervedly riſe and fall: and the other parts, according as they <lb></lb>are neerer to the middle, riſe the leſſe; and the more remote, <lb></lb>more. </s><s>The third is, that whereas the parts about the midſt do <lb></lb>make little alteration in riſing and falling, in reſpect of the wa <lb></lb>ters of the ſides; on the contrary, they run forwards and back <lb></lb>wards very much, in compariſon of the extreams. </s><s>Now, my <lb></lb>Maſters, that which the Bark doth, in reſpect of the water by it <lb></lb>contained, and that which the water contained doth, in re <lb></lb>ſpect of the Bark its container, is the ſelf-ſame, to an hair, with <lb></lb>that which the Mediterranean Veſſel doth, in reſpect of the wa <lb></lb>ters in it contained, and that which the waters contained do, in <lb></lb><arrow.to.target n="marg752"></arrow.to.target> <lb></lb>reſpect of the Mediterranean Veſſel their container. </s><s>It follow <lb></lb>eth now that we demonſtrate how, and in what manner it is true, <lb></lb>that the Mediterrane, and all the other Straits; and in a word, <lb></lb>all the parts of the Earth do all move, with a motion notably <lb></lb>uneven, though no motion that is not regular and uniforme, is <lb></lb>thereby aſſigned to all the ſaid Globe taken collectively.</s></p> <pb xlink:href="040/01/411.jpg" pagenum="389"></pb><p type="margin"><s><margin.target id="marg748"></margin.target><emph type="italics"></emph>Two ſorts of <lb></lb>motions of the con <lb></lb>taining Veſſel, may <lb></lb>make the contai <lb></lb>ned water to riſe <lb></lb>and fall.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg749"></margin.target><emph type="italics"></emph>The Cavities of <lb></lb>the Earth cannot <lb></lb>approach or go far <lb></lb>ther from the cen <lb></lb>tre of the ſame.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg750"></margin.target><emph type="italics"></emph>The progpeſſive <lb></lb>and uneven motion <lb></lb>may make the wa <lb></lb>ter contained in a <lb></lb>Veſſel to run to <lb></lb>and fro.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg751"></margin.target>+ A Town ly <lb></lb>ing S. E. of <emph type="italics"></emph>Venice<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg752"></margin.target><emph type="italics"></emph>The parts of the <lb></lb>terreſtrial Globe <lb></lb>accelerate and re <lb></lb>tard in their moti <lb></lb>on.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>This Propoſition, at firſt ſight to me, that am neither <lb></lb>Geometrician nor Aſtronomer, hath the appearance of a very <lb></lb>great Paradox; and if it ſhould be true, that the motion of the <lb></lb><emph type="italics"></emph>whole,<emph.end type="italics"></emph.end> being regular, that of the parts, which are all united to <lb></lb>their <emph type="italics"></emph>whole,<emph.end type="italics"></emph.end> may be irregular, the Paradox will overthrow the <lb></lb>Axiome that affirmeth, <emph type="italics"></emph>Eandem eſſe rationem totius & par <lb></lb>tium.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>I will demonſtrate my Paradox, and leave it to your <lb></lb>care, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> to defend the Axiome from it, or elſe to re <lb></lb>concile them; and my demonſtration ſhall be ſhort and fa <lb></lb>miliar, depending on the things largely handled in our prece <lb></lb>dent conferences, without introducing the leaſt ſyllable, in fa <lb></lb>vour of the flux and reflux.</s></p><p type="main"><s>We have ſaid, that the motions aſſigned to the Terreſtrial <lb></lb><arrow.to.target n="marg753"></arrow.to.target> <lb></lb>Globe are two, the firſt Annual, made by its centre about the <lb></lb>circumference of the Grand Orb, under the Ecliptick, according <lb></lb>to the order of the Signes, that is, from Weſt to Eaſt; the other <lb></lb>made by the ſaid Globe revolving about its own centre in twenty <lb></lb>four hours; and this likewiſe from Weſt to Eaſt: though a <lb></lb>bout an Axis ſomewhat inclined, and not equidiſtant from that <lb></lb>of the Annual converſion. </s><s>From the mixture of theſe two mo <lb></lb>tions, each of it ſelf uniform, I ſay, that there doth reſult an <lb></lb>uneven and deformed motion in the parts of the Earth. </s><s>Which, <lb></lb>that it may the more eaſily be underſtood, I will explain, by <lb></lb>drawing a Scheme thereof. </s><s>And firſt, about the centre A [<emph type="italics"></emph>in <lb></lb>Fig. </s><s>1. of this Dialogue<emph.end type="italics"></emph.end>] I will deſcribe the circumference of <lb></lb><arrow.to.target n="marg754"></arrow.to.target> <lb></lb>the Grand Orb B C, in which any point being taken, as B, <lb></lb>about it as a centre we will deſcribe this leſſer circle D E F G, <lb></lb>repreſenting the Terreſtrial Globe; the which we will ſuppoſe <lb></lb>to run thorow the whole circumference of the Grand Orb, with <lb></lb>its centre B, from the Weſt towards the Eaſt, that is, from the <lb></lb>part B towards C; and moreover we will ſuppoſe the Terre <lb></lb>ſtrial Globe to turn about its own centre B likewiſe from Weſt <lb></lb>to Eaſt, that is, according to the ſucceſſion of the points <lb></lb>D E F G, in the ſpace of twenty four hours. </s><s>But here we <lb></lb>ought carefully to note, that a circle turning round upon its <lb></lb>own centre, each part of it muſt, at different times, move with <lb></lb>contrary motions: the which is manifeſt, conſidering that whilſt <lb></lb>the parts of the circumference, about the point D move to the <lb></lb>left hand, that is, towards E, the oppoſite parts that are about F, <lb></lb>approach to the right hand, that is, towards G; ſo that when <lb></lb>the parts D ſhall be in F, their motion ſhall be contrary to what <lb></lb>it was before. </s><s>when it was in D. Furthermore, the ſame time <lb></lb>that the parts E deſcend, if I may ſo ſpeak, towards F, thoſe in <lb></lb>G aſcend towards D. </s><s>It being therefore preſuppoſed, that <pb xlink:href="040/01/412.jpg" pagenum="390"></pb><arrow.to.target n="marg755"></arrow.to.target> <lb></lb>there are ſuch contrarieties of motions in the parts of the Terre <lb></lb>ſtrial Surface, whilſt it turneth round upon its own centre, it is <lb></lb>neceſſary, that in conjoyning this Diurnal Motion, with the other <lb></lb>Annual, there do reſult an abſolute motion for the parts of the <lb></lb>ſaid Terreſtrial Superficies, one while very accelerate, and ano <lb></lb>ther while as ſlow again. </s><s>The which is manifeſt, conſidering <lb></lb>firſt the parts about D, the abſolute motion of which ſhall be <lb></lb>extream ſwift, as that which proceedeth from two motions made <lb></lb>both one way, namely, towards the left hand; the firſt of <lb></lb>which is part of the Annual Motion, common to all the parts of <lb></lb>the Globe, the other is that of the ſaid point D., carried likewiſe <lb></lb>to the left, by the Diurnal Revolution; ſo that, in this caſe, the <lb></lb>Diurnal motion increaſeth and accelerateth the Annual. </s><s>The <lb></lb>contrary to which happeneth in the oppoſite part F, which, whilſt <lb></lb>it is by the common annual motion carried, together with the <lb></lb>whole Globe, towards the left, it happeneth to be carried by the <lb></lb>Diurnal converſion alſo towards the right: ſo that the Diur <lb></lb>nal motion by that means detracteth from the Annual, where <lb></lb>upon the abſolute motion, reſulting from the compoſition of both <lb></lb>the other, is much retarded. </s><s>Again, about the points E and G, <lb></lb>the abſolute motion becometh in a manner equal to the ſimple <lb></lb>Annual one, in regard that little or nothing increaſeth or dimi <lb></lb>niſheth it, as not tending either to the left hand, or to the right, <lb></lb>but downwards and upwards. </s><s>We will conclude therefore, that <lb></lb>like as it is true, that the motion of the whole Globe, and of <lb></lb>each of its parts, would be equal and uniforme, in caſe they did <lb></lb>move with one ſingle motion, whether it were the meer Annual, <lb></lb>or the ſingle Diurnal Revolution, ſo it is requiſite, that mixing <lb></lb>thoſe two motions together, there do reſult thence for the parts <lb></lb>of the ſaid Globe irregular motions, one while accelerated, and <lb></lb>another while retarded, by means of the additions or ſubſtracti <lb></lb>ons of the Diurnal converſion from the annual circulation. </s><s>So <lb></lb>that, if it be true (and moſt true it is, as experience proves) that <lb></lb>the acceleration and retardation of the motion of the Veſ <lb></lb>ſel, makes water contained therein to run to and again the long <lb></lb>waves of it, and to riſe and fall in its extreames, who will make <lb></lb>ſcruple of granting, that the ſaid effect may, nay ought to ſuc <lb></lb>ceed in the Sea-waters, contained within their Veſſels, ſubject to <lb></lb>ſuch like alterations, and eſpecially in thoſe that diſtend them <lb></lb>ſelves long-wayes from Weſt to Eaſt, which is the courſe that <lb></lb><arrow.to.target n="marg756"></arrow.to.target> <lb></lb>the motion of thoſe ſame Veſſels ſteereth? </s><s>Now this is the <lb></lb>moſt potent and primary cauſe of the ebbing and flowing, with <lb></lb>out the which no ſuch effect would enſue. </s><s>But becauſe the par <lb></lb>ticular accidents are many and various, that in ſeveral places and <lb></lb>times are obſerved, which muſt of neceſſity have dependance <pb xlink:href="040/01/413.jpg" pagenum="391"></pb>on other different concomitant cauſes, although they ought all <lb></lb>to have connexion with the primary; therefore it is convenient <lb></lb>that we propound and examine the ſeveral accidents that may <lb></lb>be the cauſes of ſuch different effects.</s></p><p type="margin"><s><margin.target id="marg753"></margin.target><emph type="italics"></emph>Demonſtrations <lb></lb>how the parts of <lb></lb>the terreſtriall <lb></lb>Globe accelerats <lb></lb>and ratard.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg754"></margin.target><emph type="italics"></emph>The parts of a <lb></lb>Circle regularly <lb></lb>moved about its <lb></lb>own centre move in <lb></lb>divers times with <lb></lb>contrary motions.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg755"></margin.target><emph type="italics"></emph>The mixture of <lb></lb>the two motions <lb></lb>annnal and diur <lb></lb>nal, cauſeth the <lb></lb>inequality in the <lb></lb>motion of the parts <lb></lb>of the terreſtrial <lb></lb>Globe.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg756"></margin.target><emph type="italics"></emph>The moſt potent <lb></lb>and primary cauſe <lb></lb>of the ebbing and <lb></lb>flowing.<emph.end type="italics"></emph.end></s></p><p type="main"><s>The firſt of which is, that when ever the water, by means of a <lb></lb><arrow.to.target n="marg757"></arrow.to.target> <lb></lb>notable retardation or acceleration of the motion of the Veſſel, <lb></lb>its container, ſhall have acquired a cauſe of running towards this <lb></lb><arrow.to.target n="marg758"></arrow.to.target> <lb></lb>or that extream, and ſhall be raiſed in the one, and abated in the <lb></lb><arrow.to.target n="marg759"></arrow.to.target> <lb></lb>other, it ſhall not nevertheleſſe continue, for any time in that <lb></lb>ſtate, when once the primary cauſe is ceaſed: but by vertue of <lb></lb>its own gravity and natural inclination to level and grow, even it <lb></lb>ſhall ſpeedily return backwards of its own accord, and, as being <lb></lb>grave and fluid, ſhall not only move towards <emph type="italics"></emph>Æquilibrium<emph.end type="italics"></emph.end>; but <lb></lb>being impelled by its own <emph type="italics"></emph>impetus,<emph.end type="italics"></emph.end> ſhall go beyond it, riſing in <lb></lb>the part, where before it was loweſt; nor ſhall it ſtay here, but <lb></lb>returning backwards anew, with more reiterated reciprocations of <lb></lb>its undulations, it ſhall give us to know, that it will not from a <lb></lb>velocity of motion, once conceived, reduce it ſelf, in an inſtant, <lb></lb>to the privation thereof, and to the ſtate of reſt, but will ſucceſ <lb></lb>ſively, by decreaſing a little and a little, reduce it ſelf unto the <lb></lb>ſame, juſt in the ſame manner as we ſee a weight hanging at a <lb></lb>cord, after it hath been once removed from its ſtate of reſt, that <lb></lb>is, from its perpendicularity, of its own accord, to return thither <lb></lb>and ſettle it ſelf, but not till ſuch time as it ſhall have often <lb></lb>paſt to one ſide, and to the other, with its reciprocall vi <lb></lb>brations.</s></p><p type="margin"><s><margin.target id="marg757"></margin.target><emph type="italics"></emph>Sundry accidents <lb></lb>that happen in the <lb></lb>ebbings & flowings<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg758"></margin.target><emph type="italics"></emph>The first acci <lb></lb>dent.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg759"></margin.target><emph type="italics"></emph>The Water rai <lb></lb>ſed in one end of <lb></lb>the Veſſel return <lb></lb>eth of its ſelf to<emph.end type="italics"></emph.end> <lb></lb>Æquilibrium.</s></p><p type="main"><s>The ſecond accident to be obſerved is, that the before <lb></lb><arrow.to.target n="marg760"></arrow.to.target> <lb></lb>declared reciprocations of motion come to be made and repeated <lb></lb>with greater or leſſer frequency, that is, under ſhorter or longer <lb></lb>times, according to the different lengths of the Veſſels contain <lb></lb>ing the waters; ſo that in the ſhorter ſpaces the reciprocati <lb></lb>ons are more frequent, and in the longer more rare: juſt as in <lb></lb>the former example of pendent bodies, the vibrations of thoſe <lb></lb>that are hanged to longer cords are ſeen to be leſſe frequent, <lb></lb>than thoſe of them that hang at ſhorter ſtrings.</s></p><p type="margin"><s><margin.target id="marg760"></margin.target><emph type="italics"></emph>In the ſhorter <lb></lb>Viſſels the undula <lb></lb>tions of waters are <lb></lb>more frequent.<emph.end type="italics"></emph.end></s></p><p type="main"><s>And here, for a third obſervation, it is to be noted, that not <lb></lb><arrow.to.target n="marg761"></arrow.to.target> <lb></lb>onely the greater or leſſer length of the Veſſel is a cauſe that <lb></lb>the water maketh its reciprocations under different times; but <lb></lb>the greater or leſſer profundity worketh the ſame effect. </s><s>And <lb></lb>it happeneth, that of waters contained in receptacles of equall <lb></lb>length, but of unequal depth, that which ſhall be the deepeſt, <lb></lb>maketh its undulations under ſhorter times, and the reciprocati <lb></lb>ons of the ſhallower waters are leſſe frequent.</s></p><p type="margin"><s><margin.target id="marg761"></margin.target><emph type="italics"></emph>The greater <lb></lb>profundity maketh <lb></lb>the undulations of <lb></lb>waters more fre <lb></lb>quent.<emph.end type="italics"></emph.end></s></p><p type="main"><s>Fourthly, there are two effects worthy to be noted, and di <lb></lb>ligently obſerved, which the water worketh in thoſe its vibra <pb xlink:href="040/01/414.jpg" pagenum="392"></pb><arrow.to.target n="marg762"></arrow.to.target> <lb></lb>tions; the one is its riſing and falling alternately towards the <lb></lb>one and other extremity; the other is its moving and running, to <lb></lb>ſo ſpeak, Horizontally forwards and backwards. </s><s>Which two dif <lb></lb>ferent motions differently reſide in divers parts of the Water: <lb></lb>for its extream parts are thoſe which moſt eminently riſe and fall; <lb></lb>thoſe in the middle never abſolutely moving upwards and down <lb></lb>wards, of the reſt ſucceſſively thoſe that are neereſt to the ex <lb></lb>treams riſe and fall proportionally more than the remote: but on <lb></lb>the contrary, touching the other progreſſive motion forwards <lb></lb>and backwards, the middle parts move notably, going and re <lb></lb>turning, and the waters that are in the extream parts gain no <lb></lb>ground at all; ſave onely in caſe that in their riſing they over <lb></lb>flow their banks, and break forth of their firſt channel and re <lb></lb>ceptacle; but where there is the obſtacle of banks to keep them <lb></lb>in, they onely riſe and fall; which yet hindereth not the waters <lb></lb>in the middle from fluctuating to and again; which likewiſe <lb></lb>the other parts do in proportion, undulating more or leſſe, <lb></lb>according as they are neerer or more remote from the middle. <lb></lb><arrow.to.target n="marg763"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg762"></margin.target><emph type="italics"></emph>Water riſeth & <lb></lb>falleth in the ex <lb></lb>tream parts of the <lb></lb>Veſſel, and runneth <lb></lb>to and fro in the <lb></lb>midst.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg763"></margin.target><emph type="italics"></emph>An accident of <lb></lb>the Earths motions <lb></lb>impoſſible to be re <lb></lb>duced to practice <lb></lb>by art.<emph.end type="italics"></emph.end></s></p><p type="main"><s>The fifth particular accident ought the more attentively to be <lb></lb>conſidered, in that it is impoſſible to repreſent the effect there <lb></lb>of by an experiment or example; and the accident is this. </s><s>In <lb></lb>the veſſels by us framed with art, and moved, as the above <lb></lb>named Bark, one while more, and another while leſſe ſwiftly, <lb></lb>the acceleration and retardation is imparted in the ſame manner <lb></lb>to all the veſſel, and to every part of it; ſo that whilſt <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> the <lb></lb>Bark forbeareth to move, the parts precedent retard no more <lb></lb>than the ſubſequent, but all equally partake of the ſame re <lb></lb>tardment; and the ſelf-ſame holds true of the acceleration, <lb></lb>namely, that conferring on the Bark a new cauſe of grea <lb></lb>ter velocity, the Prow and Poop both accelerate in one and <lb></lb>the ſame manner. </s><s>But in huge great veſſels, ſuch as are the very <lb></lb>long bottomes of Seas, albeit they alſo are no other than cer <lb></lb>tain cavities made in the ſolidity of the Terreſtrial Globe, <lb></lb>it alwayes admirably happeneth, that their extreams do not <lb></lb>unitedly equall, and at the ſame moments of time increaſe <lb></lb>and diminiſh their motion, but it happeneth that when one of its <lb></lb>extreames hath, by vertue of the commixtion of the two <lb></lb>Motions, Diurnal, and Annual, greatly retarded its velocity, <lb></lb>the other extream is animated with an extream ſwift motion. <lb></lb></s><s>Which for the better underſtanding of it we will explain, reaſ <lb></lb>ſuming a Scheme like to the former; in which if we do but ſup <lb></lb>poſe a tract of Sea to be long, <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> a fourth part, as is the arch <lb></lb>B C [<emph type="italics"></emph>in Fig.<emph.end type="italics"></emph.end> 2.] becauſe the parts B are, as hath been already <lb></lb>declared, very ſwift in motion, by reaſon of the union of the <lb></lb>two motions diurnal and annual, towards one and the ſame way, <pb xlink:href="040/01/415.jpg" pagenum="393"></pb>but the part C at the ſame time is retarded in its motion, as be <lb></lb>ing deprived of the progreſſion dependant on the diurnal motion: <lb></lb>If we ſuppoſe, I ſay, a tract of Sea as long as the arch B C, we <lb></lb>have already ſeen, that its extreams ſhall move in the ſame time <lb></lb>with great inequality. </s><s>And extreamly different would the velo <lb></lb>cities of a tract of Sea be that is in length a ſemicircle, and pla <lb></lb>ced in the poſition B C D, in regard that the extream B would <lb></lb>be in a moſt accelerate motion, and the other D, in a moſt ſlow <lb></lb>one; and the intermediate parts towards C, would be in a <lb></lb>moderate motion. </s><s>And according as the ſaid tracts of Sea ſhall <lb></lb>be ſhorter, they ſhall leſſe participate of this extravagant acci <lb></lb>dent, of being in ſome hours of the day with their parts diverſly <lb></lb>affected by velocity and tardity of motion. </s><s>So that, if, as in the firſt <lb></lb>caſe, we ſee by experience that the acceleration and retardation, <lb></lb>though equally imparted to all the parts of the conteining Veſſel, <lb></lb>is the cauſe that the water contained, fluctuates too and again, what <lb></lb>may we think would happen in a Veſſel ſo admirably diſpoſed, <lb></lb>that retardation and acceleration of motion is very unequally <lb></lb>contributed to its parts? </s><s>Certainly we muſt needs grant that <lb></lb>greater and more wonderful cauſes of the commotions in the <lb></lb>Water ought to be looked for. </s><s>And though it may ſeem im <lb></lb>poſſible to ſome, that in artificial Machines and Veſſels we ſhould <lb></lb>be able to experiment the effects of ſuch an accident; yet ne <lb></lb>vertheleſſe it is not abſolutely impoſſible to be done; and I have <lb></lb>by me the model of an Engine, in which the effect of theſe admi <lb></lb>rable commixtions of motions may be particularly obſerved. </s><s>But <lb></lb>as to what concerns our preſent purpoſe, that which you may <lb></lb>have hitherto comprehended with your imagination may ſuf <lb></lb>fice.</s></p><p type="main"><s>SAGR. </s><s>I for my own particular very well conceive that this <lb></lb>admirable accident ought neceſſarily to evene in the Straights of <lb></lb>Seas, and eſpecially in thoſe that diſtend themſelves for a great <lb></lb>length from Weſt to Eaſt; namely according to the courſe of <lb></lb>the motions of the Terreſtrial Globe; and as it is in a certain <lb></lb>manner unthought of, and without a preſident among the moti <lb></lb>ons poſſible to be made by us, ſo it is not hard for me to believe, <lb></lb>that effects may be derived from the ſame, which are not to be i <lb></lb>mitated by our artificial experiments.</s></p><p type="main"><s>SALV. </s><s>Theſe things being declared, it is time that we pro <lb></lb>ceed to examine the particular accidents, which, together with <lb></lb>their diverſities, are obſerved by experience in the ebbing and <lb></lb>flowing of the waters. </s><s>And firſt we need not think it hard to </s></p><p type="main"><s><arrow.to.target n="marg764"></arrow.to.target> <lb></lb>gueſſe whence it happeneth, that in Lakes, Pooles, and alſo in the <lb></lb>leſſer Seas there is no notable flux and reflux; the which hath <lb></lb>two very ſolid reaſons. </s><s>The one is, that by reaſon of the ſhort <pb xlink:href="040/01/416.jpg" pagenum="394"></pb><arrow.to.target n="marg765"></arrow.to.target> <lb></lb>neſſe of the Veſſel, in its acquiring in ſeveral hours of the day <lb></lb>ſeveral degrees of velocity, they are with very little difference <lb></lb>acquired by all its parts; for as well the precedent as the ſubſe <lb></lb>quent, that is to ſay, both the Eaſtern and Weſtern parts, do <lb></lb>accelerate and retard almoſt in the ſame manner; and withal <lb></lb>making that alteration by little and little, and not by giving the <lb></lb>motion of the conteining Veſſel a ſudden check, and retard <lb></lb>ment, or a ſudden and great impulſe or acceleration; both it <lb></lb>and all its parts, come to be gently and equally impreſſed with <lb></lb>the ſame degrees of velocity; from which uniformity it follow <lb></lb>eth, that alſo the conteined water with but ſmall reſiſtance and <lb></lb>oppoſition, receiveth the ſame impreſſions, and by conſequence <lb></lb>doth give but very obſcure ſignes of its riſing or falling, or of its <lb></lb>running towards one part or another. </s><s>The which effect is likewiſe <lb></lb>manifeſtly to be ſeen in the little artificial Veſſels, wherein the <lb></lb>contained water doth receive the ſelf ſame impreſſions of veloci <lb></lb>ty; when ever the acceleration and retardation is made by gentle <lb></lb>and uniform proportion. </s><s>But in the Straights and Bays that for a <lb></lb>great length diſtend themſelves from Eaſt to Weſt, the accele <lb></lb>ration and retardation is more notable and more uneven, for <lb></lb>that one of its extreams ſhall be much retarded in motion, and <lb></lb>the other ſhall at the ſame time move very ſwiftly: The reci <lb></lb>procal libration or levelling of the water proceeding from the <emph type="italics"></emph>im <lb></lb>petus<emph.end type="italics"></emph.end> that it had conceived from the motion of its container. <lb></lb></s><s>The which libration, as hath been noted, hath its undulations <lb></lb>very frequent in ſmall Veſſels; from whence enſues, that though <lb></lb>there do reſide in the Terreſtrial motions the cauſe of confer <lb></lb>ring on the waters a motion onely from twelve hours to twelve <lb></lb>hours, for that the motion of the conteining Veſſels do ex <lb></lb>treamly accelerate and extreamly retard but once every day, <lb></lb>and no more; yet nevertheleſſe this ſame ſecond cauſe depend <lb></lb>ing on the gravity of the water which ſtriveth to reduce it ſelf to <lb></lb>equilibration, and that according to the ſhortneſſe of the Veſ <lb></lb>ſel hath its reciprocations of one, two, three, or more hours, this <lb></lb>intermixing with the firſt, which alſo it ſelf in ſmall Veſſels is <lb></lb>very little, it becommeth upon the whole altogether inſenſible. <lb></lb></s><s>For the primary cauſe, which hath the periods of twelve hours, <lb></lb>having not made an end of imprinting the precedent commoti <lb></lb>on, it is overtaken and oppoſed by the other ſecond, depen <lb></lb>dant on the waters own weight, which according to the brevity <lb></lb>and profundity of the Veſſel, hath the time of its undulations of <lb></lb>one, two, three, four, or more hours; and this contending <lb></lb>with the other former one, diſturbeth and removeth it, not per <lb></lb>mitting it to come to the height, no nor to the half of its moti <lb></lb>on; and by this conteſtation the evidence of the ebbing and <pb xlink:href="040/01/417.jpg" pagenum="395"></pb>flowing is wholly annihilated, or at leaſt very much obſcured. <lb></lb></s><s>I paſſe by the continual alteration of the air, which diſquieting <lb></lb>the water, permits us not to come to a certainty, whether any, <lb></lb>though but ſmall, encreaſe or abatement of half an inch, or <lb></lb>leſſe, do reſide in the Straights, or receptacles of water not a <lb></lb>bove a degree or two in length.</s></p><p type="margin"><s><margin.target id="marg764"></margin.target><emph type="italics"></emph>Reaſons renew <lb></lb>ed of the particu <lb></lb>lar accidents ob <lb></lb>ſerved in the eb <lb></lb>bings and flowings.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg765"></margin.target><emph type="italics"></emph>Second cauſes <lb></lb>why in ſmall Seas <lb></lb>and in Lakes there <lb></lb>are no ebbings and <lb></lb>flowings.<emph.end type="italics"></emph.end></s></p><p type="main"><s>I come in the ſecond place to reſolve the queſtion, why, there <lb></lb><arrow.to.target n="marg766"></arrow.to.target> <lb></lb>not reſiding any vertue in the primary principle of commoving <lb></lb>the waters, ſave onely every twelve hours, that is to ſay, once <lb></lb>by the greateſt velocity, and once by the greateſt tardity of <lb></lb>motion; the ebbings and flowings ſhould yet nevertheleſſe ap <lb></lb>pear to be every ſix hours. </s><s>To which is anſwered, that this de <lb></lb>termination cannot any wayes be taken from the primary cauſe <lb></lb>onely; but there is a neceſſity of introducing the ſecondary cau <lb></lb>ſes, as namely the greater or leſſe length of the Veſſels, and <lb></lb>the greater or leſſe depth of the waters in them conteined. <lb></lb></s><s>Which cauſes although they have not any operation in the moti <lb></lb>ons of the waters, thoſe operations belonging to the ſole prima <lb></lb>ry cauſe, without which no ebbing or flowing would happen, <lb></lb>yet nevertheleſſe they have a principal ſhare in determining the <lb></lb>times or periods of the reciprocations, and herein their influ <lb></lb>ence is ſo powerful, that the primary cauſe muſt of force give <lb></lb>way unto them. </s><s>The period of ſix hours therefore is no more <lb></lb>proper or natural than thoſe of other intervals of times, though <lb></lb>indeed its the moſt obſerved, as agreeing with our Mediterrane, <lb></lb>which was the onely Sea that for many Ages was navigated: <lb></lb>though neither is that period obſerved in all its parts; for <lb></lb>that in ſome more anguſt places, ſuch as are the <emph type="italics"></emph>Helle <lb></lb>ſpont,<emph.end type="italics"></emph.end> and the <emph type="italics"></emph>Ægean<emph.end type="italics"></emph.end> Sea, the periods are much ſhorter, <lb></lb>and alſo very divers amongſt themſelves; for which diver <lb></lb>ſities, and their cauſes incomprehenſible to <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> ſome <lb></lb>ſay, that after he had a long time obſerved it upon ſome <lb></lb>cliffes of <emph type="italics"></emph>Negropont,<emph.end type="italics"></emph.end> being brought to deſperation, he threw <lb></lb>himſelf into the adjoyning <emph type="italics"></emph>Euripus,<emph.end type="italics"></emph.end> and voluntarily drowned <lb></lb>himſelf.</s></p><p type="margin"><s><margin.target id="marg766"></margin.target><emph type="italics"></emph>The reaſon gi <lb></lb>ven, why the eb <lb></lb>bings and flowings, <lb></lb>for the moſt part, <lb></lb>are every ſix <lb></lb>hours.<emph.end type="italics"></emph.end></s></p><p type="main"><s>In the third place we have the reaſon ready at hand, whence <lb></lb><arrow.to.target n="marg767"></arrow.to.target> <lb></lb>it commeth to paſſe, that ſome Seas, although very long, as is <lb></lb>the Red Sea, are almoſt altogether exempt from Tides, which <lb></lb>happeneth becauſe their length extendeth not from Eaſt to <lb></lb>Weſt, but rather tranſverſly from the Southeaſt to the North <lb></lb>weſt; but the motions of the Earth going from Weſt to Eaſt; <lb></lb>the impulſes of the water, by that means, alwayes happen to fall <lb></lb>in the Meridians, and do not move from parallel to parallel; <lb></lb>inſomuch that in the Seas that extend themſelves athwart to <lb></lb>wards the Poles, and that the contrary way are narrow, there is <pb xlink:href="040/01/418.jpg" pagenum="396"></pb>no cauſe of ebbing and flowing, ſave onely by the participation <lb></lb>of another Sea, wherewith it hath communication, that is ſub <lb></lb>ject to great commotions. <lb></lb><arrow.to.target n="marg768"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg767"></margin.target><emph type="italics"></emph>The cauſe why <lb></lb>ſome Seas, though <lb></lb>very long, ſuffer <lb></lb>no ebbing and <lb></lb>flowing.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg768"></margin.target><emph type="italics"></emph>Ebbings and <lb></lb>flowings why grea <lb></lb>teſt in the extre <lb></lb>mities of gulphs, <lb></lb>and leaſt in the <lb></lb>middle parts.<emph.end type="italics"></emph.end></s></p><p type="main"><s>In the fourth place we ſhall very eaſily find out the reaſon <lb></lb>why the fluxes and refluxes are greateſt, as to the waters riſing <lb></lb>and falling in the utmoſt extremities of Gulphs, and leaſt in the <lb></lb>intermediate parts; as daily experience ſheweth here in <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> <lb></lb>lying in the farther end of the <emph type="italics"></emph>Adriatick<emph.end type="italics"></emph.end> Sea, where that diffe <lb></lb>rence commonly amounts to five or ſix feet; but in the places <lb></lb>of the Mediterrane, far diſtant from the extreams, that mutati <lb></lb>on is very ſmall, as in the Iſles of <emph type="italics"></emph>Corſica<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Sardinnia,<emph.end type="italics"></emph.end> and <lb></lb>in the Strands of <emph type="italics"></emph>Rome<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ligorne,<emph.end type="italics"></emph.end> where it exceeds not half a <lb></lb>foot; we ſhall underſtand alſo, why on the contrary, where <lb></lb>the riſings and fallings are ſmall, the courſes and recourſes are <lb></lb>great: I ſay it is an eaſie thing to underſtand the cauſes of theſe <lb></lb>accidents, ſeeing that we meet with many manifeſt occurrences <lb></lb>of the ſame nature in every kind of Veſſel by us artificially com <lb></lb>poſed, in which the ſame effects are obſerved naturally to fol <lb></lb>low upon our moving it unevenly, that is, one while faſter, and <lb></lb>another while ſlower.</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"></emph>Why in narrow <lb></lb>places the courſe <lb></lb>of the waters is <lb></lb>more ſwift than in <lb></lb>larger.<emph.end type="italics"></emph.end></s></p><p type="main"><s>Moreover, conſidering in the fifth place, that the ſame <lb></lb>quantity of Water being moved, though but gently, in a ſpatious <lb></lb>Channel, comming afterwards to go through a narrow paſſage, <lb></lb>will of neceſſity run, with great violence, we ſhall not finde it hard <lb></lb>to comprehend the cauſe of the great Currents that are made <lb></lb>in the narrow Channel that ſeparateth <emph type="italics"></emph>Calabria<emph.end type="italics"></emph.end> from <emph type="italics"></emph>Sicilia:<emph.end type="italics"></emph.end> <lb></lb>for that all the Water that, by the ſpaciouſneſſe of the Iſle, <lb></lb>and by the <emph type="italics"></emph>Ionick<emph.end type="italics"></emph.end> Gulph, happens to be pent in the Eaſtern <lb></lb>part of the Sea, though it do in that, by reaſon of its largeneſs, <lb></lb>gently deſcend towards the Weſt, yet nevertheleſſe, in that it <lb></lb>is pent up in the <emph type="italics"></emph>Boſphorus,<emph.end type="italics"></emph.end> it floweth with great violence be <lb></lb>tween <emph type="italics"></emph>Scilla<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Caribdis,<emph.end type="italics"></emph.end> and maketh a great agitation. </s><s>Like to <lb></lb>which, and much greater, is ſaid to be betwixt <emph type="italics"></emph>Africa<emph.end type="italics"></emph.end> and the <lb></lb>great Iſle of St. <emph type="italics"></emph>Lorenzo,<emph.end type="italics"></emph.end> where the Waters of the two vaſt <lb></lb>Seas, <emph type="italics"></emph>Indian<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ethiopick,<emph.end type="italics"></emph.end> that lie round it, muſt needs be <lb></lb>ſtraightned into a leſſe Channel between the ſaid Iſle and the <lb></lb><emph type="italics"></emph>Ethiopian<emph.end type="italics"></emph.end> Coaſt. </s><s>And the Currents muſt needs be very great <lb></lb>in the Straights of <emph type="italics"></emph>Magellanes,<emph.end type="italics"></emph.end> which joyne together the <lb></lb>vaſt Oceans of <emph type="italics"></emph>Ethiopia,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Del Zur,<emph.end type="italics"></emph.end> called alſo the <emph type="italics"></emph>Pacifick<emph.end type="italics"></emph.end> <lb></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"></emph>A diſcuſſion of <lb></lb>ſome more abſtruſe <lb></lb>accidents obſerved <lb></lb>in the ebbing and <lb></lb>flowing.<emph.end type="italics"></emph.end></s></p><p type="main"><s>It follows now, in the ſixth place, that to render a reaſon of <lb></lb>ſome more abſtruſe and incredible accidents, which are obſer <lb></lb>ved upon this occaſion, we make a conſiderable reflection upon <lb></lb>the two principal cauſes of ebbings and flowings, afterwards <lb></lb>compounding and mixing them together. </s><s>The firſt and ſimpleſt <pb xlink:href="040/01/419.jpg" pagenum="397"></pb>of which is (as hath often been ſaid) the determinate accelera <lb></lb>tion and retardation of the parts of the Earth, from whence <lb></lb>the Waters have a determinate period put to their decurſions <lb></lb>towards the Eaſt, and return towards the Weſt, in the time of <lb></lb>twenty ſour hours. </s><s>The other is that which dependeth on the pro <lb></lb>per gravity of the Water, which being once commoved by the <lb></lb>primary cauſe, ſeeketh, in the next place, to reduce it ſelf to <emph type="italics"></emph>Æ <lb></lb>quilibrium,<emph.end type="italics"></emph.end> with iterated reciprocations; which are not deter <lb></lb>mined by one ſole and prefixed time; but have as many varie <lb></lb>ties of times as are the different lengths and profundities of the <lb></lb>receptacles, and Straights of Seas; and by what dependeth on <lb></lb>this ſecond principle, they would ebbe. </s><s>and flow, ſome in one <lb></lb>hour, others in two, in four, in ſix, in eight, in ten, &c. </s><s>Now if <lb></lb>we begin to put together the firſt cauſe, which hath its ſet Period <lb></lb>from twelve hours to twelve hours, with ſome one of the ſecon <lb></lb>dary, that hath its Period <emph type="italics"></emph>verb. </s><s>grat.<emph.end type="italics"></emph.end> from five hours to five <lb></lb>hours, it would come to paſſe, that at ſometimes the primary <lb></lb>cauſe and ſecondary would accord to make impulſes both one <lb></lb>and the ſame way; and in this concurrency, and (as one may call <lb></lb>it) unanimous conſpiration the flowings ſhall be great. </s><s>At other <lb></lb>times it happening that the primary impulſe doth, in a certain <lb></lb>manner, oppoſe that which the ſecondary Period would make, <lb></lb>and in this conteſt one of the Principles being taken away, that <lb></lb>which the other would give, will weaken the commotion of the <lb></lb>Waters, and the Sea will return to a very tranquil State, and <lb></lb>almoſt immoveable. </s><s>And at other times, according as the two <lb></lb>aforeſaid Principles ſhall neither altogether conteſt, nor altoge <lb></lb>ther concur, there ſhall be other kinds of alterations made in <lb></lb>the increaſe and diminution of the ebbing and flowing. </s><s>It may <lb></lb>likewiſe fall out that two Seas, conſiderably great and which <lb></lb>communicate by ſome narrow Channel, may chance to have, by <lb></lb>reaſon of the mixtion of the two Principles of motion, one <lb></lb>cauſe to flow at the time that the other hath cauſe to move a <lb></lb>contrary way; in which caſe in the Channel, whereby they diſ <lb></lb>imbogue themſelves into each other, there do extraordinary <lb></lb>conturbations inſue, with oppoſite and vortick motions, and <lb></lb>moſt dangerous boilings and breakings, as frequent relations <lb></lb>and experiences do aſſure us. </s><s>From ſuch like diſcordant moti <lb></lb>ons, dependent not onely on the differenr poſitions and longi <lb></lb>tudes, but very much alſo upon the different profundities of the <lb></lb>Seas, which have the ſaid intercourſe there do happen at ſome <lb></lb>times different commotions in the Waters, irregular, and that <lb></lb>can be reduced to no rules of obſervation, the reaſons of which <lb></lb>have much troubled, and alwayes do trouble Mariners, for that <lb></lb>they meet with them without ſeeing either impulſe of winds, or <pb xlink:href="040/01/420.jpg" pagenum="398"></pb>other eminent aereal alteration that might occaſion the ſame; of <lb></lb>which diſturbance of the Air we ought to make great account <lb></lb>in other accidents, and to take it for a third and accidental <lb></lb>cauſe, able to alter very much the obſervation of the effects de <lb></lb>pending on the ſecondary and more eſſential cauſes. </s><s>And it is <lb></lb>not to be doubted, but that impetuous windes, continuing to <lb></lb>blow, for example, from the Eaſt, they ſhall retein the Waters <lb></lb>and prohibit the reflux or ebbing; whereupon the ſecond and <lb></lb>third reply of the flux or tide overtaking the former, at the <lb></lb>hours prefixed, they will ſwell very high; and being thus born <lb></lb>up for ſome dayes, by the ſtrength of the Winds, they ſhall riſe <lb></lb>more than uſual, making extraordinary inundations.</s></p><p type="main"><s>We ought alſo, (and this ſhall ſerve for a ſeventh Probleme) <lb></lb>to take notice of another cauſe of motion dependant on the <lb></lb>great abundance of the Waters of great Rivers that diſcharge </s></p><p type="main"><s><arrow.to.target n="marg771"></arrow.to.target> <lb></lb>themſelves into Seas of no great capacity, whereupon in the <lb></lb>Straits or <emph type="italics"></emph>Boſphori<emph.end type="italics"></emph.end> that communicate with thoſe Seas, the Waters <lb></lb>are ſeen to run always one way: as it happeneth in the <emph type="italics"></emph>Thraci <lb></lb>an Boſphorus<emph.end type="italics"></emph.end> below <emph type="italics"></emph>Conſtantinople,<emph.end type="italics"></emph.end> where the water alwayes <lb></lb>runneth from the <emph type="italics"></emph>Black-Sea,<emph.end type="italics"></emph.end> towards the <emph type="italics"></emph>Propontis<emph.end type="italics"></emph.end>: For in the <lb></lb>ſaid <emph type="italics"></emph>Black-Sea<emph.end type="italics"></emph.end> by reaſon of its ſhortneſſe, the principal cauſes <lb></lb>of ebbing and flowing are but of ſmall force. </s><s>But, on the con <lb></lb>trary, very great Rivers falling into the ſame, thoſe huge de <lb></lb>fluxions of water being to paſſe and diſgorge themſelves by the <lb></lb><arrow.to.target n="marg772"></arrow.to.target> <lb></lb>the Straight, the ^{*}courſe is there very notable and alwayes to <lb></lb>wards the South. </s><s>Where moreover we ought to take notice, that <lb></lb>the ſaid Straight or Channel, albeit very narrow, is not ſubject <lb></lb>to perturbations, as the Straight of <emph type="italics"></emph>Soilla<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Carybdis<emph.end type="italics"></emph.end>; for that <lb></lb>that hath the <emph type="italics"></emph>Black-Sea<emph.end type="italics"></emph.end> above towards the North, and the <emph type="italics"></emph>Pro <lb></lb>pontis,<emph.end type="italics"></emph.end> the <emph type="italics"></emph>Ægean,<emph.end type="italics"></emph.end> and the <emph type="italics"></emph>Mediterranean<emph.end type="italics"></emph.end> Seas joyned unto it, <lb></lb>though by a long tract towards the South; but now, as we have <lb></lb>obſerved, the Seas, though of never ſo great length, lying North <lb></lb>and South, are not much ſubject to ebbings and flowings; but <lb></lb>becauſe the <emph type="italics"></emph>Sicilian<emph.end type="italics"></emph.end> Straight is ſituate between the parts of the <lb></lb>Mediterrane diſtended for a long tract or diſtance from Weſt to <lb></lb>Eaſt, that is, according to the courſe of the fluxes and refluxes, <lb></lb>therefore in this the agitations are very great; and would be <lb></lb>much more violent between <emph type="italics"></emph>Hercules Pillars,<emph.end type="italics"></emph.end> in caſe the <lb></lb>Straight of <emph type="italics"></emph>Gibraltar<emph.end type="italics"></emph.end> did open leſſe; and thoſe of the Straight of <lb></lb><emph type="italics"></emph>Magellanes<emph.end type="italics"></emph.end> are reported to be extraordinary violent.</s></p><p type="margin"><s><margin.target id="marg771"></margin.target><emph type="italics"></emph>The cauſe why, <lb></lb>in ſome narrow <lb></lb>Channels, we ſee <lb></lb>the Sea-waters run <lb></lb>alwayes one way.<emph.end type="italics"></emph.end></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 preſent, cometh into my mind to ſay unto <lb></lb>you about the cauſes of this firſt period diurnal of the Tide, and <lb></lb>its various accidents, touching which, if you have any thing to <lb></lb>offer, you may let us hear it, that ſo we may afterwards pro <lb></lb>ceed to the other two periods, monethly and annual.</s></p> <pb xlink:href="040/01/421.jpg" pagenum="399"></pb><p type="main"><s>SIMP. </s><s>In my opinion, it cannot be denied, but that your diſ <lb></lb>courſe carrieth with it much of probability, arguing, as we ſay, <lb></lb><emph type="italics"></emph>ex ſuppoſitione,<emph.end type="italics"></emph.end> namely, granting that the Earth moveth with <lb></lb>the two motions aſſigned it by <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end>: but if that motion <lb></lb><arrow.to.target n="marg773"></arrow.to.target> <lb></lb>be diſproved, all that you have ſaid is vain, and inſignificant: <lb></lb>and for the diſproval of that <emph type="italics"></emph>Hypotheſis,<emph.end type="italics"></emph.end> it is very manifeſtly <lb></lb>hinted by your Diſcourſe it ſelf. </s><s>You, with the ſuppoſition of <lb></lb>the two Terreſtrial motions, give a reaſon of the ebbing and <lb></lb>flowing; and then again, arguing circularly, from the ebbing <lb></lb>and flowing, draw the reaſon and confirmation of thoſe very <lb></lb>motions; aud ſo proceeding to a more ſpecious Diſcourſe, you <lb></lb>ſay that the Water, as being a fluid body, and not tenaciouſly <lb></lb>annexed to the Earth, is not conſtrained punctually to obey eve <lb></lb>ry of its motions, from which you afterwards infer its ebbing <lb></lb>and flowing, Now I, according to your own method, argue <lb></lb>the quite contrary, and ſay; the Air is much more tenuous, and <lb></lb>fluid than the Water, and leſſe annexed to the Earths ſuperfici <lb></lb>es, to which the Water, if it be for nothing elſe, yet by reaſon <lb></lb>of its gravity that preſſeth down upon the ſame more than the <lb></lb>light Air, adhereth; therefore the Air is much obliged to fol <lb></lb>low the motions of the Earth: and therefore were it ſo, that the <lb></lb>Earth did move in that manner, we the inhabitants of it, and <lb></lb>carried round with like velocity by it, ought perpetually to feel <lb></lb>a Winde from the Eaſt that beateth upon us with intolerable <lb></lb>force. </s><s>And that ſo it ought to fall out, quotidian experience aſ <lb></lb>ſureth us: for if with onely riding poſt, at the ſpeed of eight or <lb></lb>ten miles an hour in the tranquil Air, the incountering of it with <lb></lb>our face ſeemeth to us a Winde that doth not lightly blow upon <lb></lb>us, what ſhould we expect from our rapid courſe of 800. or a <lb></lb>thouſand miles an hour, againſt the Air, that is, free from that <lb></lb>motion? </s><s>And yet, notwithſtanding we cannot perceive any <lb></lb>thing of that nature.</s></p><p type="margin"><s><margin.target id="marg773"></margin.target><emph type="italics"></emph>The Hypotheſir <lb></lb>of the Earths mo <lb></lb>bility taken in fa <lb></lb>vour of the Tide, <lb></lb>oppoſed.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>To this objection that hath much of likelihood in it, I <lb></lb><arrow.to.target n="marg774"></arrow.to.target> <lb></lb>reply, that its true, the Air is of greater tenuity and levity; and, <lb></lb>by reaſon of its levity, leſſe adherent to the Earth than Water ſo <lb></lb>much more grave and ^{*}bulky; but yet the conſequence is falſe <lb></lb>that you infer from theſe qualities; namely, that upon account <lb></lb><arrow.to.target n="marg775"></arrow.to.target> <lb></lb>of that its levity, tenuity, and leſſe adherence to the Earth, it <lb></lb>ſhould be more exempt than the Water from following the <lb></lb>Terreſtrial Motions; ſo as that to us, who abſolutely pertake of <lb></lb>of them, the ſaid exemption ſhould be ſenſible and manifeſt; <lb></lb>nay, it happeneth quite contrary; for, if you well remember, the <lb></lb>cauſe of the ebbing and flowing of the Water aſſigned by us, <lb></lb>conſiſteth in the Waters not following the unevenneſſe of the <lb></lb>motion of its Veſſel, but retaining the <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> conceived before, <pb xlink:href="040/01/422.jpg" pagenum="400"></pb>without diminiſhing or increaſing it according to the preciſe rate <lb></lb>of its diminiſhing or increaſing in its Veſſel. </s><s>Becauſe therefore <lb></lb><arrow.to.target n="marg776"></arrow.to.target> <lb></lb>that in the conſervation and retention of the <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> before con <lb></lb>ceived, the diſobedience to a new augmentation or diminution of <lb></lb>motion conſiſteth, that moveable that ſhall be moſt apt for ſuch <lb></lb>a retention, ſhall be alſo moſt commodious to demonſtrate the <lb></lb>effect that followeth in conſequence of that retention. </s><s>Now how <lb></lb>much the Water is diſpoſed to maintain ſuch a conceived agita <lb></lb>tion; though the cauſes ceaſe that impreſs the ſame, the experi <lb></lb>ence of the Seas extreamly diſturbed by impetuous Winds ſhew <lb></lb>eth us; the Billows of which, though the Air be grown calm, and <lb></lb>the Wind laid, for a long time after continue in motion: As the <lb></lb>Sacred Poet pleaſantly ſings,</s></p><p type="margin"><s><margin.target id="marg774"></margin.target><emph type="italics"></emph>The anſwer to <lb></lb>the objections <lb></lb>made againſt the <lb></lb>motion of the Ter <lb></lb>reſtrial Globe.<emph.end type="italics"></emph.end></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"></emph>The Water more <lb></lb>apt to conſerve an<emph.end type="italics"></emph.end> <lb></lb>impetus <emph type="italics"></emph>conceived, <lb></lb>then the Air.<emph.end type="italics"></emph.end></s></p><p type="head"><s><emph type="italics"></emph>Qual l'alto Egeo,<emph.end type="italics"></emph.end> &c.----------</s></p><p type="main"><s>And that long continuing rough after a ſtorm, dependeth on <lb></lb><arrow.to.target n="marg777"></arrow.to.target> <lb></lb>the gravity of the water: For, as I have elſewhere ſaid, light bo <lb></lb>dies are much eaſier to be moved than the more grave, but yet <lb></lb>are ſo much the leſs apt to conſerve the motion imparted, when <lb></lb>once the moving cauſe ceaſeth. </s><s>Whence it comes that the Aire, <lb></lb>as being of it ſelf very light and thin, is eaſily mov'd by any very <lb></lb>ſmall force, yet it is withall very unable to hold on its motion, <lb></lb>the Mover once ceaſing. </s><s>Therefore, as to the Aire which envi <lb></lb>rons the Terreſtrial Globe, I would fay, that by reaſon of its <lb></lb>adherence, it is no leſſe carried about therewith then the Water; <lb></lb>and eſpecially that part which is contained in its veſſels; which <lb></lb><arrow.to.target n="marg778"></arrow.to.target> <lb></lb>veſſels are the valleys encloſed with Mountains. </s><s>And we may <lb></lb>with much more reaſon affirm that this ſame part of the Air is <lb></lb>carried round, and born forwards by the rugged parts of the <lb></lb>Earth, than that the higher is whirl'd about by the motion of the <lb></lb>Heavens, as ye <emph type="italics"></emph>Peripateticks<emph.end type="italics"></emph.end> maintain.</s></p><p type="margin"><s><margin.target id="marg777"></margin.target><emph type="italics"></emph>Light bodies eaſier <lb></lb>to be moved than <lb></lb>beavy, but leſs aut <lb></lb>to conſerve the mo <lb></lb>tion.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg778"></margin.target><emph type="italics"></emph>Its more rational <lb></lb>that the Air be <lb></lb>commoved by the <lb></lb>rugged ſurface of <lb></lb>the Earth than <lb></lb>by the Celeſtial <lb></lb>motion.<emph.end type="italics"></emph.end></s></p><p type="main"><s>What hath been hitherto ſpoken, ſeems to me a ſufficient an <lb></lb><arrow.to.target n="marg779"></arrow.to.target> <lb></lb>ſwer to the allega ion of <emph type="italics"></emph>Simputius<emph.end type="italics"></emph.end>; yet nevertheleſs with a new <lb></lb>inſtance and ſolution, founded upon an admirable experiment, I <lb></lb>will ſuperabundantly ſatisfie him, and confirm to <emph type="italics"></emph>Sagredus<emph.end type="italics"></emph.end> the <lb></lb>mobility of the Earth. </s><s>I have told you that the Air, and in par <lb></lb>ticular that part of it which aſcendeth not above the tops of the <lb></lb>higheſt Mountains, is carried round by the uneven parts of the <lb></lb>Earths ſurface: from whence it ſhould ſeem, that it muſt of con <lb></lb>ſequence come to paſſe, that in caſe the ſuperficies of the Earth <lb></lb>were not uneven, but ſmooth and plain, no cauſe would remain <lb></lb>for drawing the Air along with it, or at leaſt for revolving it with <lb></lb>ſo much uniformity. </s><s>Now the ſurface of this our Globe, is not <lb></lb>all craggy and rugged, but there are exceeding great tracts very <pb xlink:href="040/01/423.jpg" pagenum="401"></pb>even, to wit, the ſurfaces of very vaſt Seas, which being alſo far <lb></lb>remote from the continuate ledges of Mountains which environ <lb></lb>it, ſeem to have no faculty of carrying the ſuper-ambient Air <lb></lb>along therewith: and not carrying it about, we may perceive what <lb></lb>will of conſequence enſue in thoſe places.</s></p><p type="margin"><s><margin.target id="marg779"></margin.target><emph type="italics"></emph>The revolution of <lb></lb>the Earth con <lb></lb>firmed by a new <lb></lb>argument taken <lb></lb>from the Air.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I was about to propoſe the very ſame difficulty, which <lb></lb>I think is of great validity.</s></p><p type="main"><s>SALV. </s><s>You ſay very well <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> for from the not finding <lb></lb>in the Air that which of conſequence would follow, did this our <lb></lb>Globe move round; you argue its immoveableneſſe. </s><s>But in caſe <lb></lb>that this which you think ought of neceſſary conſequence to be <lb></lb>found, be indeed by experience proved to be ſo; will you accept <lb></lb>it for a ſufficient teſtimony and an argument for the mobility of <lb></lb>the ſaid Globe?</s></p><p type="main"><s>SIMP. </s><s>In this caſe it is not requiſite to argue with me alone, <lb></lb>for if it ſhould ſo fall out, and that I could not comprehend the <lb></lb>cauſe 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 ſhall never get, but <lb></lb>be alwayes on the loſing hand; and therefore it would be better <lb></lb>to give over: Nevertheleſs, that we may not cheat our third man <lb></lb>we will play on. </s><s>We ſaid even now, and with ſome addition we <lb></lb>reitterate it, that the Ayr as if it were a thin and fluid body, and <lb></lb>not ſolidly conjoyned with the Earth, ſeem'd not to be neceſſi <lb></lb>tated to obey its motion; unleſſe ſo far as the craggineſs of the <lb></lb>terreſtrial ſuperficies, tranſports and carries with it a part there <lb></lb>of contigious thereunto; which doth not by any great ſpace ex <lb></lb>ceed the greateſt altitude of Mountains: the which portion of Air <lb></lb>ought to be ſo much leſs repugnant to the terreſtrial converſion, <lb></lb><arrow.to.target n="marg780"></arrow.to.target> <lb></lb>by how much it is repleat with vapours, fumes, and exhalations, <lb></lb>matters all participating of terrene qualities, and conſequently <lb></lb>apt of their own nature to the ſame motions. </s><s>But where there are <lb></lb>wanting the cauſes of motion, that is, where the ſurface of the <lb></lb>Globe hath great levels, and where there is leſs mixture of the <lb></lb>terrene vapours, there the cauſe whereby the ambient Air is con <lb></lb>ſtrained to give entire obedience to the terreſtrial converſion will <lb></lb>ceaſe in part; ſo that in ſuch places, whilſt the Earth revolveth to <lb></lb>wards the Eaſt, there will be continually a wind perceived which <lb></lb>will beat upon us, blowing from the Eaſt towards the Weſt: <lb></lb>and ſuch gales will be the more ſenſible, where the revolution of <lb></lb>the Globe is moſt ſwift; which will be in places more remote from <lb></lb>the Poles, and approaching to the greateſt Circle of the diurnal <lb></lb>converſion. </s><s>But now <emph type="italics"></emph>de facto<emph.end type="italics"></emph.end> experience much confi meth this <lb></lb>Phyloſophical argumentation; for in the ſpatious Seas, and in their <lb></lb>parts moſt remote from Land, and ſituate under the Torrid Zone, <lb></lb>that is bounded by the Tropicks, where there are none of thoſe <pb xlink:href="040/01/424.jpg" pagenum="402"></pb><arrow.to.target n="marg781"></arrow.to.target> <lb></lb>ſame terreſtrial evaporations, we finde a perpetual gale move <lb></lb>from the Eaſt with ſo conſtant a blaſt, that ſhips by favour there <lb></lb>of ſail proſperouſly to the <emph type="italics"></emph>West-India's.<emph.end type="italics"></emph.end> And from the ſame <lb></lb>coaſting along the <emph type="italics"></emph>Mexican<emph.end type="italics"></emph.end> ſhore, they with the ſame felicity paſs <lb></lb>the <emph type="italics"></emph>Pacifick<emph.end type="italics"></emph.end> Ocean towards the <emph type="italics"></emph>India's<emph.end type="italics"></emph.end>; which to us are Eaſt, but <lb></lb><arrow.to.target n="marg782"></arrow.to.target> <lb></lb>to them are Weſt. </s><s>Whereas on the contrary the Courſe from <lb></lb>thence towards the Eaſt is difficult and uncertain, and not to be <lb></lb>made by the ſame Rhumb, but muſt vere more to Land-ward, to <lb></lb>recover other Winds, which we may call accidentary and tumul <lb></lb>tuary, produced from other Principles, as thoſe that inhabit the <lb></lb>continent find by experience. </s><s>Of which productions of Winds, <lb></lb>the Cauſes are many and different, which ſhall not at this time be <lb></lb><arrow.to.target n="marg783"></arrow.to.target> <lb></lb>mentioned. </s><s>And theſe accidentary Winds are thoſe which blow <lb></lb>indifferently from all parts of the Eatth, and make rough the Seas <lb></lb>remote from the Equinoctial, and environed by the rugged Sur <lb></lb>face of the Earth; which is as much as to ſay environ'd with <lb></lb>thoſe perturbations of Air, that confound that primary Gale. <lb></lb></s><s>The which, in caſe theſe accidental impediments were removed, <lb></lb>would be continually felt, and eſpecially upon the Sea. </s><s>Now <lb></lb>ſee how the effect of the Water and Air ſeem wonderfully to ac <lb></lb>cord with the Celeſtial obſervations, to confirm the mobility of <lb></lb>our Terreſtrial Globe. <lb></lb><arrow.to.target n="marg784"></arrow.to.target></s></p><p type="margin"><s><margin.target id="marg780"></margin.target><emph type="italics"></emph>The vaporous <lb></lb>parts of the earth, <lb></lb>partake of its mo <lb></lb>tions.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg781"></margin.target><emph type="italics"></emph>Conſtant gales <lb></lb>within the Tro <lb></lb>pieks blow towards <lb></lb>the Weſt.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg782"></margin.target><emph type="italics"></emph>The courſe to the <lb></lb>Weſt<emph.end type="italics"></emph.end>-India's <emph type="italics"></emph>ea <lb></lb>ſie, the return dif <lb></lb>ficult.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg783"></margin.target><emph type="italics"></emph>Winds from Land <lb></lb>make rough the <lb></lb>Seas.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg784"></margin.target><emph type="italics"></emph>Another obſerva <lb></lb>tion taken from the <lb></lb>Air in confirmati <lb></lb>on of the motion of <lb></lb>the Earth.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I alſo for a final cloſe will relate to you one particular, <lb></lb>which as I believe is unknown unto you, and which likewiſe may <lb></lb>ſerve to confirm the ſame concluſion: You <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> alledged, <lb></lb>That Accident which Sailers meet with between the Tropicks; <lb></lb>I mean that perpetual Gale of Winde that beats upon them from <lb></lb>the Eaſt, of which I have an account from thoſe that have many <lb></lb>times made the Voyage: And moreover (which is very obſer <lb></lb>vable) I underſtand that the Mariners do not call it a <emph type="italics"></emph>Wind,<emph.end type="italics"></emph.end> but </s></p><p type="main"><s><arrow.to.target n="marg785"></arrow.to.target> <lb></lb>by another ^{*} name, which I do not now remember, taken haply <lb></lb>from its ſo fixed and conſtant Tenor; which when they have met <lb></lb>with, they tie up their ſhrouds and other cordage belonging to <lb></lb>the Sails, and without any more need of touching them, though <lb></lb>they be in a ſleep, they can continue their courſe. </s><s>Now this conſtant <lb></lb>Trade-wind was known to be ſuch by its continual blowing with <lb></lb>out interruptions; for if it were interrupted by other Windes, it <lb></lb>would not have been acknowledged for a ſingular Effect, and <lb></lb>different from the reſt: from which I wlll infer, That it may be <lb></lb>that alſo our Mediterranean Sea doth partake of the like accident; <lb></lb>but it is not obſerved, as being frequently altered by the conflu <lb></lb>ence of other windes. </s><s>And this I ſay, not without good grounds, <lb></lb>yea upon very probable conjectures whch came unto my know <lb></lb>ledge, from that which tendred it ſelf to my notice on occaſion of <lb></lb>the voyage that I made into <emph type="italics"></emph>Syria,<emph.end type="italics"></emph.end> going Conſul for this Nation <pb xlink:href="040/01/425.jpg" pagenum="403"></pb>to <emph type="italics"></emph>Aleppo,<emph.end type="italics"></emph.end> and this it is: That keeping a particular account and <lb></lb><arrow.to.target n="marg786"></arrow.to.target> <lb></lb>memorial of the dayes of the departure and arrival of the Ships in <lb></lb>the Ports of <emph type="italics"></emph>Alexandria,<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Alexandretta,<emph.end type="italics"></emph.end> and this of <emph type="italics"></emph>Venice<emph.end type="italics"></emph.end>; in <lb></lb>comparing ſundry of them, which I did for my curioſity, I found <lb></lb>that in exactneſs of account the returns hither, that is the voiages <lb></lb>from Eaſt to Weſt along the Mediterrane, are made in leſs time <lb></lb>then the contrary courſes by 25. in the Hundred: So that we ſee <lb></lb>that one with another, the Eaſtern windes are ſtronger then the <lb></lb>Weſtern.</s></p><p type="margin"><s><margin.target id="marg785"></margin.target>Which Wind <lb></lb>with our Engliſh <lb></lb>Mariners is called <lb></lb>the <emph type="italics"></emph>Trade-wind.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg786"></margin.target><emph type="italics"></emph>The voiages in the <lb></lb>Mediterrane from <lb></lb>Eaſt to Weſt are <lb></lb>made in ſhorter <lb></lb>times than from <lb></lb>Weſt to Eaſt.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>I am very glad I know this particular, which doth not <lb></lb>a little make for the confirmation of the Earths mobility. </s><s>And <lb></lb>although it may be alledged, That all the Water of the Mediter <lb></lb>rane runs perpetually towards the Straits-mouth, as being to <lb></lb>diſimbogue into the Ocean, the waters of as many Rivers, as do <lb></lb>diſcharge themſelves into the ſame; I do not think that that cur <lb></lb>rent can be ſo great, as to be able of it ſelf alone to make ſo no <lb></lb>table a difference: which is alſo manifeſt by obſerving that the <lb></lb>water in the Pharo of <emph type="italics"></emph>Sicily<emph.end type="italics"></emph.end> runneth back again no leſs towards <lb></lb>the Eaſt, than it runneth forwards towards the Weſt.</s></p><p type="main"><s>SAGR. I, that have not as <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> an inclination to ſatiſ <lb></lb>fie any one beſides my ſelf, am ſatisfied with what hath been ſaid <lb></lb>as to this firſt particular: Therefore <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> when you think <lb></lb>it fit to proceed forward, I am prepared to hear you.</s></p><p type="main"><s>SALV. </s><s>I ſhall do as you command me, but yet I would fain <lb></lb>hear the opinion alſo of <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> from whoſe judgement I can <lb></lb>argue how much I may promiſe to my ſelf touching theſe diſ <lb></lb>courſes from the <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> Schools, if ever they ſhould come <lb></lb>to their ears.</s></p><p type="main"><s>SIMP. </s><s>I deſire not that my opinion ſhould ſerve or ſtand for <lb></lb>a meaſure, whereby you ſhould judge of others thoughts; for <lb></lb>as I have often ſaid, I am inconſiderable in theſe kinde of ſtudies, <lb></lb>and ſuch things may come into the mindes of thoſe that are enter <lb></lb>ed into the deepeſt paſſages of Philoſophy, as I could never think <lb></lb>of; as having (according to the Proverb) ſcarce kiſt her Maid: <lb></lb>yet nevertheleſs, to give you my ſudden thoughts, I ſhall tell <lb></lb>you, That of thoſe effects by you recounted, and particularly the <lb></lb>laſt, there may in my judgement very ſufficient Reaſons be given <lb></lb>without the Earths mobility, by the mobility of the Heavens one <lb></lb>ly; never introducing any novelty more, than the inverſion of <lb></lb>that which you your ſelf propoſe unto us. </s><s>It hath been received <lb></lb><arrow.to.target n="marg787"></arrow.to.target> <lb></lb>by the <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> Schools, that the Element of Fire, and alſo a <lb></lb>great part of the Aire is carried about according to the Diurnal <lb></lb>converſion from Eaſt to Weſt, by the contact of the Concave of <lb></lb>the Lunar Orb, as by the Veſſel their container. </s><s>Now without <lb></lb>going out of your track, I will that we determine the Quantity of <pb xlink:href="040/01/426.jpg" pagenum="404"></pb><arrow.to.target n="marg788"></arrow.to.target> <lb></lb>the Aire which partaketh of that motion to diſtend ſo low as to <lb></lb>the Tops of the higheſt Hills, and that likewiſe they would reach <lb></lb>to the Earth, if thoſe Mountains did not impede them, which <lb></lb>agreeth with what you ſay: For as you affirm, the Air, which is <lb></lb>invironed by ledges of Mountains, to be carried about by the <lb></lb>aſperity of the moveable Earth; we on the contrary ſay, That <lb></lb>the whole Element of Air is carried about by the motion of <lb></lb>Heaven, that part only excepted which lyeth below thoſe bodies, <lb></lb>which is hindred by the aſperity of the immoveable Earth. </s><s>And <lb></lb>whereas you ſaid, That in caſe that aſperity ſhould be removed, <lb></lb>the Air would alſo ceaſe to be whirld about; we may ſay, <lb></lb>That the ſaid aſperity being removed, the whole Aire would con <lb></lb>tinue its motion. </s><s>Whereupon, becauſe the ſurfaces of ſpacious <lb></lb>Seas are ſmooth, and even; the Airs motion ſhall continue upon <lb></lb>thoſe, alwaies blowing from the Eaſt: And this is more ſenſibly <lb></lb>perceived in Climates lying under the Line, and within the Tro <lb></lb>picks, where the motion of Heaven is ſwifter; and like as that <lb></lb>Celeſtial motion is able to bear before it all the Air that is at <lb></lb>liberty, ſo we may very rationally affirm that it contributeth the <lb></lb>ſame motion to the Water moveable, as being fluid and not con <lb></lb>nected to the immobility of the Earth: And with ſo much the <lb></lb><arrow.to.target n="marg789"></arrow.to.target> <lb></lb>more confidence may we affirm the ſame, in that by your con <lb></lb>feſſion, that motion ought to be very ſmall in reſect of the efficient <lb></lb>Cauſe; which begirting in a natural day the whole Terreſtrial <lb></lb>Globe, paſſeth many hundreds of miles an hour, and eſpecially <lb></lb>towards the Equinoctial; whereas in the currents of the open Sea, <lb></lb>it moveth but very few miles an hour. </s><s>And thus the voiages to <lb></lb>wards the Weſt ſhall come to be commodious and expeditious, <lb></lb>not onely by reaſon of the perpetual Eaſtern Gale, but of the <lb></lb>courſe alſo of the Waters; from which courſe alſo perhaps the <lb></lb>Ebbing and Flowing may come, by reaſon of the different ſcitu <lb></lb><arrow.to.target n="marg790"></arrow.to.target> <lb></lb>ation of the Terreſtrial Shores: againſt which the Water coming <lb></lb>to beat, may alſo return backwards with a contrary motion, like <lb></lb>as experience ſheweth us in the courſe of Rivers; for according as <lb></lb>the Water in the unevenneſs of the Banks, meeteth with ſome <lb></lb>parts that ſtand out, or make with their Meanders ſome Reach or <lb></lb>Bay, here the Water turneth again, and is ſeen to retreat back <lb></lb>a conſiderable ſpace. </s><s>Upon this I hold, That of thoſe effects <lb></lb>from which you argue the Earths mobility, and alledge it as a <lb></lb>cauſe of them, there may be aſſigned a cauſe ſufficiently valid, <lb></lb>retaining the Earth ſtedfaſt, and reſtoring the mobility of <lb></lb>Heaven.</s></p><p type="margin"><s><margin.target id="marg787"></margin.target><emph type="italics"></emph>It is demonſtra <lb></lb>ted inverting the <lb></lb>argument, that <lb></lb>the perpetual mo <lb></lb>tion of the Air <lb></lb>from Eaſt to Weſt <lb></lb>cometh from the <lb></lb>motion of Heaven?<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg788"></margin.target><emph type="italics"></emph>It is demonſtrated <lb></lb>inverting the ar <lb></lb>gument, that the <lb></lb>perpetual motion of <lb></lb>the Air from Eaſt <lb></lb>to Weſt, cometh <lb></lb>from the motion of <lb></lb>Heaven.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg789"></margin.target><emph type="italics"></emph>The motion of the <lb></lb>Water dependeth <lb></lb>on the motion of <lb></lb>Heaven.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg790"></margin.target><emph type="italics"></emph>The flux and re <lb></lb>flux may depend <lb></lb>on the diurual mo <lb></lb>tion of Heaven.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SALV. </s><s>It cannot be denied, but that your diſcourſe is ingenious, <lb></lb>& hath much of probability, I mean probability in appearance, but <lb></lb>not in reality & exiſtence: It conſiſteth of two parts: In the firſt it <pb xlink:href="040/01/427.jpg" pagenum="405"></pb>aſſignes a reaſon of the continual motion of the Eaſtern Winde, <lb></lb>and alſo of a like motion in the Water. </s><s>In the ſecond, It would <lb></lb>draw from the ſame Sourſe the cauſe of the Ebbing and Flowing. <lb></lb></s><s>The firſt part hath (as I have ſaid) ſome appearance of probabi <lb></lb>lity, but yet extreamly leſs then that which we take from the <lb></lb>Terreſtrial motion. </s><s>The ſecond is not onely wholly improbable, <lb></lb>but altogether impoſſible and falſe. </s><s>And coming to the firſt, <lb></lb><arrow.to.target n="marg791"></arrow.to.target> <lb></lb>whereas it is ſaid that the Concave of the Moon carrieth about <lb></lb>the element of Fire, and the whole Air, even to the tops of the <lb></lb>higher Mountains. </s><s>I anſwer firſt, that it is dubious whether <lb></lb>there be any element of Fire: But ſuppoſe there be, it is much <lb></lb>doubted of the Orbe of the Moon, as alſo of all the reſt; that is, <lb></lb>Whether there be any ſuch ſolid bodies and vaſt, or elſs, Whether <lb></lb>beyond the Air there be extended a continuate expanſion of a <lb></lb>ſubſtance of much more tenuity and purity than our Air, up and <lb></lb>down which the Planets go wandring, as now at laſt a good part <lb></lb>of thoſe very Phyloſophers begin to think: But be it in this or in <lb></lb><arrow.to.target n="marg792"></arrow.to.target> <lb></lb>that manner, there is no reaſon for which the Fire, by a ſimple <lb></lb>contract to a ſuperficies, which you your ſelf grant to be ſmooth <lb></lb>and terſe, ſhould be according to its whole depth carried round in <lb></lb>a motion different from its natural inclination; as hath been de <lb></lb>fuſely proved, and with ſenſible reaſons demonſtrated by^{+} <emph type="italics"></emph>Il Sag-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg793"></arrow.to.target> <lb></lb><emph type="italics"></emph>giatore<emph.end type="italics"></emph.end>: Beſides the other improbability of the ſaid motions <lb></lb>transfuſing it ſelf from the ſubtileſt Fire throughout the Air, much <lb></lb>more denſe; and from that alſo again to the Water. </s><s>But that <lb></lb>a body of rugged and mountainous ſurface, by revolving in it <lb></lb>ſelf, ſhould carry with it the Air contiguous to it, and againſt <lb></lb>which its promontaries beat, is not onely probable but neceſſary, <lb></lb>and experience thereof may be daily ſeen; though without ſee <lb></lb>ing it, I believe that there is no judgement that doubts thereof. <lb></lb></s><s>As to the other part, ſuppoſing that the motion of Heaven did <lb></lb>carry round the Air, and alſo the Water; yet would that motion <lb></lb>for all that have nothing to do with the Ebbing and Flowing. <lb></lb></s><s>For being that from one onely and uniform cauſe, there can fol <lb></lb><arrow.to.target n="marg794"></arrow.to.target> <lb></lb>low but one ſole and uniform effect; that which ſhould be diſco <lb></lb>vered in the Water, would be a continuate and uniform courſe <lb></lb>from Eaſt to Weſt; and in that a Sea onely, which running com <lb></lb>paſs environeth the whole Globe. </s><s>But in determinate Seas, ſuch <lb></lb>as is the Mediterrane ſhut up in the Eaſt, there could be no ſuch <lb></lb>motion. </s><s>For if its Water might be driven by the courſe of <lb></lb>Heaven towards the Weſt, it would have been dry many ages <lb></lb>ſince: Beſides that our Water runneth not onely towards the <lb></lb>Weſt, But returneth backwards towards the Eaſt, and that in or <lb></lb>dinal Periods: And whereas you ſay by the example of Rivers, <lb></lb>that though the courſe of the Sea were Originally that onely <pb xlink:href="040/01/428.jpg" pagenum="406"></pb>from Eaſt to Weſt, yet nevertheleſs the different Poſition of the <lb></lb>Shores may make part of the Water regurgitate, and return <lb></lb>backwards: I grant it you, but it is neceſſary that you take no <lb></lb>tice my <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that where the Water upon that account <lb></lb>returneth backwards, it doth ſo there perpetually; and where <lb></lb>it runneth ſtraight forwards, it runneth there alwayes in the ſame <lb></lb>manner; for ſo the example of the Rivers ſhewes you: But in the <lb></lb>caſe of the ebbing and flowing, you muſt finde and give us ſome <lb></lb>reaſon why it doth in the ſelf ſame place run one while one way, <lb></lb>and another while another; Effects that being contrary & irregular, <lb></lb>can never be deduced from any uniform and conſtant Cauſe: <lb></lb>And this Argument, that overthrows the Hypotheſis of the mo <lb></lb>tion contributed to the Sea from the Heavens diurnal motion, <lb></lb>doth alſo confute that Poſition of thoſe who would admit the ſole <lb></lb>diurnal motion of the Earth, and believe that they are able with <lb></lb>that alone to give a reaſon of the Flux and Reflux: Of which <lb></lb>effect ſince it is irregular, the cauſe muſt of neceſſity be irregular <lb></lb>and alterable.</s></p><p type="margin"><s><margin.target id="marg791"></margin.target><emph type="italics"></emph>A reaſon of the <lb></lb>continual motion of <lb></lb>the Air and Wa <lb></lb>ter may be given, <lb></lb>making the Earth <lb></lb>moveable, then by <lb></lb>making it immove <lb></lb>able.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg792"></margin.target><emph type="italics"></emph>Its improbable that <lb></lb>the element of Fire <lb></lb>ſhould be carried <lb></lb>round by the Con <lb></lb>cave of the Moon.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg793"></margin.target>+ A Treatiſe of our <lb></lb>Author formerly <lb></lb>cited.</s></p><p type="margin"><s><margin.target id="marg794"></margin.target><emph type="italics"></emph>The Ebbing and <lb></lb>Flowing cannot de <lb></lb>pend on the motion <lb></lb>of Heaven.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SIMP. </s><s>I have nothing to reply, neither of my own, by reaſon <lb></lb>of the weakneſs of my underſtanding; nor of that of others, for <lb></lb>that the Opinion is ſo new: But I could believe that if it were <lb></lb>ſpread amongſt the Schools, there would not want Phyloſophers <lb></lb>able to oppoſe it.</s></p><p type="main"><s>SAGR. </s><s>Expect ſuch an occaſion; and we in the mean time <lb></lb>if it ſeem good to <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> will proceed forward.</s></p><p type="main"><s>SALV. </s><s>All that which hath been ſaid hitherto, pertaineth to <lb></lb>the diurnal period of the ebbing and flowing; of which we have in <lb></lb>the firſt place demonſtrated in general the primary and univerſal <lb></lb>Cauſe, without which, no ſuch effect would follow: Afterw ds <lb></lb>paſſing to the particular Accidents, various, and in a certain ſort <lb></lb>irregular, that are obſerved therein: We have handled the ſecon <lb></lb>dary and concommitant Cauſes upon which they depend. </s><s>Now <lb></lb>follow the two other Periods, Monethly, and Annual, which do <lb></lb>not bring with them new and different Accidents, other than <lb></lb>thoſe already conſidered in the diurnal Period; but they ope <lb></lb>rate on the ſame Accidents, by rendring them greater and leſſer <lb></lb>in ſeveral parts of the Lunar Moneth, and in ſeveral times of <lb></lb>the Solar Year; as if that the Moon and Sun did each conceive <lb></lb>it ſelf apart in operating and producing of thoſe Effects; a thing <lb></lb>that totally claſheth with my underſtanding, which ſeeing how <lb></lb>that this of Seas is a local and ſenſible motion, made in an im <lb></lb>menſe maſs of Water, it cannot be brought to ſubſcribe to <lb></lb>Lights, to temperate Heats, to predominacies by occult Quali <lb></lb>ties, and to ſuch like vain Imaginations, that are ſo far from be <lb></lb>ing, or being poſſible to be Cauſes of the Tide; that on the con <pb xlink:href="040/01/429.jpg" pagenum="407"></pb>trary, the Tide is the cauſe of them, that is, of bringing them <lb></lb>into the brains more apt for loquacity and oſtentation, than for <lb></lb>the ſpeculation and diſcovering of the more abſtruſe ſecrets of <lb></lb>Nature; which kind of people, before they can be brought to <lb></lb>prononnce that wiſe, ingenious, and modeſt ſentence, <emph type="italics"></emph>I know it <lb></lb>not,<emph.end type="italics"></emph.end> ſuffer to eſcape from their mouths and pens all manner of ex <lb></lb>travagancies. </s><s>And the onely obſerving, that the ſame Moon, and <lb></lb>the ſame Sun operate not with their light with their motion, with <lb></lb>great heat, or with temperate, on the leſſer reeeptaces of Water, <lb></lb>but that to effect their flowing by heat, they muſt be reduced to <lb></lb>little leſſe than boiling, and in ſhort, we not being able artificially <lb></lb>to imitate any way the motions of the Tide, ſave only by the mo <lb></lb>tion of the Veſſel, ought it not to ſatisfie every one, that all <lb></lb>the other things alledged, as cauſes of thoſe eſſects, are <lb></lb>vaine fancies, and altogether eſtranged from the Truth. </s><s>I <lb></lb><arrow.to.target n="marg795"></arrow.to.target> <lb></lb>ſay, therefore, that if it be true, that of one effect there is but <lb></lb>one ſole primary cauſe, and that between the cauſe and effect, <lb></lb>there is a firm and conſtant connection; it is neceſſary that when <lb></lb>ſoever there is ſeen a firm and conſtant alteration in the effect, <lb></lb>there be a firm and conſtant alteration in the cauſe. </s><s>And be <lb></lb>cauſe the alterations that happen in the ebbing and flowing in <lb></lb>ſeveral parts of the Year and Moneths, have their periods firm and <lb></lb>conſtant, it is neceſſary to ſay, that a regular alteration in thoſe <lb></lb>ſame times happeneth in the primary cauſe of the ebbings and <lb></lb>flowings. </s><s>And as for the alteration that in thoſe times happens <lb></lb><arrow.to.target n="marg796"></arrow.to.target> <lb></lb>in the ebbings and flowings conſiſteth onely in their greatneſs; <lb></lb>that is, in the Waters riſing and falling more or leſſe, and in <lb></lb>running with greater or leſſe <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end>; therefore it is neceſſary, <lb></lb>that that which is the primary cauſe of the ebbing and flowing, <lb></lb>doth in thoſe ſame determinate times increaſe and diminiſh its <lb></lb>force. </s><s>But we have already concluded upon the inequality and <lb></lb>irregularity of the motion of the Veſſels containing the Water to <lb></lb>be the primary cauſe of the ebbings and flowings. </s><s>Therefore <lb></lb>it is neceſſary, that that irregularity, from time to time, corre <lb></lb>ſpondently grow more irregular, that is, grow greater and leſſer. <lb></lb></s><s>Now it is requiſite, that we call to minde, that the irregularity, <lb></lb>that is, the different velocity of the motions of the Veſſels, to <lb></lb>wit, of the parts of the Terreſtrial Superficies, dependeth on <lb></lb>their moving with a compound motion, reſulting from the com <lb></lb>mixtion of the two motions, Annual and Diurnal, proper to the <lb></lb>whole Terreſtrial Globe; of which the Diurnal converſion, by <lb></lb>one while adding to, and another while ſubſtracting from, the <lb></lb>Annual motion, is that which produceth the irregularity in the <lb></lb>compound motion; ſo that, in the additions and ſubſtractions, <lb></lb>that the Diurnal revolution maketh from the Annual motion, <pb xlink:href="040/01/430.jpg" pagenum="408"></pb>conſiſteth the original cauſe of the irregular motion of the Veſ <lb></lb>ſels, and conſequently of the Ebbing and Flowing: inſomuch <lb></lb><arrow.to.target n="marg797"></arrow.to.target> <lb></lb>that if theſe additions and ſubſtractions ſhould alwayes proceed <lb></lb>in the ſame proportion, in reſpect of the Annual motion, the <lb></lb>cauſe of the Ebbing and Flowing would indeed continue, but <lb></lb>yet ſo as that they would perpetually return in the ſelf ſame man <lb></lb>ner: But we are to finde out the cauſe of making the ſame Eb <lb></lb>bings and Flowings in divers times greater and leſſer: There <lb></lb>fore we muſt (if we will retain the identity of the cauſe) find the <lb></lb>alteration in theſe additions and ſubſtractions, that make them <lb></lb>more & leſs potent, in producing thoſe effects which depend there <lb></lb>upon. </s><s>But I ſee not how that potency and impotence can be intro <lb></lb>duced, unleſſe by making the ſame additions and ſubſtractions, <lb></lb>one while greater, and another while leſſer; ſo that the accelera <lb></lb>tion and the retardment of the compound motion, may be made, <lb></lb>ſometimes in greater, and ſometimes in leſſer proportion.</s></p><p type="margin"><s><margin.target id="marg795"></margin.target><emph type="italics"></emph>The alterations <lb></lb>in the effects argue <lb></lb>alteration in the <lb></lb>cauſe.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg796"></margin.target><emph type="italics"></emph>The cauſes at <lb></lb>large aſſigned of <lb></lb>the Periods Mo <lb></lb>nethly and Annu <lb></lb>al of the ebbing <lb></lb>and flowing.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg797"></margin.target><emph type="italics"></emph>The monethly <lb></lb>and annual altera <lb></lb>tions of the tide can <lb></lb>depend upon no <lb></lb>thing, ſave on the <lb></lb>alteration of the <lb></lb>additions & ſub <lb></lb>ſtractions of the <lb></lb>diurnal period from <lb></lb>the annual.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I feel my ſelf very gently led, as it were, by the hand, <lb></lb>and though I finde no rubs in the way, yet nevertheleſſe, like a <lb></lb>blind man, I ſee not whether your Clue leadeth me, nor can I <lb></lb>imagine where ſuch a Journey will end.</s></p><p type="main"><s>SALV. </s><s>Though there be a great difference between my ſlow <lb></lb>pac't Philoſophy, and your more nimble Reaſon, yet neverthe <lb></lb>leſſe, in this particular which we are now upon, I do not much <lb></lb>wonder, if the apprehenſiveneſſe of your wit be a little obſcu <lb></lb>red by the dark and thick miſt that hides the mark, at which we <lb></lb>aime: and that which leſſeneth my admiration is, the remem <lb></lb>brance of the many hours, many dayes, yea more, many nights <lb></lb>that I have conſumed in this contemplation, and of the many <lb></lb>times that, deſpairing to bring it to a period, I have, for an in <lb></lb>couragement of my ſelf, indeavoured to believe, by the exam <lb></lb>ple of the unfortunate <emph type="italics"></emph>Orlando,<emph.end type="italics"></emph.end> that that might not poſſibly be <lb></lb>true, which yet the teſtimony of ſo many credible men ſet be <lb></lb>fore my eyes: wonder not, therefore, if this once, contrary to <lb></lb>your cuſtome, you do not foreſee what I intend: and if you will <lb></lb>needs admire, I believe that the event, as far as I can judge un <lb></lb>expected, will make you ceaſe your wonderment.</s></p><p type="main"><s>SAGR. </s><s>I thank God, that he did not permit that deſperation <lb></lb>of yours to end in the <emph type="italics"></emph>Exit<emph.end type="italics"></emph.end> that is fabled of the miſerable <emph type="italics"></emph>Or <lb></lb>lando,<emph.end type="italics"></emph.end> nor in that which haply is no leſſe fabulouſly related of <lb></lb><emph type="italics"></emph>Ariſtotle,,<emph.end type="italics"></emph.end> that ſo neither my ſelf nor others ſhould be deprived <lb></lb>of the diſcovery of a thing, as abſtruſe as it was deſirable: I <lb></lb>beſeech you, therefore, to ſatisfie my eager appetite as ſoon as <lb></lb>you can.</s></p><p type="main"><s>SALV. </s><s>I am ready to ſerve you: We were upon an inquiry <lb></lb>in what manner the additions and ſubſtractions of the Terreſtri <pb xlink:href="040/01/431.jpg" pagenum="409"></pb>all converſion from the Annual motion, could be made, one <lb></lb>while in a greater, and another while in a leſſer proportion; <lb></lb>which diverſity, and no other thing, could be aſſigned for the <lb></lb>cauſe of the alterations, Monethly and Annual, that are ſeen in <lb></lb>the greatneſſe of the Ebbings and Flowings. </s><s>I will now con <lb></lb>ſider how this proportion of the additions and ſubſtractions of <lb></lb><arrow.to.target n="marg798"></arrow.to.target> <lb></lb>the Diurnal Revolution, and Annual motion may grow greater <lb></lb>and leſſer three ſeveral wayes. </s><s>One is by increaſing and dimi <lb></lb>niſhing the velocity of the Annual motion, retaining the additi <lb></lb>ons and ſubſtractions made by the Diurnal converſion in the <lb></lb>ſame greatneſſe, becauſe the Annual motion being about three <lb></lb>times greater, that is, more velocious than the Diurnal motion <lb></lb>(conſidered likewiſe in the Grand Circle) if we increaſe it <lb></lb>anew, the additions and ſubſtractions of the Diurnal motion <lb></lb>will occaſion leſſe alteration therein: but, on the other ſide, <lb></lb>making it more ſlow, it will be altered in greater proportion, by <lb></lb>that ſame diurnal motion, juſt as the adding or ſubſtracting <lb></lb>four degrees of velocity from one that moveth with twenty de <lb></lb>grees, altereth his courſe leſſe, than thoſe very four degrees would <lb></lb>do, added or ſubſtracted from one that ſhould move onely with <lb></lb>ten degrees. </s><s>The ſecond way would be, by making the additi <lb></lb>ons and ſubſtractions greater and leſſer, retaining the annual mo <lb></lb>tion in the ſame velocity; which is as eaſie to be underſtood, as it <lb></lb>is manifeſt, that a velocity <emph type="italics"></emph>v. </s><s>gr.<emph.end type="italics"></emph.end> of 20. degr. </s><s>is more altered by the <lb></lb>addition or ſubſtraction of 10. deg. </s><s>than by the addition or ſubſtra <lb></lb>ction of 4. The third way would be, in caſe theſe two were joyned <lb></lb>together, diminiſhing the annual motion, & increaſing the diurnal <lb></lb>additions and ſubſtractions. </s><s>Hitherto, as you ſee, it was no <lb></lb>hard matter to attain, but yet it proved to me very hard to find <lb></lb>by what means this might be effected in Nature. </s><s>Yet in the end, <lb></lb><arrow.to.target n="marg799"></arrow.to.target> <lb></lb>I finde that ſhe doth admirably make uſe thereof, and in wayes <lb></lb>almoſt incredible: I mean, admirable and incredible to us, but <lb></lb>not to her, who worketh even thoſe very things, which, to our <lb></lb>capacity, are of infinite wonder, with extraordinary facility and <lb></lb>ſimplicity: and that which it is hard for us to underſtand, is ea <lb></lb>ſie for her to effect. </s><s>Now to proceed, having ſhewn that the <lb></lb>proportion between the additions and ſubſtractions of the Diur <lb></lb>nal converſion and Annual motion may be made greater and leſ <lb></lb>ſer, two wayes, (and I ſay two, becauſe the third is comprized in <lb></lb>the two firſt) I adde, that Nature maketh uſe of them both: <lb></lb>and farthermore, I ſubjoyn, that if ſhe did make uſe but of one <lb></lb>alone, it would be neceſſary to take away one of the two Perio <lb></lb>dical alterations. </s><s>That of the Monethly Period would ceaſe, if <lb></lb><arrow.to.target n="marg800"></arrow.to.target> <lb></lb>the annual motion ſhould not alter. </s><s>And in caſe the additions <lb></lb>and ſubſtractions of the diurnal revolution ſhould continually <pb xlink:href="040/01/432.jpg" pagenum="410"></pb>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"></emph>Three wayes of <lb></lb>altering the pro <lb></lb>portion of the ad <lb></lb>ditions of the diur <lb></lb>nal Revolution to <lb></lb>the annual motion.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg799"></margin.target><emph type="italics"></emph>That which to <lb></lb>us is hard to be un <lb></lb>derſtood, is with <lb></lb>Nature eaſie to be <lb></lb>effected.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg800"></margin.target><emph type="italics"></emph>If the Diurnal <lb></lb>motion ſhould not <lb></lb>alter, the annual <lb></lb>Period would ceaſe<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>It ſeems then, that the Monethly alteration of eb <lb></lb>bings and flowings dependeth on the alteration of the annual <lb></lb>motion of the Earth? </s><s>And the annual alteration of thoſe eb <lb></lb>bings and flowings do, it ſeems, depend on the additions and <lb></lb>ſubſtractions of the diurnal converſion? </s><s>And here now I finde <lb></lb>my ſelf worſe puzzled than before, and more out of hope of <lb></lb>being able to comprehend how this intricacy may be, which is <lb></lb>more inextricable, in my judgment, than the Gordian knot. </s><s>And <lb></lb>I envy <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> from whoſe ſilence I argue that he doth ap <lb></lb>prehend the whole buſineſſe, and is acquit of that confuſion <lb></lb>which greatly puzzleth my brains.</s></p><p type="main"><s>SIMP. </s><s>I believe verily, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> that you are put to a <lb></lb>a ſtand; and I believe that I know alſo the cauſe of your con <lb></lb>fuſion, which, if I miſtake not, riſeth from your underſtanding <lb></lb>part of thoſe particulars but even now alledged by <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> <lb></lb>and but a part. </s><s>It is true likewiſe that I find my ſelf free from the <lb></lb>like confuſion; but not for that cauſe as you think, to wit, be <lb></lb>cauſe I apprehend the whole, nay it happens upon the quite <lb></lb>contrary account; namely, from my not comprehending any <lb></lb>thing; and confuſion is in the plurality of things, and not in <lb></lb>nothing.</s></p><p type="main"><s>SAGR. </s><s>You ſee <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> how a few checks given to <emph type="italics"></emph>Simpli <lb></lb>cius<emph.end type="italics"></emph.end> in the dayes preceding, have rendered him gentle, and <lb></lb>brought him from the <emph type="italics"></emph>capriol<emph.end type="italics"></emph.end> to the <emph type="italics"></emph>amble.<emph.end type="italics"></emph.end> But I beſeech you <lb></lb>without farther delay, put us both out of ſuſpence.</s></p><p type="main"><s>SALV. </s><s>I will endeavour it to the utmoſt of my harſh way of <lb></lb>expreſſing my ſelf, the obtuſeneſſe of which, the acuteneſſe of <lb></lb>your wit ſhall ſupply. </s><s>The accidents of which we are to enquire <lb></lb>the cauſes are two: The firſt reſpecteth the varieties that happen <lb></lb>in the ebbings and flowings in the Monethly Period; and the o <lb></lb>thr relateth to the Annual. </s><s>We will firſt ſpeak of the Moneth <lb></lb>ly, and then treat of the Annual; and it is convenient that we <lb></lb>reſolve them all according to the Fundamentals and Hypotheſis <lb></lb>already laid down, without introducing any novelty either in A <lb></lb>ſtronomy, or in the Univerſe, in favour of the ebbings and flow <lb></lb>ings; therefore let us demonſtrate that of all the ſeveral acci <lb></lb>dents in them obſerved, the cauſes reſide in the things already <lb></lb><arrow.to.target n="marg801"></arrow.to.target> <lb></lb>known, and received for true and undoubted. </s><s>I ſay therefore, <lb></lb>that it is a truly natural, yea neceſſary thing, that one and the ſame <lb></lb>moveable made to move round by the ſame moving virtue in a <lb></lb>longer time, do make its courſe by a greater circle, rather than <lb></lb>by a leſſer; and this is a truth received by all, and con <lb></lb>firmed by all experiments, of which we will produce a few. <lb></lb><arrow.to.target n="marg802"></arrow.to.target> <lb></lb>In the wheel-clocks, and particularly in the great ones, to mo <pb xlink:href="040/01/433.jpg" pagenum="411"></pb>derate the time, the Artificers that make them accomodate a cer <lb></lb>tain voluble ſtaffe horozontally, and at each end of it they fa <lb></lb>ſten two Weights of Lead, and when the time goeth too ſlow, <lb></lb>by the onely removing thoſe Leads a little nearer to the centre <lb></lb>of the ſtaffe, they render its vibrations more frequent; and on <lb></lb>the contrary to retard it, it is but drawing thoſe Weights more <lb></lb>towards the ends; for ſo the vibrations are made more ſeldome, <lb></lb>and conſequently the intervals of the hours are prolonged.</s></p><p type="margin"><s><margin.target id="marg801"></margin.target><emph type="italics"></emph>The true Hypo <lb></lb>theſis may diſpatch <lb></lb>its revolutions in a <lb></lb>ſhorter time, in <lb></lb>leſſer circles than <lb></lb>in greater; the <lb></lb>which is proved by <lb></lb>two examples.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg802"></margin.target><emph type="italics"></emph>The firſt ex <lb></lb>ample.<emph.end type="italics"></emph.end></s></p><p type="main"><s>Here the movent vertue is the ſame, namely the counterpoiſe, <lb></lb><arrow.to.target n="marg803"></arrow.to.target> <lb></lb>the moveables are thoſe ſame Weights of lead, and their vi <lb></lb>brations are more frequent when they are neerer to the centre, <lb></lb>that is, when they move by leſſer circles. </s><s>Hanging equal <lb></lb>Weights at unequal cords, and being removed from their per <lb></lb>pendicularity, letting them go; we ſhall ſee thoſe that are pen <lb></lb>dent at the ſhorter cords, to make their vibrations under ſhorter <lb></lb>times, as thoſe that move by leſſer circles. </s><s>Again, let ſuch a <lb></lb>kind of Weight be faſtened to a cord, which cord let play upon <lb></lb>a ſtaple faſtened in the Seeling, and do you hold the other end <lb></lb>of the cord in your hand, and having given the motion to the <lb></lb>pendent Weight, whilſt it is making its vibrations, pull the <lb></lb>end of the cord that you hold in your hand, ſo that the Weight <lb></lb>may riſe higher and higher: In its riſing you ſhall ſee the fre <lb></lb>quency of its vibrations encreaſe, in regard that they are made <lb></lb>ſucceſſively by leſſer and leſſer circies. </s><s>And here I deſire you to <lb></lb><arrow.to.target n="marg804"></arrow.to.target> <lb></lb>take notice of two particulars worthy to be obſerved. </s><s>One is <lb></lb>that the vibrations of one of thoſe plummets are made with ſuch <lb></lb>a neceſſity under ſuch determinate times, that it is altogether <lb></lb>impoſſible to cauſe them to be made under other times, unleſſe <lb></lb>it be by prolonging, or abreviating the cord; of which you <lb></lb>may alſo at this very inſtant aſcertain your ſelves by experience, <lb></lb>tying a ſtone to a pack-threed, and holding the other end in <lb></lb>your hand, trying whether you can ever by any artifice be able <lb></lb>to ſwing it this way and that way in other than one determinate <lb></lb>time, unleſſe by lengthening or ſhortening the ſtring, which <lb></lb>you will find to be abſolutely impoſſible. </s><s>The other particular <lb></lb>truly admirable is, that the ſelf ſame <emph type="italics"></emph>pendulum<emph.end type="italics"></emph.end> makes its vibra <lb></lb>tions with one and the ſame frequency, or very little, and as it <lb></lb>were inſenſibly different, whether they be made by very great, <lb></lb>or very ſmall arches of the ſelf-ſame circumference. </s><s>I mean that <lb></lb>whether we remove the <emph type="italics"></emph>pendulum<emph.end type="italics"></emph.end> from perpendicularity one, two, <lb></lb>or three degrees onely, or whether we remove it 70. 80. nay to <lb></lb>an entire quadrant, it being let go, will in the one caſe and in <lb></lb>the other make its vibrations with the ſame frequency, as well <lb></lb>the former where it is to move by an arch of but four or ſix de <lb></lb>grees, as the ſecond, where it is to paſſe arches of 160. or more <pb xlink:href="040/01/434.jpg" pagenum="412"></pb>degrees. </s><s>Which may the better be ſeen, by hanging two weights <lb></lb>at two ſtrings of equal length, and then removing them from per <lb></lb>pendicularity, one a little way, and the other very far; the which <lb></lb>being ſet at liberty, will go & return under the ſame times, the one <lb></lb>by arches very ſmall, & the other by very great ones, from whence <lb></lb>followeth the concluſion of an admirable Problem; which is, <lb></lb><arrow.to.target n="marg805"></arrow.to.target> <lb></lb>That a Quadrant of a Circle being given (take a little diagram of <lb></lb>the ſame, [in <emph type="italics"></emph>Fig.<emph.end type="italics"></emph.end> 3.]) as for inſtance: A B erect to the Hori <lb></lb>zon, ſo as that it reſt upon the plain touching in the point B. and <lb></lb>an Arch being made with a Hoop well plained and ſmoothed in <lb></lb>the concave part, bending it according to the curvity of the Cir <lb></lb>cumference A D B. </s><s>So that a Bullet very round and ſmooth <lb></lb>may freely run to and again within it (the rim of a Sieve is very <lb></lb>proper for the experiment) I ſay, that the Bullet being put in any <lb></lb>what ever place, neer or far from the loweſt term B. </s><s>As for in <lb></lb>ſtance, putting it in the point C, or here in D, or in E; and then <lb></lb>let go, it will in equal times, or inſenſibly different arrive at the <lb></lb>term B, departing from C, or from D, or from E, or from what <lb></lb>ever other place; an accident truly wonderfull. </s><s>We may add <lb></lb>another accident no leſs ſtrange than this, which is, That more <lb></lb>over by all the cords drawn from the point B to the points C, <lb></lb>D, E; and to any other whatſoever, taken not onely in the Qua <lb></lb>drant B A, but in all the whole circumference of the Circle the <lb></lb>ſaid moveable ſhall deſcend in times abſolutely equal; inſomuch <lb></lb>that it ſhall be no longer in deſcending by the whole Diameter <lb></lb>erect perpendicularly upon the point B, then it ſhall in deſcend <lb></lb>ing by B. C. although it do ſublend but one ſole degree, or a leſ <lb></lb>ſer Arch. </s><s>Let us add the other wonder, which is, That the mo <lb></lb>tions of the falling bodies made by the Arches of the Quadrant <lb></lb>A B; are made in ſhorter times than thoſe that are made by the <lb></lb>cords of thoſe ſame Arches; ſo that the ſwifteſt motion, and <lb></lb>made by a moveable in the ſhorteſt time, to arrive from the <lb></lb>point A, to the term B, ſhall be that which is made, not by the <lb></lb>right line A, B, (although it be the ſhorteſt of all thoſe that can <lb></lb>de drawn between the points A. B.) but by the circumference <lb></lb>A D B. </s><s>And any point being taken in the ſaid Arch; as for <lb></lb>example: The point D. and two cords drawn A D, and D. B. <lb></lb>the moveable departing from the qoint A, ſhall in a leſs time <lb></lb>come to B, moving by the two cords A D and D B. than by the <lb></lb>ſole cord A, B. </s><s>But the ſhorteſt of all the times ſhall be that of <lb></lb>the fall by the Arch A D B. </s><s>And the ſelf ſame accidents are <lb></lb>to be underſtood of all the other leſſer Arches taken from the <lb></lb>lowermoſt term B. upwards.</s></p><p type="margin"><s><margin.target id="marg803"></margin.target><emph type="italics"></emph>The ſecond ex <lb></lb>ample.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg804"></margin.target><emph type="italics"></emph>Two particular <lb></lb>notable accidents <lb></lb>in the<emph.end type="italics"></emph.end> penduli <emph type="italics"></emph>and <lb></lb>their vibrations.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg805"></margin.target><emph type="italics"></emph>Admirable Pro <lb></lb>blems of movea <lb></lb>bles deſcending by <lb></lb>the Quadrant of a <lb></lb>Circle, and of thoſe <lb></lb>deſcending by all <lb></lb>the cords of the <lb></lb>whole Circle.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>No more, no more; for you ſo confund and fill me <lb></lb>with Wonders, and diſtract my thoughts ſo many ſeveral wayes, <pb xlink:href="040/01/435.jpg" pagenum="413"></pb>that I fear I ſhall have but a ſmall part of it left free and diſin <lb></lb>gaged, to apply to the principal matter that is treated of, and <lb></lb>which of it ſelf is but even too obſcure and intricate: So that <lb></lb>I intreat you to vouchſafe me, having once diſpatcht the buſineſs <lb></lb>of the ebbings and flowings, to do this honour to my houſe (and <lb></lb>yours) ſome other dayes, and to diſcourſe upon the ſo many other <lb></lb>Problems that we have left in ſuſpence; and which perhaps are <lb></lb>no leſs curious and admirable, than this that hath been diſcuſſed <lb></lb>theſe dayes paſt, and that now ought to draw to a con <lb></lb>cluſion.</s></p><p type="main"><s>SALV. </s><s>I ſhall be ready to ſerve you, but we muſt make more <lb></lb>than one or two Seſſions; if beſides the other queſtions reſerved <lb></lb>to be handled apart, we would diſcuſſe thoſe many that pertain <lb></lb>to the local motion, as well of natural moveables, as of the reject <lb></lb>ed: an Argument largely treated of by our <emph type="italics"></emph>Lyncean Accade <lb></lb>mick.<emph.end type="italics"></emph.end> But turning to our firſt purpoſe, where we were about to <lb></lb>declare, That the bodies moving circularly by a movent virtue, <lb></lb>which continually remaineth the ſame, the times of the circula <lb></lb>tions were prefixt and determined, and impoſſible to be made <lb></lb>longer or ſhorter, having given examples, and produced experi <lb></lb>ments thereof, ſenſible, and feaſible, we may confirm the ſame <lb></lb>truth by the experiences of the Celeſtial motions of the Planets; <lb></lb>in which we ſee the ſame rule obſerved; for thoſe that move by <lb></lb>greater Circles, confirm longer times in paſſing them. </s><s>A moſt <lb></lb>pertinent obſervation of this we have from the <emph type="italics"></emph>Medicæan<emph.end type="italics"></emph.end> Pla <lb></lb>nets, which in ſhort times make their revolutions about <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end>: <lb></lb>Inſomuch that it is not to be queſtioned, nay we may hold it for <lb></lb>ſure and certain, that if for example, the Moon continuing to be <lb></lb>moved by the ſame movent faculty, ſhould retire by little and <lb></lb>little in leſſer Circles, it would acquire a power of abreviating <lb></lb>the times of its Periods, according to that <emph type="italics"></emph>Pendulum,<emph.end type="italics"></emph.end> of which in <lb></lb>the courſe of its vibrations, we by degrees ſhortned the cord, that <lb></lb>is contracted the Semidiameter of the circumferences by it paſſed. <lb></lb></s><s>Know now that this that I have alledged an example of it in the <lb></lb>Moon, is ſeen and verified eſſentially in fact. </s><s>Let us call to mind, <lb></lb>that it hath been already concluded by us, together with <emph type="italics"></emph>Coperni-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg806"></arrow.to.target> <lb></lb><emph type="italics"></emph>cus,<emph.end type="italics"></emph.end> That it is not poſſible to ſeparate the Moon from the Earth, <lb></lb>about which it without diſpute revolveth in a Moneth: Let us <lb></lb>remember alſo that the Terreſtrial Globe, accompanyed alwayes <lb></lb>by the Moon, goeth along the circumference of the Grand Orb <lb></lb>about the Sun in a year, in which time the Moon revolveth about <lb></lb>the Earth almoſt thirteen times; from which revolution it follow <lb></lb>eth, that the ſaid Moon ſometimes is found near the Sun; that is, <lb></lb>when it is between the Sun and the Earth, and ſometimes <lb></lb>much more remote, that is, when the Earth is ſituate between <pb xlink:href="040/01/436.jpg" pagenum="414"></pb>the Moon and Sun; neer, in a word, at the time of its conjun <lb></lb>ction and change; remote, in its Full and Oppoſition; and the <lb></lb>greateſt vicinity differ the quantity of the Diameter of the Lu <lb></lb>nar Orb. </s><s>Now if it be true that the virtue which moveth the <lb></lb>Earth and Moon, about the Sun, be alwayes maintained in <lb></lb>the ſame vigour; and if it be true that the ſame moveable <lb></lb>moved by the ſame virtue, but in circles unequal, do in ſhorter <lb></lb>times paſſe like arches of leſſer circles, it muſt needs be granted, <lb></lb>that the Moon when it is at a leſſe diſtance from the Sun, that is <lb></lb>in the time of conjunction, paſſeth greater arches of the Grand <lb></lb>Orb, than when it is at a greater diſtance, that is in its Opppſition <lb></lb>and Full. </s><s>And this Lunar inequality muſt of neceſſity be imparted <lb></lb>to the Earth alſo; for if we ſhall ſuppoſe a right line produced from <lb></lb>the centre of the Sun by the centre of the Terreſtrial Globe, and <lb></lb>prolonged as far as the Orb of the Moon, this ſhall be the ſemi <lb></lb>diameter of the Grand Orb, in which the Earth, in caſe it were <lb></lb>alone, would move uniformly, but if in the ſame ſemidiameter we <lb></lb>ſhould place another body to be carried about, placing it one <lb></lb>while between the Earth and Sun, and another while beyond <lb></lb>the Earth, at a greater diſtance from the Sun, it is neceſſary, <lb></lb>that in this ſecond caſe the motion common to both, according <lb></lb>to the circumference of the great Orb by means of the diſtance <lb></lb>of the Moon, do prove a little ſlower than in the other caſe, <lb></lb>when the Moon is between the Earth and Sun, that is at a leſſer <lb></lb>diſtance. </s><s>So that in this buſineſſe the very ſame happeneth that <lb></lb>befals in the time of the clock; that lead which is placed one <lb></lb>while farther ſrom the centre, to make the vibrations of the <lb></lb>ſtaffe or ballance leſſe frequent, and another while nearer, to <lb></lb>make them thicker, repreſenting the Moon. </s><s>Hence it may be <lb></lb>manifeſt, that the annual motion of the Earth in the Grand <lb></lb>Orb, and under the Ecliptick, is not uniform, and that its ir <lb></lb>regularity proceedeth from the Moon, and hath its Monethly <lb></lb>Periods and Returns. </s><s>And becauſe it hath been concluded, that <lb></lb>the Monethly and Annual Periodick alterations of the ebbings <lb></lb>and flowings, cannot be deduced from any other cauſe than <lb></lb>from the altered proportion between the annual motion and the <lb></lb>additions and ſubſtractions of the diurnal converſion; and that <lb></lb>thoſe alterations might be made two wayes, that is by altering <lb></lb>the annual motion, keeping the quantity of the additions un <lb></lb>altered, or by changing of the bigneſſe of theſe, reteining the <lb></lb>uniformity of annual motion. </s><s>We have already found the firſt <lb></lb>of theſe, depending on the irregularity of the annual motion <lb></lb>occaſioned by the Moon, and which hath its Monethly Periods. <lb></lb></s><s>It is therefore neceſſary, that upon that account the ebbings <lb></lb>and flowings have a Monethly Period in which they do grow <pb xlink:href="040/01/437.jpg" pagenum="415"></pb>greater and leſſer. </s><s>Now you ſee that the cauſe of the Monethly <lb></lb>Period reſideth in the annual motion; and withal you ſee how <lb></lb>much the Moon is concerned in this buſineſs, and how it is there <lb></lb>with interrupted apart, without having any thing to do with either, <lb></lb>with Seas or Waters.</s></p><p type="margin"><s><margin.target id="marg806"></margin.target><emph type="italics"></emph>The Earths an <lb></lb>nual motion by the <lb></lb>Ecliptick, unequal <lb></lb>by means of the <lb></lb>Moons motion.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>If one that never had ſeen any kinde of Stairs or La <lb></lb>der, were ſhewed a very high Tower, and asked if ever he hoped <lb></lb>to climb to the top of it, I verily believe that he would anſwer he <lb></lb>did not, not conceiving how one ſhould come thither any way <lb></lb>except by flying; but ſhewing him a ſtone of but a foot high, and <lb></lb>asking him whether he thought he could get to the top of that, <lb></lb>I am certain that he would anſwer he could; and farther, that he <lb></lb>would not deny, but that it was not onely one, but ten, twenty, <lb></lb>and an hundred times eaſier to climb that: But now if he ſhould <lb></lb>be ſhewed the Stairs, by means whereof, with the facility by him <lb></lb>granted, it is poſſible to get thither, whither he a little before had <lb></lb>affirmed it was impoſſible to aſcend, I do think that laughing at <lb></lb>himſelf he would confeſs his dulneſs of apprehenſion. </s><s>Thus, <lb></lb><emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> have you ſtep by ſtep ſo gently lead me, that, not <lb></lb>without wonder, I finde that I am got with ſmall pains to that <lb></lb>height which I deſpaired of arriving at. 'Tis true; that the Stair <lb></lb>caſe having been dark, I did not perceive that I was got nearer <lb></lb>to, or arrived at the top, till that coming into the open Air I diſ <lb></lb>covered a great Sea, and ſpacious Country: And as in aſcending <lb></lb>one ſtep, there is no labour; ſo each of your propoſitions by it <lb></lb>ſelf ſeemed to me ſo plain, that thinking I heard but little or no <lb></lb>thing that was new unto me, I conceived that my benefit thereby <lb></lb>had been little or none at all: Whereupon I was the more ama <lb></lb>zed at the unexpected <emph type="italics"></emph>exit<emph.end type="italics"></emph.end> of this diſcourſe, that hath guided me <lb></lb>to the knowledge of a thing which I held impoſſible to be de <lb></lb>monſtrated. </s><s>One doubt onely remains, from which I deſire to <lb></lb>be freed, and this it is; Whether that if the motion of the Earth <lb></lb>together with that of the Moon under the Zodiack are irregular <lb></lb>motions, thoſe irregularities ought to have been obſerved and ta <lb></lb>ken notice of by <emph type="italics"></emph>Aſtronomers,<emph.end type="italics"></emph.end> which I do not know that they <lb></lb>are: Therefore I pray you, who are better acquainted with theſe <lb></lb>things than I, to free me from this doubt, and tell me how the <lb></lb>caſe ſtands.</s></p><p type="main"><s>SALV. </s><s>You ask a rational queſtion, and anſwering to the Ob <lb></lb><arrow.to.target n="marg807"></arrow.to.target> <lb></lb>jection, I ſay; That although <emph type="italics"></emph>Aſtronomy<emph.end type="italics"></emph.end> in the courſes of many <lb></lb>ages hath made a great progreſs in diſcovering the conſtitution <lb></lb>and motions of the Celeſtial bodies, yet is it not hitherto arrived <lb></lb>at that height, but that very many things remain undecided, and <lb></lb>haply many others alſo undiſcovered. </s><s>It is to be ſuppoſed that the <lb></lb>firſt obſervers of Heaven knew no more but one motion common <pb xlink:href="040/01/438.jpg" pagenum="416"></pb>to all the Stars, as is this diurnal one: yet I believe that in few <lb></lb>dayes they perceived that the Moon was inconſtant in keeping <lb></lb>company with the other Stars; but yet withal, that many years <lb></lb>paſt, before that they diſtinguiſhed all the Planets: And in par <lb></lb>ticular, I conceit that <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> by its ſlowneſs, and <emph type="italics"></emph>Mercury<emph.end type="italics"></emph.end> by rea <lb></lb><arrow.to.target n="marg808"></arrow.to.target> <lb></lb>ſon of its ſeldom appearing, were the laſt that were obſerved to <lb></lb>be wandring and errant. </s><s>It is to be thought that many more <lb></lb>years run out before the ſtations and retrogradations of the three <lb></lb>ſuperiour Planets were known, as alſo their approximations and <lb></lb>receſſions from the Earth, neceſſary occaſions of introducing the <lb></lb>Eccentrix and Epicicles, things unknown even to <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> for <lb></lb>that he makes no mention thereof. <emph type="italics"></emph>Mercury,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> with <lb></lb>their admirable apparitions; how long did they keep Aſtrono <lb></lb>mers in ſuſpence, before that they could reſolve (not to ſpeak of <lb></lb>any other of their qualities) upon their ſituation? </s><s>Inſomuch <lb></lb>that the very order onely of the Mundane bodies, and the inte <lb></lb>gral ſtructure of the parts of the Univerſe by us known, hath been <lb></lb>doubted of untill the time of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> who hath at laſt given <lb></lb>us notice of the true conſtitution, and real ſyſteme, according to <lb></lb>which thoſe parts are diſpoſed; ſo that at length we are certain <lb></lb>that <emph type="italics"></emph>Mercury, Venus,<emph.end type="italics"></emph.end> and the other Planets do revolve about <lb></lb>the Sun; and that the Moon revolveth about the Earth. </s><s>But <lb></lb><arrow.to.target n="marg809"></arrow.to.target> <lb></lb>how each Planet governeth it ſelf in its particular revolution, and <lb></lb>how preciſely the ſtructure of its Orb is framed; which is that <lb></lb>which is vulgarly called the <emph type="italics"></emph>Theory<emph.end type="italics"></emph.end> of the <emph type="italics"></emph>Planets,<emph.end type="italics"></emph.end> we cannot as <lb></lb>yet undoubtedly reſolve. <emph type="italics"></emph>Mars,<emph.end type="italics"></emph.end> that hath ſo much puzled our <lb></lb>Modern Aſtronomers, is a proof of this: And to the Moon her <lb></lb>ſelf there have been aſſigned ſeveral Theories, after that the ſaid <lb></lb><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> had much altered it from that of <emph type="italics"></emph>Ptolomy.<emph.end type="italics"></emph.end> And to <lb></lb>deſcend to our particular caſe, that is to ſay, to the apparent mo <lb></lb>tion of the Sun and Moon; touching the former, there hath been <lb></lb>obſerved a certain great irregularity, whereby it paſſeth the two <lb></lb><arrow.to.target n="marg810"></arrow.to.target> <lb></lb>ſemicircles of the Ecliptick, divided by the points of the Equi <lb></lb>noxes in very different times; in paſſing one of which, it ſpend <lb></lb>eth about nine dayes more than in paſſing the other; a difference, <lb></lb>as you ſee, very great and notable. </s><s>But if in paſſing ſmall arches, <lb></lb>ſuch for example as are the twelve Signs, he maintain a moſt re <lb></lb>gular motion, or elſe proceed with paces, one while a little more <lb></lb>ſwift, and another more ſlow, as it is neceſſary that it do, in caſe <lb></lb>the annual motion belong to the Sun onely in appearance, but <lb></lb>in reality to the Earth in company with the Moon, it is what hath <lb></lb>not hitherto been obſerved, nor it may be, ſought. </s><s>Touching <lb></lb><arrow.to.target n="marg811"></arrow.to.target> <lb></lb>the Moon in the next place, whoſe reſtitutions have been prin <lb></lb>cipally lookt into an account of the Eclipſes, for which it is ſuf <lb></lb>ficient to have an exact knowledge of its motion about the Earth, <pb xlink:href="040/01/439.jpg" pagenum="417"></pb>it hath not been likewiſe with a perfect curioſity inquired, what <lb></lb>its courſe is thorow the particular arches of the Zodiack. </s><s>That <lb></lb>therefore the Earth and Moon in running through the Zodiack, <lb></lb>that is round the Grand Orb, do ſomewhat accellerate at the <lb></lb>Moons change, and retard at its full, ought not to be doubted; <lb></lb>for that the ſaid difference is not manifeſt, which cometh to be <lb></lb>unobſerved upon two accounts; Firſt, Becauſe it hath not been <lb></lb>lookt for. </s><s>Secondly, Becauſe that its poſſible it may not be very <lb></lb>great. </s><s>Nor is there any need that it ſhould be great, for the pro <lb></lb>ducing the effect that we ſee in the alteration of the greatneſs of <lb></lb>ebbings and flowings. </s><s>For not onely thoſe alterations, but the <lb></lb><arrow.to.target n="marg812"></arrow.to.target> <lb></lb>Tides themſelves are but ſmall matters in reſpect of the grandure <lb></lb>of the ſubjects on which they work; albeit that to us, and to our <lb></lb>littleneſs they ſeem great. </s><s>For the addition or ſubduction of <lb></lb>one degree of velocity where there are naturally 700, or 1000, <lb></lb>can be called no great alteration, either in that which conferreth <lb></lb>it, or in that Which receiveth it: the Water of our Mediterrane <lb></lb>carried about by the diurnal revolution, maketh about 700 miles <lb></lb>an hour, (which is the motion common to the Earth and to it, and <lb></lb>therefore not perceptible to us) & that which we ſenſibly diſcern <lb></lb>to be made in the ſtreams or currents, is not at the rate of full one <lb></lb>mile an hour, (I ſpeak of the main Seas, and not of the Straights) <lb></lb>and this is that which altereth the firſt, naturall, and grand mo <lb></lb>tion; and this motion is very great in reſpect of us, and of Ships: <lb></lb>for a Veſſel that in a ſtanding Water by the help of Oares can <lb></lb>make <emph type="italics"></emph>v. </s><s>g.<emph.end type="italics"></emph.end> three miles an hour, in that ſame current will row <lb></lb>twice as far with the ſtream as againſt it: A notable difference <lb></lb>in the motion of the Boat, though but very ſmall in the motion <lb></lb>of the Sea, which is altered but its ſeven hundredth part. </s><s>The <lb></lb>like I ſay of its riſing, and falling one, two, or three feet; and <lb></lb>ſcarcely four or five in the utmoſt bounds of a ſtreight, two thou <lb></lb>ſand, or more miles long, and where there are depths of hundreds <lb></lb>of feet; this alteration is much leſs than if in one of the Boats <lb></lb>that bring us freſh Water, the ſaid Water upon the arreſt of the <lb></lb>Boat ſhould riſe at the Prow the thickneſs of a leaf. </s><s>I conclude <lb></lb>therefore that very ſmall alterations in reſpect of the immenſe <lb></lb>greatneſs, and extraordinary velocity of the Seas, is ſufficient to <lb></lb>make therein great mutations in relation to our ſmallneſs, and to <lb></lb>our accidents.</s></p><p type="margin"><s><margin.target id="marg807"></margin.target><emph type="italics"></emph>Many things <lb></lb>may remain as yet <lb></lb>unobſerved in A <lb></lb>ſtronomy.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg808"></margin.target>Saturn <emph type="italics"></emph>for its <lb></lb>ſlowneſs, and<emph.end type="italics"></emph.end> Mer <lb></lb>cury <emph type="italics"></emph>for its rare <lb></lb>neſs of appearing <lb></lb>were amongſt thoſe <lb></lb>that were laſt ob <lb></lb>ſerved.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg809"></margin.target><emph type="italics"></emph>Particular ſtru <lb></lb>ctures of the Orbs <lb></lb>of the Planets not <lb></lb>yet well reſolved.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg810"></margin.target><emph type="italics"></emph>The Sun paſſ <lb></lb>eth one half of the <lb></lb>Zodiack nine days <lb></lb>ſooner than the <lb></lb>other.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg811"></margin.target><emph type="italics"></emph>The Moons mo <lb></lb>tion principally <lb></lb>ſought in the ac <lb></lb>count of Eclipſes.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg812"></margin.target><emph type="italics"></emph>Ebbings and <lb></lb>flowings are petty <lb></lb>things in compari <lb></lb>ſon of the vaſtneſs <lb></lb>of Seas, and of the <lb></lb>velocity of the mo <lb></lb>tion of the Terre <lb></lb>ſtrial Globe.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I am fully ſatisfied as to this particular; it remains to <lb></lb>declare unto us how thoſe additions and ſubſtractions derived <lb></lb>from the diurnal <emph type="italics"></emph>Vertigo<emph.end type="italics"></emph.end> are made one while greater, and ano <lb></lb>ther while leſſer; from which alterations you hinted that the an <lb></lb>nual period of the augmentations and diminutions of the eb <lb></lb>bings and flowings did depend.</s></p> <pb xlink:href="040/01/440.jpg" pagenum="418"></pb><p type="main"><s>SALV. </s><s>I will uſe my utmoſt endeavours to render my ſelf <lb></lb><arrow.to.target n="marg813"></arrow.to.target> <lb></lb>intelligible, but the difficulty of the accident it ſelf, and the <lb></lb>great attention of mind requiſite for the comprehending of it, <lb></lb>conſtrains me to be obſcure. </s><s>The unequalities of the additions <lb></lb>and ſubſtractions, that the diurnal motion maketh to or from <lb></lb>the annual dependeth upon the inclination of the Axis of the di <lb></lb>urnal motion upon the plane of the Grand Orb, or, if you pleaſe, <lb></lb>of the Ecliptick; by means of which inclination the Equinoctial <lb></lb>interſecteth the ſaid Ecliptick, remaining inclined and oblique <lb></lb>upon the ſame according to the ſaid inclination of Axis. </s><s>And the <lb></lb>quantity of the additions importeth as much as the whole diame <lb></lb>ter of the ſaid Equinoctial, the Earths centre being at the ſame <lb></lb>time in the Solſtitial points; but being out of them it importeth <lb></lb>leſſe and leſſe, according as the ſaid centre ſucceſſively approa <lb></lb>cheth to the points of the Equinoxes, where thoſe additions are <lb></lb>leſſer than in any other places. </s><s>This is the whole buſineſſe, but <lb></lb>wrapt up in the obſcurity that you ſee.</s></p><p type="margin"><s><margin.target id="marg813"></margin.target><emph type="italics"></emph>The cauſes of <lb></lb>the inequality of <lb></lb>the additions and <lb></lb>ſubſtractions of the <lb></lb>diurnal converſion <lb></lb>from the annual <lb></lb>motion.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>Rather in that which I do no not ſee; for hitherto I <lb></lb>comprehend nothing at all.</s></p><p type="main"><s>SALV. </s><s>I have already foretold it. </s><s>Nevertheleſſe we will try <lb></lb>whether by drawing a Diagram thereof, we can give ſome <lb></lb>ſmall light to the ſame; though indeed it might better be ſet <lb></lb>forth by ſolid bodies than by bare Schemes; yet we will help our <lb></lb>ſelves with Perſpective and fore-ſhortning. </s><s>Let us draw there <lb></lb>fore, as before, the circumference of the Grand Orb, [<emph type="italics"></emph>as in <lb></lb>Fig.<emph.end type="italics"></emph.end> 4.] in which the point A is underſtood to be one of the <lb></lb>Solſtitials, and the diameter A P the common Section of the <lb></lb>Solſtitial Colure, and of the plane of the Grand Orb or Eclip <lb></lb>tick; and in that ſame point A let us ſuppoſe the centre of the <lb></lb>Terreſtrial Globe to be placed, the Axis of which C A B, in <lb></lb>clined upon the Plane of the Grand Orb, falleth on the plane of <lb></lb>the ſaid Colure that paſſeth thorow both the Axis of the Equino <lb></lb>ctial, and of the Ecliptick. </s><s>And for to prevent confuſion, let <lb></lb>us only draw the Equinoctial circle, marking it with theſe chara <lb></lb>cters D G E F, the common ſection of which, with the plane of <lb></lb>the grand Orb, let be the line D E, ſo that half of the ſaid E <lb></lb>quinoctial D F E will remain inclined below the plane of the <lb></lb>Grand Orb, and the other half D G E elevated above. </s><s>Let <lb></lb>now the Revolution of the ſaid Equinoctial be made, according <lb></lb>to the order of the points D G E F, and the motion of the cen <lb></lb>tre from A towards E. </s><s>And becauſe the centre of the Earth <lb></lb>being in A, the Axis C B (which is erect upon the diameter of <lb></lb>the Equinoctial D E) falleth, as hath been ſaid, in the Solſti <lb></lb>tial Colure, the common Section of which and of the <lb></lb>Grand Orb, is the diameter P A, the ſaid line P A ſhall <pb xlink:href="040/01/441.jpg" pagenum="419"></pb>be perpendicular to the ſame D E, by reaſon that the Colure is <lb></lb>erect upon the grand Orb; and therefore the ſaid D E, <lb></lb>ſhall be the Tangent of the grand Orb in the point A. <lb></lb></s><s>So that in this Poſition the motion of the Centre by the arch <lb></lb>A E; that is, of one degree every day differeth very little; yea, <lb></lb>is as if it were made by the Tangent D A E. </s><s>And becauſe by <lb></lb>means of the diurnal motion the point D, carried about by G, <lb></lb>unto E, encreaſeth the motion of the Centre moved almoſt in the <lb></lb>ſame line D E, as much as the whole diameter D E amounts <lb></lb>unto; and on the other ſide diminiſheth as much, moving about <lb></lb>the other ſemicircle E F D. </s><s>The additions and ſubductions <lb></lb>in this place therefore, that is in the time of the ſolſtice, ſhall be <lb></lb>meaſured by the whole diameter D E.</s></p><p type="main"><s>Let us in the next place enquire, Whether they be of the ſame <lb></lb>bigneſs in the times of the <emph type="italics"></emph>E<emph.end type="italics"></emph.end>quinoxes; and tranſporting the <lb></lb>Centre of the Earth to the point I, diſtant a Quadrant of a <lb></lb>Circle from the point A. </s><s>Let us ſuppoſe the ſaid Equinoctial <lb></lb>to be G E F D, its common ſection with the grand Orb D E, the <lb></lb>Axis with the ſame inclination C B; but the Tangent of the grand <lb></lb>Orb in the point I ſhall be no longer D E, but another which <lb></lb>ſhall cut that at right Angles; and let it be this marked H I L, <lb></lb>according to which the motion of the Centre I, ſhall make its pro <lb></lb>greſs, proceeding along the circumference of this grand Orb. <lb></lb></s><s>Now in this ſtate the Additions and Subſtractions are no longer <lb></lb>meaſured by the diameter D E, as before was done; becauſe that <lb></lb>diameter not diſtending it ſelf according to the line of the annual <lb></lb>motion H L, rather cutting it at right angles, thoſe terms D E, do <lb></lb>neither add nor ſubſtract any thing; but the Additions and <lb></lb>Subſtractons are to be taken from that diameter that falleth <lb></lb>in the plane that is errect upon the plane of the grand Orb, and <lb></lb>that interſects it according to the line H L; which diameter in this <lb></lb>caſe ſhall be this G F and the Adjective, if I may ſo ſay, ſhall <lb></lb>be that made by the point G, about the ſemicircle G E F, and the <lb></lb>Ablative ſhall be the reſt made by the other ſemicircle F D G. <lb></lb></s><s>Now this diameter, as not being in the ſame line H L of the <lb></lb>annual motion, but rather cutting it, as we ſee in the point I, the <lb></lb>term G being elevated above, and E depreſſed below the plane <lb></lb>of the grand Orb, doth not determine the Additions and Sub <lb></lb>ſtractions according to its whole length, but the quantity of thoſe <lb></lb>firſt ought to be taken from the part of the line H L, that is in <lb></lb>tercepted between the perpendiculars drawn upon it from the <lb></lb>terms G F; namely, theſe two G S, and F V: So that the mea <lb></lb>ſure of the additions is the line S V leſſer then G F, or then D E; <lb></lb>which was the meaſure of the additions in the Solſtice A. </s><s>And <lb></lb>ſo ſucceſſively, according as the centre of the Earth ſhall be con <pb xlink:href="040/01/442.jpg" pagenum="420"></pb>ſtituted in other points of the Quadrant A I, drawing the Tan <lb></lb>gents in the ſaid points, and the perpndiculars upon the ſame fal <lb></lb>ling from the terms of the diameters of the Equinoctial drawn <lb></lb>from the errect planes by the ſaid Tangents to the plane of the <lb></lb>grand Orb; the parts of the ſaid Tangents (which ſhall conti <lb></lb>nually be leſſer towards the Equinoctials, and greater towards the <lb></lb>Solſtices) ſhall give us the quantities of the additions and ſubſtra <lb></lb>ctions. </s><s>How much in the next place the leaſt additions differ from <lb></lb>the greateſt, is eaſie to be known, becauſe there is the ſame dif <lb></lb>ference betwixt them, as between the whole Axis or Diameter of <lb></lb>the Sphere, and the part thereof that lyeth between the Polar <lb></lb>Circles; the which is leſs than the whole diameter by very near a <lb></lb>twelfth part, ſuppoſing yet that we ſpeak of the additions and <lb></lb>ſubſtractions made in the Equinoctial; but in the other Paral <lb></lb>lels they are leſſer, according as their diameters do diminiſh.</s></p><p type="main"><s>This is all that I have to ſay upon this Argument, and all perhaps <lb></lb>that can fall under the comprehenſion of our knowledge, which, <lb></lb>as you well know, may not entertain any concluſions, ſave onely <lb></lb>thoſe that are firm and conſtant, ſuch as are the three kinds of Pe <lb></lb>riods of the ebbings and flowings; for that they depend on cauſes <lb></lb>that are invariable, ſimple, and eternal. </s><s>But becauſe that ſe <lb></lb>condary and particular cauſes, able to make many alterations, in <lb></lb>termix with theſe that are the primary and univerſal; and theſe <lb></lb>ſecondary cauſes being part of them inconſtant, and not to be <lb></lb>obſerved; as for example, The alteration of Winds, and part <lb></lb>(though terminate and fixed) unobſerved for their multiplicity, <lb></lb>as are the lengths of the Straights, their various inclinations to <lb></lb>wards this or that part, the ſo many and ſo different depths of the <lb></lb>Waters, who ſhall be able, unleſs after very long obſervations, and <lb></lb>very certain relations, to frame ſo expeditious Hiſtories thereof, as <lb></lb>that they may ſerve for Hypoth eſes, and certain ſuppoſitions to <lb></lb>ſuch as will by their combinations give adequate reaſons of all the <lb></lb>appearances, and as I may ſay, Anomalie, and particular irregula <lb></lb>rities that may be diſcovered in the motions of the Waters? </s><s>I <lb></lb>will content my ſelf with advertiſing you, that the accidental <lb></lb>cauſes are in nature, and are able to produce many alterations; <lb></lb>for the more minute obſervations, I remit them to be made by <lb></lb>thoſe that frequent ſeveral Seas: and onely by way of a conclu <lb></lb>ſion to this our conference, I will propoſe to be conſidered, how <lb></lb>that the preciſe times of the fluxes and refluxes do not onely hap <lb></lb>pen to be altered by the length of Straights, and by the diffe <lb></lb>rence of depths; but I believe that a notable alteration may alſo <lb></lb>proceed from the comparing together of ſundry tarcts of Sea, <lb></lb>different in greatneſs; and in poſition, or, if you will, inclina <lb></lb>tion; which difference happeneth exactly here in the <emph type="italics"></emph>Adriatick<emph.end type="italics"></emph.end> <pb xlink:href="040/01/443.jpg" pagenum="421"></pb>Gulph, leſſe by far than the reſt of the Mediterrane, and placed in <lb></lb>ſo different an inclination, that whereas that hath its bounds that <lb></lb>incloſeth it on the Eaſtern part, as are the Coaſts of <emph type="italics"></emph>Syria,<emph.end type="italics"></emph.end> this is <lb></lb>ſhut up in its more Weſterly part: and becauſe the ebbings and <lb></lb>flowings are much greater towards the extremities, yea, becauſe <lb></lb>the Seas riſings and fallings are there onely greateſt, it may pro <lb></lb>bably happen that the times of Flood at <emph type="italics"></emph>Venice<emph.end type="italics"></emph.end> may be the time of <lb></lb>low Water in the other Sea, which, as being much greater, and <lb></lb>diſtended more directly from Weſt to Eaſt, cometh in a certain <lb></lb>ſort to have dominion over the <emph type="italics"></emph>Adriatick:<emph.end type="italics"></emph.end> and therefore it <lb></lb>would be no wonder, in caſe the effects depending on the pri <lb></lb>mary cauſes, ſhould not hold true in the times that they ought, <lb></lb>and that correſpond to the periods in the <emph type="italics"></emph>Adriatick,<emph.end type="italics"></emph.end> as it doth <lb></lb>in the reſt of the Mediterrane. </s><s>But theſe Particularities require <lb></lb>long Obſervations, which I neither have made as yet, nor ſhall I <lb></lb>ever be able to make the ſame for the future.</s></p><p type="main"><s>SAGR. </s><s>You have, in my opinion, done enough in opening us <lb></lb>the way to ſo lofty a ſpeculation, of which, if you had given us <lb></lb>no more than that firſt general Propoſition that ſeemeth to me to <lb></lb>admit of no reply, where you declare very rationally, that the <lb></lb>Veſſels containing the Sea-waters continuing ſtedfaſt, it would <lb></lb>be impoſſible, according to the common courſe of Nature, that <lb></lb>thoſe motions ſhould follow in them which we ſee do follow; <lb></lb>and that, on the other ſide, granting the motions aſcribed, for o <lb></lb>ther reſpects, by <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> to the Terreſtrial Globe, theſe ſame <lb></lb>alterations ought to enſue in the Seas, if I ſay you had told us no <lb></lb>more, this alone in my judgment, ſo far exceeds the vanities in <lb></lb>troduced by ſo many others, that my meer looking on them <lb></lb>makes me nauſeate them, and I very much admire, that among <lb></lb>men of ſublime wit, of which nevertheleſs there are not a few, <lb></lb>not one hath ever conſidered the incompatibility that is between <lb></lb>the reciprocal motion of the Water contained, and the immobi <lb></lb>lity of the Veſſel containing, which contradiction ſeemeth to me <lb></lb>now ſo manifeſt.</s></p><p type="main"><s>SALV. </s><s>It is more to be admired, that it having come into the <lb></lb><arrow.to.target n="marg814"></arrow.to.target> <lb></lb>thoughts of ſome to refer the cauſe of the Tide to the motion of <lb></lb>the Earth, therein ſhewing a more than common apprehenſion, <lb></lb>they ſhould, in afterwards driving home the motion cloſe with <lb></lb>no ſide; and all, becauſe they did not ſee that one ſimple and <lb></lb>uniform motion, as <emph type="italics"></emph>v. </s><s>gr.<emph.end type="italics"></emph.end> the ſole diurnal motion of the Terre <lb></lb>ſtrial Globe, doth not ſuffice, but that there is required an une <lb></lb>ven motion, one while accelerated, and another while retarded: <lb></lb>for when the motion of the Veſſels are uniforme, the waters <lb></lb>contained will habituate themſelves thereto, without ever ma <lb></lb>king any alteration. </s><s>To ſay alſo (as it is related of an ancient <pb xlink:href="040/01/444.jpg" pagenum="422"></pb><arrow.to.target n="marg815"></arrow.to.target> <lb></lb>Mathematician) that the motion of the Earth meeting with the <lb></lb>motion of the Lunar Orb, the concurrence of them occaſioneth <lb></lb>the Ebbing and Flowing, is an abſolute vanity, not onely be <lb></lb>cauſe it is not expreſt, nor ſeen how it ſhould ſo happen, but the <lb></lb>falſity is obvious, for that the Revolution of the Earth is not con <lb></lb>trary to the motion of the Moon, but is towards the ſame way. <lb></lb></s><s>So that all that hath been hitherto ſaid, and imagined by others, <lb></lb>is, in my judgment, altogether invalid. </s><s>But amongſt all the <lb></lb>famous men that have philoſophated upon this admirable effect <lb></lb><arrow.to.target n="marg816"></arrow.to.target> <lb></lb>of Nature, I more wonder at <emph type="italics"></emph>Kepler<emph.end type="italics"></emph.end> than any of the reſt, who <lb></lb>being of a free and piercing wit, and having the motion aſcri <lb></lb>bed to the Earth, before him, hath for all that given his ear and <lb></lb>aſſent to the Moons predominancy over the Water, and to oc <lb></lb>cult properties, and ſuch like trifles.</s></p><p type="margin"><s><margin.target id="marg814"></margin.target><emph type="italics"></emph>One ſingle moti <lb></lb>on of the terreſtri <lb></lb>al Globe ſufficeth <lb></lb>not to produce the <lb></lb>Ebbing & Flowing<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg815"></margin.target><emph type="italics"></emph>The opinion of<emph.end type="italics"></emph.end> <lb></lb>Seleucus <emph type="italics"></emph>the Ma <lb></lb>thematician cenſu <lb></lb>red.<emph.end type="italics"></emph.end></s></p><p type="margin"><s><margin.target id="marg816"></margin.target>Kepler <emph type="italics"></emph>is with <lb></lb>veſpect blamed.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>I am of opinion, that to theſe more ſpaculative per <lb></lb>ſons the ſame happened, that at preſent befalls me, namely, the <lb></lb>not underſtanding the intricate commixtion of the three Periods <lb></lb>Annual, Monethly, and Diurnal; And how their cauſes ſhould <lb></lb>ſeem to depend on the Sun, and on the Moon, without the Suns <lb></lb>or Moons having any thing to do with the Water; a buſineſſe, <lb></lb>for the full underſtanding of which I ſtand in need of a little <lb></lb>longer time to conſider thereof, which the novelty and difficulty <lb></lb>of it hath hitherto hindred me from doing: but I deſpair not, but <lb></lb>that when I return in my ſolitude and ſilence to ruminate that <lb></lb>which remaineth in my fancy, not very well digeſted, I ſhall <lb></lb>make it my own. </s><s>We have now, from theſe four dayes Diſ <lb></lb>courſe, great atteſtations, in favour of the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Syſteme, <lb></lb>amongſt which theſe three taken: the firſt, from the Stations and <lb></lb>Retrogradations of the Planets, and from their approaches, and <lb></lb>receſſions from the Earth; the ſecond, from the Suns revolving <lb></lb>in it ſelf, and from what is obſerved in its ſpots; the third, from <lb></lb>the Ebbing and Flowing of the Sea do ſhew very rational and <lb></lb>concluding.</s></p><p type="main"><s>SALV. </s><s>To which alſo haply, in ſhort, one might adde a <lb></lb>fourth, and peradventure a fifth; a fourth, I ſay, taken from <lb></lb>the fixed ſtars, ſeeing that in them, upon exact obſervations, thoſe <lb></lb>minute mutations appear, that <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> thought to have been <lb></lb>inſenſible. </s><s>There ſtarts up, at this inſtant, a fifth novelty, from <lb></lb>which one may argue mobility in the Terreſtrial Globe, by <lb></lb><arrow.to.target n="marg817"></arrow.to.target> <lb></lb>means of that which the moſt Illuſtrious <emph type="italics"></emph>Signore Cæſare,<emph.end type="italics"></emph.end> of the <lb></lb>noble Family of the <emph type="italics"></emph>Marſilii<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Bologna,<emph.end type="italics"></emph.end> and a <emph type="italics"></emph>Lyncean<emph.end type="italics"></emph.end> Aca <lb></lb>demick, diſcovereth with much ingenuity, who in a very learned <lb></lb>Tract of his, ſheweth very particularly how that he had obſerved <lb></lb>a continual mutation, though very ſlow in the Meridian line, <lb></lb>of which Treatiſe, at length, with amazement, peruſed by me, <pb xlink:href="040/01/445.jpg" pagenum="423"></pb>I hope he will communicate Copies to all thoſe that are Students <lb></lb>of Natures Wonders.</s></p><p type="margin"><s><margin.target id="marg817"></margin.target>Sig. </s><s>Cæſare Mar <lb></lb>ſilius <emph type="italics"></emph>obſerveth the <lb></lb>Meridian to be <lb></lb>moveable.<emph.end type="italics"></emph.end></s></p><p type="main"><s>SAGR. </s><s>This is not the firſt time that I have heard ſpeak of <lb></lb>the exquiſite Learning of this Gentleman, and of his ſhewing <lb></lb>himſelf a zealous Patron of all the Learned, and if this, or any <lb></lb>other of his Works ſhall come to appear in publique, we may be <lb></lb>aforehand aſſured, that they will be received, as things of great <lb></lb>value.</s></p><p type="main"><s>SALV. </s><s>Now becauſe it is time to put an end to our Diſcour <lb></lb>ſes, it remaineth, that I intreat you, that if, at more leaſure go <lb></lb>ing over the things again that have been alledged you meet <lb></lb>with any doubts, or ſcruples not well reſolved, you will excuſe <lb></lb>my overſight, as well for the novelty of the Notion, as for the <lb></lb>weakneſſe of my wit, as alſo for the grandure of the Subject, <lb></lb>as alſo finally, becauſe I do not, nor have pretended to that aſ <lb></lb>ſent from others, which I my ſelf do not give to this conceit, <lb></lb>which I could very eaſily grant to be a <emph type="italics"></emph>Chymæra,<emph.end type="italics"></emph.end> and a meer <lb></lb>paradox; and you <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> although in the Diſcourſes paſt <lb></lb>you have many times, with great applauſe, declared, that you <lb></lb>were pleaſed with ſome of my conjectures, yet do I believe, that <lb></lb>that was in part more occaſioned by the novelty than by the cer <lb></lb>tainty of them, but much more by your courteſie, which did <lb></lb>think and deſire, by its aſſent, to procure me that content which <lb></lb>we naturally uſe to take in the approbation and applauſe of our <lb></lb>own matters: and as your civility hath obliged me to you; ſo <lb></lb>am I alſo pleaſed with the ingenuity of <emph type="italics"></emph>Simplicius.<emph.end type="italics"></emph.end> Nay, his <lb></lb>conſtancy in maintaining the Doctrine of his Maſter, with ſo <lb></lb>much ſtrength & undauntedneſs, hath made me much to love him. <lb></lb></s><s>And as I am to give you thanks, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> for your courteous aſ <lb></lb>fection; ſo of <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> I ask pardon, if I have ſometimes <lb></lb>moved him with my too bold and reſolute ſpeaking: and let him <lb></lb>be aſſured that I have not done the ſame out of any inducement <lb></lb>of ſiniſter affection, but onely to give him occaſion to ſet before <lb></lb>us more lofty fancies that might make me the more knowing.</s></p><p type="main"><s>SIMP. </s><s>There is no reaſon why you ſhould make all theſe ex <lb></lb>cuſes, that are needleſſe, and eſpecially to me, that being accu <lb></lb>ſtomed to be at Conferences and publique Diſputes, have an <lb></lb>hundred times ſeen the Diſputants not onely to grow hot and an <lb></lb>gry at one another, but likewiſe to break forth into injurious <lb></lb>words, and ſometimes to come very neer to blows. </s><s>As for the <lb></lb>paſt Diſcourſes, and particulatly in this laſt, of the reaſon of <lb></lb>the Ebbing and Flowing of the Sea, I do not, to ſpeak the truth, <lb></lb>very well apprehend the ſame, but by that ſlight <emph type="italics"></emph>Idea,<emph.end type="italics"></emph.end> what e <lb></lb>ver it be, that I have formed thereof to my ſelf, I confeſſe that <lb></lb>your conceit ſeemeth to me far more ingenuous than any of all <pb xlink:href="040/01/446.jpg" pagenum="424"></pb>thoſe that I ever heard beſides, but yet nevertheleſſe I eſteem it <lb></lb>not true and concluding: but keeping alwayes before the eyes <lb></lb>of my mind a ſolid Doctrine that I have learn't from a moſt <lb></lb>learned and ingenuous perſon, and with which it is neceſſary to <lb></lb>ſit down; I know that both you being asked, Whether God, by <lb></lb>his infinite Power and Wiſdome might confer upon the Element <lb></lb>of Water the reciprocal motion which we obſerve in the ſame in <lb></lb>any other way, than by making the containing Veſſel to move; I <lb></lb>know, I ſay, that you will anſwer, that he might, and knew how <lb></lb>to have done the ſame many wayes, and thoſe unimaginable to <lb></lb>our ſhallow underſtanding: upon which I forthwith conclude, <lb></lb>that this being granted, it would be an extravagant boldneſſe <lb></lb>for any one to goe about to limit and confine the Divine <lb></lb>Power and Wiſdome to ſome one particular conjecture of <lb></lb>his own.</s></p><p type="main"><s>SALV. </s><s>This of yours is admirable, and truly Angelical Do <lb></lb>ctrine, to which very exactly that other accords, in like manner <lb></lb>divine, which whilſt it giveth us leave to diſpute, touching the <lb></lb>conſtitution of the World, addeth withall (perhaps to the end, <lb></lb>that the exerciſe of the minds of men might neither be diſcou <lb></lb>raged, nor made bold) that we cannot find out the works made <lb></lb>by his hands. </s><s>Let therefore the Diſquiſition permitted and or <lb></lb>dain'd us by God, aſſiſt us in the knowing, and ſo much more <lb></lb>admiring his greatneſſe, by how much leſſe we finde our ſelves <lb></lb>too dull to penetrate the profound Abyſſes of his infinite Wiſ <lb></lb>dome.</s></p><p type="main"><s>SAGR. </s><s>And this may ſerve for a final cloſe of our four dayes <lb></lb>Diſputations, after which, if it ſeem good to <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> to take <lb></lb>ſome time to reſt himſelf, our curioſity muſt, of neceſſity, grant <lb></lb>him the ſame, yet upon condition, that when it is leſſe incommo <lb></lb>dious for him, he will return and ſatisfie my deſire in particular <lb></lb>concerning the Problemes that remain to be diſcuſt, and that I <lb></lb>have ſet down to be propounded at one or two other Conferen <lb></lb>ces, according to our agreement: and above all, I ſhall very <lb></lb>impatiently wait to hear the Elements of the new Science of our <lb></lb><emph type="italics"></emph>Academick<emph.end type="italics"></emph.end> about the natural and violent local Motions. </s><s>And <lb></lb>in the mean time, we may, according to our cuſtome, ſpend an <lb></lb>hour in taking the Air in the <emph type="italics"></emph>Gondola<emph.end type="italics"></emph.end> that waiteth for us.</s></p><p type="head"><s><emph type="italics"></emph>FINIS.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/447.jpg"></pb><figure id="id.040.01.447.1.jpg" xlink:href="040/01/447/1.jpg"></figure><figure id="id.040.01.447.2.jpg" xlink:href="040/01/447/2.jpg"></figure><figure id="id.040.01.447.3.jpg" xlink:href="040/01/447/3.jpg"></figure><figure id="id.040.01.447.4.jpg" xlink:href="040/01/447/4.jpg"></figure><p type="caption"><s><emph type="italics"></emph>Place this Plate <lb></lb> at the end of <lb></lb>the fourth<emph.end type="italics"></emph.end><lb></lb>Dialogue</s></p></chap> <pb xlink:href="040/01/448.jpg"></pb><pb xlink:href="040/01/449.jpg"></pb><chap><p type="head"> <s>THE <lb></lb>Ancient and Modern <lb></lb>DOCTRINE <lb></lb>OF <lb></lb>Holy Fathers, <lb></lb>AND <lb></lb>Iudicious Divines,</s></p><p type="head"> <s>CONCERNING</s></p><p type="head"> <s>The raſh citation of the Teſtimony of SACRED <lb></lb>SCRIPTURE, in Concluſions meerly Natural, and <lb></lb>that may be proved by Senſible Experiments, and <lb></lb>Neceſſary Demonſtrations.</s></p><p type="head"> <s>Written, ſome years ſince, to Gratifie The moſt SERENE <lb></lb>CHRISTINA LOTHARINGA, <emph type="italics"></emph>Arch<lb></lb>Dutcheſs<emph.end type="italics"></emph.end> of <emph type="italics"></emph>TVSCANR<emph.end type="italics"></emph.end>;</s></p><p type="head"> <s>By GALILÆO GALILÆI, A Gentleman of <lb></lb><emph type="italics"></emph>Florence,<emph.end type="italics"></emph.end> and Chief Philoſopher and Mathematician to <lb></lb>His moſt Serene Highneſs the Grand <emph type="italics"></emph>DVKE.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>And now rendred into Engliſh from the Italian,<emph.end type="italics"></emph.end><lb></lb>BY <lb></lb>THOMAS SALUSBURY.</s></p><p type="main"> <s><emph type="italics"></emph>Naturam Rerum invenire, difficile; & ubi inveneris, indicare <lb></lb>in vulgus, nefas.<emph.end type="italics"></emph.end> Plato.</s></p><p type="head"> <s><emph type="italics"></emph>LONDON,<emph.end type="italics"></emph.end><lb></lb>Printed by WILLIAM LEYBOURN, 1661.</s></p> </chap> <pb xlink:href="040/01/450.jpg"></pb><chap><pb xlink:href="040/01/451.jpg" pagenum="427"></pb><p type="head"> <s>TO <lb></lb>Her moſt Serene <lb></lb>HIGHNES <lb></lb>THE <lb></lb>Gran Ducheſs Mother.</s></p><p type="main"> <s>Some years ſince, as Your moſt Serene Highneſs well <lb></lb>knoweth, I did diſcover many particulars in Hea<lb></lb>ven that had been unſeen and unheard of untill <lb></lb>this our Age; which, as well for their Novelty, as <lb></lb>for certain conſequences which depend upon <lb></lb>them, claſhing with ſome Phyſical Propoſitions commonly recei<lb></lb>ved by the Schools, did ſtir up againſt me no ſmall number of <lb></lb>ſuch as profeſſed the vulgar Philoſophy in the Univerſities; as if <lb></lb>I had with my own hand newly placed theſe things in Heaven to <lb></lb>obſcure and diſturb Nature and the Sciences: who forgetting <lb></lb>that the multitude of Truths contribute, and concur to the inve<lb></lb>ſtigation, augmentation, and eſtabliſhment of the Arts, and not to <lb></lb>their diminution, and deſtruction; and at the ſame time ſhewing <lb></lb>themſelves more affectionate to their own Opinions, than to <lb></lb>Truth, went about to deny, and to diſprove thoſe Novelties; of <lb></lb>which their very ſenſe, had they but pleaſed to have intenſly be<lb></lb>held them, would have rendered them thorowly aſſured. </s> <s>And <lb></lb>to this purpoſe they alledged ſundry things, and publiſhed cer<lb></lb>tain Papers fraughted with vain diſcourſes; and which was a <lb></lb>more groſs errour, interwoven with the atteſtations of the Sacred <lb></lb>Scriptures, taken from places by them not rightly underſtood, <lb></lb>and which did not any thing concern the point for which they <lb></lb>were produced Into which errour perhaps they would not <lb></lb>have run, if they had but been advertiſed of a moſt profitable <lb></lb>Document which S. <emph type="italics"></emph>Auguſtine<emph.end type="italics"></emph.end> giveth us, concerning our pro<lb></lb>ceeding warily, in making poſitive determinations in points that <pb xlink:href="040/01/452.jpg" pagenum="428"></pb>are obſcure and hard to be underſtood by the meer help of <lb></lb>ratiocination; where treating (as we) of a certain natural conclu<lb></lb>ſion concerning Celeſtial Bodies, he thus writes: <emph type="italics"></emph>(a) But now<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg818"></arrow.to.target><lb></lb><emph type="italics"></emph>having evermore a reſpect to the moderation of pious Gravity, <lb></lb>we ought to believe nothing unadviſedly in a doubtful point; leſt <lb></lb>we conceive a prejudice againſt that, in favour to our Errour, <lb></lb>which Truth hereafter may diſcover to be no wiſe contrary to the <lb></lb>Sacred Books either of the Old, or New Teſtament.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg818"></margin.target><emph type="italics"></emph>(a) Nunc au<lb></lb>tem, ſervatâ ſem<lb></lb>per moderatione piæ <lb></lb>gravitatis, nihil <lb></lb>credere de re ob<lb></lb>ſcurâ temerè de<lb></lb>bemus, ne fortè, <lb></lb>quod poſtea veritas <lb></lb>patefecerit, quam<lb></lb>vis Libris Sanct is, <lb></lb>ſive Teſtamenti <lb></lb>Veteris, ſive No<lb></lb>vi, nisllo modo eſſe <lb></lb>poſſit adverſum, <lb></lb>tamen propter a<lb></lb>morem noſtri erro<lb></lb>ris, oderimus.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>It hath ſince come to paſs, that Time hath by degrees diſco<lb></lb>vered to every one the truths before by me indicated: and to<lb></lb>gether with the truth of the fact, a diſcovery hath been made of <lb></lb>the difference of humours between thoſe who ſimply and with<lb></lb>out paſſion did refuſe to admit ſuch like <emph type="italics"></emph>Phænomena<emph.end type="italics"></emph.end> for true, and <lb></lb>thoſe who to their incredulity had added ſome diſcompoſed af<lb></lb>fection: For as thoſe who were better grounded in the Science of <lb></lb><arrow.to.target n="marg819"></arrow.to.target><lb></lb>Aſtronomy, and Natural Philoſophy, became ſatisfied upon my <lb></lb>firſt ntimation of the news; ſo all thoſe who ſtood not in the <lb></lb>Negative, or in doubt for any other reaſon, but becauſe it was <lb></lb>an unlookt-for-Novelty, and becauſe they had not an occaſion of <lb></lb>ſeeing a ſensible experiment thereof, did by degrees come to ſa<lb></lb>risfie themſelves: But thoſe, who beſides the love they bore to <lb></lb>their firſt Errour, have I know not what imaginary intereſs to <lb></lb>render them diſaffected; not ſo much towards the things, as to<lb></lb>wards the Author of them, not being able any longer to deny <lb></lb>them, conceal themſelves under an obſtinate ſilence; and being <lb></lb>exaſperated more than ever by that whereby thoſe others were <lb></lb>ſatisfied and convinced, they divert their thoughts to other pro<lb></lb>jects, and ſeek to prejudice me ſome other wayes: of whom I <lb></lb>proreſs that I would make no more account than I have done of <lb></lb>thoſe who heretofore have contradicted me (at whom I alwaies <lb></lb>laugh, as being aſſured of the iſſue that the buſineſs is to have) <lb></lb>but that I ſee that thoſe new Calumnies and Perſecutions do not <lb></lb>determine in our greater or leſier Learning (in which I will ſcarce <lb></lb>pretend to any thing) but extend ſo far as to attempt to aſperſe <lb></lb>me with Crimes which ought to be, and are more abhorred by me <lb></lb>than Death it ſelf: Nor ought I to content my ſelf that they <lb></lb>are known to be unjuſt by thoſe onely who know me and them, <lb></lb>but by all men whatſoever. </s> <s>They perſiſting therefore in their <lb></lb>firſt Reſolution, Of ruining me and whatſoever is mine, by all <lb></lb>imaginable waies; and knowing how that I in my Studies of <lb></lb>Aſtronomy and Philoſophy hold, as to the Worlds Syſteme, <lb></lb>That the Sun, without changing place, is ſituate in the Centre <lb></lb>of the Converſion of the Celeſtial Orbes; and that the Earth, <lb></lb>convertible about its own Axis, moveth it ſelf about the Sun: <lb></lb>And moreover underſtanding, that I proceed to maintain this Po<pb xlink:href="040/01/453.jpg" pagenum="429"></pb>ſition, not onely by refuting the Reaſons of <emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ariſto<lb></lb>tle,<emph.end type="italics"></emph.end> but by producing many on the contrary; and in particular, <lb></lb>ſome Phyſical pertaining to Natural Effects, the cauſes of which <lb></lb>perhaps can be by no other way aſſigned; and others Aſtrono<lb></lb>mical depending upon many circumſtances and encounters of <lb></lb>new Diſcoveries in Heaven, which manifeſtly confute the Ptolo<lb></lb>maick Syſteme, and admirably agree with and confirm this other <lb></lb>Hypotheſis: and poſſibly being aſhamed to ſee the known truth <lb></lb>of other Poſitions by me aſſerted, different from thoſe that have <lb></lb>been commonly received; and therefore diſtruſting their de<lb></lb>fence ſo long as they ſhould continue in the Field of Philoſo<lb></lb>phy: for theſe reſpects, I ſay, they have reſolved to try whe<lb></lb>ther they could make a Shield for the fallacies of their Argu<lb></lb>ments of the Mantle of a feigned Religion, and of the Autho<lb></lb>rity of the Sacred Scriptures, applyed by them with little judg<lb></lb>ment to the confutation of ſuch Reaſons of mine as they had <lb></lb>neither underſtood, nor ſo much as heard.</s></p><p type="margin"> <s><margin.target id="marg819"></margin.target>Lib_{+} 2. Geneſi <lb></lb>ad Literam in <lb></lb>fine.</s></p><p type="main"> <s>And firſt, they have indeavoured, as much as in them lay, to <lb></lb>divulge an opiniou thorow the Univerſe, that thoſe Propoſitions <lb></lb>are contrary to the Holy Letters, and conſequently Damnable <lb></lb>and Heretical: And thereupon perceiving, that for the moſt <lb></lb>part, the inclination of Mans Nature is more prone to imbrace <lb></lb>thoſe enterprizes, whereby his Neighbour may, although un<lb></lb>juſtly, be oppreſſed, than thoſe from whence he may receive <lb></lb>juſt incouragement; it was no hard matter to find thoſe Com<lb></lb>plices, who for ſuch (that is, for Damnable and Heretical) did <lb></lb>from their Pulpits with unwonted confidence preach it, with but <lb></lb>an unmerciful and leſs conſiderate injury, not only to this Do<lb></lb>ctrine, and to its followers, but to all Mathematicks and Ma<lb></lb>thematicians together. </s> <s>Hereupon aſſuming greater confidence, <lb></lb>and vainly hoping that that Seed which firſt took root in their un<lb></lb>ſound mindes, might ſpread its branches, and aſcend towards <lb></lb>Heaven, they went ſcattering rumours up and down among the <lb></lb>People, That it would, ere long be condemned by Supreme Au<lb></lb>thority: and knowing that ſuch a <emph type="italics"></emph>Cenſure<emph.end type="italics"></emph.end> would ſupplant <lb></lb>not onely theſe two Concluſions of the Worlds Syſteme, but <lb></lb>would make all other Aſtronomical and Phyſical Obſervations <lb></lb>that have correſpondence and neceſſary connection therewith to <lb></lb>become damnable, to facilitate the buſineſs they ſeek all they <lb></lb>can to make this opinion (at leaſt among the vulgar) to ſeem new, <lb></lb>and peculiar to my ſelf, not owning to know that <emph type="italics"></emph>Nicholas Coper<lb></lb>nicus<emph.end type="italics"></emph.end> was its Authour, or rather Reſtorer and Confirmer: a per<lb></lb>ſon who was not only a Catholick, but a Prieſt, Canonick, and <lb></lb>ſo eſteemed, that there being a Diſpute in the <emph type="italics"></emph>Lateran Council,<emph.end type="italics"></emph.end><lb></lb>under <emph type="italics"></emph>Leo<emph.end type="italics"></emph.end> X. touching the correction of the Eccleſiaſtick Ca<pb xlink:href="040/01/454.jpg" pagenum="430"></pb>lendar, he was ſent for to <emph type="italics"></emph>Rome<emph.end type="italics"></emph.end> from the remoteſt parts of <lb></lb><emph type="italics"></emph>Germany,<emph.end type="italics"></emph.end> for to aſſiſt in this Reformation, which for that time <lb></lb>was left imperfect, onely becauſe as then the true meaſure of <lb></lb>the Year and Lunar Moneth was not exactly known: whereupon <lb></lb>it was given him in charge by the Biſhop of <emph type="italics"></emph>Sempronia,<emph.end type="italics"></emph.end> at that <lb></lb>time Super-intendent in that Affair, to ſearch with reiterated <lb></lb>ſtudies and pains for greater light and certainty, touching thoſe <lb></lb>Cœleſtial Motions. </s> <s>Upon which, with a Labour truly <emph type="italics"></emph>Atlantick<emph.end type="italics"></emph.end><lb></lb>and with his admirable Wit, ſetting himſelf again to that Study, <lb></lb>he made ſuch a progreſs in theſe Sciences, and reduced the <lb></lb>knowledge of the Cœleſtial Motions to ſuch exactneſſe, that he <lb></lb>gained the title of an Excellent <emph type="italics"></emph>Aſtronomer.<emph.end type="italics"></emph.end> And, according <lb></lb>unto his Doctrine, not only the Calendar hath been ſince regu<lb></lb>lated, but the Tables of all the Motions of the Planets have al<lb></lb>ſo been calculated: and having reduced the ſaid Doctrine into <lb></lb>ſix Books, he publiſhed them to the World at the inſtance of <lb></lb>the Cardinal of <emph type="italics"></emph>Capua,<emph.end type="italics"></emph.end> and of the Biſhop of <emph type="italics"></emph>Culma.<emph.end type="italics"></emph.end> And in <lb></lb>regard that he had re-aſſumed this ſo laborious an enterprize by <lb></lb>the order of The Pope; he dedicated his Book <emph type="italics"></emph>De Revolutioni<lb></lb>bus Cœleſtibus<emph.end type="italics"></emph.end> to His Succeſſour, namely <emph type="italics"></emph>Paul<emph.end type="italics"></emph.end> III. which, being <lb></lb>then alſo Printed, hath been received by The Holy Church, and <lb></lb>read and ſtudied by all the World, without any the leaſt um<lb></lb>brage of ſcruple that hath ever been conceived at his Doctrine; <lb></lb>The which, whilſt it is now proved by manifeſt Experiments and <lb></lb>neceſſary Demonſtrations to have been well grounded, there <lb></lb>want not perſons that, though they never ſaw that ſame Book in<lb></lb>tercept the reward of thoſe many Labours to its Authour, by <lb></lb>cauſing him to be cenſured and pronounced an Heretick; and <lb></lb>this, only to ſatisfie a particular diſpleaſure conceived, without <lb></lb>any cauſe, againſt another man, that hath no other intereſt in <lb></lb><emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> but only as he is an approver of his Doctrine.</s></p><p type="main"> <s>Now in regard of theſe falſe aſperſions, which they ſo unjuſtly <lb></lb>ſeek to throw upon me, I have thought it neceſſary for my juſti<lb></lb>fication before the World (of whoſe judgment in matters of <lb></lb>Religion and Reputation I ought to make great eſteem) to <lb></lb>diſcourſe concerning thoſe Particulars, which theſe men produce <lb></lb>to ſcandalize and ſubvert this Opinion, and in a word, to con<lb></lb>demn it, not only as falſe, but alſo as Heretical; continually <lb></lb>making an Hipocritical Zeal for Religion their Shield; going a<lb></lb>bout moreover to intereſt the Sacred Scriptures in the Diſpute, <lb></lb>and to make them in a certain ſenſe Miniſters of their deceiptful <lb></lb>purpoſes: and farthermore deſiring, if I miſtake not, contrary to <lb></lb>the intention of them, and of the Holy Fathers to extend (that I <lb></lb>may not ſay abuſe) their Authority, ſo as that even in Concluſions <lb></lb>meerly Natural, and not <emph type="italics"></emph>de Fide,<emph.end type="italics"></emph.end> they would have us altogether <pb xlink:href="040/01/455.jpg" pagenum="431"></pb>leave Senſe and Demonſtrative Reaſons, for ſome place of Scri<lb></lb>pture which ſometimes under the apparent words may contain <lb></lb>a different ſenſe. </s> <s>Now I hope to ſhew with how much <lb></lb>greater Piety and Religious Zeal I proceed, than they do, in that <lb></lb>I propoſe not, that the Book of <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> is not to be condemn<lb></lb>ed, but that it is not to be condemned, as they would have it; <lb></lb>without underſtanding it, hearing it, or ſo much as ſeeing it; <lb></lb>and eſpecially he being an Author that never treateth of matters <lb></lb>of Religion or Faith; nor by Reaſons any way depending on the <lb></lb>Authority of Sacred Scripoures whereupon he may have erroni<lb></lb>ouſly interpreted them; but alwaies inſiſts upon Natural Conclu<lb></lb>ſions belonging to the Celeſtial Motions, handled with Aſtrono<lb></lb>mical and Geometrical Demonſtrations. </s> <s>Not that he had not a <lb></lb><arrow.to.target n="marg820"></arrow.to.target><lb></lb>reſpect to the places of the Sacred Leaves, but becauſe he knew <lb></lb>very well that his ſaid Doctrine being demonſtrated, it could <lb></lb>not contradict the Scriptures, rightly, and according to their true <lb></lb>meaning underſtood. </s> <s>And therefore in the end of his Epiſtle <lb></lb>Dedicatory, ſpeaking to The Pope, he ſaith thus: <emph type="italics"></emph>(b) If there <lb></lb>ſhould chance to be any Matæologiſts, who though ignorant in all <lb></lb>the Mathematicks, yet pretending a skill in thoſe Learnings, <lb></lb>ſhould dare, upon the authority of ſome place of Scripture wreſted <lb></lb>to their purpoſe, to condemn and cenſure this my Hypotheſis, I <lb></lb>value them not, but ſhall ſlight their inconſiderate Judgement. </s> <s>For <lb></lb>it is not unknown, that<emph.end type="italics"></emph.end> Lactantius (<emph type="italics"></emph>otherwiſe a Famous Author, <lb></lb>though mean Mathematician) writeth very childiſhly touching the <lb></lb>Form of the Earth, when he ſcoffs at thoſe who affirm the Earth to <lb></lb>be in Form of a Globe. </s> <s>So that it ought not to ſeem ſtrange to the <lb></lb>Ingenious, if any ſuch ſhould likewiſe now deride us. </s> <s>The Ma<lb></lb>thematicks are written for Mathematitians, to whom (if I deceive <lb></lb>not my ſelf) theſe Labours of mine ſhall ſeem to add ſomething, <lb></lb>as alſo to the Common-weale of the Church, whoſe Government is <lb></lb>now in the hands of Your Holineſs.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg820"></margin.target><emph type="italics"></emph>(c) Si fort aſſeerunt <lb></lb>Matæologi, qui <lb></lb>cum omnium Ma<lb></lb>thematicum igna<lb></lb>ri ſint, tamen de tis <lb></lb>judicium aſſu<lb></lb>munt, propter ali<lb></lb>quem locum Scri<lb></lb>ptur æ, malè ad ſu<lb></lb>um propoſitum, de<lb></lb>tortum, auſi fue<lb></lb>rint hoc meum in<lb></lb>ſtitutum reprehen<lb></lb>dere ac inſectari, <lb></lb>illos nihil moror, <lb></lb>adeò ut etiam illo<lb></lb>rum judicium, tan<lb></lb>guam temera ium <lb></lb>contemnam. </s> <s>Non <lb></lb>enim obſcurum eſt, <lb></lb>Lact antium, cele<lb></lb>lebrem alioqui <lb></lb>Scriptorem, ſed <lb></lb>Mathematicum <lb></lb>parvum, admodum <lb></lb>pueriliter de forma <lb></lb>Terræ loqui, cùm <lb></lb>deridet eos, qui <lb></lb>Terram, Globi for<lb></lb>mam habere prodi<lb></lb>derunt. </s> <s>Itaque non <lb></lb>debet mirum vide<lb></lb>ri ſtudioſis, ſi qui <lb></lb>tales, nos ettam ri<lb></lb>debunt. </s> <s>Mathema<lb></lb>ta Mathematicis <lb></lb>ſcribuntur; quibus <lb></lb>& hi noſtri labo<lb></lb>res, (ſi me non fal<lb></lb>lit opinio) vide<lb></lb>buntur etiam Rei<lb></lb>publicæ Eccleſia<lb></lb>ſticæ conducere a<lb></lb>liquid, cujus Prin<lb></lb>cipatum Tua San<lb></lb>ctitas nunc teness.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And of this kinde do theſe appear to be who indeavour to <lb></lb>perſwade that <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> may be condemned before his Book is <lb></lb>read; and to make the World believe that it is not onely lawfull <lb></lb>but commendable ſo to do, produce certain Authorities of the <lb></lb>Scripture, of Divines, and of Councils; which as they are by me <lb></lb>had in reverence, and held of Supream Authority, inſomuch that <lb></lb>I ſhould eſteem it high temerity for any one to contradict them <lb></lb>whilſt they are uſed according to the In ſtitutes of Holy Church, <lb></lb>ſo I believe that it is no errour to ſpeak, ſo long as one hath rea<lb></lb>ſon to ſuſpect that a perſon hath a deſire, for ſome concern of <lb></lb>his own, to produce and alledge them, to purpoſes different from <lb></lb>thoſe that are in the moſt Sacred intention of The Holy Church. <lb></lb></s> <s>Therefore I not onely proteſt (and my ſincerity ſhall manifeſt it <pb xlink:href="040/01/456.jpg" pagenum="432"></pb>ſelf) that I intend to ſubmit my ſelf freely to renounce thoſe et<lb></lb>rors, into which, through ignorance, I may run in this Diſcourſe <lb></lb>of matters pertaining to Religion; but I farther declare, that I <lb></lb>deſire not in theſe matters to engage diſpute with any one, al<lb></lb>though it ſhould be in points that are diſputable: for my end <lb></lb>endeth onely to this, That if in theſe conſiderations, beſides my <lb></lb>own profeſſion, amongſt the errours that may be in them, there <lb></lb>be any thing apt to give others an hint of ſome Notion beneficial <lb></lb>to the Holy Church, touching the determining about the <emph type="italics"></emph>Coper<lb></lb>nican<emph.end type="italics"></emph.end> Syſteme, it may be taken and improved as ſhall ſeem beſt <lb></lb>to my Superiours: If not, let my Book be torn and burnt; for <lb></lb>that I do neither intend, nor pretend to gain to my ſelf any fruit <lb></lb>from my writings, that is not Pious and Catholick. </s> <s>And more<lb></lb>over, although that many of the things that I obſerve have been <lb></lb>ſpoken in my own hearing, yet I ſhall freely admit and grant to <lb></lb>thoſe that ſpake them, that they never ſaid them, if ſo they <lb></lb>pleaſe, but confeſs that I might have been miſtaken: And <lb></lb>therefore what I ſay, let it be ſuppoſed to be ſpoken not by them, <lb></lb>but by thoſe which were of this opinion.</s></p><p type="main"> <s>The motive therefore that they produce to condemn the Opi<lb></lb>nion of the Mobility of the Earth, and Stability of the Sun, is, that <lb></lb>reading in the Sacred Leaves, in many places, that the Sun mo<lb></lb>veth, that the Earth ſtandeth ſtill; and the Scripture not being <lb></lb>capable of lying, or erring, it followeth upon neceſſary conſe<lb></lb>quence, that the Poſition of thoſe is Erronious and Heretical, who <lb></lb>maintain that the Sun of it ſelf is immoveable, and the Earth <lb></lb>moveable.</s></p><p type="main"> <s>Touching this Reaſon I think it fit in the firſt place, to con<lb></lb>ſider, That it is both piouſly ſpoken, and prudently affirmed, That <lb></lb>the Sacred Scripture can never lye, when ever its true meaning is <lb></lb>underſtood: Which I believe none will deny to be many times <lb></lb>very abſtruce, and very different from that which the bare ſound <lb></lb>of the words ſignifieth. </s> <s>Whence it cometh to paſs, that if ever <lb></lb>any one ſhould conſtantly confine himſelf to the naked Gram<lb></lb>matical Sence, he might, erring himſelf, make not only Contra<lb></lb>dictions and Propoſitions remote from Truth to appear in the <lb></lb>Scriptures, but alſo groſs Hereſies and Blaſphemies: For that we <lb></lb>ſhould be forced to aſſign to God feet, and hands, and eyes, yea <lb></lb>more corporal and humane affections, as of Anger, of Repen<lb></lb>tance, of Hatred, nay, and ſometimes the Forgetting of things <lb></lb>paſt, and Ignorance of thoſe to come: Which Propoſitions, like <lb></lb>as (ſo the Holy Ghoſt affirmeth) they were in that manner pro<lb></lb>nounced by the Sacred Scriptures, that they might be accommo<lb></lb>dated to the Capacity of the Vulgar, who are very rude and un<lb></lb>learned; ſo likewiſe, for the ſakes of thoſe that deſerve to be di<pb xlink:href="040/01/457.jpg" pagenum="433"></pb>ſtinguiſhed from the Vulgar, it is neceſſary that grave and skilful <lb></lb>Expoſitors produce the true ſenſes of them, and ſhew the parti<lb></lb>cular Reaſons why they are dictated under ſuch and ſuch words. <lb></lb></s> <s>And this is a Doctrine ſo true and common amongſt Divines, <lb></lb>that it would be ſuperfluous to produce any atteſtation <lb></lb>thereof.</s></p><p type="main"> <s>Hence methinks I may with much more reaſon conclude, that <lb></lb>the ſame holy Writ, when ever it hath had occaſion to pronounce <lb></lb>any natural Concluſion, and eſpecially, any of thoſe which are <lb></lb>more abſtruce, and difficult to be underſtood, hath not failed to <lb></lb>obſerve this Rule, that ſo it might not cauſe confuſion in the <lb></lb>mindes of thoſe very people, and render them the more contu<lb></lb>macious againſt the Doctrines that were more ſublimely myſteri<lb></lb>ous: For (like as we have ſaid, and as it plainly appeareth) out <lb></lb>of the ſole reſpect of condeſcending to Popular Capacity, the <lb></lb>Scripture hath not ſcrupled to ſhadow over moſt principal and <lb></lb>fundamental Truths, attributing, even to God himſelf, qualities <lb></lb>extreamly remote from, and contrary unto his Eſſence. </s> <s>Who <lb></lb>would poſitively affirm that the Scripture, laying aſide that re<lb></lb>ſpect, in ſpeaking but occaſionally of the Earth, of the Water, of <lb></lb>the Sun, or of any other Creature, hath choſen to confine it <lb></lb>ſelf, with all rigour, within the bare and narrow literal ſenſe of <lb></lb>the words? </s> <s>And eſpecially, in mentioning of thoſe Crea<lb></lb>tures, things not at all concerning the primary Inſtitution of <lb></lb>the ſame Sacred Volume, to wit, the Service of God, and the <lb></lb>ſalvation of Souls, and in things infinitely beyond the appre<lb></lb>henſion of the Vulgar?</s></p><p type="main"> <s>This therefore being granted, methinks that in the Diſcuſſion <lb></lb>of Natural Problemes, we ought not to begin at the authority <lb></lb>of places of Scripture; but at Senſible Experiments and Ne<lb></lb>ceſſary Demonſtrations: For, from the Divine Word, the <lb></lb>Sacred Scripture and Nature did both alike proceed; the firſt, <lb></lb>as the Holy Ghoſts Inſpiration; the ſecond, as the moſt obſer<lb></lb>vant Executrix of Gods Commands: And moreover it being <lb></lb>convenient in the Scriptures (by way of condeſcenſion to the <lb></lb>underſtanding of all men) to ſpeak many things different, in <lb></lb>appearance; and ſo far as concernes the naked ſigniſication of <lb></lb>the words, from abſolute truth: But on the contrary, Nature <lb></lb>being inexorable and immutable, and never paſſing the bounds <lb></lb>of the Laws aſſigned her, as one that nothing careth whether <lb></lb>her abſtruſe reaſons and methods of operating be, or be not ex<lb></lb>poſed to the Capacity of Men; I conceive that that, concer<lb></lb>ning Natural Effects, which either Senſible Experience ſets be<lb></lb>fore our eyes, or Neceſſary Demonſtrations do prove unto us, <lb></lb>ought not, upon any account, to be called into queſtion, much <pb xlink:href="040/01/458.jpg" pagenum="434"></pb>leſs condemned upon the teſtimony of Texts of Scripture, which <lb></lb>may, under their words, couch Senſes ſeemingly contrary there<lb></lb>to; In regard that every Expreſſion of Scripture is not tied to <lb></lb>ſo ſtrict conditions, as every Effect of Nature: Nor doth God <lb></lb>leſs admirably diſcover himſelf unto us in Nature's Actions, than <lb></lb>in the Scriptures Sacred Dictions. </s> <s>Which peradventure <emph type="italics"></emph>Tertul-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg821"></arrow.to.target><lb></lb><emph type="italics"></emph>lian<emph.end type="italics"></emph.end> intended to expreſs in thoſe words<emph type="italics"></emph>: (c) We conclude, God <lb></lb>is known; firſt, by Nature, and then again more particularly <lb></lb>known by Doctrine: by Nature, in his Works; by Doctrine, in his <lb></lb>Word preached.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg821"></margin.target><emph type="italics"></emph>Nos definimus, <lb></lb>Deum, primò N.<lb></lb>tura cognoſcen<lb></lb>dum; Deinde, Do<lb></lb>ctrina recognoſcen<lb></lb>dum: Natura ex <lb></lb>operibus; Doctri<lb></lb>na ex pr ædicatio<lb></lb>nibus.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>But I will not hence affirm, but that we ought to have an ex<lb></lb>traordinary eſteem for the Places of Sacred Scripture, nay, being <lb></lb><arrow.to.target n="marg822"></arrow.to.target><lb></lb>come to a certainty in any Natural Concluſions, we ought <lb></lb>to make uſe of them, as moſt appoſite helps to the true Expo<lb></lb>ſition of the ſame Scriptures, and to the inveſtigation of thoſe <lb></lb>Senſes which are neceſſarily conteined in them, as moſt true, and <lb></lb>concordant with the Truths demonſtrated.</s></p><p type="margin"> <s><margin.target id="marg822"></margin.target>Tertul. </s> <s>adver. <lb></lb></s> <s>Marcion. </s> <s>lib. 1. <lb></lb>cap. 18.</s></p><p type="main"> <s>This maketh me to ſuppoſe, that the Authority of the Sacred <lb></lb>Volumes was intended principally to perſwade men to the be<lb></lb>lief of thoſe Articles and Propoſitions, which, by reaſon they <lb></lb>ſurpaſs all humane diſcourſe, could not by any other Science, or <lb></lb>by any other means be made credible, than by the Mouth of <lb></lb>the Holy Spirit it ſelf. </s> <s>Beſides that, even in thoſe Propoſitions, <lb></lb>which are not <emph type="italics"></emph>de Fide,<emph.end type="italics"></emph.end> the Authority of the ſame Sacred Leaves <lb></lb>ought to be preferred to the Authority of all Humane Sciences <lb></lb>that are not written in a Demonſtrative Method, but either with <lb></lb>bare Narrations, or elſe with probable Reaſons; and this I hold <lb></lb>to be ſo far convenient and neceſſary, by how far the ſaid Di<lb></lb>vine Wiſdome ſurpaſſeth all humane Judgment and Conjecture. <lb></lb></s> <s>But that that ſelf ſame God who hath indued us with Senſes, <lb></lb>Diſcourſe, and Underſtanding hath intended, laying aſide the <lb></lb>uſe of theſe, to give the knowledg of thoſe things by other means, <lb></lb>which we may attain by theſe, ſo as that even in thoſe Natural <lb></lb>Concluſions, which either by Senſible Experiments or Neceſſary <lb></lb>Demonſtrations are ſet before our eyes, or our Underſtanding, we <lb></lb>ought to deny Senſe and Reaſon, I do not conceive that I am <lb></lb>bound to believe it; and eſpecially in thoſe Sciences, of which <lb></lb>but a ſmall part, and that divided into Concluſions is to be <lb></lb>found in the Scripture: Such as, for inſtance, is that of <emph type="italics"></emph>Aſtro<lb></lb>nomy,<emph.end type="italics"></emph.end> of which there is ſo ſmall a part in Holy Writ, that it doth <lb></lb>not ſo much as name any of the Planets, except the Sun and the <lb></lb>Moon, and once or twice onely <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> under the name of <emph type="italics"></emph>Luci<lb></lb>fer.<emph.end type="italics"></emph.end> For if the Holy Writers had had any intention to perſwade <lb></lb>People to believe the Diſpoſitions and Motions of the Cœleſtial <lb></lb>Bodies; and that conſequently we are ſtill to derive that know<pb xlink:href="040/01/459.jpg" pagenum="435"></pb>ledge from the Sacred Books they would not, in my opinion, have <lb></lb>ſpoken ſo little thereof, that it is as much as nothing, in compa<lb></lb>riſon of the infinite admirable Concluſions, which in that Sci<lb></lb>ence are comprized and demonſtrated Nay, that the Authours <lb></lb>of the Holy Volumes did not only not pretend to teach us the <lb></lb>Conſtitutions and Motions of the Heavens and Stars, their Fi<lb></lb>gures, Magnitudes, and Diſtances, but that intentionally (al<lb></lb>beit that all theſe things were very well known unto them) they <lb></lb><arrow.to.target n="marg823"></arrow.to.target><lb></lb>forbore to ſpeak of them, is the opinion of the Moſt Holy & Moſt <lb></lb>Learned Fathers: and in S. <emph type="italics"></emph>Auguſtine<emph.end type="italics"></emph.end> we read the following words. <lb></lb><emph type="italics"></emph>(c) It is likewiſe commonly asked, of what Form and Figure <lb></lb>we may believe Heaven to be, according to the Scriptures: For <lb></lb>many contend much about thoſe matters, which the greater pru<lb></lb>dence of our Authors hath forborn to ſpeak of, as nothing further<lb></lb>ing their Learners in relation to ableſſed life; and, (which is <lb></lb>the chiefeſt thing) taking up much of that time which ſhould be <lb></lb>ſpent in holy exerciſes. </s> <s>For what is it to me whether Heaven, as <lb></lb>a Sphere, doth on all ſides environ the Earth, a Maſs ballanced in <lb></lb>the middle of the World; or whether like a Diſh it doth onely cover <lb></lb>or overcaſt the ſame? </s> <s>But becauſe belief of Scripture is urged for <lb></lb>that cauſe, which we have oft mentioned, that is, That none through <lb></lb>ignorance of Divine Phraſes, when they ſhall find any thing of this <lb></lb>nature in, or hear any thing cited out of our Bibles which may ſeem <lb></lb>to oppoſe manifeſt Concluſions, ſhould be induced to ſuſpect their <lb></lb>truth, when they admoniſh, relate, & deliver more profitable matters <lb></lb>Briefly be it ſpoken, touching the Figure of Heaven, that our Au<lb></lb>thors knew the truth: But the H. </s> <s>Spirit would not, that men ſhould <lb></lb>learn what is profitable to none for ſalvation.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg823"></margin.target><emph type="italics"></emph>(c) Quæri etiam<lb></lb>ſolet, quæ forma & <lb></lb>figura Cæli cre<lb></lb>denda ſit ſecun<lb></lb>dum Scripturas <lb></lb>noſtras: Multi e<lb></lb>nim multum diſ<lb></lb>put ant de iis rebus, <lb></lb>quas majori pru<lb></lb>dentia noſtri Auto<lb></lb>res omiſerunt, ad <lb></lb>beatam vitam non <lb></lb>profutur as diſcen<lb></lb>libus, & occupan<lb></lb>tes (quod prius eſt) <lb></lb>multum prolixa, <lb></lb>& rebus ſalubri<lb></lb>bus impendenda <lb></lb>temporum ſpatia. <lb></lb></s> <s>Quid enim ad me <lb></lb>pertinet, utrum <lb></lb>Cælum, ſicut Sphæ<lb></lb>ra, undique conclu<lb></lb>dat Terram, in <lb></lb>media. </s> <s>Mundi mo<lb></lb>le libratam; an <lb></lb>eam ex una par<lb></lb>te deſuper, ve<lb></lb>lut diſcus, ope<lb></lb>riat? </s> <s>Sed quia de Fide agitur S cripiurærum, propter illam cauſam, quam non ſemel commemoravimus, Ne ſcilicet <lb></lb>quiſquam eloquia divina non intelligens, cum de his rebus tale aliquid vel invenerit in Libris Noſtris, vel ex illis <lb></lb>audiverit, quod perceptis aſſertionibus adver ſari videatur, nullo modo eis, cetera utilia monentibus, vel narrantibus, <lb></lb>vel pranuntiantibus, credat: Breviter diſcendum eſt, de figura Cæli, hoc ſciſſe Autores noſtros, quod verit as ha<lb></lb>bet: Sed Spiritum Dei, qui per ipſos loquebstur, noluiſſe iſta docere homines, nulli ad ſalutem profutura.<emph.end type="italics"></emph.end> D. <lb></lb>Auguſt. </s> <s>Lib. 2. De Gen. </s> <s>ad literam, Cap. </s> <s>9. Idem etiam legitur apud <emph type="italics"></emph>Petrum Lombardum<emph.end type="italics"></emph.end> Magiſtrum Sententiarum.</s></p><p type="main"> <s>And the ſame intentional ſilence of theſe ſacred Penmen in <lb></lb>determining what is to be believed of theſe accidents of the Ce<lb></lb>leſtial Bodies, is again hinted to us by the ſame Father in the en<lb></lb>ſuing 10. Chapter upon the Queſtion, Whether we are to believe <lb></lb>that Heaven moveth, or ſtandeth ſtill, in theſe words: <emph type="italics"></emph>(d) There<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg824"></arrow.to.target><lb></lb><emph type="italics"></emph>are ſome of the Brethren that ſtart a queſtion concerning the motion <lb></lb>of Heaven, Whether it be fixed, or moved: For if it be moved <lb></lb>(ſay they) how is it a Firmament? </s> <s>If it ſtand ſtill, how do theſe <lb></lb>Stars which are held to be fixed go round from Eaſt to Weſt, the <lb></lb>more Norchern performing ſhorter Circuits near the Pole; ſo that <lb></lb>Heaven, if there be another Pole, to us unknown, may ſeem to re<lb></lb>volve upon ſome other Axis; but if there be not another Pole, it <lb></lb>may be thought to move as a Diſcus? </s> <s>To whom I reply, That<emph.end type="italics"></emph.end><pb xlink:href="040/01/460.jpg" pagenum="436"></pb><emph type="italics"></emph>theſe points require many ſubtil and profound Reaſons, for the <lb></lb>making out whether they be really ſo, or no; the undertakeing and <lb></lb>diſeuſſing of which is neither conſiſtent with my leaſure, nor their <lb></lb>duty, vvhom I deſire to inſtruct in the neceſſary matters more di<lb></lb>rectly conducing to their ſalvation, and to the benefit of The Holy <lb></lb>Church.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg824"></margin.target><emph type="italics"></emph>(d) De Motu <lb></lb>etiam Cæli, non<lb></lb>nulli fratres quæ<lb></lb>ſtionem movent, u<lb></lb>trum ſtet, an mo<lb></lb>veatur; quia ſi mo<lb></lb>vetur, inquiunt, <lb></lb>quomodo Firma<lb></lb>mentum eſt? </s> <s>Si <lb></lb>autem ſtat, quomo<lb></lb>do Sydera quæ in<lb></lb>ipſo fixa credun<lb></lb>tur, ab Oriente in <lb></lb>Occidentem circum<lb></lb>eunt, Septentrio<lb></lb>nalibus breviores <lb></lb>gyros juxta cardi<lb></lb>nem perag entibus; <lb></lb>ut Cælum, ſi est a<lb></lb>lius nobis occultus <lb></lb>cardo, ex alio ver<lb></lb>tice, ſicut Sphæra; <lb></lb>ſi autem nullus a<lb></lb>lius cardo eſt, vel <lb></lb>uti diſcus rotari <lb></lb>videatur? </s> <s>Quibus <lb></lb>reſpondeo, Multum <lb></lb>ſubtilibus & labo<lb></lb>rioſis rationibus <lb></lb>iſta perquiri, ut ve<lb></lb>re percipiatur, u<lb></lb>trum ita, an non <lb></lb>ita ſit, quibus ine<lb></lb>undis atque tra<lb></lb>ctandis, nec mihi <lb></lb>jam tempus eſt, nec <lb></lb>illis eſſe debet, quos <lb></lb>ad ſalutem ſuam, <lb></lb>è Sanctæ Eccleſiæ <lb></lb>neceſſaria utilitate <lb></lb>cupimus informa<lb></lb>ri:<emph.end type="italics"></emph.end></s></p><p type="main"> <s>From which (that we may come nearer to our particular caſe) <lb></lb>it neceſſarily followeth, that the Holy Ghoſt not having intend<lb></lb>ed to teach us, whether Heaven moveth or ſtandeth ſtill; nor <lb></lb>whether its Figure be in Form of a Sphere, or of a Diſcus, or di<lb></lb>ſtended <emph type="italics"></emph>in Planum<emph.end type="italics"></emph.end>: Nor whether the Earth be contained in the <lb></lb>Centre of it, or on one ſide; he hath much leſs had an intention <lb></lb>to aſſure us of other Concluſions of the ſame kinde, and in ſuch <lb></lb>a manner, connected to theſe already named, that without the <lb></lb>dedermination of them, one can neither affirm one or the other <lb></lb>part; which are, The determining of the Motion and Reſt of the <lb></lb>ſaid Earth, and of the Sun. </s> <s>And if the ſame Holy Spirit hath <lb></lb>purpoſely pretermitted to teach us thoſe Propoſitions, as nothing <lb></lb>concerning his intention, that is, our ſalvation; how can it be af<lb></lb>firmed, that the holding of one part rather than the other, ſhould <lb></lb>be ſo neceſſary, as that it is <emph type="italics"></emph>de Fide,<emph.end type="italics"></emph.end> and the other erronious? <lb></lb></s> <s>Can an Opinion be Heretical, and yet nothing concerning the <lb></lb>ſalvation of ſouls? </s> <s>Or can it be ſaid that the Holy Ghoſt purpo<lb></lb>ſed not to teach us a thing that concerned our ſalvation? </s> <s>I might <lb></lb><arrow.to.target n="marg825"></arrow.to.target><lb></lb>here inſert the Opinion of an Eccleſiaſtical ^{*} Perſon, raiſed to the <lb></lb><arrow.to.target n="marg826"></arrow.to.target><lb></lb>degree of <emph type="italics"></emph>Eminentiſſimo,<emph.end type="italics"></emph.end> to wit, <emph type="italics"></emph>That the intention of the Holy <lb></lb>Ghoſt, is to teach us how we ſhall go to Heaven, and not how Hea<lb></lb>ven goeth.<emph.end type="italics"></emph.end></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"></emph>Spiritu ſancti <lb></lb>mentem fuiſſe, nos <lb></lb>docere, quomodo ad <lb></lb>Cælum eatur: non <lb></lb>autem, quomodo <lb></lb>Cælum gradiatur.<emph.end type="italics"></emph.end><lb></lb>Cardinal. </s> <s>Bar.</s></p><p type="main"> <s>But let us return to conſider how much neceſſary Demonſtra<lb></lb>tions, and ſenſible Experiments ought to be eſteemed in Natural <lb></lb>Concluſions; and of what Authority Holy and Learned Divines <lb></lb>have accounted them, from whom amongſt an hundred other atte<lb></lb><arrow.to.target n="marg827"></arrow.to.target><lb></lb>ſtations, we have theſe that follow: <emph type="italics"></emph>(e) We must alſo carefully <lb></lb>heed and altogether avoid in handling the Doctrine of<emph.end type="italics"></emph.end> Moſes, <emph type="italics"></emph>to <lb></lb>avouch or ſpeak any thing affirmatively and confidently which <lb></lb>contradicteth the manifeſt Experiments and Reaſons of Philoſo<lb></lb>phy, or other Sciences. </s> <s>For ſince all Truth is agreeable to Truth, <lb></lb>the Truth of Holy Writ cannot be contrary to the ſolid Reaſons <lb></lb>and Experiments of Humane Learning.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg828"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg827"></margin.target><emph type="italics"></emph>(e) Illud etiam <lb></lb>diligenter caven<lb></lb>dum, & emnino <lb></lb>fugiendum eſt, ne <lb></lb>in tractanda<emph.end type="italics"></emph.end> Mo<lb></lb>ſis <emph type="italics"></emph>Dectrina, quic<lb></lb>quam affirmate & <lb></lb>aſſeveranter ſen<lb></lb>tiamus & dica<lb></lb>mus, quod repug<lb></lb>net manifeſtis ex<lb></lb>perimentis & rationibus Philoſophiæ, vel aliarum Diſciplinarum. </s> <s>Namque cum Verum omne ſemper cum Vero <lb></lb>congruat, non poteſt Verit as Sacrarum Litterarum, Veris Rationibus & Experimentis Humanarum Doctrina<lb></lb>rum eſſe contraria.<emph.end type="italics"></emph.end> Perk. in Gen. circa Principium.</s></p><p type="margin"> <s><margin.target id="marg828"></margin.target><emph type="italics"></emph>(f) Si manife<lb></lb>ſtæ certæque Rati<lb></lb>oni, velut ſancta<lb></lb>rum Litterarum <lb></lb>objicitur autori<lb></lb>ritas, non intelli<lb></lb>git, qui hoc facit; <lb></lb>& non Scripturæ <lb></lb>ſenſum (ad quem <lb></lb>penetrare non po<lb></lb>tuit) ſed ſuum po<lb></lb>tius objicit verita<lb></lb>ti: nec id quod in <lb></lb>sa, ſed quod in ſe<lb></lb>ipſo velue pro ea<lb></lb>invenit, opponit.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And in St. <emph type="italics"></emph>Auguſtine<emph.end type="italics"></emph.end> we read: <emph type="italics"></emph>(f) If any one ſhall object <lb></lb>the Authority of Sacred Writ, againſt clear and manifeſt Reaſon, <lb></lb>he that doth ſo, knows not what he undertakes: For he objects<emph.end type="italics"></emph.end><pb xlink:href="040/01/461.jpg" pagenum="437"></pb><emph type="italics"></emph>againſt the Truth, not the ſenſe of the Scripture (which is be<lb></lb>yond his comprehenſion) but rather his own; not what is in it, but <lb></lb>what, finding it in himſelf, he fancyed to be in it.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>This granted, and it being true, (as hath been ſaid) that two <lb></lb>Truths cannot be contrary to each other, it is the office of a <lb></lb>Judicious Expoſitor to ſtudy to finde the true Senſes of Sacred <lb></lb>Texts, which undoubtedly ſhall accord with thoſe Natural Con<lb></lb>cluſions, of which manifeſt Senſe and Neceſſary Demonſtrations </s></p><p type="main"> <s><arrow.to.target n="marg829"></arrow.to.target><lb></lb>had before made us ſure and certain. </s> <s>Yea, in regard that the <lb></lb>Scriptures (as hath been ſaid) for the Reaſons alledged, admit in <lb></lb>many places Expoſitions far from the Senſe of the words; and <lb></lb>moreover, we not being able to affirm, that all Interpreters <lb></lb>ſpeak by Divine Inſpiration; For (if it were ſo) then there <lb></lb>would be no difference between them about the Senſes of the <lb></lb>ſame places; I ſhould think that it would be an act of great pru<lb></lb>dence to make it unlawful for any one to uſurp Texts of Scri<lb></lb>pture, and as it were to force them to maintain this or that Natu<lb></lb>rall Concluſion for truth, of which Sence, & Demonſtrative, and <lb></lb>neceſſary Reaſons may one time or other aſſure us the contrary. <lb></lb></s> <s>For who will preſcribe bounds to the Wits of men? </s> <s>Who will <lb></lb>aſſert that all that is ſenſible and knowable in the World is al<lb></lb>ready diſcovered and known? </s> <s>Will not they that in other points <lb></lb>diſagree with us, confeſs this (and it is a great truth) that <emph type="italics"></emph>Ea <lb></lb>quæ ſcimus, ſint minima pars eorum quæ ignoramus<emph.end type="italics"></emph.end>? </s> <s>That thoſe <lb></lb>Truths which we know, are very few, in compariſon of thoſe <lb></lb>which we know not? </s> <s>Nay more, if we have it from the Mouth <lb></lb><arrow.to.target n="marg830"></arrow.to.target><lb></lb>of the Holy Ghoſt, that <emph type="italics"></emph>Deus tradidit Mundum diſputationi <lb></lb>eorum, ut non inveniat homo opus, quod operatus eſt Deus ab <lb></lb>initio ad finem:<emph.end type="italics"></emph.end> One ought not, as I conceive, to ſtop the way <lb></lb>to free Philoſophating, touching the things of the World, and of <lb></lb>Nature, as if that they were already certainly found, and all ma<lb></lb>nifeſt: nor ought it to be counted raſhneſs, if one do not fit <lb></lb>down ſatisfied with the opinions now become as it were com<lb></lb>mune; nor ought any perſons to be diſpleaſed, if others do not <lb></lb>hold, in natural Diſputes to that opinion which beſt pleaſeth <lb></lb>them; and eſpecially touching Problems that have, for thouſands <lb></lb>of years, been controverted amongſt the greateſt Philoſophers, as is <lb></lb>the Stability of the Sun, and Mobility of the Earth, an opinion <lb></lb>held by <emph type="italics"></emph>Pythagoras,<emph.end type="italics"></emph.end> and by his whole Sect; by <emph type="italics"></emph>Heraclides Pon<lb></lb>ticus,<emph.end type="italics"></emph.end> who was of the ſame opininion; by <emph type="italics"></emph>Phylolaus,<emph.end type="italics"></emph.end> the Maſter <lb></lb>of <emph type="italics"></emph>Plato<emph.end type="italics"></emph.end>; and by <emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> himſelf, as <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> relateth, and of <lb></lb>which <emph type="italics"></emph>Plutarch<emph.end type="italics"></emph.end> writeth in the life of <emph type="italics"></emph>Numa,<emph.end type="italics"></emph.end> that the ſaid <emph type="italics"></emph>Plato,<emph.end type="italics"></emph.end><lb></lb>when he was grown old, ſaid, It is a moſt abſurd thing to think <lb></lb>otherwiſe: The ſame was believed by <emph type="italics"></emph>Ariſtarchus Samius,<emph.end type="italics"></emph.end> as <lb></lb>we have it in <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end>; and probably by <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> him<pb xlink:href="040/01/462.jpg" pagenum="438"></pb>ſelf; by <emph type="italics"></emph>Nicetas<emph.end type="italics"></emph.end> the Philoſopher, upon the teſtimony of <emph type="italics"></emph>Scicero,<emph.end type="italics"></emph.end><lb></lb>and by many others. </s> <s>And this opinion hath, finally, been am<lb></lb>plified, and with many Obſervations and Demonſtrations con<lb></lb>firmed by <emph type="italics"></emph>Nicholaus Copernicus.<emph.end type="italics"></emph.end> And <emph type="italics"></emph>Seneca,<emph.end type="italics"></emph.end> a moſt eminent <lb></lb>Philoſopher, in his Book <emph type="italics"></emph>De Cometis,<emph.end type="italics"></emph.end> advertizeth us that we <lb></lb>ought, with great diligence, ſeek for an aſſured knowledge, <lb></lb>whether it be Heaven, or the Earth, in which the Diurnal Con<lb></lb>verſion reſides.</s></p><p type="margin"> <s><margin.target id="marg829"></margin.target>Epiſt. </s> <s>7. ad Mar<lb></lb>cellinum.</s></p><p type="margin"> <s><margin.target id="marg830"></margin.target>Eccleſiaſt. </s> <s>cap. 3.</s></p><p type="main"> <s>And for this cauſe, it would probably be prudent and proſi<lb></lb>table counſel, if beſides the Articles which concern our Salvati<lb></lb>on, and the eſtabliſhment of our Faith (againſt the ſtability of <lb></lb>which there is no fear that any valid and ſolid Doctrine can e<lb></lb>ver riſe up) men would not aggregate and heap up more, with<lb></lb>out neceſſity: And if it be ſo, it would certainly be a prepoſte<lb></lb>rous thing to introduce ſuch Articles at the requeſt of perſons <lb></lb>who, beſides that we know not that they ſpeak by inſpiration <lb></lb>of Divine Grace, we plainly ſee that there might be wiſhed in <lb></lb>them the underſtanding which would be neceſſary firſt to enable <lb></lb>them to comprehend, and then to diſcuſs the Demonſtrations <lb></lb>wherewith the ſubtiler Sciences proceed in confirming ſuch like <lb></lb>Concluſions. </s> <s>Nay, more I ſhould ſay, (were it lawful to ſpeak <lb></lb>my judgment freely on this Argument) that it would haply <lb></lb>more ſuit with the <emph type="italics"></emph>Decorum<emph.end type="italics"></emph.end> and Majeſty of thoſe Sacred Vo<lb></lb>lumes, if care were taken that every ſhallow and vulgar Writer <lb></lb>might not authorize his Books (which are not ſeldome grounded <lb></lb>upon fooliſh fancies) by inſerting into them Places of Holy Scri<lb></lb>pture, interpreted, or rather diſtorted to Senſes as remote from <lb></lb>the right meaning of the ſaid Scripture, as they are neer to deri<lb></lb>riſion, who not without oſtentation flouriſh out their Writings <lb></lb>therewith. </s> <s>Examples of ſuch like abuſes there might many be <lb></lb>produced, but for this time I will confine my ſelf to two, not <lb></lb>much beſides theſe matters of <emph type="italics"></emph>Aſtronomy:<emph.end type="italics"></emph.end> One of which, is that <lb></lb>of thoſe Pamphlets which were publiſhed againſt the <emph type="italics"></emph>Medicean<emph.end type="italics"></emph.end><lb></lb>Planets, of which I had the fortune to make the diſcovery; a<lb></lb>gainſt the exiſtence of which there were brought many places of <lb></lb>Sacred Sctipture: Now, that all the World ſeeth them to be <lb></lb>Planets, I would gladly hear with what new interpretations <lb></lb>thoſe very Antagoniſts do expound the Scripture, and excuſe their <lb></lb>own ſimplicity. </s> <s>The other example is of him who but very <lb></lb>lately hath Printed againſt <emph type="italics"></emph>Aſtronomers<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Philoſophers,<emph.end type="italics"></emph.end> that <lb></lb>the Moon doth not receive its light from the Sun, but is of its own <lb></lb>nature reſplendent: which imagination he in the cloſe confirm<lb></lb>eth, or, to ſay better, perſwadeth himſelf that he confirmeth by <lb></lb>ſundry Texts of Scripture, which he thinks cannot be reconciled <lb></lb>unleſſe his opinion ſhould be true and neceſſary. </s> <s>Nevertheleſſe, <pb xlink:href="040/01/463.jpg" pagenum="439"></pb>the Moon of it ſelf is Tenebroſe, and yet it is no leſſe lucid than <lb></lb>the Splendor of the Sun.</s></p><p type="main"> <s>Hence it is manifeſt, that theſe kinde of Authors, in regard they <lb></lb>did not dive into the true Sence of the Scriptures, would (in caſe <lb></lb>their authority were of any great moment) have impoſed a neceſ<lb></lb>ſity upon others to believe ſuch Concluſions for true as were re<lb></lb>pugnant to manifeſt Reaſon, and to Senſe. </s> <s>Which abuſe <emph type="italics"></emph>Deus <lb></lb>avertat,<emph.end type="italics"></emph.end> that it do not gain Countenance and Authority; for if it <lb></lb>ſhould, it would in a ſhort time be neceſſary to proſcribe and in<lb></lb>hibit all the Contemplative Sciences. </s> <s>For being that by nature <lb></lb>the number of ſuch as are very unapt to underſtand perfectly <lb></lb>both the Sacred Scriptures, and the other Sciences is much great<lb></lb>er than that of the skilfull and intelligene; thoſe of the firſt ſort <lb></lb>ſuperficially running over the Scriptures, would arrogate to them<lb></lb>ſelves an Authority of decreeing upon all the Queſtions in Na<lb></lb>ture, by vertue of ſome Word by them miſonderſtood, and pro<lb></lb>duced by the Sacred Pen-men to another purpoſe: Nor would <lb></lb>the ſmall number of the Intelligent be able to repreſs the furious <lb></lb>Torrent of thoſe men, who would finde ſo many the more fol<lb></lb>lowers, in that the gaining the reputation of Wiſe men without <lb></lb>pains or Study, is far more grateful to humane Nature, than the <lb></lb>conſuming our ſelves with reſtleſs contemplations about the moſt <lb></lb>painfull Arts. </s> <s>Therefore we ought to return infinite thanks to <lb></lb>Almighty God, who of his Goodneſs freeth us from this fear, in <lb></lb>that he depriveth ſuch kinde of perſons of all Authority and, re<lb></lb>poſeth the Conſulting, Reſolving, and Decreeing upon ſo im<lb></lb>portant Determinations in the extraordinary Wiſdom and Can<lb></lb>dor of moſt Sacred Fathers; and in the Supream Authority of <lb></lb>thoſe, who being guided by his Holy Spirit, cannot but determin <lb></lb>Holily: So ordering things, that of the levity of thoſe other men, <lb></lb>there is no account made. </s> <s>This kinde of men are thoſe, as I be<lb></lb>lieve, againſt whom, not without Reaſon, Grave, and Holy Wri<lb></lb>ters do ſo much inveigh; and of whom in particular S. <emph type="italics"></emph>Hierom<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg831"></arrow.to.target><lb></lb>writeth: <emph type="italics"></emph>(g) This<emph.end type="italics"></emph.end> (Scilicet <emph type="italics"></emph>the Sacred Scripture) the talking <lb></lb>old woman, the doting old man, the talkative Sophiſter, all venture <lb></lb>upon, lacerate, teach, and that before they have learnt it. </s> <s>Others <lb></lb>induced by Pride, diving into hard words, Philoſophate amongſt <lb></lb>Women, touching the Holy Scriptures. </s> <s>Others (Oh ſhame<lb></lb>ful!) Learn of Women what they teach to Men; and, as if this <lb></lb>were nothiug, in a certain facility of words, I may ſay of confi<lb></lb>dence, expound to others what they underſtand not themſelves. </s> <s>I <lb></lb>forbear to ſpeak of thoſe of my own Profeſſion, who, if after Hu<lb></lb>mane Learning they chance to attain to the Holy Scriptures, and <lb></lb>tickle the ears of the people with affected and Studied expreſſions, <lb></lb>they affirm that all they ſay, is to be entertained as the Law of God<emph.end type="italics"></emph.end>; <pb xlink:href="040/01/464.jpg" pagenum="440"></pb><emph type="italics"></emph>and not ſtooping to learn what the Prophets and Apoſtles held, <lb></lb>they force incongruous teſtimonies to their own Senſe: As if it <lb></lb>were the genuine, and not corrupt way of teaching to deprave Sen<lb></lb>tences, and Wreſt the Scripture according to their own ſingular and <lb></lb>contradictory humour.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg831"></margin.target><emph type="italics"></emph>(g) Hanc (Sci<lb></lb>licer Sacram Scri<lb></lb>pturam) garrula <lb></lb>arus, hanc deli<lb></lb>rus ſenex hanc So<lb></lb>phiſta verboſus, <lb></lb>h<gap></gap> univerſi præ<lb></lb>ſumunt, lacerant, <lb></lb>docent, anteguans <lb></lb>diſcant. </s> <s>Alij, <lb></lb>addacto ſupercilio, <lb></lb>grandia verba <lb></lb>trutinantes, inter <lb></lb>mulierculas, de <lb></lb>Sacris Litteris <lb></lb>Philoſophantur. <lb></lb></s> <s>Alij diſcunt, prob <lb></lb>pudor! à fæminis, <lb></lb>quod viros docent, <lb></lb>& ne parum hoc <lb></lb>ſit, quadam faci<lb></lb>litate verborum, <lb></lb>imo audaciâ, ediſ<lb></lb>ſerunt aliis, quod <lb></lb>ipſi non intelli<lb></lb>gunt. </s> <s>Taceo de <lb></lb>mei ſimilibus, qui <lb></lb>ſi fortè ad Scriptu<lb></lb>ras Sanctas, poſt <lb></lb>ſeculares litteras <lb></lb>venerint, & ſer<lb></lb>mone compoſito, <lb></lb>aurem populi mul<lb></lb>ſerint; quicquid <lb></lb>dixerint, hoc le<lb></lb>gem Dei putant: <lb></lb>nec ſcire dignan<lb></lb>tur, quid Prophe<lb></lb>tæ, quid Apoſtoli <lb></lb>ſenſerint, ſed ad <lb></lb>ſenſum ſuum, in<lb></lb>congrua aptant te<lb></lb>ſtimonia: Quaſi <lb></lb>grande ſit, & non <lb></lb>vitiociſſimum do<lb></lb>cendi genus, de<lb></lb>pravare ſententi<lb></lb>as, & ad volun<lb></lb>tatem ſuam Scri<lb></lb>pturamtrahere re<lb></lb>pugnantem.<emph.end type="italics"></emph.end> Je<lb></lb>ron. </s> <s>Epiſt. </s> <s>ad <lb></lb><emph type="italics"></emph>Paul.<emph.end type="italics"></emph.end> 103.</s></p><p type="main"> <s>I will not rank among theſe ſame ſecular Writers any <emph type="italics"></emph>Theo<lb></lb>logiſts,<emph.end type="italics"></emph.end> whom I repute to be men of profound Learning, and ſo<lb></lb>ber Manners, and therefore hold them in great eſteem and vene<lb></lb>ration: Yet I cannot deny but that I have a certain ſcruple in <lb></lb>my mind, and conſequently am deſirous to have it removed, <lb></lb>whilſt I hear that they pretend to a power of conſtraining others <lb></lb>by Authority of the Scriptures to follow that opinion in Natu<lb></lb>ral Diſputations, which they think moſt agreeth with the Texts <lb></lb>of that: Holding withall, that they are not bound to anſwer <lb></lb>the Reaſons and Experiments on the contrary: In Explication <lb></lb>and Confirmation of which their judgement they ſay, That <emph type="italics"></emph>The<lb></lb>ologie<emph.end type="italics"></emph.end> being the Queen of all the Sciences, ſhe ought not upon <lb></lb>any account to ſtoop to accomodate her ſelf to the Poſitions of <lb></lb>the reſt, leſs worthy, and inferior to her: But that they ought <lb></lb>to refer themſelves to her (as to their Supream Empereſs) and <lb></lb>change and alter their Concluſions, according to <emph type="italics"></emph>Theological<emph.end type="italics"></emph.end><lb></lb>Statutes and Decrees. </s> <s>And they further add, That if in the <lb></lb>inferior Science there ſhould be any Concluſion certain by ver<lb></lb>tue of Demonſtrations or experiments, to which there is found <lb></lb>in Scripture another Concluſion repugnant; the very Profeſſors <lb></lb>of that Science ought of themſelves to reſolve their Demonſtrati<lb></lb>ons, and diſcover the falacies of their own Experiments, without <lb></lb>repairing to Theologers and Textuaries, it not ſuiting (as hath <lb></lb>been ſaid) with the dignity of <emph type="italics"></emph>Theologie<emph.end type="italics"></emph.end> to ſtoop to the inveſtiga<lb></lb>tion of the falacies of the inferior Sciences: But it ſufficeth her, <lb></lb>to determine the truth of the Concluſion with her abſolute Au<lb></lb>thority, and by her infallibility. </s> <s>And then the Natural Conclu<lb></lb>ſions in which they ſay that we ought to bide by the meer Au<lb></lb>thority of the Scripture, without gloſſing, or expounding it to <lb></lb>Senſes different from the Words, they affirm to be Thoſe of <lb></lb>which the Scripture ſpeaketh alwaies in the ſame manner; and <lb></lb>the Holy Fathers all receive, and expound to the ſame <lb></lb>Senſe.</s></p><p type="main"> <s>Now as to theſe Determinations, I have had occaſion to conſi<lb></lb>der ſome particulars (which I will purpoſe) for that I was made <lb></lb>cautious thereof, by thoſe who underſtand more than I in theſe <lb></lb>buſineſſes, and to whoſe judgments I alwaies ſubmit my ſelf. <lb></lb></s> <s>And firſt I could ſay, that there might poſſibly a certain kinde of <lb></lb>equivocation interpoſe, in that they do not diſtinguiſh the prehe<lb></lb>minences whereby Sacred <emph type="italics"></emph>Theologie<emph.end type="italics"></emph.end> meriteth the Title of Queen. <pb xlink:href="040/01/465.jpg" pagenum="441"></pb>For it might be called ſo, either becauſe that that which is taught <lb></lb>by all the other Sciences, is found to be comprized and demonſtra<lb></lb>ted in it, but with more excellent means, and with more ſublime <lb></lb>Learning; in like manner, as for example; The Rules of meaſuring <lb></lb>of Land, & of Accountantſhip are much more excellently contain<lb></lb>ed in the Arithmatick and Geometry of <emph type="italics"></emph>Euclid,<emph.end type="italics"></emph.end> than in the Practi<lb></lb>ſes of Surveyours and Accomptants: Or becauſe the Subject about <lb></lb>which <emph type="italics"></emph>Theologie<emph.end type="italics"></emph.end> is converſant, excelleth in Dignity all the other <lb></lb>Subjects, that are the Matters of other Sciences: As alſo becauſe <lb></lb>its Documents are divulged by nobler waies. </s> <s>That the Title <lb></lb>and Authority of Queen belongeth to <emph type="italics"></emph>Theologie<emph.end type="italics"></emph.end> in the firſt <lb></lb>Senſe, I think that no Theologers will affirm, that have but any <lb></lb>in-ſight into the other Sciences; of which there are none (as I be<lb></lb>lieve) that will ſay that Geometry, Aſtronomy Muſick, and Me<lb></lb>dicine are much more excellently and exactly contained in the <lb></lb>Sacred Volumes, than in the Books of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Ptolomy,<emph.end type="italics"></emph.end> in <lb></lb><emph type="italics"></emph>Boetius,<emph.end type="italics"></emph.end> and in <emph type="italics"></emph>Galen.<emph.end type="italics"></emph.end> Therefore it is probable that the Regal <lb></lb>Preheminence is given her upon the ſecond account, namely, By <lb></lb>reaſon of the Subject, and the admirable communicating of the <lb></lb>Divine Revelations in thoſe Concluſions which by other means <lb></lb>could not be conceived by men, and which chiefly concern the <lb></lb>acquiſt of eternal Beatitude. </s> <s>Now if <emph type="italics"></emph>Theologie<emph.end type="italics"></emph.end> being conver<lb></lb>ſant about the loftieſt Divine Contemplation, and reſiding for <lb></lb>Dignity in the Regal Throne of the Sciences, (whereby ſhe be<lb></lb>cometh of higheſt Authority) deſcendeth not to the more mean <lb></lb>and humble Speculations of the inferior Sciences: Nay; (as hath <lb></lb>been declared above) hath no regard to them, as not concerning <lb></lb>Bearitude; the Profeſſors thereof ought not to arrogate to them<lb></lb>ſelves the Authority to determin of Controverſies in thoſe Pro<lb></lb>feſſions which have been neither practiſed nor ſtudied by them. <lb></lb></s> <s>For this would be as if an Abſolute Prince, knowing that he <lb></lb>might freely command, and cauſe himſelf to be obeyed, ſhould <lb></lb>(being neither Phiſitian nor Architect) undertake to adminiſter <lb></lb>Medicines, and erect Buildings after his own faſhion, to the great <lb></lb>endangering af the lives of the poor Patients, and to the manifeſt <lb></lb>deſtruction of the Edifices.</s></p><p type="main"> <s>Again, to command the very Profeſſors of <emph type="italics"></emph>Aſtronomy,<emph.end type="italics"></emph.end> that <lb></lb>they of themſelves ſee to the confuting of their own Obſerva<lb></lb>tions and Demonſtrations, as thoſe that can be no other but <lb></lb>Falacies and Sophiſmes, is to enjoyn a thing beyond all poſſibi<lb></lb>lity of doing: For it is not onely to command them that they do <lb></lb>not ſee that which they ſee, and that they do not underſtand <lb></lb>that which they underſtand; but that in ſeeking, they finde the <lb></lb>contrary of that which they happen to meet with. </s> <s>Therefore be<lb></lb>fore that this is to be done, it would be neceſſary that they were <pb xlink:href="040/01/466.jpg" pagenum="442"></pb>ſhewed the way how to make the Powers of the Soul to command <lb></lb>one another, and the inferior the Superior; ſo that the imaginati<lb></lb>on and will might, and ſhould believe contrary to what the Intel<lb></lb>lect underſtands: I ſtill mean in Propoſitions purely Natural, and <lb></lb>which are not <emph type="italics"></emph>de Fide,<emph.end type="italics"></emph.end> and not in the Supernatural, which are <lb></lb><emph type="italics"></emph>de Fide.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>I would entreat theſe Wiſe and Prudent Fathers, that they <lb></lb>would withal diligence conſider the difference that is between <lb></lb>Opinable and Demonſtrative Doctrines: To the end, that well <lb></lb>weighing in their minds with what force Neceſſary Illations ob<lb></lb>lige, they might the better aſcertain themſelves, that it is not in <lb></lb>the Power of the Profeſſors of Demonſtrative Sciences to change <lb></lb>their Opinions at pleaſure, and apply themſelves one while to <lb></lb>one ſide, and another while to another; and that there is a great <lb></lb>difference between commanding a Methametitian or a Philoſo<lb></lb>pher, and the diſpoſing of a Lawyer or a Merchant; and that the <lb></lb>demonſtrated Concluſions touching the things of Nature and of <lb></lb>the Heavens cannot be changed with the ſame facility, as the <lb></lb>Opinions are touching what is lawful or not in a Contract, Bar<lb></lb>gain, or Bill of Exchange. </s> <s>This difference was well underſtood <lb></lb>by the Learned and Holy Fathers, as their having been at great <lb></lb>pains to confute many Arguments, or to ſay better, many Phi<lb></lb><arrow.to.target n="marg832"></arrow.to.target><lb></lb>loſophical Fallacies, doth prove unto us; and as may expreſly be <lb></lb>read in ſome of them, and particularly we have in S. <emph type="italics"></emph>Auguſtine<emph.end type="italics"></emph.end><lb></lb>the following words: <emph type="italics"></emph>(g) This is to be held for an undoubt<lb></lb>ed Truth, That we may be confident, that whatever the Sages of <lb></lb>this World have demonſtrated touching Natural Points, is no waies <lb></lb>contrary to our Bibles: And in caſe they teach any thing in their <lb></lb>Books that is contrary to the Holy Scriptures, we may without any <lb></lb>ſcruple conclude it to be moſt falſe; And aceording to our ability <lb></lb>let us make the ſame appear: And let us ſo keep the Faith of our <lb></lb>Lord, in whom are hidden all the Treaſures of Wiſdom; that we <lb></lb>be neither ſeduced with the Loquacity of falſe Philoſophy, nor <lb></lb>ſcared by the ſuperſtition of a counterfeit Religion.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg832"></margin.target><emph type="italics"></emph>(g) Hoc indu<lb></lb>bitanter tenendum <lb></lb>eſt, ut quicquid <lb></lb>Sapientes hujus <lb></lb>Mundi, de Natu<lb></lb>ra rerum veraci<lb></lb>ter demonſtrare <lb></lb>potuerint, oſtenda<lb></lb>mus, noſtris libris <lb></lb>non eſſe contrari<lb></lb>um: quicquid au<lb></lb>tem illi, in ſuis vo<lb></lb>lumintbus, contra<lb></lb>rium Sacris Lit<lb></lb>teris docent, ſine <lb></lb>ulla dubitatione <lb></lb>credamus, id falſiſ<lb></lb>ſimum eſſe, & quo<lb></lb>quo modo poſſu<lb></lb>mus, etiam oſten<lb></lb>damus; atque it a <lb></lb>teneamus Fidem <lb></lb>Domini noſtri, in <lb></lb>quaſunt abſconditi <lb></lb>omnes theſauri <lb></lb>Sapientiæ, ut ne<lb></lb>que falſæ Philoſo<lb></lb>phiæ loquacitate <lb></lb>ſeducamur, neque <lb></lb>ſimulata Religio<lb></lb>nis ſuperſtitione <lb></lb>terreamur.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>From which words, I conceive that I may collect this Do<lb></lb>ctrine, namely, That in the Books of the Wiſe of this World, <lb></lb>there are contained ſome Natural truths that are ſolidly demon<lb></lb>ſtrated, and others again that are barely taught; and that as to <lb></lb>the firſt ſort, it is the Office of wiſe Divines to ſhew that they <lb></lb>are not contrary to the Sacred Scriptures; As to the reſt, taught, <lb></lb>but not neceſſarily demonſtrated, if they ſhall contain any thing <lb></lb>contrary to the Sacred Leaves, it ought to be held undoubtedly <lb></lb>falſe, and ſuch it ought by all poſſible waies to be demon<lb></lb>ſtrated.<lb></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></lb><emph type="italics"></emph>lib<emph.end type="italics"></emph.end> I. Cap. 25.</s></p><p type="main"> <s>If therefore Natural Concluſions veritably demonſtrated, are <pb xlink:href="040/01/467.jpg" pagenum="443"></pb>not to be poſtpoſed to the Places of Scripture, but that it ought <lb></lb>to be ſhewn how thoſe Places do not interfer with the ſaid Con<lb></lb>cluſions; then its neceſſary before a Phyſical Propoſition be <lb></lb>condemned, to ſhew that it is not neceſſarily demonſtrated; and <lb></lb>this is to be done not by them who hold it to be true, but by thoſe <lb></lb>who judge it to be falſe. </s> <s>And this ſeemeth very reaſonable, <lb></lb>and agreeable to Nature; that is to ſay, that they may much <lb></lb>more eaſily find the fallacies in a Diſcourſe, who believe it to be <lb></lb>falſe, than thoſe who account it true and concludent. </s> <s>Nay, in <lb></lb>this particular it will come to paſſe, that the followers of this o<lb></lb>pinion, the more that they ſhall turn over Books, examine the <lb></lb>Arguments, repeat the Obſervations, and compare the Experi<lb></lb>ments, the more ſhall they be confirmed in this belief. </s> <s>And your <lb></lb>Highneſs knoweth what happened to the late Mathematick Pro<lb></lb>feſſor in the Univerſity of <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> Who betook himſelf in his old <lb></lb>age to look into the Doctrine of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> with hope that he <lb></lb>might be able ſolidly to confute it (for that he held it ſo far to <lb></lb>be falſe, as that he had never ſtudied it) but it was his fortune, <lb></lb>that as ſoon as he had underſtood the grounds, proceedings, and <lb></lb>demonſtrations of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> he found himſelf to be perſwaded, <lb></lb>and of an oppoſer became his moſt confident Defender. </s> <s>I <lb></lb>might alſo nominate other ^{*} Mathematicians, who being moved </s></p><p type="main"> <s><arrow.to.target n="marg834"></arrow.to.target><lb></lb>by my laſt Diſcoveries, have confeſſed it neceſsary to change the <lb></lb>formerly received Conſtitution of the World, it not being able <lb></lb>by any means to ſubſiſt any longer.</s></p><p type="margin"> <s><margin.target id="marg834"></margin.target>* P. </s> <s>Clavius the <lb></lb>Jeſuite.</s></p><p type="main"> <s>If for the baniſhing this Opinion and Hypotheſis out of the <lb></lb>World, it were enough to ſtop the mouth of one alone, as it <lb></lb>may be they perſwade themſelves who meaſuring others judge<lb></lb>ments by their own, think it impoſſible that this Doctrine ſhould <lb></lb>be able to ſubſiſt and finde any followers, this would be very ea<lb></lb>ſie to be done, but the buſineſs ſtandeth otherwiſe: For to <lb></lb>execute ſuch a determination, it would be neceſſary to prohibite <lb></lb>not onely the Book of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> and the Writings of the o<lb></lb>ther Authors that follow the ſame opinion, but to interdict the <lb></lb>whole Science of <emph type="italics"></emph>Aſtronomy<emph.end type="italics"></emph.end>; and which is more, to forbid men <lb></lb>looking towards Heaven, that ſo they might not ſee <emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> and <lb></lb><emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> at one time neer to the Earth, and at another farther off, <lb></lb>with ſuch a difference that the latter is found to be fourty times, <lb></lb>and the former ſixty times bigger in ſurface at one time than at <lb></lb>another; and to the end, that the ſame <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> might not be <lb></lb>diſcovered to be one while round, and another while forked, with <lb></lb>moſt ſubtil hornes: and many other ſenſible Obſervations which <lb></lb>can never by any means be reconciled to the <emph type="italics"></emph>Ptolomaick<emph.end type="italics"></emph.end> Syſteme, <lb></lb>but are unanſwerable Arguments for the <emph type="italics"></emph>Copernican.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>But the prohibiting of <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> his Book, now that by many <pb xlink:href="040/01/468.jpg" pagenum="444"></pb>new Obſervations, and by the application of many of the Lear<lb></lb>ned to the reading of him, his Hypotheſis and Doctrine doth <lb></lb>every day appear to be more true, having admitted and tolerated <lb></lb>it for ſo many years, whilſt he was leſſe followed, ſtudied, and <lb></lb>confirmed, would ſeem, in my judgment, an affront to Truth, <lb></lb>and a ſeeking the more to obſcure and ſuppreſſe her, the more <lb></lb>ſhe ſheweth her ſelf clear and perſpicuous.</s></p><p type="main"> <s>The aboliſhing and cenſuring, not of the whole Book, but <lb></lb>onely ſo much of it as concerns this particular opinion of the <lb></lb><emph type="italics"></emph>Earths Mobility,<emph.end type="italics"></emph.end> would, if I miſtake not, be a greater detriment <lb></lb>to ſouls, it being an occaſion of great ſcandal, to ſee a Poſition <lb></lb>proved, and to ſee it afterwards made an Hereſie to believe it.</s></p><p type="main"> <s>The prohibiting of the whole Science, what other would it <lb></lb>be but an open contempt of an hundred Texts of the Holy Scri<lb></lb>ptures, which teach us, That the Glory, and the Greatneſſe of <lb></lb>Almighty God is admirably diſcerned in all his Works, and di<lb></lb>vinely read in the Open Book of Heaven? </s> <s>Nor let any one <lb></lb>think that the Lecture of the lofty conceits that are written in <lb></lb>thoſe Leaves finiſh in only beholding the Splendour of the Sun, <lb></lb>and of the Stars, and their riſing and ſetting, (which is the term <lb></lb>to which the eyes of bruits and of the vulgar reach) but there <lb></lb>are couched in them myſteries ſo profound, and conceipts ſo ſub<lb></lb>lime, that the vigils, labours, and ſtudies of an hundred and an <lb></lb>hundred acute Wits, have not yet been able thorowly to dive <lb></lb>into them after the continual diſquiſition of ſome thouſands of <lb></lb>years. </s> <s>But let the Unlearned believe, that like as that which <lb></lb>their eyes diſcern in beholding the aſpect of a humane body, is <lb></lb>very little in compariſon of the ſtupendious Artifices, which an <lb></lb>exquiſite and curious Anatomiſt or Philoſopher finds in the ſame <lb></lb>when he is ſearching for the uſe of ſo many Muſcles, Tendons, <lb></lb>Nerves, and Bones; and examining the Offices of the Heart, <lb></lb>and of the other principal Members, ſeeking the ſeat of the vi<lb></lb>tal Faculties, noting and obſerving the admirable ſtructures of <lb></lb>the Inſtruments of the Senſes, and, without ever making an end <lb></lb>of ſatisfying his curioſity and wonder, contemplating the Re<lb></lb>ceptacles of the Imagination, of the Memory, and of the Un<lb></lb>derſtanding; So that which repreſents it ſelf to the meer ſight, <lb></lb>is as nothing in compariſon and proportion to the ſtrange Won<lb></lb>ders, that by help of long and accurate Obſervations the Wit <lb></lb>of Learned Men diſcovereth in Heaven. </s> <s>And this is the ſub<lb></lb>ſtance of what I had to conſider touching this particular.</s></p><p type="main"> <s>In the next place, as to thoſe that adde, That thoſe Natural <lb></lb>Propoſitions of which the Scripture ſtill ſpeaks in one conſtant <lb></lb>tenour, and which the Fathers all unanimouſly receive in the <lb></lb>ſame ſenſe, ought to be accepted according to the naked and <pb xlink:href="040/01/469.jpg" pagenum="445"></pb>literal ſenſe of the Words, without gloſſes and interpretations; <lb></lb>and received and held for moſt certain and true; and that con<lb></lb>ſequently the Mobility of the Sun, and Stability of the Earth, <lb></lb>as being ſuch, are <emph type="italics"></emph>de Fide<emph.end type="italics"></emph.end> to be held for true, and the contrary <lb></lb>opinion to be deemed Heretical: I ſhall propoſe to conſidera<lb></lb>tion, in the firſt place, That of Natural Propoſitions, ſome there <lb></lb>are, of which all humane Science and Diſcourſe can furniſh us <lb></lb>only with ſome plauſible opinion, and probable conjecture ra<lb></lb>ther than with any certain and demonſtrative knowledge; as for <lb></lb>example, whether the Stars be animated: Others there are, of <lb></lb>which we have, or may confidently believe that we may have, <lb></lb>by Experiments, long Obſervations, and Neceſſary Demonſtra<lb></lb>tions an undubitable aſſurance; as for inſtance, whether the <lb></lb>Earth and Heavens move, or not; whether the Heavens are <lb></lb>Spherical, or otherwiſe. </s> <s>As to the firſt ſort, I doubt not in the <lb></lb>leaſt, that if humane Ratiocinations cannot reach them, and <lb></lb>that conſequently there is no Science to be had of them, but on<lb></lb>ly an Opinion or Belief, we ought fully and abſolutely to com<lb></lb>ply with the meer Verbal Senſe of the Scripture: But as to the <lb></lb>other Poſitions, I ſhould think (as hath been ſaid above) That <lb></lb>we are firſt to aſcertain our ſelves of the fact it ſelf, which will <lb></lb>aſſiſt us in finding out the true ſenſes of the Scriptures; which <lb></lb>ſhall moſt certainly be found to accord with the fact demonſtra<lb></lb>ted, for two truths can never contradict each other. </s> <s>And <lb></lb>this I take to be a Doctrine orthodox and undoubted, for that I <lb></lb>ſinde it written in Saint <emph type="italics"></emph>Auguſtine,<emph.end type="italics"></emph.end> who ſpeaking to our point <lb></lb>of the Figure of Heaven, and what it is to be believed to be, in <lb></lb>regard that which Aſtronomers affirm concerning it ſeemeth to <lb></lb>be, contrary to the Scripture, (they holding it to be rotund, <lb></lb>and the Scripture calling it as it were a ^{*} Curtain, determi<lb></lb><arrow.to.target n="marg835"></arrow.to.target><lb></lb>neth that we are not at all to regard that the Scripture contra<lb></lb>dicts Aſtronomers; but to believe its Authority, if that which <lb></lb>they ſay ſhall be falſe, and founded, only on the conjectures of <lb></lb>humane infirmity: but if that which which they affirm be pro<lb></lb>ved by indubitable Reaſons, this Holy Father doth not ſay, <lb></lb>that the Aſtronomers are to be enjoyned, that they themſelves <lb></lb>reſolving and renouncing their Demonſtrations do declare their <lb></lb>Concluſion to be falſe, but ſaith, that it ought to be de<lb></lb>monſtrated, That what is ſaid in Scripture of a Curtain is not <lb></lb>contrary to their true Demonſtrations. </s> <s>Theſe are his words: <lb></lb><arrow.to.target n="marg836"></arrow.to.target><lb></lb><emph type="italics"></emph>(h) But ſome object; How doth it appear, that the ſaying in our <lb></lb>Bibles,<emph.end type="italics"></emph.end> Who ſtretcheth out the Heaven as a Curtain, <emph type="italics"></emph>maketh <lb></lb>not againſt thoſe who maintain the Heavens to be in figure of a <lb></lb>Sphere? </s> <s>Let it be ſo, if that be falſe which they affirme: For <lb></lb>that is truth which is ſpoke by Divine Authority, rather than<emph.end type="italics"></emph.end> <pb xlink:href="040/01/470.jpg" pagenum="446"></pb><emph type="italics"></emph>that which proceeds from Humane Inſirmity. </s> <s>But if peradven<lb></lb>ture they ſhould be able to prove their Poſition by ſuch Experiments <lb></lb>as puts it out of queſtion, it is to be proved, that what is ſaid in <lb></lb>Scripture concerning a Curtain, doth in no wiſe contradict <lb></lb>their manifeſt Reaſons.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg835"></margin.target>* <emph type="italics"></emph>Pelle,<emph.end type="italics"></emph.end> a Skin in <lb></lb>the Original, out <lb></lb>in our Bibles a <lb></lb>Curtain.</s></p><p type="margin"> <s><margin.target id="marg836"></margin.target>(h) <emph type="italics"></emph>Sed ait ali<lb></lb>quis, quomodo non <lb></lb>eſt coutrarium iis, <lb></lb>qui figur am Sphæ<lb></lb>ræ Cœlo tribunt, <lb></lb>quod ſcriptum eſt <lb></lb>en Libris Noſtris,<emph.end type="italics"></emph.end><lb></lb>Qui extendit Cœ<lb></lb>lum, ſicut pellem? <lb></lb><emph type="italics"></emph>Stt ſane contrari<lb></lb>um, ſi falſum eſt, <lb></lb>quod illi dicunt: <lb></lb>hoc enim verum <lb></lb>eſt, quod Divina <lb></lb>dicit authoritas, <lb></lb>potius quans illud, <lb></lb>quod humana in<lb></lb>firmitas conjicit. <lb></lb></s> <s>Sed ſi forte illud <lb></lb>talibus illi docu<lb></lb>mentis probare po<lb></lb>tuerint, at dubi<lb></lb>tari inde non debe<lb></lb>at; demonſtrandum <lb></lb>eſt, hoc quod apud <lb></lb>nos eſt de Pelle di<lb></lb>ctum, veris illis <lb></lb>rationibus non eſſe <lb></lb>contrarium.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>He proceedeth afterwards to admoniſh us that we ought to be <lb></lb>no leſs careful and obſervant in reconciling a Text of Scripture <lb></lb>with a demonſtrated Natural Propoſition, than with another <lb></lb>Text of Scripture which ſhould ſound to a contrary Senſe. </s> <s>Nay <lb></lb>methinks that the circumſpection of this Saint is worthy to be ad<lb></lb>mired and imitated, who even in obſcure Concluſions, and of <lb></lb>which we may aſſure our ſelves that we can have no knowledge <lb></lb>or Science by humane demonſtration, is very reſerved in deter<lb></lb>mining what is to be believed, as we ſee by that which he wri<lb></lb>teth in the end of his ſecond Book, <emph type="italics"></emph>de Geneſi ad Litteram,<emph.end type="italics"></emph.end> ſpeak<lb></lb>ing, whether the Stars are to be believed animate: <emph type="italics"></emph>(i) Which<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg837"></arrow.to.target><lb></lb><emph type="italics"></emph>particular, although (at preſent) it cannot eaſily be comprehended, <lb></lb>yet I ſuppoſe in our farther Progreſs of bandling the Scriptures, <lb></lb>we may meet with ſome more pertinent places, upon which it will <lb></lb>be permitted us (if not to determin any thing for certain, yet) to <lb></lb>ſuggeſt ſomewhat concerning this matter, according to the dictates <lb></lb>of Sacred Authority. </s> <s>But now, the moderation of pious gravity <lb></lb>being alwaies obſerved, we ought to receive nothing raſhly in <lb></lb>a doubtful point, leaſt perhaps we reject that out of reſpect to <lb></lb>our Errour, which hereafter Truth may diſcover, to be in no <lb></lb>wiſe repugnant to the Sacred Volumes of the Old and New Te<lb></lb>ſtament.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg837"></margin.target><emph type="italics"></emph>(i) Quod licet in <lb></lb>praſenti facile non <lb></lb>poſſit comprehendi; <lb></lb>arbitror tamen, in <lb></lb>proceſſis tract an<lb></lb>dærum Scriptura<lb></lb>rum, opportuntora <lb></lb>loca poſſe occurre<lb></lb>re, ubinobis de hac <lb></lb>re, ſecundum San<lb></lb>ctæ auctoritatis <lb></lb>Litteras, etſi non <lb></lb>oſtendere certum <lb></lb>aliquid, tamen cre<lb></lb>dere licebit. </s> <s>Nunc <lb></lb>autem, ſervat â <lb></lb>ſemper moderatio<lb></lb>ne piæ gravitatis, <lb></lb>nihil credere dere <lb></lb>obſcura temere <lb></lb>debemus; ne fortè, <lb></lb>quoà poſtea verit as <lb></lb>patefecerit, quam<lb></lb>vis Libris San<lb></lb>ctis, ſive Teſta<lb></lb>menti veteris, ſive, <lb></lb>novi nullo modo eſ<lb></lb>ſe poſſit æeverſum, <lb></lb>tamen propter a<lb></lb>morem noſtri er<lb></lb>roris, oderimus.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>By this and other places (if I deceive not my ſelf) the intent <lb></lb>of the Holy Fathers appeareth to be, That in Natural queſtions, <lb></lb>and which are not <emph type="italics"></emph>de Fide,<emph.end type="italics"></emph.end> it is firſt to be conſidered, whether <lb></lb>they be indubitably demonſtrated, or by ſenſible Experiments <lb></lb>known; or whether ſuch a knowledge and demonſtration is to be <lb></lb>had; which having obtained, and it being the gift of God, it <lb></lb>ought to be applyed to find out the true Sences of the Sacred Pa<lb></lb>ges in thoſe places, which in appearance might ſeem to ſpeak to <lb></lb>a contrary meaning: Which will unqueſtionably be pierced into <lb></lb>by Prudent Divines, together with the occaſions that moved the <lb></lb><arrow.to.target n="marg838"></arrow.to.target><lb></lb>Holy Ghoſt, (for our exerciſe, or for ſome other reaſon to me un<lb></lb>known) to veil it ſelf ſometimes under words of different ſigni<lb></lb>fications.</s></p><p type="margin"> <s><margin.target id="marg838"></margin.target>Id. </s> <s>D Aug. </s> <s>in <lb></lb>Gen. <emph type="italics"></emph>ad Lute<lb></lb>ram,<emph.end type="italics"></emph.end> lib. 1. <emph type="italics"></emph>in fine.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>As to the other point, Of our regarding the Primary Scope of <lb></lb>thoſe Sacred Volumes, I cannot think that their having ſpoken <lb></lb>alwaies in the ſame tenour, doth any thing at all diſturb this <lb></lb>Rule. </s> <s>For if it hath been the Scope of the Scripture by way of <lb></lb>condeſcention to the capacity of the Vulgar at any time, to ex <pb xlink:href="040/01/471.jpg" pagenum="447"></pb>preſs a Propoſition in words, that bear a ſenſe different from the <lb></lb>Eſſence of the ſaid Propoſition; why might it not have obſerved <lb></lb>the ſame, and for the ſame reſpect, as often as it had occaſion to <lb></lb>ſpeak of the ſame thing? </s> <s>Nay I conceive, that to have done <lb></lb>otherwiſe, would but have encreaſed the confuſion, and dimi<lb></lb>niſhed the credit that theſe Sacred Records ought to have a<lb></lb>mongſt the Common People.</s></p><p type="main"> <s>Again, that touching the Reſt and Motion of the Sun and <lb></lb>Earth, it was neceſſary, for accommodation. </s> <s>to Popular Capa<lb></lb>city, to aſſert that which the Litteral ſenſe of the Scripture im<lb></lb>porteth, experience plainly proveth: For that even to our dayes <lb></lb>people far leſs rude, do continue in the ſame Opinion upon Rea<lb></lb>ſons, that if they were well weighed and examined, would be <lb></lb>found to be extream trivial, and upon Experiments, either whol<lb></lb>ly falſe, or altogether beſides the purpoſe. </s> <s>Nor is it worth <lb></lb>while to go about to remove them from it, they being incapable <lb></lb>of the contrary Reaſons that depend upon too exquiſite Obſer<lb></lb>vations, and too ſubtil Demonſtrations, grounded upon Abſtra<lb></lb>ctions, which, for the comprehending of them, require too ſtrong <lb></lb>an Imagination. </s> <s>Whereupon, although that the Stability of <lb></lb>Heaveu, and Motion of the Earth ſhould be more than certain <lb></lb>and demonſtrated to the Wiſe; yet nevertheleſs it would be <lb></lb>neceſſary, for the conſervation of credit amongſt the Vulgar, to <lb></lb>affirm the contrary: For that of a thouſand ordinary men, that <lb></lb>come to be queſtioned concerning theſe particulars, its probab e <lb></lb>that there will not be found ſo much as one that will not an<lb></lb>ſwer that he thinketh, and ſo certainly he doth, that the Sun <lb></lb>moveth, and the Earth ſtandeth ſtill. </s> <s>But yet none ought to <lb></lb>take this common Popular Aſſent to be any Argument of the <lb></lb>truth of that which is affirmed: For if we ſhould examine <lb></lb>theſe very men touching the grounds and motives by which they <lb></lb>are induced to believe in that manner; and on the other ſide <lb></lb>ſhould hear what Experiments and Demonſtrationslperſwade <lb></lb>thoſe few others to believe the contrary, we ſhould finde theſe <lb></lb>latter to be moved by moſt ſolid Reaſons, and the former by <lb></lb>ſimple appearances, and vain and ridiculous occurrences. </s> <s>That <lb></lb>therefore it was neceſſary to aſſign Motion to the Sun, and Reſt <lb></lb>to the earth, leſt the ſhallow capacity of the Vulgar ſhould be <lb></lb>confounded, amuſed, and rendred obſtinate and contumacious, <lb></lb>in giving credit to the principal Articles, and which are abſolute<lb></lb>ly <emph type="italics"></emph>de fide,<emph.end type="italics"></emph.end> it is ſufficiently obvious. </s> <s>And if it was neceſſary ſo <lb></lb>to do, it is not at all to be wondred at, that it was with extraor<lb></lb>dinary Wiſdom ſo done, in the Divine Scriptures.</s></p><p type="main"> <s>But I will alledge further, That not onely a reſpect to the <lb></lb>Incapacity of the Vulgar, but the current Opinion of thoſe times <pb xlink:href="040/01/472.jpg" pagenum="448"></pb>made the Sacred Writers, in the points that were not neceſſary <lb></lb>to ſalvation, to accommodate themſelves more to the received <lb></lb>uſe, than to the true Eſſence of things: Of which S. <emph type="italics"></emph>Hierom<emph.end type="italics"></emph.end><lb></lb>treating, writeth: <emph type="italics"></emph>(k) As if many things were not ſpoken in<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg839"></arrow.to.target><lb></lb><emph type="italics"></emph>the Holy Scriptures according to the judgement of thoſe times <lb></lb>in which they were acted, and not according to that which <lb></lb>truth contained.<emph.end type="italics"></emph.end> And elſewhere, the ſame Saint: <emph type="italics"></emph>(l) It is the cu<lb></lb>ſtome for the Pen-men of Scripture, to deliver their Judgments in <lb></lb>many things, according to the common received opinion that their <lb></lb>times had of them.<emph.end type="italics"></emph.end> And ^{*} S. <emph type="italics"></emph>Thomas Aquinas<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Job<emph.end type="italics"></emph.end> upon thoſe <lb></lb>words, <emph type="italics"></emph>Qui extendit Aquilonem ſuper vacuum, & appendit<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg840"></arrow.to.target><lb></lb><emph type="italics"></emph>Terram ſuper nihilum<emph.end type="italics"></emph.end>: Noteth that the Scripture calleth that <lb></lb>ſpace <emph type="italics"></emph>Vacuum<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Nihilum,<emph.end type="italics"></emph.end> which imbraceth and invironeth the <lb></lb>Earth, and which we know, not to be empty, bat filled with Air; <lb></lb>Nevertheleſſe, ſaith he, The Scripture to comply with the appre<lb></lb>henſion of the Vulgar, who think that in that ſame ſpace there <lb></lb>is nothing, calleth it <emph type="italics"></emph>Vacuum<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Nihilum.<emph.end type="italics"></emph.end> Here the words of <lb></lb><arrow.to.target n="marg841"></arrow.to.target><lb></lb>S. <emph type="italics"></emph>Thomas, Quod de ſuperiori Hæmiſphærio Cœli nibil nobis ap<lb></lb>paret, niſi ſpatium aëre plenum, quod vulgares homines reputant <lb></lb>Vacnum; loquitur enim ſecundum exiſtimationem vulgarium ho<lb></lb>minum, prout eſt mos in Sacra Scriptura.<emph.end type="italics"></emph.end> Now from this Place <lb></lb>I think one may very Logically argue, That the Sacred Scripture <lb></lb>for the ſame reſpect had much more reaſon to phraſe the Sun mo<lb></lb>veable, and the Earth immoveable. </s> <s>For if we ſhould try the ca<lb></lb>pacity of the Common People, we ſhould find them much more <lb></lb>unapt to be perſwaded of the ſtability of the Sun, and Motion <lb></lb>of the Earth, than that the ſpace that environeth it is full of Air. <lb></lb></s> <s>Therefore if the ſacred Authors, in this point, which had not ſo <lb></lb>much difficulty to be beat into the capacity of the Vulgar, have <lb></lb>notwithſtanding forborn to attempt perſwading them unto it, it <lb></lb>muſt needs ſeem very reaſonable that in other Propoſitions much <lb></lb>more abſtruſe they have obſerved the ſame ſtile. </s> <s>Nay <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end><lb></lb>himſelf, knowing what power an antiquated cuſtome and way <lb></lb>of conceiving things become familiar to us from our infancy <lb></lb>hath in our Fancy, that he might not increaſe confuſion and dif<lb></lb>ficulty in our apprehenſions, after he had firſt demonſtrated, <lb></lb>That the Motions which appear to us to belong to the Sun, or to <lb></lb>the Firmament, are really in the Earth; in proceeding after<lb></lb>wards to reduce rhem into Tables, and to apply them to uſe, he <lb></lb>calleth them the Motions of the Sun, and of the Heaven that is <lb></lb>above the Planets; expreſly terming them the Riſing and Set<lb></lb>ting of the Sun and Stars; and mutations in the obliquity of <lb></lb>the Zodiack, and variations in the points of the Equinoxes, the <lb></lb>Middle Motion, <emph type="italics"></emph>Anomalia, Proſthaphæreſis<emph.end type="italics"></emph.end> of the Sun; and ſuch <lb></lb>other things; which do in reality belong to the Earth: But be <pb xlink:href="040/01/473.jpg" pagenum="449"></pb>cauſe being joyned to it, and conſequently having a ſhare in eve<lb></lb>ry of its motions, we cannot immediately diſcern them in her, but <lb></lb>are forced to refer them to the Celeſtial Bodies in which they <lb></lb>appear; therefore we call them as if they were made there, where <lb></lb>they ſeem to us to be made. </s> <s>Whence it is to be noted how ne<lb></lb>neſſary it is to accommodate our diſcourſe to our old and accu<lb></lb>ſtomed manner of underſtanding.</s></p><p type="margin"> <s><margin.target id="marg839"></margin.target>(k) <emph type="italics"></emph>Quaſi non <lb></lb>multa in Scriptu<lb></lb>ris Sanctis dican<lb></lb>tur juxta opinio<lb></lb>nem illius tempor is <lb></lb>quo geſt a referant, <lb></lb>& non juxta quod <lb></lb>rei veritas contine<lb></lb>bat.<emph.end type="italics"></emph.end> D. Hiero. </s> <s>in c. <lb></lb></s> <s>28. Jerem.</s></p><p type="margin"> <s><margin.target id="marg840"></margin.target>(l) <emph type="italics"></emph>Conſuctudi<lb></lb>nis Scripturarum <lb></lb>eſt, ut opinionem <lb></lb>multarum rerum <lb></lb>ſic narret Hiſtori<lb></lb>cus, quomodo eo <lb></lb>tempore ab omni<lb></lb>bus credebatur.<emph.end type="italics"></emph.end> In <lb></lb>cap. 13. Matth.</s></p><p type="margin"> <s><margin.target id="marg841"></margin.target>* D. Thomas, in <lb></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 conſent of Fathers, in re<lb></lb>ceiving a Natural Propoſition of Scripture, all in the ſame ſenſe <lb></lb>ought to Authorize it ſo far, as to make it become a matter of <lb></lb>Faith to believe it to be ^{*} ſo, I ſhould think that it ought at moſt <lb></lb><arrow.to.target n="marg842"></arrow.to.target><lb></lb>to be underſtood of thoſe Concluſions onely, which have beenby <lb></lb>the ſaid Fathers diſcuſſed, and ſifted with all poſſible diligence, <lb></lb>and debated on the one ſide, and on the other, and all things in <lb></lb>the end concurring to diſprove the one, and prove the other. </s> <s>But <lb></lb>the Mobility of the Earth, and Stability of the Sun, are not of <lb></lb>this kinde; For, that the ſaid Opinion was in thoſe times total<lb></lb>ly buried, and never brought amongſt the Queſtions of the Schools, <lb></lb>and not conſidered, much leſs followed by any one: So that it is to <lb></lb>be believed that it never ſo much as entered into the thought of <lb></lb>the Fathers to diſpute it, the Places of Scripture, their own Opinion, <lb></lb>and the aſſent of men having all concurred in the ſame judgement, <lb></lb>without the contradiction of any one, ſo far as we can finde.</s></p><p type="margin"> <s><margin.target id="marg842"></margin.target>* Namely, ac<lb></lb>cording to the Lit<lb></lb>teral Senſe.</s></p><p type="main"> <s>Beſides, it is not enough to ſay that the Fathers all admit the <lb></lb>ſtability of the Earth, &c. </s> <s>Therefore to believe it is a matter of <lb></lb>Faith: But its neceſſary to prove that they have condemned the <lb></lb>contrary Opinion: For I may affirm and bide by this, That their <lb></lb>not having occaſion to make ſatisfaction upon the ſame, and to <lb></lb>diſcuſs it, hath made them to omit and admit it, onely as cur<lb></lb>rent, but not as reſolved and proved And I think I have very <lb></lb>good Reaſon for what I ſay; For either the Fathers did make <lb></lb>reflection upon this Concluſion as controverted, or not: If not, <lb></lb>then they could determin nothing concerning it no not in their <lb></lb>private thoughts; and their incogitance doth not oblige us to <lb></lb>receive thoſe Precepts which they have not, ſo much as in their <lb></lb>intentions enjoyned. </s> <s>But if they did reflect and conſider there<lb></lb>on, they would long ſince have condemned it, if they had judged <lb></lb>it erroneous; which we do not find that they have done. </s> <s>Nay, after <lb></lb>that ſome Divines have began to conſider it, we find that they <lb></lb>have not deem'd it erroneous; as we read in the Commentaries of <lb></lb><emph type="italics"></emph>Didacus a Stunica<emph.end type="italics"></emph.end> upon <emph type="italics"></emph>Job,<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Cap. 9, v. </s> <s>6.<emph.end type="italics"></emph.end> on the words, <emph type="italics"></emph>Qui com<lb></lb>movet Terram de loco ſuo,<emph.end type="italics"></emph.end> &c. </s> <s>Where he at large diſcourſeth upon <lb></lb>the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Hypotheſis, and concludeth, <emph type="italics"></emph>That the Mobility <lb></lb>of the Earth, is not contrary to Scripture.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Withal, I may juſtly queſtion the truth of that determination, <lb></lb>namely, That the Church enjoyneth us to hold ſuch like Natural <pb xlink:href="040/01/474.jpg" pagenum="450"></pb>Concluſions as matters of Faith, onely becauſe they bear the <lb></lb>ſtamp of an unanimous Interpretation of all the Fathers: And <lb></lb>I do ſuppoſe that it may poſſibly be, that thoſe who hold in this <lb></lb>manner, might poſſibly have gone about in favour of their own <lb></lb>Opinion, to have amplified the Decretal of the Councils; which <lb></lb>I cannot finde in this caſe to prohibit any other, ſave onely, <emph type="italics"></emph>Per<lb></lb>verting to Senſes contrary to that of Holy Church, or of the <lb></lb>concurrent conſent of Fathers, thoſe places, and thoſe onely that <lb></lb>do pertain either to Faith or Manners, or concern our edification <lb></lb>in the Doctrine of Chriſtianity: And thus ſpeaks the Council of <lb></lb>Trent. </s> <s>Seſſ.<emph.end type="italics"></emph.end> 4. But the Mobility or Stability of the Earth, or <lb></lb><arrow.to.target n="marg843"></arrow.to.target><lb></lb>of the Sun, are not matters of Faith, nor contrary to Manners, <lb></lb>nor is there any one, that for the ſtabliſhing of this Opinion, <lb></lb>will pervert places of Scripture in oppoſition to the Holy Church, <lb></lb>or to the Fathers: Nay, Thoſe who have writ of this Doctrine, <lb></lb>did never make uſe of Texts of Scripture; that they might leave <lb></lb>it ſtill in the breaſts of Grave and Prudent Divines to interpret <lb></lb>the ſaid Places, according to their true meaning.</s></p><p type="margin"> <s><margin.target id="marg843"></margin.target><emph type="italics"></emph>Concil. </s> <s>Trid. </s> <s>Seſſ.<emph.end type="italics"></emph.end><lb></lb>4.</s></p><p type="main"> <s>And how far the Decrees of Councills do comply with the Ho<lb></lb>ly Fathers in theſe particulars, may be ſufficiently manifeſt, in <lb></lb>that they are ſo far from enjoyning to receive ſuch like Natural <lb></lb>Concluſions for matters of Faith, or from cenſuring the contrary <lb></lb>Opinions as erronious; that rather reſpecting the Primitive and <lb></lb>primary intention of the Holy Church, they do adjudge it un<lb></lb>profitable to be buſied in examining the truth thereof. </s> <s>Let <lb></lb>your Highneſs be pleaſed to hear once again what S. <emph type="italics"></emph>Auguſtine<emph.end type="italics"></emph.end><lb></lb>anſwers to to thoſe Brethren who put the Queſtion, Whether it <lb></lb><arrow.to.target n="marg844"></arrow.to.target><lb></lb>be true that Heaven moveth, or ſtandeth ſtill? (*) <emph type="italics"></emph>To theſe I <lb></lb>anſwer, That Points of this nature require a curious and pro<lb></lb>found examination, that it may truly appear whether they be <lb></lb>true or falſe; a work inconſiſtent with my leaſure to under<lb></lb>take or go thorow with, nor is it any way neceſſary for thoſe, <lb></lb>whom we deſire to inform of the things that more nearly <lb></lb>concern their own ſalvation and The Churches Be<lb></lb>nefit.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg844"></margin.target>(*) <emph type="italics"></emph>His re<lb></lb>ſpondeo, multum <lb></lb>ſubüliter, & labo<lb></lb>rioſis ratiombus, <lb></lb>iſta perquirere, ut <lb></lb>vere percipiatur, <lb></lb>ntrum ita, an non <lb></lb>ita ſit: quibus in<lb></lb>eundis atque tra<lb></lb>ctandis, nec mihi <lb></lb>jam tempus eſt, <lb></lb>nec illis eſſe debet, <lb></lb>quos ad ſalutem <lb></lb>ſuam, Sanctæ Ec<lb></lb>cleſiæ neceſſariam <lb></lb>utilitatem cupi <lb></lb>mus informari.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>But yet although in Natural Propoſitions we were to take the <lb></lb>reſolution of condemning or admitting them from Texts of Scri<lb></lb>pture unanimouſly expounded in the ſame Senſe by all the Fa<lb></lb>thers, yet do I not ſee how this Rule can hold in our Caſe; for that <lb></lb>upon the ſame Places we read ſeveral Expoſitions in the Fathers; <lb></lb><arrow.to.target n="marg845"></arrow.to.target><lb></lb><emph type="italics"></emph>(m) Dionyſius Areopagita<emph.end type="italics"></emph.end> ſaying, <emph type="italics"></emph>That the Primum Mobile, and <lb></lb>not the Sun ſtand ſtill.<emph.end type="italics"></emph.end> Saint <emph type="italics"></emph>Auguſtine<emph.end type="italics"></emph.end> is of the ſame Opinion; <lb></lb><emph type="italics"></emph>(n) All the Celeſtial Bodies were immoveable.<emph.end type="italics"></emph.end> And with them <lb></lb><arrow.to.target n="marg846"></arrow.to.target><lb></lb>concurreth <emph type="italics"></emph>Abulenſis.<emph.end type="italics"></emph.end> But which is more, amongſt the Jewiſh <lb></lb>Authors (whom <emph type="italics"></emph>Joſephus<emph.end type="italics"></emph.end> applauds) ſome have held, <emph type="italics"></emph>(o) That<emph.end type="italics"></emph.end> <pb xlink:href="040/01/475.jpg" pagenum="451"></pb><emph type="italics"></emph>The Sun did not really ſtand ſtill, but ſeemed ſo to do, during the<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg847"></arrow.to.target><lb></lb><emph type="italics"></emph>ſhort time in which Iſrael gave the overthrow to their Enemies.<emph.end type="italics"></emph.end><lb></lb>So for the Miracle in the time of <emph type="italics"></emph>Hezekiah, Paulus Burgenſis<emph.end type="italics"></emph.end> is of <lb></lb>opinion that it was not wrought on the Sun, but on the Diall. <lb></lb></s> <s>But that, in ſhort, it is neceſſary to Gloſſe and Interpret the <lb></lb>words of the Text in <emph type="italics"></emph>Joſhua,<emph.end type="italics"></emph.end> when ever the Worlds Syſteme <lb></lb><arrow.to.target n="marg848"></arrow.to.target><lb></lb>is in diſpute, I ſhall ſhew anon. </s> <s>Now finally, granting to theſe <lb></lb>Gentlemen more than they demand, to wit, That we are whol<lb></lb>ly to acquieſce in the judgment of Judicious Divines, and that <lb></lb>in regard that ſuch a particular Diſquiſition is not found to <lb></lb>have been made by the Ancient Fathers, it may be undertaken <lb></lb>by the Sages of our Age, who having firſt heard the Experiments, <lb></lb>Obſervations, Reaſons, and Demonſtrations of Philolophers and <lb></lb>Aftronomers, on the one ſide, and on the other (ſeeing that the <lb></lb>Controverſie is about Natural Problems, and Neceſſary <emph type="italics"></emph>Dilem<lb></lb>ma's,<emph.end type="italics"></emph.end> and which cannot poſſibly be otherwiſe than in one of <lb></lb>the two manners in controverſie) they may with competent cer<lb></lb>tainty determine what Divine Inſpirations ſhall dictate to them. <lb></lb></s> <s>But that without minutely examining and diſcuſſing all the Rea<lb></lb>ſons on both ſides; and without ever comming to any certainty <lb></lb>of the truth of the Caſe, ſnch a Reſolution ſhould be taken, Is <lb></lb>not to be hoped from thoſe who do not ſtick to hazzard the Ma<lb></lb>jeſty and Dignity of the Sacred Scripture, in defending the re<lb></lb>putation of their vain Fancies; Nor to be feared from thoſe <lb></lb>who make it their whole buſineſſe, to examine with all in<lb></lb>tenſneſs, what the Grounds of this Doctrine are; and that only <lb></lb>in an Holy Zeal for Truth, the Sacred Scriptures, and for the <lb></lb>Majeſty, Dignity, and Authority, in which every Chriſtian <lb></lb>ſhould indeavour to have them maintained. </s> <s>Which Dignity, <lb></lb>who ſeeth not that it is with greater Zeal deſired and procured <lb></lb>by thoſe who, abſolutely ſubmitting themſelves to the Holy <lb></lb>Church, deſire, not that this, or that opinion may be prohibi<lb></lb>ted, but onely that ſuch things may be propoſed to conſidera<lb></lb>tion, as may the more aſcertain her in the ſafeſt choice, than by <lb></lb>thoſe who being blinded by their particular Intereſt, or ſtimula<lb></lb>ted by malitious ſuggeſtions, preach that ſhe ſhould, without <lb></lb>more ado, thunder out Curſes, for that ſhe had power ſo to do: <lb></lb>Not conſidering that all that may be done is not alwayes conve<lb></lb>nient to be done. </s> <s>The Holy Fathers of old were not of this <lb></lb>opinion, but rather knowing of how great prejudice, and how <lb></lb>much againſt the primary intent of the Catholick Church, it <lb></lb>would be to go about from Texts of Scripture to decide Natu<lb></lb>ral Concluſions, touching which, either Experiments or neceſſary <lb></lb>Demonſtrations, might in time to come evince the contrary, of <lb></lb>that which the naked ſenſe of the Words ſoundeth, they have <pb xlink:href="040/01/476.jpg" pagenum="452"></pb>not only proceeded with great circumſpection, but have left the <lb></lb>following Precepts for the inſtruction of others. <emph type="italics"></emph>(p) In points<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg849"></arrow.to.target><lb></lb><emph type="italics"></emph>obſcure and remote from our Sight, if we come to read any thing <lb></lb>out of Sacred Writ, that, with a<emph.end type="italics"></emph.end> Salvo <emph type="italics"></emph>to the Faith that we have <lb></lb>imbued, may correſpond with ſeveral conſtructions, let us not ſo <lb></lb>farre throw our ſelves upon any of them with a precipitous ob<lb></lb>ſtinacy, as that if, perhaps the Truth being more diligently ſearch't <lb></lb>into, it ſhould juſtly fall to the ground, we might fall together <lb></lb>with it: and ſo ſhew that we contend not for the ſenſe of Divine <lb></lb>Scriptures, but our own, in that we would have that which is <lb></lb>our own to be the ſenſe of Scriptures, when as we ſhould ra<lb></lb>ther deſire the Scriptures meaning to be ours.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg845"></margin.target><emph type="italics"></emph>(m) Non Solem, ſed <lb></lb>Primum Mobile <lb></lb>immotum conſti<lb></lb>tiſſe<emph.end type="italics"></emph.end>: Dioniſ. <lb></lb></s> <s>Areop.</s></p><p type="margin"> <s><margin.target id="marg846"></margin.target><emph type="italics"></emph>(n) Omnia cor<lb></lb>pora Cæleſtia, im<lb></lb>mota ſubſtitiſſe<emph.end type="italics"></emph.end>:</s></p><p type="margin"> <s><margin.target id="marg847"></margin.target><emph type="italics"></emph>(o) Solem re<lb></lb>vera non ſubſtitiſ<lb></lb>ſe immorum, ſed <lb></lb>pro brevi tempore, <lb></lb>intra quod Iſræeli<lb></lb>tæ, hoſtes ſuos fu<lb></lb>derunt, id ita vi<lb></lb>ſum eſſe.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg848"></margin.target>Iſa. Cap. 38.</s></p><p type="margin"> <s><margin.target id="marg849"></margin.target>(p) <emph type="italics"></emph>In rebus ob<lb></lb>ſouris, atque a no<lb></lb>ſtris oculis remi<lb></lb>tiſſimis, ſiqua inde <lb></lb>ſcripta etiam divi<lb></lb>næ legerimus, quæ <lb></lb>poſſint ſalva fide, <lb></lb>qua imbuimur, a<lb></lb>liis atque altis pa<lb></lb>rere ſentextiis, in <lb></lb>nullam earum nos <lb></lb>præcipiti affirma<lb></lb>tione ita projici<lb></lb>amus, ut ſi forte <lb></lb>ailigentiùs diſcuſ<lb></lb>ſa veritas <expan abbr="eã">eam</expan> recte <lb></lb>labefact averit, corruamus: non pro ſententia Divinarum Scripturarum, ſed pro noſtra ita dimicantes, ut eam <lb></lb>velimus Scripturarum eſſe, quæ noſtra eſt, cum potius eam quæ Scripturarum eſt, noſtram eſſe velle debeamus,<emph.end type="italics"></emph.end><lb></lb>Divus Auguſtin. </s> <s>in Gen. </s> <s>ad Litteram, lib. 2. c. </s> <s>18. & <expan abbr="ſeq.">ſeque</expan></s></p><p type="main"> <s>He goeth on, and a little after teacheth us, that no Propoſi<lb></lb>tion can be againſt the Faith, unleſſe firſt it be demonſtrated <lb></lb><arrow.to.target n="marg850"></arrow.to.target><lb></lb>falſe; ſaying, <emph type="italics"></emph>(q) Tis not all the while contrary to Faith, until it <lb></lb>be diſproved by moſt certain Truth, which if it ſhould ſo be, the Holy <lb></lb>Scripture affirm'd it not, but Humane Ignorance ſuppoſed it.<emph.end type="italics"></emph.end><lb></lb>Whereby we ſee that the ſenſes which we impoſe on Texts of <lb></lb>Scripture, would be falſe, when ever they ſhould diſagree with <lb></lb>Truths demonſtrated. </s> <s>And therefore we ought, by help of de<lb></lb>monſtrated Truth, to ſeek the undoubted ſenſe of Scripture: <lb></lb>and not according to the ſound of the words, that may ſeem <lb></lb>true to our weakneſſe, to go about, as it were, to force Na<lb></lb>ture, and to deny Experiments and Neceſſary Demonſtra<lb></lb>tions.</s></p><p type="margin"> <s><margin.target id="marg850"></margin.target>(q) <emph type="italics"></emph>Tam diu non <lb></lb>eſt extra fidem, do<lb></lb>nec Veritate cer<lb></lb>tiſſima refellatur. <lb></lb></s> <s>Quod ſi fæctum <lb></lb>fuerit, non hoc ha<lb></lb>bebut Divina Scri<lb></lb>ptura, ſed hoc ſen<lb></lb>ſer at humana Ig<lb></lb>norantia.<emph.end type="italics"></emph.end> Ibid.</s></p><p type="main"> <s>Let Your Highneſſe be pleaſed to obſerve farther, with how <lb></lb>great circumſpection this Holy Man proceedeth, before he af<lb></lb>firmeth any Interpretation of Scripture to be ſure, and in ſuch <lb></lb>wiſe certain, as that it need not fear the encounter of any diffi<lb></lb>culty that may procure it diſturbance, for not contenting <lb></lb>himſelf that ſome ſenſe of Scripture agreeth with ſome Demon<lb></lb><arrow.to.target n="marg851"></arrow.to.target><lb></lb>ſtration, he ſubjoynes. <emph type="italics"></emph>(r) But if right Reaſon ſhall demon<lb></lb>ſtrate this to be true, yet is it queſtionable whether in theſe words <lb></lb>of Sacred Scripture the Pen-man would have this to be under<lb></lb>ſtood, or ſomewhat elſe, no leſſe true. </s> <s>And in caſe the Context <lb></lb>of his Words ſhall prove that he intended not this, yet will not <lb></lb>that which he would have to be underſtood be therefore falſe, but <lb></lb>moſt true, aad that which is more profitable to be known.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg851"></margin.target>(r) <emph type="italics"></emph>Si autem <lb></lb>hoc verum eſſe ve<lb></lb>ra ratio demon<lb></lb>ſtraverit, adhuc <lb></lb>incertum erit, u<lb></lb>trum hoc in illis <lb></lb>verbis Sanctorum <lb></lb>Librorum, Scrip<lb></lb>tor ſentiri volue<lb></lb>rit, an aliquid a<lb></lb>liud non minus ve<lb></lb>rum. </s> <s>Quod ſi cætera contextio ſermonis non hoc eum voluiſſe probaverit, non ideo falſum erit aliud, quod ipſe <lb></lb>intelligi voluit, ſed & verum, & quod utilius cognoſcatur.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>But that which increaſeth our wonder concerning the cir <pb xlink:href="040/01/477.jpg" pagenum="453"></pb>cumſpection, wherewith this Pious Authour proceedeth, is, <lb></lb><arrow.to.target n="marg852"></arrow.to.target><lb></lb>that not truſting to his obſerving, that both Demonſtrative <lb></lb>Reaſons, and the ſenſe that the words of Scripture and the reſt <lb></lb>of the Context both precedent and ſubſequent, do conſpire to <lb></lb>prove the ſame thing, he addeth the following words.</s></p><p type="margin"> <s><margin.target id="marg852"></margin.target><emph type="italics"></emph>(ſ) Si autem con<lb></lb>textio Scripturæ, <lb></lb>hoc voluiſſe intel<lb></lb>ligi Scriptorem, <lb></lb>non repugnaverit, <lb></lb>adhuc reſtabit <lb></lb>quærere, utrum & <lb></lb>aliud non potuerit.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>(ſ) But if the Context do not hold forth any thing that may<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg853"></arrow.to.target><lb></lb><emph type="italics"></emph>diſprove this to be the Authors Senſé, it yet remains to enquire, <lb></lb>Whether the other may not be intended alſo.<emph.end type="italics"></emph.end> And not yet reſolving <lb></lb>to accept of one Senſe, or reject another, but thinking that he <lb></lb>could never uſe ſufficient caution, he proceedeth: <emph type="italics"></emph>(t) But if <lb></lb>ſo be we finde that the other may be alſo meant, it will be doubted <lb></lb>which of them he would have to ſtand; or which in probability he <lb></lb>may be thought to aim at, if the true circumſtances on both ſides be <lb></lb>weighed.<emph.end type="italics"></emph.end> And laſtly, intending to render a Reaſon of this his <lb></lb><arrow.to.target n="marg854"></arrow.to.target><lb></lb>Rule, by ſhewing us to what perils thoſe men expoſe the Scri<lb></lb>ptures, and the Church; who, more reſpecting the ſupport of <lb></lb>their own errours, than the Scriptures Dignity, would ſtretch its <lb></lb>Authority beyond the Bounds which it preſcribeth to it ſelf, he <lb></lb>ſubjoyns the enſuing words, which of themſelves alone might <lb></lb>ſuffice to repreſs and moderate the exceſſive liberty, which ſome <lb></lb>think that they may aſſume to themſelves: <emph type="italics"></emph>(u) For it many <lb></lb>times falls out, that a Chriſtian may not ſo fully underſtand a <lb></lb>Point concerning the Earth, lieaven, and the reſt of this Worlds <lb></lb>Elements; the Motion, Converſion, Magnitude, and Diſtances of <lb></lb>the Stars, the certain defects of the Sun and Moon, the Revoluti<lb></lb>ons of Years and Times, the Nature of Animals, Fruits, Stones, <lb></lb>and other things of like nature, as to defend the ſame by right <lb></lb>Reaſon, or make it out by Experiments. </s> <s>But its too great an ab<lb></lb>ſurdity, yea moſt pernicious, and chiefly to be avoided, to let an <lb></lb>Infidel finde a Chriſtian ſo ſtupid, that he ſhould argue theſe mat<lb></lb>ters; as if they were according to Chriſtian Doctrine; and make <lb></lb>him (as the Proverb ſaith) ſcarce able to contain his laughter, ſee<lb></lb>ing him ſo far from the Mark Nor is the matter ſo much that one <lb></lb>in an errour ſhould be laught at, but that our Authors ſhould be <lb></lb>thought by them that are without, to be of the ſame Opinion, and to <lb></lb>the great prejudice of thoſe, whoſe ſalvation we wait for, ſenſurcd <lb></lb>and rejected as unlearned. </s> <s>For when they ſhal confute any one of the <lb></lb>Chriſtians in that matter, which they themſelvs thorowly under<lb></lb>ſtand, and ſhall thereupon expreſs their light eſteem of our Books; <lb></lb>how ſhall theſe Volumes be believed touching the Reſurrection of <lb></lb>the Dead, the Hope of eternal Life, and the Kingdom of Heaven; <lb></lb>when, as to theſe Points which admit of preſent Demonſtration, <lb></lb>or undoubted Reaſons, they conceive them to be falſly written.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/478.jpg" pagenum="454"></pb><p type="margin"> <s><margin.target id="marg853"></margin.target><emph type="italics"></emph>(t) Quod ſi & <lb></lb>aliud potuiſſe inve<lb></lb>nerimus, incertum <lb></lb>erit; quidnam eo<lb></lb>rum ille voluerit: <lb></lb>aut utrumque vo<lb></lb>luiſſe non inconve<lb></lb>nienter creditur, ſi <lb></lb>utriuſque ſententiæ <lb></lb>certa circumſt an<lb></lb>tia ſufragatur.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg854"></margin.target><emph type="italics"></emph>(u) Plerumque <lb></lb>enim accidit, at a<lb></lb>liquid de Terra, de<lb></lb>Celo, de ceter is hu<lb></lb>jus mundi elemen<lb></lb>tis, de motu, con<lb></lb>verſione, vel ctiam <lb></lb>magnitudine & <lb></lb>intervallis Syde<lb></lb>rum, de certis de<lb></lb>fectibus Solis, & <lb></lb>Lunæ, de eircuiti<lb></lb>bus annorum & <lb></lb>temporum; de Na<lb></lb>turis animalium, <lb></lb>fruticum, lapidum, <lb></lb>atque bujuſmodi <lb></lb>ceter is, etiam non <lb></lb>Chriſtianus ita no<lb></lb>verit, ut cirtiſſima <lb></lb>ratione vel experi<lb></lb>entiâ teneat. </s> <s>Tur<lb></lb>pe autem eſt nimis <lb></lb>& pernicioſum, ae <lb></lb>maxime caven<lb></lb>dum, at Chriſtia<lb></lb>num de his rebus <lb></lb>quaſi ſecundum <lb></lb>Chriſtianaslitter as <lb></lb>loquentem, ita de<lb></lb>lirare quilibet in<lb></lb>fiàelis audiat, ut, <lb></lb>quemadmodum di<lb></lb>citur, toto Cælo er<lb></lb>ræreconſpiciens, <expan abbr="ri-ſũtenere">ri<lb></lb>ſuntenere</expan> vix poſſit: <lb></lb>& non tam mole<lb></lb>ſtum eſt, quod er<lb></lb>rans homo deride<lb></lb>retur, ſed quod au<lb></lb>ctores noſtri, ab tis <lb></lb>qui foris ſunt, ta<lb></lb>lia ſenſiſſe credun<lb></lb>tur, & cum magno exitio eorum, de quorum ſalute ſatagimus, tanquam indocti reprehenduntur atque reſpuuntur. <lb></lb></s> <s>Cum enim quemquam de numero Chriſtiano um eainre, quam ip ſi optime norunt, deprehenderint, & venam ſenten<lb></lb>tiam ſuam de noſtris libris aſſerent; quo pacto illis Libris credituri ſunt, de Reſurrectione Mortuorum, & de ſpe<lb></lb>vit æ eternæ, Regnoque Celorum; quando de his rebus quas jam experiri, vel indubitatis rationibus percipere potuerunt<lb></lb>fallaciter putaverint eſſe conſcriptos.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And how much the truly Wiſe and Prudent Fathers are diſ<lb></lb>pleaſed with theſe men, who in defence of Propoſitions which <lb></lb>they do not underſtand, do apply, and in a certain ſenſe pawn <lb></lb>Texts of Scripture, and afterwards go on to encreaſe their firſt <lb></lb>Errour, by producing other places leſs underſtood than the for<lb></lb>mer. </s> <s>The ſame Saint declareth in the expreſſions following: <lb></lb><arrow.to.target n="marg855"></arrow.to.target><lb></lb><emph type="italics"></emph>(x) What trouble and ſorrow weak undertakers bring upon <lb></lb>their knowing Brethren, is not to be expreſſed; ſince when they <lb></lb>begin to be told and convinced of their falſe and unſound Opinion, <lb></lb>by thoſe who have no reſpect for the Authority of our Scriptures, <lb></lb>in defence of what through a fond Temerity, and moſt manifeſt fal<lb></lb>ſity, they have urged; they fall to citing the ſaid Sacred Books <lb></lb>for proof of it, or elſe repeat many words by heart out of them, <lb></lb>which they conceive to make for their purpoſe; not knowing <lb></lb>either what they ſay, or whereof they affirm.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg855"></margin.target><emph type="italics"></emph>(y) Quid enim <lb></lb>moleſtiæ, triſtiæque <lb></lb>ingerant prudenti<lb></lb>bus fratribus, te<lb></lb>nerarij præſumpto<lb></lb>res, ſatis dici non <lb></lb>poteſt, cum, ſi <lb></lb>quando de falſa & <lb></lb>prava opinione ſua <lb></lb>reprehendi & con<lb></lb>vinci cæperint, ab <lb></lb>iis qui noſtrorum <lb></lb>librorum auctori<lb></lb>tate, & aperliſſima <lb></lb>falfitate dixerunt, <lb></lb>eoſdnm libros San<lb></lb>ctos, unde id pro<lb></lb>bent, proferre co<lb></lb>nantur; vel etiam <lb></lb>memoriter, quæ ad <lb></lb>teſtimonium vale<lb></lb>re arbitrantur, <lb></lb>multa inde verba <lb></lb>pronunciant, non <lb></lb>intelligentes, neque <lb></lb>quæ loquuntur, ne<lb></lb>que de quibus af<lb></lb>firmant.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>In the number of theſe we may, as I conceive, account thoſe, <lb></lb>who, being either unwilling or unable to underſtand the De<lb></lb>monſtrations and Experiments, wherewith the Author and fol<lb></lb>lowers of this Opinion do confirm it, run upon all occaſions to <lb></lb>the Scriptures, not conſidering that the more they cite them, and <lb></lb>the more they perſiſt in affirming that they are very clear, and <lb></lb>do admit no other ſenſes, ſave thoſe which they force upon <lb></lb>them, the greater injury they do to the Dignity of them (if we <lb></lb>allowed that their judgments were of any great Authority) in <lb></lb>caſe that the Truth coming to be manifeſtly known to the con<lb></lb>trary, ſhould occaſion any confuſion, at leaſt to thoſe who are <lb></lb>ſeparated from the Holy Church; of whom yet ſhe is very ſolici<lb></lb>tous, and like a tender Mother, deſirous to recover them again <lb></lb>into her Lap. </s> <s>Your Highneſs therefore may ſee how præpoſterouſ<lb></lb>ly thoſe Perſons proceed, who in Natural Diſputations do range <lb></lb>Texts of Scripture in the Front for their Arguments; and ſuch <lb></lb>Texts too many times, as are but ſuperficially underſtood by them.</s></p><p type="main"> <s>But if theſe men do verily think, & abſolutely believe that they <lb></lb>have the true ſence of Such a particular place of Scripture, it muſt <lb></lb>needs follow of conſequence, that they do likewiſe hold for certain, <lb></lb>that they have found the abſolute truth of that Natural Concluſi<lb></lb>on, which they intend to diſpute:</s> <s> And that withall, they do know <lb></lb>that they have a great advantage of their Adverſary, whoſe Lot it <lb></lb>is to defend the part that is falſe; in regard that he who maintain<lb></lb>eth the Truth, may have many ſenſible experiments, and many ne<lb></lb>ceſſary Demonſtrations on his ſide; whereas his Antagoniſt can <lb></lb>make uſe of no other than deceitful appearances, <emph type="italics"></emph>Paralogiſms<emph.end type="italics"></emph.end> and <lb></lb><emph type="italics"></emph>Sophiſms.<emph.end type="italics"></emph.end> Now if they keeping within natural bounds, & produ<lb></lb>cing no other Weapons but thoſe of Philoſophy, pretend however, <lb></lb>to have ſo much advantage of their Enemy; why do they after <pb xlink:href="040/01/479.jpg" pagenum="455"></pb>wards in coming to engage, preſently betake themſelves to a Wea<lb></lb>pon inevitable & dreadful to terrifie their Opponent with the ſole <lb></lb>beholding of it? </s> <s>But if I may ſpeak the truth, I believe that they are <lb></lb>the firſt that are affrighted, and that perceiving themſelves unable <lb></lb>to bear up againſt the aſſaults of their Adverſary, go about to find <lb></lb>out ways how to keep them far enough off, forbidding unto them <lb></lb>the uſe of the Reaſon which the Divine Bounty had vouchſafed <lb></lb>them, & abuſing the moſt equitable Authority of ſacred Scripture, <lb></lb>which rightly underſtood and applyed, can never, according to <lb></lb>the common Maxime of Divines, oppoſe the Manifeſt Experi<lb></lb>ments, or Neceſſary Demonſtrations. </s> <s>But theſe mens running <lb></lb>to the Scriptures for a Cloak to their inability to comprehend, <lb></lb>not to ſay reſolve the Reaſons alledged againſt them, ought (if I <lb></lb>be not miſtaken) to ſtand them in no ſtead: the Opinion which <lb></lb>they oppoſe having never as yet been condemned by Holy <lb></lb>Church. </s> <s>So that if they would proceed with Candor, they <lb></lb>ſhould either by ſilence confeſs themſelves unable to handle ſuch <lb></lb>like points, or firſt conſider that it is not in the power of them or <lb></lb>others, but onely in that of the Pope, and of Sacred Councils to <lb></lb><arrow.to.target n="marg856"></arrow.to.target><lb></lb>cenſure a Poſition to be Erroneous: But that it is left to their <lb></lb>freedome to diſpute concerning its falſity. </s> <s>And thereupon, <lb></lb>knowing that it is impoſſible that a Propoſition ſhould at the <lb></lb>ſame time be True and Heretical; they ought, I ſay, to imploy <lb></lb>themſelves in that work which is moſt poper to them, namely, <lb></lb>in demonſtrating the falſity thereof: whereby they may ſee <lb></lb>how needleſſe the prohibiting of it is, its falſhood being once <lb></lb>diſcovered, for that none would follow it: or the Prohibition <lb></lb>would be ſafe, and without all danger of Scandal. </s> <s>Therefore <lb></lb>firſt let theſe men apply themſelves to examine the Arguments <lb></lb>of <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> and others; and leave the condemning of them <lb></lb>for Erroneous and Heretical to whom it belongeth: But yet let <lb></lb>them not hope ever to finde ſuch raſh and precipitous Determina<lb></lb>tions in the Wary and Holy Fathers, or in the abſolute Wiſ<lb></lb>dome of him that cannot erre, as thoſe into which they ſuffer <lb></lb>themſelves to be hurried by ſome particular Affection or Inte<lb></lb>reſt of their own. </s> <s>In theſe and ſuch other Poſitions, which are <lb></lb>not directly <emph type="italics"></emph>de Fide,<emph.end type="italics"></emph.end> certainly no man doubts but His Holineſs <lb></lb>hath alwayes an abſolute power of Admitting or Condemn<lb></lb>ing them, but it is not in the power of any Creature to make <lb></lb>them to be true or falſe, otherwiſe than of their own nature, <lb></lb>and <emph type="italics"></emph>de facto<emph.end type="italics"></emph.end> they are.</s></p><p type="margin"> <s><margin.target id="marg856"></margin.target>If this paſſage <lb></lb>ſeem harſh, the <lb></lb>Reader muſt re<lb></lb>member that I do <lb></lb>but Tranſlate.</s></p><p type="main"> <s>Therefore it is in my judgment more diſcretion to aſſure us <lb></lb>firſt of the neceſſary and immutable Truth of the Fact, (over <lb></lb>which none hath power) than without that certainty by condem<lb></lb>ning one part to deprive ones ſelf of that authority of freedome <pb xlink:href="040/01/480.jpg" pagenum="456"></pb>to elect, making thoſe Determinations to become neceſſary, <lb></lb>which at preſent are indifferent and arbitrary, and reſt in the <lb></lb>will of Supreme Authority. </s> <s>And in a word, if it be not poſ<lb></lb>ſible that a Concluſion ſhould be declared Heretical, whilſt we <lb></lb>are not certain, but that it may be true, their pains are in vain <lb></lb>who pretend to condemn the Mobility of the Earth and Stabili<lb></lb>ty of the Sun, unleſſe they have firſt demonſtrated it to be im<lb></lb>poſſible and falſe.</s></p><p type="main"> <s>It remaineth now, that we conſider whether it be true, that <lb></lb>the Place in <emph type="italics"></emph>Joſhuab<emph.end type="italics"></emph.end> may be taken without altering the pure ſig<lb></lb>nification of the words: and how it can be that the Sun, obey<lb></lb>ing the command of <emph type="italics"></emph>Joſhuah,<emph.end type="italics"></emph.end> which was, <emph type="italics"></emph>That it ſhould ſtand <lb></lb>ſtill,<emph.end type="italics"></emph.end> the day might thereupon be much lengthened. </s> <s>Which bu<lb></lb>ſineſſe, if the Celeſtial Motions be taken according to the <emph type="italics"></emph>Ptolo<lb></lb>maick<emph.end type="italics"></emph.end> Syſteme, can never any wayes happen, for that the Sun <lb></lb>moving thorow the Ecliptick, according to the order of the <lb></lb>Signes, which is from Eaſt to Weſt (which is that which maketh <lb></lb>Day and Night) it is a thing manifeſt, that the Sun ceaſing its <lb></lb>true and proper Motion, the day would become ſhorter and not <lb></lb>longer; and that on the contrary, the way to lengthen it would <lb></lb>be to haſten and velocitate the Suns motion; inſomuch that to <lb></lb>cauſe the Sun to ſtay above the Horizon for ſome time, in one <lb></lb>and the ſame place, without declining towards the Weſt, it would <lb></lb>be neceſſary to accelerate its motion in ſuch a manner as that it <lb></lb>might ſeem equal to that of the <emph type="italics"></emph>Primum Mobile,<emph.end type="italics"></emph.end> which would be <lb></lb>an accelerating it about three hundred and ſixty times more than <lb></lb>ordinary. </s> <s>If therefore <emph type="italics"></emph>Joſhuah<emph.end type="italics"></emph.end> had had an intention that his <lb></lb>words ſhould be taken in their pure and proper ſignification, he <lb></lb>would have bid the Sun to have accelerated its Motion ſo, that <lb></lb>the Rapture of the <emph type="italics"></emph>Primum Mobile<emph.end type="italics"></emph.end> might not carry it to the <lb></lb>Weſt: but becauſe his words were heard by people which hap<lb></lb>ly knew no other Celeſtial Motion, ſave this grand and common <lb></lb>one, from Eaſt to Weſt, ſtooping to their Capacity, and having <lb></lb>no intention to teach them the Conſtitution of the Spheres, but <lb></lb>only that they ſhould perceive the greatneſs of the Miracle <lb></lb>wrought, in the lengthening of the Day, he ſpoke according to <lb></lb>their apprehenſion. </s> <s>Poſſibly this Conſideration moved <emph type="italics"></emph>Diony<lb></lb>ſius Areopagita<emph.end type="italics"></emph.end> to ſay that in this Miracle the <emph type="italics"></emph>Primum Mobile<emph.end type="italics"></emph.end><lb></lb>ſtood ſtill, and this ſtopping, all the Celeſtial Spheres did of <lb></lb>conſequence ſtay: of which opinion is S. <emph type="italics"></emph>Auguſtine<emph.end type="italics"></emph.end> himſelf, and <lb></lb><emph type="italics"></emph>Abulenſis<emph.end type="italics"></emph.end> at large confirmeth it. </s> <s>Yea, that <emph type="italics"></emph>Joſhua's<emph.end type="italics"></emph.end> intention <lb></lb>was, that the whole Syſteme of the Celeſtial Spheres ſhould <lb></lb>ſtand ſtill, is collected from the command he gave at the ſame <lb></lb>time to the Moon, although that it had nothing to do in the <lb></lb>lengthening of the day; and under the injunction laid upon the <pb xlink:href="040/01/481.jpg" pagenum="457"></pb>Moon, we are to underſtand the Orbes of all the other Planets, <lb></lb>paſſed over in ſilence here, as alſo in all other places of the Sacred <lb></lb>Scriptures; the intention of which, was not to reach us the Aſtro<lb></lb>nomical Sciences. </s> <s>I ſuppoſe therefore, (if I be not deceived) <lb></lb>that it is very plain, that if we allow the <emph type="italics"></emph>Ptolemaick<emph.end type="italics"></emph.end> Syſteme, we <lb></lb>muſt of neceſſity interpret the words to ſome ſenſe different from <lb></lb>their ſtrict ſignification. </s> <s>Which Interpretation (being admo<lb></lb>niſhed by the moſt uſefull precepts of S. <emph type="italics"></emph>Auguſtine)<emph.end type="italics"></emph.end> I will not <lb></lb>affirm to be of neceſſity this above-mentioned, ſince that ſome <lb></lb>other man may haply think of ſome other more proper, and more <lb></lb>agreeable Senſe.</s></p><p type="main"> <s>But now, if this ſame paſſage may be underſtood in the <emph type="italics"></emph>Coper<lb></lb>nican<emph.end type="italics"></emph.end> Syſteme, to agree better with what we read in <emph type="italics"></emph>Joſhuah,<emph.end type="italics"></emph.end><lb></lb>with the help of another Obſervation by me newly ſhewen in <lb></lb>the Body of the Sun; I will propound it to conſideration, ſpeak<lb></lb>ing alwaies with thoſe ſafe Reſerves; That I am not ſo affectio<lb></lb>nate to my own inventions, as to prefer them before thoſe of <lb></lb>other men, and to believe that better and more agreeable to the <lb></lb>intention of the Sacred Volumes cannot be produced.</s></p><p type="main"> <s>Suppoſing therefore in the firſt place, that in the Miracle of <lb></lb><emph type="italics"></emph>Joſhuah,<emph.end type="italics"></emph.end> the whole Syſteme of the Celeſtial Revolutions ſtood <lb></lb>ſtill, according to the judgment of the afore-named Authors: <lb></lb>And this is the rather to be admitted, to the end, that by the <lb></lb>ſtaying of one alone, all the Conſtitutions might not be con<lb></lb>founded, and a great diſorder needleſly introduced in the whole <lb></lb>courſe of Nature: I come in the ſecond place to conſider how the <lb></lb>Solar Body, although ſtable in one conſtant place, doth neverthe<lb></lb>leſs revolve in it ſelf, making an entire Converſion in the ſpace <lb></lb>of a Month, or thereabouts; as I conceive I have ſolidly demon<lb></lb>ſtrated in my Letters <emph type="italics"></emph>Delle Machie Solari<emph.end type="italics"></emph.end>: Which motion we <lb></lb>ſenſibly ſee to be in the upper part of its Globe, inclined to<lb></lb>wards the South; and thence towards the lower part, to encline <lb></lb>towards the North, juſt in the ſame manner as all the other Orbs <lb></lb>of the Planets do. </s> <s>Thirdly, If we reſpect the Nobility of the <lb></lb>Sun, and his being the Fountain of Light, by which, (as I neceſ<lb></lb>ſarily demonſtrate) not onely the Moon and Earth, but all the <lb></lb>other Planets (all in the ſame manner dark of themſelves) become <lb></lb>illuminated; I conceive that it will be no unlogicall Illation to ſay, <lb></lb>That it, as the Grand Miniſter of Nature, and in a certain ſenſe <lb></lb>the Soul and Heart of the World, infuſeth into the other Bodies <lb></lb>which environ it; not onely Light, but Motion alſo; by revol<lb></lb>ving ^{*} in it ſelf: So that in the ſame manner that the motion of <lb></lb><arrow.to.target n="marg857"></arrow.to.target><lb></lb>the Heart of an Animal ceaſing, all the other motions of its <lb></lb>Members would ceaſe; ſo, the Converſion of the Sun ceaſing, <lb></lb>the Converſions of all the Planets would ſtand ſtill. </s> <s>And though <pb xlink:href="040/01/482.jpg" pagenum="458"></pb>I could produce the teſtimonies of many grave Writers to prove <lb></lb>the admirable power and influence of the Sun, I will content my <lb></lb>ſelf with one ſole place of Holy <emph type="italics"></emph>Dioniſius Areopagita<emph.end type="italics"></emph.end> in his Book <lb></lb><arrow.to.target n="marg858"></arrow.to.target><lb></lb><emph type="italics"></emph>de Divinis Nominibus<emph.end type="italics"></emph.end>; who thus writes of the Sun: ^{(*)} <emph type="italics"></emph>His Light <lb></lb>gathereth and converts all things to himſelf, which are ſeen, <lb></lb>moved, illuſtrated, wax hot, and (in a word) thoſe things which <lb></lb>are preſerved by his ſplendor: Wherefore the Sun is called<emph.end type="italics"></emph.end> <foreign lang="grc">Hλιος,</foreign><lb></lb><emph type="italics"></emph>for that he collecteth and gathereth together all things diſperſed.<emph.end type="italics"></emph.end><lb></lb>And a little after of the Sun again he adds; ^{(*)} <emph type="italics"></emph>If this Sun which <lb></lb>wo ſee, as touching the Eſſences and Qualities of thoſe things <lb></lb>which fall within our Senſe, being very many and different; yet <lb></lb>if he who is one, and equally beſtowes his Light, doth renew, <lb></lb>nouriſh, defend, perfect, divide, conjoyn, cheriſh, make fruitfull,<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg859"></arrow.to.target><lb></lb><emph type="italics"></emph>encreaſe, change, fix, produce, move, and faſhion all living crea<lb></lb>tures: And every thing in this Vniverſe at his Pleaſure, is par<lb></lb>taker of one and the ſame Sun; and the cauſes of many things <lb></lb>which participate of him, are equally auticipated in him: Certain<lb></lb>ly by greater reaſon<emph.end type="italics"></emph.end>; &c. </s> <s>The Sun therefore being the Foun<lb></lb>tain of Light and, Principle of Motion, God intending, that at <lb></lb>the Command of <emph type="italics"></emph>Joſhua,<emph.end type="italics"></emph.end> all the Worlds Syſteme, ſhould con<lb></lb>tinue many hours in the ſame ſtate, it ſufficeth to make the Sun <lb></lb>ſtand ſtill, upon whoſe ſtay (all the other Converſions ceaſing) <lb></lb>the Earth, the Moon, the Sun did abide in the ſame Conſtitution <lb></lb>as before, as likewiſe all the other Planets: Nor in all that time <lb></lb>did the Day decline towards Night, but it was miraculouſly pro<lb></lb>longed: And in this manner, upon the ſtanding ſtill of the Sun, <lb></lb>without altering, or in the leaſt diſturbing the other Aſpects and <lb></lb>mutual Poſitions of the Stars, the Day might be lengthned on <lb></lb>Earth; which exactly agreeth with the Litteral ſenſe of the Sacred <lb></lb>Text.</s></p><p type="margin"> <s><margin.target id="marg857"></margin.target>* <emph type="italics"></emph>i. </s> <s>i.<emph.end type="italics"></emph.end> On its own <lb></lb>Axis.</s></p><p type="margin"> <s><margin.target id="marg858"></margin.target>(*) <emph type="italics"></emph>Lux ejus colli<lb></lb>git, convertitque ad <lb></lb>ſe omnia, quæ vi<lb></lb>dentur, quæ mo<lb></lb>ventur, quæ illu<lb></lb>ſtrantur, quæ ca<lb></lb>leſcunt, & uno no<lb></lb>mine ea, quæ ab e<lb></lb>jus ſplendore cen<lb></lb>tinentur. </s> <s>Itaque <lb></lb>Sol <foreign lang="grc">Hλι<34></foreign> dicitur, <lb></lb>quod omnia con<lb></lb>greger, colligatque <lb></lb>diſperſa.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg859"></margin.target>(*) <emph type="italics"></emph>Si enim <lb></lb>Sol hic quem vi<lb></lb>domus, eorum quæ <lb></lb>ſub ſenſum ca<lb></lb>dunt, eſſentias & <lb></lb>qualitates, quæ que <lb></lb>muliæ ſint ac diſ<lb></lb>ſimiles, tamen ipſe <lb></lb>qui unus eſt, æqua<lb></lb>literque lumen <lb></lb>fundit, renovat, a<lb></lb>lit, tuetur, perficit, <lb></lb>dividit, conjungit, <lb></lb>fovet, fæcunda red<lb></lb>dit, auget, mutat, <lb></lb>firmat, edit, movet, <lb></lb><expan abbr="vitaliaq;">vitaliaque</expan> facit om<lb></lb>nia: & <expan abbr="unaquæq;">unaquæque</expan> <lb></lb>res hujus univer<lb></lb>ſitatis, pro cæptu <lb></lb>ſuo, unius atque e<lb></lb>juſdem Solis eſt <lb></lb>particeps, cauſæſ<lb></lb>que multorum, <lb></lb>quæ participant, in <lb></lb>ſe æquabiliter an<lb></lb>ticipatas habet, <lb></lb>certe majori ratio<lb></lb>ne,<emph.end type="italics"></emph.end> &c.</s></p><p type="main"> <s>But that of which, if I be not miſtaken, we are to make no <lb></lb>ſmall account, is, That by help of this <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Hypotheſis, <lb></lb>we have the Litteral, apert, and Natural Senſe of another parti<lb></lb>cular that we read of in the ſame Miracle; which is, That the <lb></lb>Sun ſtood ſtill <emph type="italics"></emph>in Medio Cæli<emph.end type="italics"></emph.end>: Upon which paſſage grave Divines <lb></lb>raiſe many queſtions, in regard it ſeemeth very probable, That <lb></lb>when <emph type="italics"></emph>Joſhuah<emph.end type="italics"></emph.end> deſired the lengthning of the Day, the Sun was <lb></lb>near ſetting, and not in the Meridian; for if it had been in the <lb></lb>Meridian, it being then about the Summer <emph type="italics"></emph>Solſtice,<emph.end type="italics"></emph.end> and con<lb></lb>ſequently the dayes being at the longeſt, it doth not ſeem likely <lb></lb>that it was neceſſary to pray for the lengthning of the day, to <lb></lb>proſecute Victory in a Battail, the ſpace of ſeven hours and more, <lb></lb>which remained to Night, being ſufficient for that purpoſe. <lb></lb></s> <s>Upon which Grave Divines have been induced to think that the <lb></lb>Sun was near ſetting: And ſo the words themſelves ſeem to <pb xlink:href="040/01/483.jpg" pagenum="459"></pb>ſound, ſaying, <emph type="italics"></emph>Ne movearis Sol, ne movearis.<emph.end type="italics"></emph.end> For if it had <lb></lb>been in the Meridian, either it had been needleſs to have asked <lb></lb>a Miracle, or it would have been ſufficient to have onely praid <lb></lb>for ſome retardment. </s> <s>Of this opinion is <emph type="italics"></emph>Cajetan,<emph.end type="italics"></emph.end> to which ſub<lb></lb>ſcribeth <emph type="italics"></emph>Magaglianes,<emph.end type="italics"></emph.end> confirming it by ſaying, that <emph type="italics"></emph>Joſhua<emph.end type="italics"></emph.end> had <lb></lb>that very day done ſo many other things before his commanding <lb></lb>the Sun, as were not poſſibly to be diſpatch't in half a day. <lb></lb></s> <s>Whereupon they are forced to read the Words <emph type="italics"></emph>in Medio Cœli<emph.end type="italics"></emph.end><lb></lb>(to confeſs the truth) with a little harſhneſs, ſaying that they <lb></lb>import no more than this: <emph type="italics"></emph>That the Sun ſtood ſtill, being in our <lb></lb>Hemiſphere, that is, above the Horizon.<emph.end type="italics"></emph.end> But (if I do not erre) <lb></lb><arrow.to.target n="marg860"></arrow.to.target><lb></lb>we ſhall avoid that and all other harſh expoſitions, if according <lb></lb>to the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Syſteme we place the Sun in the midſt, that <lb></lb>is, in the Centre of the Cœleſtial Orbes, and of the Planetary <lb></lb>Converſions, as it is moſt requiſite to do. </s> <s>For ſuppoſing any <lb></lb>hour of the day (either Noon, or any other, as you ſhall pleaſe <lb></lb>neerer to the Evening) the Day was lengthened, and all the <lb></lb>Cœleſtial Revolutions ſtayed by the Suns ſtanding ſtill, <emph type="italics"></emph>In the <lb></lb>midſt,<emph.end type="italics"></emph.end> that is, <emph type="italics"></emph>in the Centre of Heaven,<emph.end type="italics"></emph.end> where it reſides: A <lb></lb>Senſe ſo much the more accomodate to the Letter (beſides what <lb></lb>hath been ſaid already) in that, if the Text had deſired to have <lb></lb>affirmed the Suns Reſt to have been cauſed at Noon-day, the <lb></lb>proper expreſſion of it had been to ſay, <emph type="italics"></emph>It ſtood ſtill at Noon-day,<emph.end type="italics"></emph.end><lb></lb>or <emph type="italics"></emph>in the Meridian Circle,<emph.end type="italics"></emph.end> and not <emph type="italics"></emph>in the midſt of Heaven<emph.end type="italics"></emph.end>: In <lb></lb>regard that the true and only <emph type="italics"></emph>Middle<emph.end type="italics"></emph.end> of a Spherical Body (as is <lb></lb>Heaven) is the Centre.</s></p><p type="margin"> <s><margin.target id="marg860"></margin.target><emph type="italics"></emph>Solem ſtetiſſe, <lb></lb>dum adhuc in He<lb></lb>miſpharto noſtro, <lb></lb>ſupra ſcilicet Ho<lb></lb>rizontem exiſteret.<emph.end type="italics"></emph.end><lb></lb>Cajetan <emph type="italics"></emph>in loce.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Again, as to other places of Scripture, which ſeem contrary to <lb></lb>this poſition, I do not doubt but that if it were acknowledged <lb></lb>for True and Demonſtrated thoſe very Divines who ſo long as <lb></lb>they repute it falſe, hold thoſe places incapable of Expoſitions <lb></lb>that agree with it would finde ſuch Interpretations for them, as <lb></lb>ſhould very well ſuit therewith; and eſpecially if to the know<lb></lb>ledge of Divine Learning they would but adde ſome knowledge <lb></lb>of the Aſtronomical Sciences: And as at preſent, whilſt they <lb></lb>deem it falſe they think they meet in Scripture only with ſuch <lb></lb>places as make againſt it, if they ſhall but once have entertained <lb></lb>another conceipt thereof, they would meet peradventure as many <lb></lb>others that accord with it, and haply would judge, that the Holy <lb></lb>Church doth very appoſitly teach, That God placed the Sun in <lb></lb>the Centre of Heaven, and that thereupon by revolving it in it <lb></lb>ſelf, after the manner of a Wheel, He contributed the ordinary <lb></lb>Courſes to the Moon and other Erratick Stars, whilſt that ſhe <lb></lb>Sings,</s></p><p type="main"> <s><emph type="italics"></emph>Cœli Deus ſanctiſſime,<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Qui lucidum Centrum Poli,<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/484.jpg" pagenum="460"></pb><p type="main"> <s><emph type="italics"></emph>Candore ping is igneo,<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Augens decoro lumine,<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Quarto die, qui flammeam<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Solis rotam conſtituens<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Lunœ miniſtras ordinem,<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Vagoſque curſus Syderum.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>They might ſay, that the Name of <emph type="italics"></emph>Firmament<emph.end type="italics"></emph.end> very well a<lb></lb>greeth, <emph type="italics"></emph>ad literam,<emph.end type="italics"></emph.end> to the Starry Sphere, and to all that which <lb></lb>is above the Planetary Converſions; which according to this Hy<lb></lb>potheſis is altogether <emph type="italics"></emph>firme<emph.end type="italics"></emph.end> and immoveable. <emph type="italics"></emph>Ad litteram<emph.end type="italics"></emph.end> (the <lb></lb>Earth moving circularly) they might underſtand its <emph type="italics"></emph>Poles,<emph.end type="italics"></emph.end><lb></lb>where it's ſaid, <emph type="italics"></emph>Nec dum Terram fecerat, & flumina, &<emph.end type="italics"></emph.end> Cardi<lb></lb>nes <emph type="italics"></emph>Orbis Terrœ,<emph.end type="italics"></emph.end> Which <emph type="italics"></emph>Cardines<emph.end type="italics"></emph.end> or ^{*} <emph type="italics"></emph>liinges<emph.end type="italics"></emph.end> ſeem to be aſcribed <lb></lb><arrow.to.target n="marg861"></arrow.to.target><lb></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"></emph>FINIS.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/485.jpg" pagenum="461"></pb><p type="head"> <s>AN <lb></lb>ABSTRACT <lb></lb>OF THE <lb></lb>Learned Treatiſe <lb></lb>OF <lb></lb>JOHANNIS KEPL<emph type="italics"></emph>E<emph.end type="italics"></emph.end>RUS, <lb></lb>The Emperours <emph type="italics"></emph>Mathematician<emph.end type="italics"></emph.end>: <lb></lb>ENTITULED <lb></lb><emph type="italics"></emph>His Introduction upon<emph.end type="italics"></emph.end> MARS:</s></p><p type="main"> <s>It muſt be confeſſed, that there are very <lb></lb>many who are devoted to Holineſſe, <lb></lb>that diſſent from the Judgment of <emph type="italics"></emph>Co<lb></lb>pernicus,<emph.end type="italics"></emph.end> fearing to give the Lye to the <lb></lb>Holy Ghoſt ſpeaking in the Scriptures, <lb></lb>if they ſhould ſay, that the Earth mo<lb></lb>veth, and the Sun ſtands ſtill. </s> <s>But let <lb></lb>ſuch conſider, that ſince we judge of ve<lb></lb>ry many, and thoſe the moſt principal <lb></lb>things by the Senſe of Seeing, it is impoſſible that we ſhould ali<lb></lb>enate our Speech from this Senſe of our Eyes. </s> <s>Therefore many <lb></lb>things daily occur, of which we ſpeak according to the Senſe of <lb></lb>Sight, when as we certainly know that the things themſelves are <lb></lb>otherwiſe. </s> <s>An Example whereof we have in that Verſe of <lb></lb><emph type="italics"></emph>Virgil<emph.end type="italics"></emph.end>;</s></p><p type="head"> <s><emph type="italics"></emph>Provehimur portu, Terrœque urbeſque recedunt.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>So when we come forth of the narrow ſtraight of ſome Val<lb></lb>ley, we ſay that a large Field diſcovereth it ſelf. </s> <s>So Chriſt to <lb></lb><emph type="italics"></emph>Peter, Duc in altum<emph.end type="italics"></emph.end>; [Lanch forth into the Deep, or on high,] <lb></lb>as if the Sea were higher than its Shores; For ſo it ſeemeth to <lb></lb>the Eye, but the Opticks ſhew the cauſe of this fallacy. </s> <s>Yet <lb></lb>Chriſt uſeth the moſt received Speech, although it proceed from <lb></lb>this deluſion of the Eyes. </s> <s>Thus we conceive of the Riſing and <pb xlink:href="040/01/486.jpg" pagenum="462"></pb>Setting of the Stars, that is to ſay, of their Aſcenſion and Deſ<lb></lb>cenſion; when at the ſame time that we affirm the Sun riſeth, o<lb></lb>thers ſay, that it goeth down. </s> <s>See my <emph type="italics"></emph>Optices Aſtronomiœ, cap.<emph.end type="italics"></emph.end><lb></lb>10. <emph type="italics"></emph>fol.<emph.end type="italics"></emph.end> 327 So in like manner, the <emph type="italics"></emph>Ptolomaicks<emph.end type="italics"></emph.end> affirm, that the <lb></lb>Planets <emph type="italics"></emph>ſtand ſtill,<emph.end type="italics"></emph.end> when for ſome dayes together they ſeem to be <lb></lb>fixed, although they believe them at that very time to be moved <lb></lb>in a direct line, either downwards to, or upwards from the <lb></lb>Earth. </s> <s>Thus the Writers of all Nations uſe the word <emph type="italics"></emph>Solſtiti<lb></lb>um,<emph.end type="italics"></emph.end> and yet they deny that the Sun doth really ſtand ſtill. </s> <s>Like<lb></lb>wiſe there will never any man be ſo devoted to <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> but <lb></lb>he will ſay, the Sun entereth into <emph type="italics"></emph>Cancer<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Leo,<emph.end type="italics"></emph.end> although he <lb></lb>granteth that the Earth enters <emph type="italics"></emph>Capricorn<emph.end type="italics"></emph.end> or <emph type="italics"></emph>Aquarius<emph.end type="italics"></emph.end>: And ſo <lb></lb>in other caſes of the like nature. </s> <s>But now the Sacred Scriptures, <lb></lb>ſpeaking to men of vulgar matters (in which they were not in<lb></lb>tended to inſtruct men) after the manner of men, that ſo they <lb></lb>might be underſtood by men, do uſe ſuch Expreſſions as are <lb></lb>granted by all, thereby to inſinuate other things more Myſterious <lb></lb>and Divine. </s> <s>What wonder is it then, if the Scripture ſpeaks <lb></lb>according to mans apprehenſion, at ſuch time when the Truth <lb></lb>of things doth diſſent from the Conception that all men, whe<lb></lb>ther Learned or Unlearned have of them? </s> <s>Who knows not <lb></lb>that it is a Poetical alluſion, <emph type="italics"></emph>Pſal.<emph.end type="italics"></emph.end> 19. where, whilſt under the ſi<lb></lb>militude of the Sun, the Courſe of the Goſpel, as alſo the Pere<lb></lb>grination of our Lord Chriſt in this World, undertaken for our <lb></lb>ſakes, is deſcribed, <emph type="italics"></emph>The Sun<emph.end type="italics"></emph.end> is ſaid <emph type="italics"></emph>to come forth of his Taberna<lb></lb>cle<emph.end type="italics"></emph.end> of the Horizon, <emph type="italics"></emph>as a Bridegroom out of his Chamber, re<lb></lb>joycing as a Giant to run a Race<emph.end type="italics"></emph.end>? </s> <s>Which <emph type="italics"></emph>Virgil<emph.end type="italics"></emph.end> thus imitates;</s></p><p type="head"> <s><emph type="italics"></emph>Tithono croceum linquens Auror a cubile<emph.end type="italics"></emph.end>:</s></p><p type="main"> <s>For the firſt Poets were amongſt the Jews. </s> <s>The Pſalmiſt knew that <lb></lb>the Sun went not forth of the Horizon, as out of its Tabernacle, <lb></lb>& yet it ſeemeth to the Eye ſo to do: Nor did he believe, that the <lb></lb>Sun moved, for that it appeared to his ſight ſo to do. </s> <s>And yet he <lb></lb>ſaith both, for that both were ſo to his ſeeming. </s> <s>Neither is it <lb></lb>to be adjudged falſe in either Senſe: for the perception of the <lb></lb>Eyes hath its verity, fit for the more ſecret purpoſe of the Pſal<lb></lb>miſt in ſhadowing forth the current paſſage oſ the Goſpel, as <lb></lb>alſo the Peregrination of the Son of God. <emph type="italics"></emph>Joſhua<emph.end type="italics"></emph.end> likewiſe <lb></lb>mentioneth the Vallies on or in, which the Sun and Moon mo<lb></lb>ved, for that they appeared to him at <emph type="italics"></emph>Jordan<emph.end type="italics"></emph.end> ſo to do: And yet <lb></lb>both theſe Pen-men may obtain their ends. <emph type="italics"></emph>David,<emph.end type="italics"></emph.end> (and with <lb></lb>him <emph type="italics"></emph>Syracides<emph.end type="italics"></emph.end>) the magnificence of God being made known, <lb></lb>which cauſed theſe things to be in this manner repreſented to <lb></lb>ſight, or otherwiſe, the myſtical meaning, by means of theſe <lb></lb>Viſibles being diſcerned: And <emph type="italics"></emph>Joſhua,<emph.end type="italics"></emph.end> in that the Sun, as to his <pb xlink:href="040/01/487.jpg" pagenum="463"></pb>Senſe of Seeing, ſtaid a whole day in the midſt of Heaven, where<lb></lb>as at the ſame time to others it lay hid under the Earth. </s> <s>But in<lb></lb>cogitant perſons onely look upon the contrariety of the words, <lb></lb><emph type="italics"></emph>The Sun ſtood ſtill,<emph.end type="italics"></emph.end> that is, <emph type="italics"></emph>The Earth ſtood ſtill<emph.end type="italics"></emph.end>; not conſidering <lb></lb>that this contradiction is confined within the limits of the Op<lb></lb>ticks and Aſtronomy: For which cauſe it is not outwardly ex<lb></lb>poſed to the notice and uſe of men: Nor will they underſtand <lb></lb>that the onely thing <emph type="italics"></emph>Joſhuah<emph.end type="italics"></emph.end> prayed for, was that the Mountains <lb></lb>might not intercept the Sun from him; which requeſt he expreſ<lb></lb>ſed in words, that ſuited with his Ocular Senſe: Beſides it had <lb></lb>been very unſeaſonable at that time to think of Aſtronomy, or <lb></lb>the Errours in Sight; for if any one ſhould have told him that <lb></lb>the Sun could not really move upon the Valley of <emph type="italics"></emph>Ajalon,<emph.end type="italics"></emph.end>, but <lb></lb>onely in relation to Senſe, would not <emph type="italics"></emph>Joſhuah<emph.end type="italics"></emph.end> have replyed, that <lb></lb>his deſire was that the day might be prolonged, ſo it were by <lb></lb>any means whatſoever? </s> <s>In like manner would he have anſwered <lb></lb>if any one had ſtarted a queſtion about the Suns Mobility, and <lb></lb>the Earths Motion. </s> <s>But God eaſily underſtood by <emph type="italics"></emph>Joſhuahs<emph.end type="italics"></emph.end><lb></lb>words what he asked for, and by arreſting the Earths Motion, <lb></lb>made the Sun in his apprehenſion ſeem to ſtand ſtill. </s> <s>For the <lb></lb>ſumm of <emph type="italics"></emph>Joſhuahs<emph.end type="italics"></emph.end> Prayer amounts to no more but this, that it <lb></lb>might thus appear to him, let it in the mean time <emph type="italics"></emph>be what it <lb></lb>would<emph.end type="italics"></emph.end> of it ſelf. </s> <s>For that its ſo ſeeming, was not in vain and <lb></lb>ridiculous, but accompanied with the deſired effect. </s> <s>But read <lb></lb>the tenth <emph type="italics"></emph>Chap.<emph.end type="italics"></emph.end> of my <emph type="italics"></emph>Book,<emph.end type="italics"></emph.end> that treats of <emph type="italics"></emph>the Optick part of A<lb></lb>ſtronomy,<emph.end type="italics"></emph.end> where thou ſhalt finde the Reaſons why the Sun doth <lb></lb>in this manner ſeem to all mens thinking to be moved, and not <lb></lb>the Earth; as namely, becauſe the Sun appeareth ſmall; and the <lb></lb>Earth bigg. </s> <s>Again, the Motion of the Sun is not diſcerned by <lb></lb>the eye, by reaſon of his ſeeming tardity, but by ratiocina<lb></lb>tion onely; in that after ſome time it varieth not its proximity to <lb></lb>ſuch and ſuch Mountains. </s> <s>Therefore it is impoſſible that Rea<lb></lb>ſon, unleſs it be firſt inſtructed, ſhould frame to it ſelf any other <lb></lb>apprehenſion, than that the Earth with Heavens Arch placed <lb></lb>over it, is as it were a great Houſe, in which, being immoveable, <lb></lb>the Sun like a Bird flying in the Air, paſſeth in ſo ſmall a Species <lb></lb>out of one Climate into another. </s> <s>Which imagination of all <lb></lb>Man-kinde being thus, gave the firſt line in the Sacred Leaves: <lb></lb>^{*} <emph type="italics"></emph>In the beginning<emph.end type="italics"></emph.end> (ſaith <emph type="italics"></emph>Moſes) God created the Heaven and the <lb></lb><arrow.to.target n="marg862"></arrow.to.target><lb></lb>Earth<emph.end type="italics"></emph.end>; for that theſe two are moſt obvious to the eye. </s> <s>As if <lb></lb><emph type="italics"></emph>Moſes<emph.end type="italics"></emph.end> ſhould have ſaid thus to Man; This whole Mundane Fa<lb></lb>brick which thou ſeeſt, lucid above, and dark, and of a vaſt ex<lb></lb>tent beneath, wherein thou haſt thy being, and with which thou <lb></lb>art covered, was created by God.</s></p><p type="margin"> <s><margin.target id="marg862"></margin.target>* Gen. <emph type="italics"></emph>Chv. </s> <s>1. <lb></lb>v.<emph.end type="italics"></emph.end> 1.</s></p><p type="main"> <s>In another place Man is queſtioned; <emph type="italics"></emph>Whether he can finde out<emph.end type="italics"></emph.end> <pb xlink:href="040/01/488.jpg" pagenum="464"></pb><emph type="italics"></emph>the height of Heaven above, or depth of the Earth beneath<emph.end type="italics"></emph.end>: for <lb></lb>that each of them appeareth to men of ordinary capacity, to have <lb></lb>equally an infinite extent. </s> <s>And yet no man that is in his right <lb></lb>mind will by theſe words circumſcribe and bound the diligence <lb></lb>of Aſtronomers, whether in demonſtrating the moſt contemptible <lb></lb>Minuity of the Earth, in compariſon of Heaven, or in ſearching <lb></lb>out Aſtronomical <emph type="italics"></emph>Diſtances<emph.end type="italics"></emph.end>: Since thoſe words ſpeak not of the <lb></lb>Rational, but real Dimention; which to a Humane Body, <lb></lb>whilſt confin'd to the Earth, and breathing in the open Air, is al<lb></lb>together impoſſible. </s> <s>Read the whole 38. Chapter of <emph type="italics"></emph>Job,<emph.end type="italics"></emph.end> and <lb></lb>compare it with thoſe Points which are diſputed in Aſtronomy, <lb></lb><arrow.to.target n="marg863"></arrow.to.target><lb></lb>and Phyſiologie. </s> <s>If any one do alledge from <emph type="italics"></emph>Pſal.<emph.end type="italics"></emph.end> 24. That ^{*} <emph type="italics"></emph>The <lb></lb>Earth is founded upon the Seas,<emph.end type="italics"></emph.end> to the end that he may thence <lb></lb>infer ſome new Principle in Philoſophy, abſurd to hear; as, That <lb></lb>the Earth doth float upon the Waters; may it not truly be told <lb></lb>him, That he ought not to meddle with the Holy Spirit, nor to <lb></lb>bring him with contempt into the School of Phyſiologie. <lb></lb></s> <s>For the Pſalmiſt in that place means nothing elſe but <lb></lb>that which men fore-know, and daily ſee by experience; namely, <lb></lb>That the Earth (being lifted up after the ſeparation of the Wa<lb></lb>ters) doth ſwim between the Grand Oceans, and float about the <lb></lb>Sea. </s> <s>Nor is it ſtrange that the expreſſion ſhould be the ſame <lb></lb>where the <emph type="italics"></emph>Iſraelites<emph.end type="italics"></emph.end> ſing, ^{*} <emph type="italics"></emph>That they ſate on the River of Baby<lb></lb><arrow.to.target n="marg864"></arrow.to.target><lb></lb>lon<emph.end type="italics"></emph.end>; that is, <emph type="italics"></emph>by<emph.end type="italics"></emph.end> the River ſide. </s> <s>or on the Banks of <emph type="italics"></emph>Euphrates<emph.end type="italics"></emph.end> and <lb></lb><emph type="italics"></emph>Tygris.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg863"></margin.target>* Pſal. </s> <s>24. 2.</s></p><p type="margin"> <s><margin.target id="marg864"></margin.target>Pſal. </s> <s>137. 1.</s></p><p type="main"> <s>If any one receive this Reading without ſcruple, why not the <lb></lb>other; that ſo in thoſe ſame Texts which are wont to be alledged <lb></lb>againſt the Motion of the Earth, we may in like manner turn our <lb></lb>eyes from Natural Philoſophy, to the ſcope and intent of Scri<lb></lb>pture. <emph type="italics"></emph>One Generation paſſeth away,<emph.end type="italics"></emph.end> (ſaith <emph type="italics"></emph>Eccleſiaſtes) and a<lb></lb><arrow.to.target n="marg865"></arrow.to.target><lb></lb>nother Generation cometh: But the Earth abideth for ever.<emph.end type="italics"></emph.end> ^{*} As <lb></lb>if <emph type="italics"></emph>Solomon<emph.end type="italics"></emph.end> did here diſpute with Aſtronomers, and not rather put <lb></lb>men in minde of their Mutability; when as the Earth, Mankindes <lb></lb>habitation, doth alwaies remain the ſame: The Suns Motion <lb></lb>doth continually return into what it was at firſt: The Wind is <lb></lb>acted in a Circle, and returns in the ſame manner: The Rivers <lb></lb>flow from their Fountains into the Sea, and return again from <lb></lb>thence unto their Fountains: To conclude, The Men of this <lb></lb>Age dying, others are born in their room; the Fable of Life is <lb></lb>ever the ſame; there is nothing new under the Sun. </s> <s>Here is no <lb></lb>reference to any Phyſical Opinion. <foreign lang="grc"><gap></gap>ον<gap></gap>εσὶα</foreign> is Moral of a thing in it <lb></lb>ſelf manifeſt, and ſeen by the eyes of all, but little regarded: Tis <lb></lb>that therefore which <emph type="italics"></emph>Solomon<emph.end type="italics"></emph.end> doth inculcate. </s> <s>For who knows not <lb></lb>that the Earth is alwaies the ſame? </s> <s>Who ſees not that the Sun <lb></lb>dothariſe from the Eaſt; That the Rivers continually run into <pb xlink:href="040/01/489.jpg" pagenum="465"></pb>the Sea; That the viciſſitudes of the Windes return into their <lb></lb>primitive State; That ſome men ſucceed others? </s> <s>But who con<lb></lb>ſidereth that the ſelf-ſame <emph type="italics"></emph>Scene<emph.end type="italics"></emph.end> of Life is ever acting, by diffe<lb></lb>rent perſons; and that nothing is <emph type="italics"></emph>new<emph.end type="italics"></emph.end> in humane affairs? </s> <s>There<lb></lb>fore <emph type="italics"></emph>Solomon<emph.end type="italics"></emph.end> inſtancing in thoſe things which all men ſee, doth <lb></lb>put men in minde of that which many thorowly know, but too <lb></lb>ſlightly conſider.</s></p><p type="margin"> <s><margin.target id="marg865"></margin.target>* Chap. </s> <s>1. v. </s> <s>4, to <lb></lb>9.</s></p><p type="main"> <s>But the 104. <emph type="italics"></emph>Pſalm<emph.end type="italics"></emph.end> is thought by ſome to contain a Diſcourſe <lb></lb>altogether Phyſical, in regard it onely concerns Natural Philoſo<lb></lb>phy. </s> <s>Now God is there ſaid, <emph type="italics"></emph>To have laid the Foundations of <lb></lb><arrow.to.target n="marg866"></arrow.to.target><lb></lb>the Earth, that it ſhould not be removed for ever.<emph.end type="italics"></emph.end> But here al<lb></lb>ſo the Pſalmiſt is far from the Speculation of Phyſical Cauſes: <lb></lb>For he doth wholly acquieſce in the Greatneſſe of God, <lb></lb>who did all theſe things, and ſings an Hymne to God the <lb></lb>Maker of them, in which he runneth over the World in order, <lb></lb>as it appeared to his eyes. </s> <s>And if you well conſider this <lb></lb>Pſalme, it is a Paraphraſe upon the ſix dayes work of the Crea<lb></lb>tion: For as in it the three firſt dayes were ſpent in the Separa<lb></lb>tion of Regions; the firſt of Light from the exteriour Dark<lb></lb>neſs; the ſecond, of the Waters from the Waters, by the inter<lb></lb>poſition of the Firm ament; the third, of the Sea from Land; <lb></lb>when alſo the Earth was cloathed with Herbage and Plants: <lb></lb>And the three laſt dayes were ſpent in the filling the Re<lb></lb>gions thus diſtinguiſhed; the fourth, of Heaven; the <lb></lb>fifth, of the Seas and Aire; the fixth, of the Earth: So <lb></lb>here in this Pſalme there are ſo many diſtinct parts pro<lb></lb>portionable to the Analogy of the ſix dayes Works. </s> <s>For <lb></lb>in <emph type="italics"></emph>Verſe<emph.end type="italics"></emph.end> 2. he cloaths and covereth the Creator with Light <lb></lb>(the firſt of Creatures, and work of the firſt day) as with a <lb></lb>Garment. </s> <s>The ſecond part beginneth at <emph type="italics"></emph>Verſe<emph.end type="italics"></emph.end> 3. and treats of <lb></lb>the Waters above the Heavens, the extent of Heaven and of Me<lb></lb>teors (which the Pſalmiſt ſeemeth to intend by the Waters a<lb></lb>bove) as namely of Clouds, Winds, Whirl-winds, Lightnings. <lb></lb></s> <s>The third part begins at <emph type="italics"></emph>Verſe<emph.end type="italics"></emph.end> 6. and doth celebrate the Earth <lb></lb>as the foundation of all thoſe things which he here conſidereth. <lb></lb></s> <s>For he referreth all things to the Earth, and to thoſe Animals <lb></lb>which inhabit it, for that in the judgment of Sight the two prin<lb></lb>cipal parts of the World are Heaven and Earth. </s> <s>He therefore <lb></lb>here obſerveth that the Earth after ſo many Ages hath not falte<lb></lb>red, tired, or decayed; when as notwithſtanding no man hath <lb></lb>yet diſcovered upon what it is founded. </s> <s>He goeth not about to <lb></lb>teach men what they do not know, but putteth them in minde <lb></lb>of what they neglect, to wit, the Greatneſſe and Power of God <lb></lb>in creating ſo huge a Maſs ſo firm and ſtedfaſt. </s> <s>If an Aſtrono<lb></lb>mer ſhould teach that the Earth is placed among the Planets, he <pb xlink:href="040/01/490.jpg" pagenum="466"></pb>overthroweth not what the Pſalmiſt here ſaith, nor doth he con<lb></lb>tradict Common Experience; for it is true notwithſtanding, <lb></lb>that the Earth, the Structure of God its Architect, doth not de<lb></lb>cay (as our Buildings are wont to do) by age, or conſume by <lb></lb>wormes, nor ſway and leane to this or that ſide; that the Seats <lb></lb>and Neſts of Living Creatures are not moleſted; that the <lb></lb>Mountains and Shores ſtand immoveable againſt the violence of <lb></lb>the Winds and Waves, as they were at the beginning. </s> <s>But the <lb></lb>Pſalmiſt addeth a moſt Elegant Hypotheſis of the Separation of <lb></lb>the Waters from the Continent or Main-land, and adorns it <lb></lb>with the production of Fountains, and the benefits that Springs <lb></lb>and Rocks exhibit to Birds and Beaſts. </s> <s>Nor doth he omit the <lb></lb>apparelling the Earths Surface, mentioned by <emph type="italics"></emph>Moſes<emph.end type="italics"></emph.end> amongſt the <lb></lb>works of the third Day, but more ſublimely deſcribeth it in his <lb></lb>Caſe in expreſſions infuſed from Divine Inſpiration; and flouri<lb></lb>ſheth out the commemoration of the many commodities which <lb></lb>redound from that Exornation for the Nouriſhment and Com<lb></lb><arrow.to.target n="marg867"></arrow.to.target><lb></lb>fort of Man, and ^{*} Covert of Beaſts. </s> <s>The fourth part begins <lb></lb>at <emph type="italics"></emph>Verſe<emph.end type="italics"></emph.end> 20. celebrating the fourth dayes work, <emph type="italics"></emph>viz.<emph.end type="italics"></emph.end> The Sun <lb></lb>and Moon, but chiefly the commodiouſneſſe of thoſe things, <lb></lb>which in their Seaſons befall to all Living Creatures and to Man; <lb></lb>this being the ſubject matter of his Diſcourſe: So that it plain<lb></lb>ly appeareth he acted not the part of an Aſtronomer. </s> <s>For if he <lb></lb>had, he would not then have omitted to mention the five Planets, <lb></lb>than whoſe moiton nothing is more admirable, nothing more ex<lb></lb>cellent, nothing that can more evidently ſet forth the Wiſdome <lb></lb>of the Creator amongſt the Learned. </s> <s>The fifth part begins, <lb></lb><emph type="italics"></emph>Verſe<emph.end type="italics"></emph.end> 25. with the fifth Dayes work. </s> <s>And it ſtores the Seas with <lb></lb>Fiſhes, and covers them with Ships. </s> <s>The ſixth part is more ob<lb></lb>ſcurely hinted at, <emph type="italics"></emph>Verſe<emph.end type="italics"></emph.end> 28. and alludeth to the Land-Creatures <lb></lb>that were created the ſixth day. </s> <s>And laſtly, he declareth the <lb></lb>goodneſſe of God in general, who daily createth and preſerveth <lb></lb>all things? </s> <s>So that whatever he ſaid of the World is in relation <lb></lb>to Living Creatures; He ſpeaks of nothing but what is granted <lb></lb>on all hands; for that it was his intent to extol things known, <lb></lb>and not to dive into hidden matters, but to invite men to con<lb></lb>template the Benefits that redouud unto them from the works of <lb></lb>each of theſe dayes.</s></p><p type="margin"> <s><margin.target id="marg866"></margin.target>Pſal. </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 alſo beſeech my Reader, not forgetting the Divine <lb></lb>Goodneſſe conferred on Mankind; the conſideration of which <lb></lb>the Pſalmiſt doth chiefly urge, that when he returneth from the <lb></lb>Temple, and enters into the School of <emph type="italics"></emph>Aſtronomy,<emph.end type="italics"></emph.end> he would <lb></lb>with me praiſe and admire the Wiſdome and Greatneſſe of the <lb></lb>Creator, which I diſcover to him by a more narrow explication <lb></lb>of the Worlds Form, the Diſquiſition of Cauſes, and Detection <pb xlink:href="040/01/491.jpg" pagenum="467"></pb>of the Errours of Sight: And ſo he will not onely extoll the <lb></lb>Bounty of God in the preſervation of Living Creatures of all <lb></lb>kindes, and eſtabliſhment of the Earth; but even in its Motion <lb></lb>alſo, which is ſo ſtrange, ſo admirable, he will acknowledge the <lb></lb>Wiſdome of the Creator. </s> <s>But he who is ſo ſtupid as not to <lb></lb>comprehend the Science of <emph type="italics"></emph>Aſtronomy,<emph.end type="italics"></emph.end> or ſo weak and ſcrupu<lb></lb>lous as to think it an offence of Piety to adhere to <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end><lb></lb>him I adviſe, that leaving the Study of <emph type="italics"></emph>Aſtronomy,<emph.end type="italics"></emph.end> and cenſuring <lb></lb>the opinions of Philoſophers at pleaſure, he betake himſelf to <lb></lb>his own concerns, and that deſiſting from further purſuit of theſe <lb></lb>intricate Studies, he keep at home and manure his own Ground; <lb></lb>and with thoſe Eyes wherewith alone he ſeeth, being eleva<lb></lb>ted towards this to be admired Heaven, let him pour forth his <lb></lb>whole heart in thanks and praiſes to God the Creator; and aſ<lb></lb>ſure himſelf that he ſhall therein perform as much Worſhip to <lb></lb>God, as the <emph type="italics"></emph>Aſtronomer,<emph.end type="italics"></emph.end> on whom God hath beſtowed this Gift, <lb></lb>that though he ſeeth more clearly with the Eye of his Under<lb></lb>ſtanding; yet whatever he hath attained to, he is both able and <lb></lb>willing to extoll his God above it.</s></p><p type="main"> <s>And thus much concerning the Authority of Sacred Scripture. <lb></lb></s> <s>Now as touching the opinions of the Saints about theſe Natural <lb></lb>Points. </s> <s>I anſwer in one word, That in Theology the weight of <lb></lb>Authority, but in Philoſophy the weight of Reaſon is to be con<lb></lb>ſidered. </s> <s>Therefore Sacred was <emph type="italics"></emph>Lactantius,<emph.end type="italics"></emph.end> who denyed the <lb></lb>Earths rotundity; Sacred was <emph type="italics"></emph>Auguſtine,<emph.end type="italics"></emph.end> who granted the Earth <lb></lb>to be round, but denyed the <emph type="italics"></emph>Antipodes<emph.end type="italics"></emph.end>; Sacred is the ^{*}Liturgy of <lb></lb><arrow.to.target n="marg868"></arrow.to.target><lb></lb>our Moderns, who admit the ſmallneſſe of the Earth, but deny <lb></lb>its Motion: But to me more ſacred than all theſe is Truth, who <lb></lb>with reſpect to the Doctors of the Church, do demonſtrate <lb></lb>from Philoſophy that the Earth is both round, circumhabited by <lb></lb><emph type="italics"></emph>Antipodes,<emph.end type="italics"></emph.end> of a moſt contemptible ſmalneſſe, and in a word, <lb></lb>that it is ranked amongſt the Planets.</s></p> <pb xlink:href="040/01/492.jpg" pagenum="468"></pb><p type="margin"> <s><margin.target id="marg868"></margin.target>* Officium</s></p><p type="head"> <s>AN <lb></lb>ABSTRACT <lb></lb>OF <lb></lb>Some paſſages in the Commentaries of <lb></lb>Didacus à Stunica, <lb></lb>OF <lb></lb>SALAMANCA <lb></lb>Upon <emph type="italics"></emph>JOB:<emph.end type="italics"></emph.end></s></p><p type="head"> <s>The Toledo Edition, Printed by <emph type="italics"></emph>JOHN RODERICK, <lb></lb>Anno<emph.end type="italics"></emph.end> 1584, in <emph type="italics"></emph>Quarto,<emph.end type="italics"></emph.end> Pag. </s> <s>205. & <emph type="italics"></emph><expan abbr="ſeqq.">ſeqque</expan><emph.end type="italics"></emph.end> on <lb></lb>theſe Words, Chap. </s> <s>9. Verſe 6.</s></p><p type="head"> <s><emph type="italics"></emph>Who ſhaketh the Earth out of her place, and the Pil<lb></lb>lars thereof Tremble.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The Sacred Pen-man here ſets down another ef<lb></lb>fect whereby God ſheweth his Ahnighty Po<lb></lb>wer, joyned with infinite Wiſdom. </s> <s>Which <lb></lb>place, though it muſt be confeſſed very diffi<lb></lb>cult to underſtand, might be greatly cleared <lb></lb>by the Opinion of the <emph type="italics"></emph>Pythagorians,<emph.end type="italics"></emph.end> who <lb></lb>hold the Earth to be moved of its own Na<lb></lb>ture, and that the Motion of the Stars can no other way be aſcer<lb></lb>tained, they being ſo extreamly different in tardity and velocity. <lb></lb></s> <s>Of which judgement was <emph type="italics"></emph>Philolaus,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Heraclides Ponticus,<emph.end type="italics"></emph.end> as <lb></lb><emph type="italics"></emph>Plutarch<emph.end type="italics"></emph.end> relateth in his Book <emph type="italics"></emph>De Placitis Philoſophorum<emph.end type="italics"></emph.end>: Who <lb></lb>were followed by <emph type="italics"></emph>Numa Pompilius,<emph.end type="italics"></emph.end> and, which I more regard, <lb></lb>The Divine <emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> in his old age; inſomuch that he affirmed that <lb></lb>it was moſt abſurd to think otherwiſe, as the ſame <emph type="italics"></emph>Plutarch<emph.end type="italics"></emph.end> tells <lb></lb>us in his ^{*} <emph type="italics"></emph>Numa.<emph.end type="italics"></emph.end> And <emph type="italics"></emph>Hypocrates<emph.end type="italics"></emph.end> in his Book <emph type="italics"></emph>De Flatibus,<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg869"></arrow.to.target><lb></lb>calleth the Air <foreign lang="grc">τησγησὀχἠμα,</foreign> <emph type="italics"></emph>i. </s> <s>e.<emph.end type="italics"></emph.end> The Earths Chariot. </s> <s>But in this <pb xlink:href="040/01/493.jpg" pagenum="469"></pb>our Age, <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> doth demonſtrate the courſes of the Pla<lb></lb>nets to be according to this Opinion. </s> <s>Nor is it to be doubted <lb></lb>but that the Planets Places may be more exactly and certainly <lb></lb>aſſigned by his Doctrine, than by <emph type="italics"></emph>Ptolomies<emph.end type="italics"></emph.end> Great Almogeſt of <lb></lb>Syſteme, or the Opinions of any others. </s> <s>For its manifeſt, that <lb></lb><emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> could never deſcribe either the Motion of the Equi<lb></lb>noxes, or aſſign the certain and poſitive beginning of the Year:<lb></lb>the which he ingeniouſly confeſſeth in <emph type="italics"></emph>Lih.<emph.end type="italics"></emph.end> 3. <emph type="italics"></emph>De Almageſt. </s> <s>Mag<lb></lb>num. </s> <s>Ch.<emph.end type="italics"></emph.end> 2. and which he leaveth to be diſcovered in after times <lb></lb>by thoſe Aſtronomers, who coming into the World much later <lb></lb>than he, might be able to invent ſome way to make more accurate <lb></lb>obſervations. </s> <s>And although the ^{*} <emph type="italics"></emph>Alphonſines & Thebith Ben Core<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg870"></arrow.to.target><lb></lb>have attempted to explain them; yet it appeareth that they have <lb></lb>done as much as nothing. </s> <s>For the Poſitions of the <emph type="italics"></emph>Alphonſines<emph.end type="italics"></emph.end><lb></lb>diſagree amongſt themſelves, as <emph type="italics"></emph>Ricius<emph.end type="italics"></emph.end> proveth. </s> <s>And although <lb></lb>the Reaſon of <emph type="italics"></emph>Thebith<emph.end type="italics"></emph.end> be more acute, and that thereby he de<lb></lb>termined the certain beginning of the year, (being that which <lb></lb><emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> ſought for) yet it is now clear, that the Progreſſions of <lb></lb>the Equinoxes are much longer than he conceived they could be. <lb></lb></s> <s>Moreover, the Sun is found to be much nearer to us than it was <lb></lb><arrow.to.target n="marg871"></arrow.to.target><lb></lb>held to be in times paſt, by above fourty thouſand ^{*} <emph type="italics"></emph>Stadia,<emph.end type="italics"></emph.end> or <lb></lb>furlongs. </s> <s>The Cauſe and Reaſon of whoſe Motion, neither <lb></lb><emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> nor any other Aſtrologers could ever comprehend: And <lb></lb>yet the Reaſons of theſe things are moſt plainly explained and <lb></lb>demonſtrated by <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> from the Motion of the Earth, with <lb></lb>which he ſheweth that all the other <emph type="italics"></emph>Phœnomena<emph.end type="italics"></emph.end> of the Univerſe <lb></lb>do more aptly accord. </s> <s>Which opinion of his is not in the leaſt <lb></lb>contradicted by what <emph type="italics"></emph>Solomon<emph.end type="italics"></emph.end> ſaith in ^{*} <emph type="italics"></emph>Eccleſiaſtes: But the <lb></lb><arrow.to.target n="marg872"></arrow.to.target><lb></lb>Earth abideth for ever.<emph.end type="italics"></emph.end> For that Text ſignifieth no more but <lb></lb>this, That although the ſucceſſion of Ages, and generations of <lb></lb>Men on Earth, be various; yet the Earth it ſelf is ſtill one and <lb></lb>the ſame, and continueth without any ſenſible alteration; For <lb></lb>the words run thus: <emph type="italics"></emph>One Generation paſſeth away, and another <lb></lb>Generation cometh; but the Earth abideth for ever.<emph.end type="italics"></emph.end> So that it <lb></lb>hath no coherence with its Context, (as Philoſophers ſhew) if it <lb></lb><arrow.to.target n="marg873"></arrow.to.target><lb></lb>be expounded to ſpeak of the Earths immobility. </s> <s>And al<lb></lb>though in this Chapter <emph type="italics"></emph>Eccleſiaſtes,<emph.end type="italics"></emph.end> and in many others, Holy <lb></lb>Writ aſcribes Motion to the Sun, which <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> will have to <lb></lb>ſtand fixed in the Centre of the Univerſe; yet it makes nothing <lb></lb>againſt his Poſition. </s> <s>For the Motion that belongs to the Earth, <lb></lb>is by way of ſpeech aſſigned to the Sun, even by <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> him<lb></lb>ſelf, and thoſe who are his followers, ſo that the Revolution of <lb></lb>the Earth is often by them phraſed, The Revolution of the Sun. <lb></lb></s> <s>To conclude, No place can be produced out of Holy Scripture, <lb></lb>which ſo clearly ſpeaks the Earths Immobility, as this doth its <pb xlink:href="040/01/494.jpg" pagenum="470"></pb>Mobility. </s> <s>Therefore this Text, of which we have ſpoken, is ea<lb></lb>ſily reconciled to this Opinion. </s> <s>And to ſet forth the Wonder<lb></lb>ful power and Wiſdome of God, who can indue and actuate the <lb></lb>Frame of the Whole Earth (it being of a monſtrous weight by <lb></lb>Nature) with Motion, this our Divine pen-man addeth; <emph type="italics"></emph>And <lb></lb>the pillars thereof tremble:<emph.end type="italics"></emph.end> As if he would teach us, from the <lb></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"></emph>In vita ejus.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg870"></margin.target>* Followers of <lb></lb>that Learned <lb></lb>Kings Hypothe<lb></lb>ſis.</s></p><p type="margin"> <s><margin.target id="marg871"></margin.target>* That is 5000 <lb></lb>miles; eight of <lb></lb>theſe making an <lb></lb><emph type="italics"></emph>Italian,<emph.end type="italics"></emph.end> or <emph type="italics"></emph>Engliſh<emph.end type="italics"></emph.end><lb></lb>mile of a 1000. <lb></lb>paces, every pace <lb></lb>containing 5. <lb></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></lb>the Earth, not a<lb></lb>gainſt Scripture.</s></p> </chap> <chap> <pb xlink:href="040/01/495.jpg"></pb><p type="head"> <s>AN <lb></lb>EPISTLE <lb></lb>Of the Reverend Father <lb></lb><emph type="italics"></emph>PAOLO ANTONIO FOSCARINI,<emph.end type="italics"></emph.end><lb></lb>A CARMELITE; <lb></lb>Concerning <lb></lb>The <emph type="italics"></emph>PYTHAGORIAN<emph.end type="italics"></emph.end> and <emph type="italics"></emph>COPERNICAN<emph.end type="italics"></emph.end> Opinion <lb></lb>OF <lb></lb>The Mobility of the <emph type="italics"></emph>EARTH,<emph.end type="italics"></emph.end><lb></lb>AND <lb></lb>Stability of the <emph type="italics"></emph>SVN;<emph.end type="italics"></emph.end><lb></lb>AND <lb></lb>Of the New Syſteme or Conſtitution <lb></lb>OF THE <lb></lb>WORLD.</s></p><p type="head"> <s>IN WHICH, <lb></lb>The Authorities of <emph type="italics"></emph>SACRED SCRIPTVRE,<emph.end type="italics"></emph.end><lb></lb>and <emph type="italics"></emph>ASSERTIONS<emph.end type="italics"></emph.end> of <emph type="italics"></emph>DIVINES,<emph.end type="italics"></emph.end><lb></lb>commonly alledged againſt this Opinion, <lb></lb>are Reconciled.</s></p><p type="head"> <s>WRITTEN <lb></lb>To the moſt Reverend FATHER, <lb></lb>SEBASTIANO FANTONI, <lb></lb>General of the Order of CARMELITES.</s></p><p type="head"> <s><emph type="italics"></emph>Engliſhed from the Original,<emph.end type="italics"></emph.end><lb></lb>BY <lb></lb><emph type="italics"></emph>THOMAS SALVSBVRIE.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>So quis indiget ſapientia, poſtulet <lb></lb>à Deo.<emph.end type="italics"></emph.end> Jacobi 1. verſu. 5.</s></p><p type="head"> <s><emph type="italics"></emph>Optavi, & datus eſt mihi ſenſus.<emph.end type="italics"></emph.end><lb></lb>Sapientiæ 7. verſu. </s> <s>7.</s></p><p type="head"> <s><emph type="italics"></emph>LONDON,<emph.end type="italics"></emph.end><lb></lb>Printed by WILLIAM LEYBOURN, MDCLXI.</s></p><pb xlink:href="040/01/496.jpg"></pb> </chap> <chap> <pb xlink:href="040/01/497.jpg" pagenum="473"></pb><p type="head"> <s>To the Moſt <lb></lb>Reverend Father <lb></lb>SEBASTIANO FANTONI, <lb></lb><emph type="italics"></emph>General of the Order of<emph.end type="italics"></emph.end><lb></lb>CARMELITES.</s></p><p type="main"> <s>In obedience to the command of the No<lb></lb>ble <emph type="italics"></emph>Signore Vincenzo Carraffa,<emph.end type="italics"></emph.end> a Neapo<lb></lb>litan, and Knight of S. <emph type="italics"></emph>John of Jeru<lb></lb>ſalem,<emph.end type="italics"></emph.end> (a perſon, to ſpeak the truth, of <lb></lb>ſo great Merit, that in him Nobility of <lb></lb>Birth, Affability of Manners, Univerſal <lb></lb>knowledge of Arts and things, Piety <lb></lb>and Vertue do all contend for prehemi<lb></lb>nence) I reſolved with my ſelf to un<lb></lb>dertake the Defence of the Writings of the New, or rather Re<lb></lb>newed, and from the Duſt of Oblivion (in which it hath long <lb></lb>lain hid) lately Revived Opinion, <emph type="italics"></emph>Of the Mobility of the Earth, <lb></lb>and Stability of the Sun,<emph.end type="italics"></emph.end> in times paſt found out firſt by <emph type="italics"></emph>Pytha<lb></lb>goras,<emph.end type="italics"></emph.end> and at laſt reduced into Practice by <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end>; who like<lb></lb>wiſe hath deduced the Poſition of the Syſteme and Conſtitution <lb></lb>of the World and its parts from that Hypotheſis: on which <lb></lb>Subject I have formerly writ to You, Moſt Reverend Sir: But <lb></lb>in regard I am bound for <emph type="italics"></emph>Rome<emph.end type="italics"></emph.end> to preach there by your Com<lb></lb>mand; and ſince this Speculation may ſeem more proper for a<lb></lb>nother Treatiſe, to wit, a Volume of <emph type="italics"></emph>Coſmography,<emph.end type="italics"></emph.end> which I am <lb></lb>in hand with, and which I am daily buſie about, that it may <lb></lb>come forth in company with my <emph type="italics"></emph>Compendium of the Liberal Arts,<emph.end type="italics"></emph.end><lb></lb>which I have already finiſhed, rather than now to diſcuſs it by it <lb></lb>ſelf, I thought to forbear, imparting what I have done for the <lb></lb>preſent; Yet I was deſirous to give, in the mean time, a brief ac<lb></lb>count of this my Determination, and to ſhew You, Moſt Reve<lb></lb>rend Father, (to whom I owe all my indeavours, and my very <lb></lb>ſelf) the Foundations on which this Opinion may be grounded, <lb></lb>leaſt, whilſt otherwiſe it is favoured with much probability, it be <lb></lb>found in reality to be extreamly repugnant (as at firſt ſight it <pb xlink:href="040/01/498.jpg" pagenum="474"></pb>ſeems) not onely to Phyſical Reaſons, and Common Principles <lb></lb>received on all hands (which cannot do ſo much harm) but alſo <lb></lb>(which would be of far worſe conſequence) to many Authori<lb></lb>ties of ſacred Scripture: Upon which account many at their <lb></lb>firſt looking into it, explode it as the moſt fond Paradox and <lb></lb>Monſtrous <emph type="italics"></emph>Capriccio<emph.end type="italics"></emph.end> that ever was heard of. </s> <s>Which thing pro<lb></lb>ceeds only from an antiquated and long confirmed Cuſtome, <lb></lb>which hath ſo hardened men in, and habituated them to Vul<lb></lb>gar, Plauſible, and for that cauſe by all men (aſwell learned as <lb></lb>unlearned) Approved Opinions, that they cannot be removed <lb></lb>one ſtep from them: So great is the force of Cuſtome (which <lb></lb>not unfitly is ſtiled a ſecond Nature) prevailing over the whole <lb></lb>World, that touching things men are rather pleaſed with, de<lb></lb>lighted in, and deſirous of thoſe, which, though evil and obnox<lb></lb>ious, are by uſe made familiar to them, than ſuch, wherewith, <lb></lb>though better, they are not accuſtomed and acquainted. </s> <s>So in <lb></lb>like manner, and that chiefly, in <emph type="italics"></emph>Opinions,<emph.end type="italics"></emph.end> which when once they <lb></lb>are rooted in the Mind, men ſtart at, and reject all others <lb></lb>whatſoever; not only thoſe that are contrary to, but even all <lb></lb>that ever ſo little diſagree with or vary from theirs, as harſh to <lb></lb>the Ear, diſcoloured to the Eye, unpleaſant to the Smell, nauſe<lb></lb>ous to the Taſt, rough to the Touch. </s> <s>And no wonder: For <lb></lb>Phyſical Truths are ordinarily judged and conſidered by men, <lb></lb>not according to their Eſſence, but according to the preſcript of <lb></lb>ſome one whoſe deſcription or definition of them gaines him <lb></lb>Authority amongſt the vulgar. </s> <s>Which authority nevertheleſs <lb></lb>(ſince 'tis no more than humane) ought not to be ſo eſteemed, as <lb></lb>that that which doth manifeſtly appear to the contrary, whether <lb></lb>from better Reaſons lately found out, or from Senſe it ſelf, ſhould <lb></lb>for its ſake be contemned and ſlighted; Nor is Poſterity ſo to be <lb></lb>confined, but that it may, and dares, not only proceed farther, <lb></lb>but alſo bring to light better and truer Experiments than thoſe <lb></lb>which have been delivered to us by the Ancients. </s> <s>For the <emph type="italics"></emph>Ge<lb></lb>nius's<emph.end type="italics"></emph.end> of the Antients, as in Inventions they did not much ſur<lb></lb>paſs the Wits of our times; ſo for the perfecting of Inventions <lb></lb>this Age of ours ſeems not only to equal, but far to excell former <lb></lb>Ages; Knowledge, whether in the Liberal or Mechanical Arts, <lb></lb>daily growing to a greater height. </s> <s>Which Aſſertion might be <lb></lb>eaſily proved, were it not that in ſo clear a caſe, there would be <lb></lb>more danger of obſcuring, than hopes of illuſtrating it with any <lb></lb>farther light.</s></p><p type="main"> <s>But (that I may not wholly be ſilent in this point) have not the <lb></lb>ſeveral Experiments of Moderns, in many things, ſtopped the <lb></lb>mouth of Venerable Antiquity, and proved many of their great<lb></lb>teſt and weightieſt Opinions, to be vain and falſe? </s> <s>The Doctrine <pb xlink:href="040/01/499.jpg" pagenum="475"></pb>of the <emph type="italics"></emph>Antipodes<emph.end type="italics"></emph.end> by many of the Antients of approved Wiſ<lb></lb>dome and Learning was held a Paradox no leſs abſurd than this <lb></lb>Our Opinion of the <emph type="italics"></emph>Earths Motion<emph.end type="italics"></emph.end> may ſeem to be; as likewiſe <lb></lb>that of the <emph type="italics"></emph>Habitableneſſe of the Torrid Zone<emph.end type="italics"></emph.end>: Of theſe Opini<lb></lb>ons, the firſt was accounted unpoſſible by many, but the latter <lb></lb>was abſolutely denyed by the unanimous conſent of all: But <lb></lb>later Authors (to the great felicity and perpetual Glory of <lb></lb>their Age) have, not ſo much by Authority, as by accurate <lb></lb>diligence and indefatigable ſtudy to finde out the truth, pro<lb></lb>ved them both to be undoubtedly true. </s> <s>Thus I affirm that <lb></lb>the Antients were deceived, and that in too lightly challenging <lb></lb>Credid and Authority for their Inventions, they diſcovered too <lb></lb>much folly. </s> <s>Here for brevities ſake I paſs by many Dreams <lb></lb>lately detected, both of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> and other of the antient Philo<lb></lb>ſophers; who in all likelihood if they had dived into the Obſer<lb></lb>vations of Modern Writers, and underſtood their Reaſons, would, <lb></lb>by changing their Judgements, have given them the precedency, <lb></lb>and would have ſubſcribed to their manifeſt Truth. </s> <s>Hereby we <lb></lb>ſee that we are not to have ſo high a reſpect for the Antiens, that <lb></lb>whatever they aſſert ſhould be taken upon truſt, and that Faith <lb></lb>ſhould be given to their ſayings, as if they were Oracles and <lb></lb>Truths ſent down from Heaven. </s> <s>But yet (which indeed is <lb></lb>chiefly to be regarded in theſe matters) if any thing be found out <lb></lb>that is repugnant to Divine Authority, or to the Sacred Leaves, <lb></lb>that were dictated by the Holy Ghoſt, and by His Inſpiration <lb></lb><arrow.to.target n="marg874"></arrow.to.target><lb></lb>expounded by the Holy Doctors of the Church, in this caſe not <lb></lb>onely Humane Reaſon, but even Senſe it ſelf is to ſubmitt: <lb></lb>which, though by all manner of weighty Conditions and circum<lb></lb>ſtances it ſhould hold forth any thing contrary to Divine Autho<lb></lb>rity, (which indeed is ſo plain, that there is no way left to evade <lb></lb>the right un erſtanding of it) yet is it to be rejected; and we <lb></lb>muſt conclude our ſelves deceived by it, and believe that that is <lb></lb>not true which Senſe and Reaſon repreſents unto us: For, however <lb></lb>we judge of things, we have, both in this and all other caſes, a <lb></lb>more certain knowledge, which proceeds from Divine Faith; as <lb></lb>S. <emph type="italics"></emph>Peter<emph.end type="italics"></emph.end> hath moſt excellently expreſt it: Who though with his <lb></lb>Senſes he ſaw, and perceived the Glory of our Lord in his <lb></lb>Transfiguration, and heard his words manifeſting his great Pow<lb></lb>er, yet nevertheleſs all theſe things compared with the Light of <lb></lb>Faith, he adds: ^{*}<emph type="italics"></emph>We have alſo a more ſure word of Prophecy,<emph.end type="italics"></emph.end> &c. <lb></lb><arrow.to.target n="marg875"></arrow.to.target><lb></lb>Wherefore ſince this Opinion of <emph type="italics"></emph>Pythagoras<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> hath <lb></lb>entred upon the Stage of the World in ſo ſtrange a Dreſs, and at <lb></lb>the firſt appearance (beſides the reſt) doth ſeem to oppoſe ſun<lb></lb>dry Authorities of Sacred Scripture, it hath (this being granted) <lb></lb>been juſtly rejected of all men as a meer abſurdity.</s></p> <pb xlink:href="040/01/500.jpg" pagenum="476"></pb><p type="margin"> <s><margin.target id="marg874"></margin.target><emph type="italics"></emph>Faith is more <lb></lb>certain, than ei<lb></lb>ther Senſe or Rea<lb></lb>ſon.<emph.end type="italics"></emph.end></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 becauſe the common Syſteme of the World deviſed by <lb></lb><emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> hath hitherto ſatisfied none of the Learned, hereupon a <lb></lb>ſuſpicion is riſen up amongſt all, even <emph type="italics"></emph>Ptolemy's<emph.end type="italics"></emph.end> followers them<lb></lb>ſelves, that there muſt be ſome other Syſteme, which is more true <lb></lb>than this of <emph type="italics"></emph>Ptolemy<emph.end type="italics"></emph.end>; For although the <emph type="italics"></emph>Phœnomena<emph.end type="italics"></emph.end> of Celeſtial <lb></lb>Bodys may ſeem to be generally reſolved by this Hypotheſis, yet <lb></lb>they are found to be involved with many difficulties, and refer<lb></lb>red to many devices; as namely of Orbes of ſundry Forms and <lb></lb>Figures, Epicicles, Equations, Differences, Excentricks, andinnu<lb></lb>merable ſuch like fancies and Chymæra's which ſavour of the <lb></lb><emph type="italics"></emph>Ens Rationis<emph.end type="italics"></emph.end> of Logicians, rather than of any <emph type="italics"></emph>Realem Eſſentiam.<emph.end type="italics"></emph.end><lb></lb>Of which kinde is that of the <emph type="italics"></emph>Rapid Motion,<emph.end type="italics"></emph.end> than which I finde <lb></lb>not any thing that can be more weakly grounded, and more eaſi<lb></lb>ly controverted and diſproved: And ſuch is that conceit of the <lb></lb>^{*} Heaven void of Stars, moving the inferior Heavens or Orbes: <lb></lb><arrow.to.target n="marg876"></arrow.to.target><lb></lb>All which are introduced upon occaſion of the variety of the <lb></lb>Motions of Celeſtial Bodyes, which ſeemed impoſſible, by any <lb></lb>other way, to be reduced to any certain and determinate Rule. <lb></lb></s> <s>So that the Aſſertors of that common Opinion, freely confeſs, <lb></lb>that in deſcribing the Worlds Syſteme, they cannot as yet diſco<lb></lb>ver, or teach the true Hypotheſis thereof: But that their endea<lb></lb>vours are onely to finde out, amongſt many things, what is moſt <lb></lb>agreeable with truth, and may, upon better and more accomo<lb></lb>date Reaſons, anſwer the Celeſtial <emph type="italics"></emph>Phœnomena.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg876"></margin.target>* Or <emph type="italics"></emph>Primum<lb></lb>Mobile.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Since that, the Teleſcope (an Optick Invention) hath been found <lb></lb>out, by help of which, many remarkable things in the Heavens, <lb></lb>moſt worthy to be known, and till then unthought of, were diſ<lb></lb>covered by manifeſt ſenſation; as for inſtance, That the Moon is <lb></lb>Mountainous; <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> Tricorporeal; and <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end><lb></lb>Quadricorporeal: Likewiſe that in the <emph type="italics"></emph>Via Lactea,<emph.end type="italics"></emph.end> in the <emph type="italics"></emph>Ple<lb></lb>iades,<emph.end type="italics"></emph.end> and in the Stars called <emph type="italics"></emph>Nobuloſœ<emph.end type="italics"></emph.end> there are many Stars, and <lb></lb>thoſe of the greateſt Magnitude which are by turns adjacent to <lb></lb>one another; and in the end it hath diſcovered to us, new fixed <lb></lb>Stars, new planets, and new Worlds. </s> <s>And by this ſame Inſtru<lb></lb>ment it appears very probable, that <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Mercury<emph.end type="italics"></emph.end> do not <lb></lb>move properly about the Earth, but rather about the Sun; and <lb></lb>that the Moon alone moveth about the Earth. </s> <s>What therefore <lb></lb>can be inferred from hence, but that the Sun doth ſtand immo<lb></lb>vable in the Centre, and that the Earth, with the other Celeſtial <lb></lb>Orbes, is circumvolved about it? </s> <s>Wherefore by this and many <lb></lb>other Reaſons it appears, That the Opinion of <emph type="italics"></emph>Pythagor as<emph.end type="italics"></emph.end> and <lb></lb><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> doth not diſagree with Aſtronomical and Coſmogra<lb></lb>phical Principles; yea, that it carryeth with it a great likelihood <lb></lb>and probability of Truth: Whereas amongſt the ſo many ſeve<lb></lb>ral Opinions, that deviate from the common Syſteme, and deviſe <pb xlink:href="040/01/501.jpg" pagenum="477"></pb>others, ſuch as were thoſe of <emph type="italics"></emph>Plato, Calippus, Eudoxus<emph.end type="italics"></emph.end>; and ſince <lb></lb><arrow.to.target n="marg877"></arrow.to.target><lb></lb>them of <emph type="italics"></emph>Averroe, ^{*} Cardanus, Fracaſtorius,<emph.end type="italics"></emph.end> and others both Anti<lb></lb>ent and Modern, there is not one found that is more facile, more <lb></lb>regularly ahd determinately, accommodated to the <emph type="italics"></emph>Phœnomena<emph.end type="italics"></emph.end><lb></lb>and Motions of the Heavens, without <emph type="italics"></emph>Epicycles, Excentrix, Ho<lb></lb>mocentricks<emph.end type="italics"></emph.end> Deferents, and the ſupputation of the Rapid Motion. <lb></lb></s> <s>And this Hypotheſis hath been aſſerted for true, not onely by <lb></lb><emph type="italics"></emph>Pythagoras,<emph.end type="italics"></emph.end> and, after him, by <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> but by many famous <lb></lb>men, as namely, <emph type="italics"></emph>Heraclitus,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ecphantus, Pythagoreans,<emph.end type="italics"></emph.end> all the <lb></lb>Diſciples of that Sect, <emph type="italics"></emph>Miceta<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Syracuſe, Martianus Capella,<emph.end type="italics"></emph.end> and <lb></lb>many more. </s> <s>Amongſt whom, thoſe (as we have ſaid) that <lb></lb>have attempted the finding out of New Syſtemes (for they refu<lb></lb>ſed both this of <emph type="italics"></emph>Pythagoras,<emph.end type="italics"></emph.end> and that of <emph type="italics"></emph>Ptolemy)<emph.end type="italics"></emph.end> are numberleſs: <lb></lb>who yet notwithſtanding allowed this Opinion of <emph type="italics"></emph>Pythagoras<emph.end type="italics"></emph.end> to <lb></lb>carry with it much probability, and indirectly confirmed it; inaſ<lb></lb>much as that they rejected the common one as imperfect, defe<lb></lb><arrow.to.target n="marg878"></arrow.to.target><lb></lb>ctive, and attended with many contradictions and difficulties. <lb></lb></s> <s>Amongſt theſe may be numbered Father ^{*} <emph type="italics"></emph>Clavius,<emph.end type="italics"></emph.end> a moſt learn<lb></lb>ed Jeſuite; who, although he refutes the Syſteme of <emph type="italics"></emph>Pythagoras,<emph.end type="italics"></emph.end><lb></lb>yet acknowledgeth the Levity of the common Syſteme, and he <lb></lb>ingeniouſly confeſſeth, that for the removal of difficulties, in which <lb></lb>the common Syſteme will not ſerve the turn, Aſtronomers are <lb></lb>forced to enquire after another Syſteme, to the diſcovery of <lb></lb>which, he doth very earneſtly exhort them.</s></p><p type="margin"> <s><margin.target id="marg877"></margin.target>* Cardan de re<lb></lb>rum variet. </s> <s>Lib. 1. <lb></lb>Cap. 1.</s></p><p type="margin"> <s><margin.target id="marg878"></margin.target>* P. </s> <s>Clavins in <lb></lb>ultima ſuor. </s> <s>Ope<lb></lb>rum editione.</s></p><p type="main"> <s>Now can there a better or more commodious Hypotheſis <lb></lb>be deviſed, than this of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end>? </s> <s>For <emph type="italics"></emph>t<emph.end type="italics"></emph.end>his Cauſe many Mo<lb></lb>dern Authors are induced to approve of, and follow it: but <lb></lb>with much hæſitancy, and fear, in regard that it ſeemeth in their <lb></lb>Opinion ſo to contradict the Holy Scriptures, as that it cannot <lb></lb>poſſibly be reconciled to them. </s> <s>Which is the Reaſon that this <lb></lb>Opinion hath been long ſuppreſt, and is now entertained by men <lb></lb>in a modeſt manner, ad as it were with a veiled Face; according <lb></lb>to that advice of the Poet:</s></p><p type="main"> <s><emph type="italics"></emph>Judicium populi nunquam contempſeris unus,<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Ne nullis place as, dum vis contemnere multos.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Upon conſideration of which, (out of my very great love to<lb></lb>wards the Sciences, and my ardent defire to ſee the encreaſe and <lb></lb>perfection of them, and the Light of Truth freed from all Er<lb></lb>rours and Obſcurities) I began to argue with my ſelf touching <lb></lb>this Point after this manner: This Opinion of the <emph type="italics"></emph>Pythagoreans<emph.end type="italics"></emph.end><lb></lb>is either true, or falſe; If falſe, it ought not to be mentioned, and <lb></lb>deſerves not to be divulged: If true, it matters not, though it <lb></lb>contradict all, as well Philoſophers as Aſtronomers: And though <lb></lb>for its eſtabliſhment and reducement to uſe a new Philoſophy <pb xlink:href="040/01/502.jpg" pagenum="478"></pb>and Aſtronomy, (ſounded upon new Principles and Hypotheſe) <lb></lb>ſhould be conſtituted: For the Authority of Sacred Scripture <lb></lb>will not oppoſe it; neither doth one Truth contradict another. <lb></lb></s> <s>If therefore the Opinion of <emph type="italics"></emph>Pythagoras<emph.end type="italics"></emph.end> be true, without doubt <lb></lb>God hath diſpoſed and dictated the words of of Holy Writ in <lb></lb>ſuch a manner, that they may admit an apt ſenſe and reconcilia<lb></lb>tion with that Hypotheſis. </s> <s>Being moved by theſe Reaſons, and <lb></lb>the probability of the ſaid Opinion, I thought good to try whe<lb></lb>ther Texts of Sacred Scripture might be expounded according to <lb></lb>Theological and Phyſical Principles, and might be reconciled to <lb></lb>it, ſo that (in regard that hitherto it hath been held probable) it <lb></lb>may in after times, coming without ſcruple to be acknowledged <lb></lb>for true, advance it ſelf, and appear in publick with an uncover<lb></lb>ed Face, without any mans prohibition, and may lawfully and <lb></lb>freely hold a Sacred intelligence with Holy Truth, ſo earneſtly <lb></lb>coveted and commended by good Men. </s> <s>Which deſigne, having hi<lb></lb><arrow.to.target n="marg879"></arrow.to.target><lb></lb>therto been undertaken by none that I know, wil, I am perſwaded, <lb></lb>be very acceptable to the Studious of theſe Learnings, eſpecially to <lb></lb>the moſt Learned <emph type="italics"></emph>Galilœo Galilœi,<emph.end type="italics"></emph.end> chief Mathematician to the <lb></lb>moſt Serene Grand Duke of <emph type="italics"></emph>Tuſcany,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>John Kepler,<emph.end type="italics"></emph.end> chief <lb></lb>Mathematician to his Sacred and invincible Majeſty, the Empe<lb></lb>rour, and to all that Illuſtrious, and much to be commended Ac<lb></lb>cademy of the <emph type="italics"></emph>Lynceans<emph.end type="italics"></emph.end>; whom, if I miſtake not, are all of this <lb></lb>Opinion. </s> <s>Although I doubt not but they, and many other <lb></lb>Learned Men might eaſily have found out theſe or the like Re<lb></lb>conciliations of Scriptural expreſſions; to whom nevertheleſs I <lb></lb>have thought fit (in reſpect of that profeſſion which I have under<lb></lb>taken, upon the faith of my ſoul, and the propenſity that I have <lb></lb>towards Truth) to offer that of the Poet,</s></p><p type="margin"> <s><margin.target id="marg879"></margin.target><emph type="italics"></emph>The Author <lb></lb>firſt Theologically <lb></lb>defendeth the <lb></lb>Earths Mobili<lb></lb>ty, approved by <lb></lb>many of the Mo<lb></lb>derns.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Nullius addictus jur are in verba Magiſtri.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And in teſtimony of my eſteem to them and all the Learned, <lb></lb>to communicate theſe my thoughts; confidently aſſuring my ſelf <lb></lb>that they will accept them, with a Candor equal to that where<lb></lb>with I have written them.</s></p><p type="main"> <s>Therefore to come to the buſineſs: All Authorities of Di<lb></lb>vine Writ which ſeem to oppoſe this Opinion, are reducible to <lb></lb>ſix Claſſes: The firſt is of thoſe that affirm the Earth to ſtand <lb></lb>ſtill, and not to move: as <emph type="italics"></emph>Pſal. </s> <s>92. He framed the round World <lb></lb>ſo ſure, that it cannot be moved<emph.end type="italics"></emph.end>: Alſo <emph type="italics"></emph>Pſal. </s> <s>104. Who laid the <lb></lb>Foundations of the Earth, that it ſhould not be removed for ever<emph.end type="italics"></emph.end>: <lb></lb>And <emph type="italics"></emph>Eccleſiaſtes 1. But the Earth abideth for ever<emph.end type="italics"></emph.end>: And others <lb></lb>of the like ſenſe.</s></p><p type="main"> <s>The ſecond is of thoſe which atteſt the Sun to move, and <pb xlink:href="040/01/503.jpg" pagenum="479"></pb>Revolve about the Earth; as <emph type="italics"></emph>Pſal. </s> <s>19. (b) In them hath be ſet a <lb></lb><arrow.to.target n="marg880"></arrow.to.target><lb></lb>Tabernacle for the Sun, which cometh forth as a Bridegroom out <lb></lb>of his chamber, and rejoyceth as a Gyant to run his Courſe. </s> <s>It <lb></lb>cometh forth from the uttermoſt part of the Heaven, and runneth <lb></lb>about unto the end of it again; and there is nothing hid from the <lb></lb>heat thereof.<emph.end type="italics"></emph.end> And <emph type="italics"></emph>Eccleſiaſt. </s> <s>1. The Sun riſeth, and the Sun go<lb></lb>eth down, and haſteth to the place where be aroſe: it goeth towards <lb></lb>the South, and turneth about unto the North.<emph.end type="italics"></emph.end> Whereupon the <lb></lb>Suns Retrogradation is mentioned as a Miracle, <emph type="italics"></emph>Iſaiah 38. The <lb></lb>Sun returned ten degrees.<emph.end type="italics"></emph.end> And <emph type="italics"></emph>Eccleſiaſticus 48. In his time the <lb></lb>Sun went backward, and lengthened the life of the King.<emph.end type="italics"></emph.end> And <lb></lb>for this reaſon it is related for a Miracle, in the Book of <emph type="italics"></emph>Joſbuah,<emph.end type="italics"></emph.end><lb></lb>that at the Prayers of that great Captain the Sun ſtood ſtill, its <lb></lb>motion being forbidden it, by him<emph type="italics"></emph>: Joſh.<emph.end type="italics"></emph.end>10. <emph type="italics"></emph>Sun ſtand thou <lb></lb>ſtill upon Gibeon.<emph.end type="italics"></emph.end> Now if the Sun ſhould ſtand ſtill, and the <lb></lb>Earth move about it, its ſtation at that time was no Miracle; <lb></lb>and if <emph type="italics"></emph>Joſhuah<emph.end type="italics"></emph.end> had intended, that the light of the day ſhould <lb></lb>have been prolonged by the Suns ſplendour, he would not have <lb></lb>ſaid, <emph type="italics"></emph>Sun ſtand thou ſtill,<emph.end type="italics"></emph.end> but rather <emph type="italics"></emph>Earth ſtand thou ſtill.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg880"></margin.target><emph type="italics"></emph>(b) Or<emph.end type="italics"></emph.end> In Sole <lb></lb>poſuit tabernacu<lb></lb>lum ſuum, <emph type="italics"></emph>accor<lb></lb>ding to the Tran<lb></lb>ſlation our Au<lb></lb>thor followeth.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The third Claſſis is of thoſe Authorities which ſay, that Hea<lb></lb>ven is <emph type="italics"></emph>above,<emph.end type="italics"></emph.end> and the Earth <emph type="italics"></emph>beneath<emph.end type="italics"></emph.end>; of which ſort is that place <lb></lb>of <emph type="italics"></emph>Joel, chap.<emph.end type="italics"></emph.end> 2. cited by S. <emph type="italics"></emph>Peter,<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Acts. </s> <s>2. I will ſhew wonders <lb></lb>in Heaven above, and ſignes in the Earth beneath,<emph.end type="italics"></emph.end> with others of <lb></lb>the like purport. </s> <s>Hereupon Chriſt at his Incarnation is ſaid to <lb></lb><emph type="italics"></emph>come down from Heaven<emph.end type="italics"></emph.end>; and after his Reſurrection to have <emph type="italics"></emph>aſ<lb></lb>cended up into heaven.<emph.end type="italics"></emph.end> But if the Earth ſhould move about <lb></lb>the Sun, it would be, as one may ſay, in Heaven, and conſe<lb></lb>quently would rather be <emph type="italics"></emph>above<emph.end type="italics"></emph.end> Heaven than <emph type="italics"></emph>beneath<emph.end type="italics"></emph.end> it. </s> <s>And <lb></lb>this is confirmed; For that the Opinion which placeth the Sun in <lb></lb>the Centre, doth likewiſe place <emph type="italics"></emph>Mercury<emph.end type="italics"></emph.end> above the Sun, and <lb></lb><emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> above <emph type="italics"></emph>Mercury<emph.end type="italics"></emph.end>; and the Earth above <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> together <lb></lb>with the Moon, which revolves about the Earth, and therefore <lb></lb>the Earth, together with the Moon, is placed in the third Heaven. <lb></lb></s> <s>If therefore in Spherical Bodies, as in the World, <emph type="italics"></emph>beneath<emph.end type="italics"></emph.end> ſigni<lb></lb><arrow.to.target n="marg881"></arrow.to.target><lb></lb>fies no more than to be neer to the centre, and <emph type="italics"></emph>above,<emph.end type="italics"></emph.end> than to <lb></lb>approach the Circumference, it muſt needs follow, that for ma<lb></lb>king good of Theological Poſitions concerning the Aſcenſion <lb></lb>and Deſcenſion of Chriſt, the Earth is to be placed in the cen<lb></lb>tre, and the Sun, with the other Heavens in the Circumference; <lb></lb>and not according to <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> whoſe Hypotheſis inverts this <lb></lb>Order: with which one cannot ſee how the true Aſcenſion and <lb></lb>Deſcenſion can be conſiſtent.</s></p><p type="margin"> <s><margin.target id="marg881"></margin.target><emph type="italics"></emph>In Spberieall <lb></lb>Bodies,<emph.end type="italics"></emph.end> Deorſum <lb></lb><emph type="italics"></emph>is the Centre, and<emph.end type="italics"></emph.end><lb></lb>Surſum <emph type="italics"></emph>the Cir<lb></lb>cumference.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The fourth Claſſis is of thoſe Authorities which make Hell to <lb></lb>be in the Centre of the World, which is the Common Opinion <lb></lb>of Divines, and confirmed by this Reaſon, That ſince Hell (ta <pb xlink:href="040/01/504.jpg" pagenum="480"></pb>ken in its ſtrict denomination) ought to be in the loweſt part of <lb></lb>the World, and ſince that in a Sphere there is no part lower <lb></lb>then the Centre, Hell ſhall be, as it were, in the Centre of the <lb></lb>World, which being of a Spherical Figure, it muſt follow, that <lb></lb><arrow.to.target n="marg882"></arrow.to.target><lb></lb>Hell is either in the Sun (foraſmuch as it is ſuppoſed by this Hy<lb></lb>potheſis to be in the Centre of the World) or elſe ſuppoſing <lb></lb>that Hell is in the Centre of the Earth, if the Earth ſhould move <lb></lb>about the Sun, it would neceſſarily enſue, that Hell, together <lb></lb>with the Earth, is in Heaven, and with it revolveth about the third <lb></lb>Heaven; than which nothing more abſurd can be ſaid or imagi<lb></lb>ned.</s></p><p type="margin"> <s><margin.target id="marg882"></margin.target><emph type="italics"></emph>Hell is in the <lb></lb>centre of the <lb></lb>Earth, not of the <lb></lb>World.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The fifth Claſſis, is of thoſe Authorities which alwayes op<lb></lb><arrow.to.target n="marg883"></arrow.to.target><lb></lb>poſe Heaven to the Earth, and ſo again the Earth to Heaven; as <lb></lb>if there were the ſame relation betwixt them, with that of the <lb></lb>Centre to the Circumference, and of the Circumference to the <lb></lb>Centre. </s> <s>But if the Earth were in Heaven, it ſhould be on one <lb></lb>ſide thereof, and would not ſtand in the Middle, and conſequent<lb></lb>ly there would be no ſuch relation betwixt them; which never<lb></lb>theleſs do, not only in Sacred Writ, but even in Common Speech, <lb></lb>ever and every where anſwer to each other with a mutual Oppo<lb></lb>fition. </s> <s>Whence that of <emph type="italics"></emph>Geneſ. </s> <s>1. In the beginning God created <lb></lb>the Heaven and the Earth<emph.end type="italics"></emph.end>: and <emph type="italics"></emph>Pſal. </s> <s>115. The Heaven, even <lb></lb>the Heavens are the Lords; but the Earth hath he given to the <lb></lb>Children of men:<emph.end type="italics"></emph.end> and our Saviour in that Prayer which he pre<lb></lb>ſcribeth to us, <emph type="italics"></emph>Matth. </s> <s>6. Thy will be done in Earth, as it is in <lb></lb>Heaven:<emph.end type="italics"></emph.end> and S. <emph type="italics"></emph>Paul, 1 Corinth. </s> <s>15. The firſt man is of the <lb></lb>Earth, earthy; the ſecond man is of Heaven, heavenly:<emph.end type="italics"></emph.end> and <lb></lb><emph type="italics"></emph>Coloſſ. </s> <s>1. By him were all things created that are in Heaven, and <lb></lb>that are in Earth<emph.end type="italics"></emph.end>: and again, <emph type="italics"></emph>Having made peace through the <lb></lb>Blood of his Croſſe for all things, whether they be things in Earth <lb></lb>or things in Heaven:<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Chap. </s> <s>3. Set your affections on things <lb></lb>above, not on things on the Earth<emph.end type="italics"></emph.end>; with innumerable other ſuch <lb></lb>like places. </s> <s>Since therefore theſe two Bodies are alwayes mu<lb></lb>tually oppoſed to each other, and Heaven, without all doubt, <lb></lb>referreth to the Circumference, it muſt of neceſſity follow, that <lb></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"></emph>Heaven and <lb></lb>Earth are always <lb></lb>mutually oppoſed <lb></lb>to each other.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The ſixth and laſt Claſſis is of thoſe Authorities, which (being <lb></lb>rather of Fathers and Divines, than of the Sacred Scripture) ſay, <lb></lb>That the Sun, after the day of Judgment ſhall ſtand immoveable <lb></lb><arrow.to.target n="marg884"></arrow.to.target><lb></lb>in the Eaſt, and the Moon in the Weſt. </s> <s>Which Station, if the <lb></lb><emph type="italics"></emph>Pythagorick<emph.end type="italics"></emph.end> Opinion hold true, ought rather to be aſcribed to <lb></lb>the Earth, than to the Sun; for if it be true, that the Earth doth <lb></lb>now move about the Sun, it is neceſſary that after the day of <lb></lb>Judgment it ſhould ſtand immoveable. </s> <s>And truth is, if it muſt <lb></lb>ſubſiſt without motion in one conſtant place, there is no reaſon <pb xlink:href="040/01/505.jpg" pagenum="481"></pb>why it ſhould rather ſtand in one ſite of that Place than in ano<lb></lb>ther, or why it ſhould rather turn one part of it than another to <lb></lb>the Sun, if ſo be that every of its parts without diſtinction, which <lb></lb>is deſtitute of the Suns light, cannot chooſe but be diſmal, and <lb></lb>much worſe affected than that part which is illuminated. </s> <s>Hence <lb></lb>alſo would ariſe many other abſurdities beſides theſe.</s></p><p type="margin"> <s><margin.target id="marg884"></margin.target><emph type="italics"></emph>After the day <lb></lb>of Judgment the <lb></lb>Earth ſhall ſtand <lb></lb>immoveable.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Theſe are the Claſſes, &c. </s> <s>from which great aſſaults are made <lb></lb>againſt the ſtructure of the Pythagorick Syſteme; yet by that <lb></lb>time I ſhall have firſt laid down ſix Maximes or Principles, as <lb></lb>impregnable Bulwarks erected againſt them, it will be eaſie to <lb></lb>batter them, and to defend the Hypotheſis of <emph type="italics"></emph>Pythagoras<emph.end type="italics"></emph.end> from <lb></lb>being attaqued by them. </s> <s>Which before I propound, I do pro<lb></lb>feſs (with that Humility and Modeſty which becometh a Chri<lb></lb>ſtian, and a perſon in Religious Orders) that I do with reverence <lb></lb>ſubmit what I am about to ſpeak to the Judgment of Holy <lb></lb>Church. </s> <s>Nor have I undertaken to write theſe things out of <lb></lb>any inducements of Temerity, or Ambition, but out of Charity <lb></lb>and a Deſire to be auxiliary to my neighbour in his inquiſition <lb></lb>after Truth. </s> <s>And there is nothing in all this Controverſie <lb></lb>maintained by me (that expect to be better inſtructed by thoſe <lb></lb>who profeſs theſe Studies) which I ſhall not retract, if any per<lb></lb>ſons ſhall by ſolid Reaſons & reiterated Experiments, prove ſome <lb></lb>other Hypotheſis to be more probable; but yet, until ſuch time as <lb></lb>they ſhall decide the Point, I ſhall labour all I can for its ſupport.</s></p><p type="main"> <s>My firſt and chiefeſt Maxime is this; When any thing is at<lb></lb>tributed in Holy Writ, to God, or to a Creature, thats not be<lb></lb>ſeeming to, or incommenſurate with them, it muſt of neceſſity <lb></lb>be received and expounded one, or more of the four following <lb></lb>wayes; Firſt, it may be ſaid to agree with them <emph type="italics"></emph>Metaphorically, <lb></lb>and Proportionally, or by Similitude.<emph.end type="italics"></emph.end> Secondly, <emph type="italics"></emph>According to <lb></lb>our manner of Conſidering, Apprehending, Conceiving, Vnderſtand<lb></lb>ing, Knowing, &c.<emph.end type="italics"></emph.end> Thirdly, <emph type="italics"></emph>according to the Opinion of the <lb></lb>Vulgar, and the Common way of Speaking:<emph.end type="italics"></emph.end> to which Vulgar <lb></lb>Speech the Holy Ghoſt doth very often with much ſtudy acco<lb></lb>modate it ſelf. </s> <s>Fourthly, <emph type="italics"></emph>In reſpect of our ſelves, and for that <lb></lb>he makes himſelf like unto us.<emph.end type="italics"></emph.end> Of each of theſe wayes there are <lb></lb>theſe examples: God doth not walk, ſince he is Infinite and Im<lb></lb>moveable; He hath no Bodily Members, ſince he is a Pure Act; <lb></lb>and conſequently is void of all Paſſion of Minde; and yet in <lb></lb>Sacred Scripture, <emph type="italics"></emph>Gen. </s> <s>3. verſ.<emph.end type="italics"></emph.end> 8. it is ſaid, <emph type="italics"></emph>He walked in the cool of <lb></lb>the day<emph.end type="italics"></emph.end>: and <emph type="italics"></emph>Job 22. verſ.<emph.end type="italics"></emph.end> 14. it is ſaid, <emph type="italics"></emph>He walketh in the ^{*} Cir<lb></lb><arrow.to.target n="marg885"></arrow.to.target><lb></lb>cuit of Heaven:<emph.end type="italics"></emph.end> and in many other places coming, departing, <lb></lb>making haſt is aſcribed to God; and likewiſe Bodily parts, as <lb></lb>Eyes, Ears, Lips, Face, Voice, Countenance, Hands, Feet, Bow<lb></lb>els, Garments, Arms; as alſo many Paſſions, ſuch as Anger, <pb xlink:href="040/01/506.jpg" pagenum="482"></pb>Sorrow, Repentance, and the like. </s> <s>What ſhall we ſay there<lb></lb>fore? </s> <s>Without doubt ſuch like Attributes agree with God (to <lb></lb>uſe the Schoolmens words <emph type="italics"></emph>Metaphorically, Proportionally, and by <lb></lb>Similitude<emph.end type="italics"></emph.end>: And touching Paſſions, it may be ſaid, that God <lb></lb>condeſcendeth to repreſent himſelf after that manner: as for <lb></lb>inſtance, <emph type="italics"></emph>The Lord is angry<emph.end type="italics"></emph.end>; i.e. <emph type="italics"></emph>He revealeth himſelf as one that <lb></lb>is angry: He grieved<emph.end type="italics"></emph.end>; i. </s> <s>e. <emph type="italics"></emph>He revealeth himſelf, as one that <lb></lb>is ſorrowful: It repented him that he had made man<emph.end type="italics"></emph.end>; i.e. <emph type="italics"></emph>He ſee<lb></lb>med as one that repented.<emph.end type="italics"></emph.end> And indeed all theſe things are <emph type="italics"></emph>Com<lb></lb>parativè ad nos,<emph.end type="italics"></emph.end> and in reſpect of us. </s> <s>So God is ſaid to be in <lb></lb>Heaven, to move in time, to ſhew himſelf, to hide himſelf, to <lb></lb>obſerve and mark our ſteps; to ſeek us, to ſtand at the door, <lb></lb>to knock at the door; not that he can be contained in a bodily <lb></lb>place, nor that he is really moved, nor in time; nor that humane <lb></lb>manners or cuſtomes can agree with him, ſave only according to <lb></lb>our manner of Apprehenſion: This Conception of ours orderly <lb></lb>diſtinguiſheth theſe Attributes in him one from another, when, <lb></lb>notwithſtanding, they are one and the ſame with him: This Ap<lb></lb>prehenſion of ours divideth alſo his actions into ſeveral times, <lb></lb>which, nevertheleſſe, for the moſt part, are produced in one and <lb></lb>the ſame inſtant: And this, to conclude, alwayes apprehendeth <lb></lb>thoſe things with ſome defect, which, notwithſtanding are in <lb></lb>God moſt perfect. </s> <s>For this reaſon doth the Sacred Scripture <lb></lb>expreſs it ſelf <emph type="italics"></emph>according to the Vulgar Opinion,<emph.end type="italics"></emph.end> whilſt it aſcribes <lb></lb>to the Earth Ends and Foundations, which yet it hath not; to <lb></lb>the Sea a Depth not to be fathomed; to Death (which is a Pri<lb></lb>vation, and conſequently a Non entity) it appropriates Actions, <lb></lb>Motion, Paſſions, and other ſuch like Accidents, of all which it is <lb></lb>deprived, as alſo Epithites and Adjuncts, which really cannot <lb></lb>ſuit with it: <emph type="italics"></emph>Is not the bitterneſſe of Death paſt<emph.end type="italics"></emph.end>? </s> <s>1 Sam. </s> <s>15. 32. <lb></lb><emph type="italics"></emph>Let death come upon them,<emph.end type="italics"></emph.end> Pſal 6. <emph type="italics"></emph>He hath prepared the Inſtru<lb></lb>ments of Death,<emph.end type="italics"></emph.end> Pſal. </s> <s>7. 14. <emph type="italics"></emph>Thou raiſeſt me from the gates of <lb></lb>Death,<emph.end type="italics"></emph.end> Pſal. </s> <s>84. <emph type="italics"></emph>In the midſt of the ſhadow of Death,<emph.end type="italics"></emph.end> Pſal. </s> <s>23. <lb></lb><emph type="italics"></emph>Love is ſtrong as Death,<emph.end type="italics"></emph.end> Cant. </s> <s>8. 9. <emph type="italics"></emph>The Firſt-Born of Death,<emph.end type="italics"></emph.end> Job <lb></lb>18. 13. <emph type="italics"></emph>Deſtruction and Death ſay, &c.<emph.end type="italics"></emph.end> Job 28. 22. And who knows <lb></lb>not that the whole Hiſtory of the rich Glutton doth conſiſt of <lb></lb><arrow.to.target n="marg886"></arrow.to.target><lb></lb>the like phraſes of <emph type="italics"></emph>Vulgar Speech<emph.end type="italics"></emph.end>? </s> <s>So <emph type="italics"></emph>Eccleſiaſticus,<emph.end type="italics"></emph.end> Chap. </s> <s>27. <lb></lb>verſ. </s> <s>11. <emph type="italics"></emph>The godly man abideth in wiſdome, as the Sun; but a <lb></lb>fool changeth as the Moon<emph.end type="italics"></emph.end>; and yet the Moon according to the <lb></lb>real truth of the matter no wayes changeth, but abides the ſame <lb></lb>for ever, as <emph type="italics"></emph>Aſtronomers<emph.end type="italics"></emph.end> demonſtrate, one half thereof remain<lb></lb>ing alwayes lucid, and the other alwayes opacous. </s> <s>Nor at any <lb></lb>time doth this ſtate vary in it, unleſſe <emph type="italics"></emph>in reſpect of us,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>ac<lb></lb>cording to the opinion of the Vulgar.<emph.end type="italics"></emph.end> Hence it is cleer, that the <lb></lb>holy Scripture ſpeaks according to the common form of ſpeech u <pb xlink:href="040/01/507.jpg" pagenum="483"></pb>ſed amongſt the unlearned, and according to the appearance of <lb></lb>things, and not according to their true Exiſtence. </s> <s>In like man<lb></lb>ner <emph type="italics"></emph>Geneſ.<emph.end type="italics"></emph.end> 1. in the deſcription of the Creation of all things, <lb></lb>the Light is ſaid to be made firſt of all, and yet it followeth in <lb></lb>the Text, <emph type="italics"></emph>And the Evening and the Morning made the firſt day<emph.end type="italics"></emph.end>: <lb></lb>and a little after the ſeveral Acts of the Creation are diſtinguiſhed <lb></lb>and aſſigned to ſeveral days, and concerning each of them it is <lb></lb>ſaid in the Text, <emph type="italics"></emph>And the Evening and the Morning made the <lb></lb>ſecond day<emph.end type="italics"></emph.end>; and then <emph type="italics"></emph>the third day, the fourth day, &c.<emph.end type="italics"></emph.end> Hence <lb></lb>many doubts ariſe, all which I ſhall propound according to the <lb></lb>common Syſteme, that it may appear even from the <emph type="italics"></emph>H<emph.end type="italics"></emph.end>ypotheſis <lb></lb>of that Syſteme, that the ſacred Scripture ſometimes, for the a<lb></lb>voyding of emergent difficulties, is to be underſtood in a vulgar <lb></lb>ſenſe and meaning, and in reſpect of us, and not according to <lb></lb>the nature of things. </s> <s>Which diſtinction even <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> himſelf <lb></lb><arrow.to.target n="marg887"></arrow.to.target><lb></lb>ſeemeth to have hinted, when he ſaith, ^{*} <emph type="italics"></emph>Some things are more <lb></lb>intelligible to us; others by nature,<emph.end type="italics"></emph.end> or <emph type="italics"></emph>ſecundum ſe.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg885"></margin.target>* Circa Cardi<lb></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 ſunt notio<lb></lb>ra nobis, alia, no<lb></lb>tiora natura, vel <lb></lb>ſecundum ſe, <emph type="italics"></emph>A<lb></lb>r ſt. </s> <s>lib. 1. Phyſ.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Firſt therefore; If the light were made before heaven, then <lb></lb>it rolled about without heaven to the making of the diſtinction <lb></lb>of Day and Night. </s> <s>Now this is contrary to the very doctrine <lb></lb>of theſe men, who affirm that no Cœleſtial Body can be moved <lb></lb>unleſſe <emph type="italics"></emph>per accidens,<emph.end type="italics"></emph.end> and by the motion of <emph type="italics"></emph>H<emph.end type="italics"></emph.end>eaven, <emph type="italics"></emph>and as a knot <lb></lb>in a board at the motion of the board.<emph.end type="italics"></emph.end> Again, if it be ſaid, that <lb></lb>the Light was created at the ſame time with <emph type="italics"></emph>H<emph.end type="italics"></emph.end>eaven, and began <lb></lb>to be moved with <emph type="italics"></emph>H<emph.end type="italics"></emph.end>eaven, another doubt ariſeth, that likewiſe <lb></lb>oppoſeth the foreſaid common <emph type="italics"></emph>Hypotheſis:<emph.end type="italics"></emph.end> For it being ſaid, <lb></lb>that Day and Night, Morning and Evening were made, that ſame <lb></lb>is either in reſpect of the Univerſe, or onely in reſpect of the <lb></lb>Earth and us. </s> <s>If ſo be that the Sun turning round (according to <lb></lb>the <emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> of the Common Syſteme) doth not cauſe the <lb></lb>Night and Day, but only to opacous Bodies which are deſtitute <lb></lb>of all other light, but that of the Sun, whilſt in their half part <lb></lb>(which is their <emph type="italics"></emph>Hemiſphœre)<emph.end type="italics"></emph.end> and no more, (for that the Suns <lb></lb>light paſſeth over but one half of an opacous Body, unleſs a ve<lb></lb>ry ſmall matter more in thoſe of leſſer bulk) they are illumina<lb></lb>ted by the Suns aſpect, the other half remaining dark and tene<lb></lb>broſe, by reaſon of a ſhadow proceeding from its own Body. <lb></lb></s> <s>Therefore the diſtinction of dayes by the light of heaven, ac<lb></lb>cording to the deſcription of them in the ſacred Scriptures, muſt <lb></lb>not be underſtood <emph type="italics"></emph>abſolutely,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>ſecundum ſe,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Nature her <lb></lb>ſelf<emph.end type="italics"></emph.end>; but in reſpect of the Earth, and of us its inhabitants, and <lb></lb>conſequently <emph type="italics"></emph>ſecundum nos.<emph.end type="italics"></emph.end> 'Tis not therefore new, nor unu<lb></lb>ſual in ſacred Scripture to ſpeak of things <emph type="italics"></emph>ſecundum nos,<emph.end type="italics"></emph.end> and on<lb></lb>ly <emph type="italics"></emph>in reſpect of us,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>ſecundum apparentiam<emph.end type="italics"></emph.end>; but not <emph type="italics"></emph>ſecundum <lb></lb>ſe,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>reinaturam,<emph.end type="italics"></emph.end> or <emph type="italics"></emph>Abſolutely<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Simply.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/508.jpg" pagenum="484"></pb><p type="main"> <s>And if any one would underſtand theſe Days of ſacred Scri<lb></lb>pture, not only <emph type="italics"></emph>ſecundum nos,<emph.end type="italics"></emph.end> but alſo <emph type="italics"></emph>ſecundum naturam,<emph.end type="italics"></emph.end> as <lb></lb>circulations of Cœleſtial Light returning to the ſelf ſame point <lb></lb>from whence it did at firſt proceed; ſo as that there needs no <lb></lb>reſpect to be had to Night or to ^{*} Darkneſſe, for which ſole rea<lb></lb><arrow.to.target n="marg888"></arrow.to.target><lb></lb>ſon we are fain to imbrace the Interpretation of ſacred Scripture <lb></lb><emph type="italics"></emph>ſecundum nos<emph.end type="italics"></emph.end>; In oppoſition to this we may thus argue: If the <lb></lb>ſacred Scripture be underſtood to ſpeak <emph type="italics"></emph>abſolutely,<emph.end type="italics"></emph.end> of iterated <lb></lb>and ſucceſſive circulations of light, and not <emph type="italics"></emph>reſpectu noſtri,<emph.end type="italics"></emph.end> as if <lb></lb>theſe words <emph type="italics"></emph>Evening and Morning<emph.end type="italics"></emph.end> had never been inſerted, which <lb></lb>in their natural acceptation denote the Suns habitude to us and to <lb></lb>the Earth: For that the <emph type="italics"></emph>Morning<emph.end type="italics"></emph.end> is that time when the Sun be<lb></lb>gins to wax light, and to riſe above the <emph type="italics"></emph>Horizon<emph.end type="italics"></emph.end> in the Eaſt, <lb></lb>and become viſible in our <emph type="italics"></emph>Hemiſphœre,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Evening<emph.end type="italics"></emph.end> is the time <lb></lb>in which the Sun declines in the Weſt, and approacheth with its <lb></lb>light neerer to the other oppoſite <emph type="italics"></emph>Horizon<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Hemiſphœre,<emph.end type="italics"></emph.end><lb></lb>which is contiguous to this of ours. </s> <s>But the word <emph type="italics"></emph>Day<emph.end type="italics"></emph.end> is a Co<lb></lb>relative to the word <emph type="italics"></emph>Night.<emph.end type="italics"></emph.end> From hence therefore it evidently <lb></lb>appeareth, that theſe three words <emph type="italics"></emph>Evening, Morning,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Day,<emph.end type="italics"></emph.end><lb></lb>cannot be underſtood of a Circulation of Light <emph type="italics"></emph>ſecundum ſe,<emph.end type="italics"></emph.end><lb></lb>and <emph type="italics"></emph>abſolutè,<emph.end type="italics"></emph.end> but only <emph type="italics"></emph>ſecundum nos,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>reſpectu noſtri<emph.end type="italics"></emph.end>; and in <lb></lb>that ſenſe indeed the <emph type="italics"></emph>Morning<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Evening<emph.end type="italics"></emph.end> do make the <emph type="italics"></emph>Night<emph.end type="italics"></emph.end><lb></lb>and <emph type="italics"></emph>Day,<emph.end type="italics"></emph.end></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"></emph>Gen.<emph.end type="italics"></emph.end> 1. 16. it is ſaid, <emph type="italics"></emph>God made two great Lights; <lb></lb>the greater Light to rule the Day, and the leſſer Light to rule the <lb></lb>Night, and the Stars.<emph.end type="italics"></emph.end> Where both in the Propoſition and in the <lb></lb>ſpecification of it, things are ſpoken which are very diſagreeing <lb></lb>with Cœleſtial Bodies. </s> <s>Therefore thoſe words are in that place <lb></lb>to be interpreted according to the foreſaid Rules; namely, ac<lb></lb>cording to the third and fourth; ſo that they may be ſaid to be <lb></lb>underſtood <emph type="italics"></emph>according to the ſenſe of the vulgar, and the common <lb></lb>way of ſpeaking,<emph.end type="italics"></emph.end> which is all one, as if we ſhould ſay, <emph type="italics"></emph>ſecundum <lb></lb>apparentiam,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>ſecundum nos, vel reſpectu noſtri.<emph.end type="italics"></emph.end> For firſt, it <lb></lb>is ſaid in the Propoſition, <emph type="italics"></emph>And God made two great Lights<emph.end type="italics"></emph.end>; <lb></lb>meaning by them the Sun and Moon, whereas according to the <lb></lb>truth of the matter theſe are not the Greater Lights; For al<lb></lb>though the Sun may be reckoned amongſt the Greater, the Moon <lb></lb>may not be ſo, unleſs <emph type="italics"></emph>in reſpect of us.<emph.end type="italics"></emph.end> Becauſe amongſt <lb></lb>thoſe that are abſolutely the Greater, and a little leſſer than the <lb></lb><arrow.to.target n="marg889"></arrow.to.target><lb></lb>Sun (nay in a manner equal to it) and far bigger than the Moon, <lb></lb>we may with great reaſon enumerate <emph type="italics"></emph>Saturn,<emph.end type="italics"></emph.end> or ſome of the <lb></lb>Fixed Stars of the firſt Magnitude, ſuch as <emph type="italics"></emph>Canopus,<emph.end type="italics"></emph.end> (otherwiſe <lb></lb>called <emph type="italics"></emph>Arcanar)<emph.end type="italics"></emph.end> in the end of a River; or the <emph type="italics"></emph>Little Dog<emph.end type="italics"></emph.end> in <lb></lb>the mouth of the <emph type="italics"></emph>Great Dog<emph.end type="italics"></emph.end>; or the Foot of <emph type="italics"></emph>Orion,<emph.end type="italics"></emph.end> called <emph type="italics"></emph>Ri<lb></lb>gel<emph.end type="italics"></emph.end>; or his <emph type="italics"></emph>Right ſhoulder,<emph.end type="italics"></emph.end> or any other of that Magnitude. <pb xlink:href="040/01/509.jpg" pagenum="485"></pb>Therefore the <emph type="italics"></emph>two great Lights<emph.end type="italics"></emph.end> are to be underſtood in reſpect of <lb></lb>us, and according to vulgar eſtimation, and not according to the <lb></lb>true and reall exiſtence of ſuch Bodies. </s> <s>Secondly, in the ſpeci<lb></lb>fication of the Propoſition it is ſaid, <emph type="italics"></emph>The greater Light to rule the <lb></lb>Day<emph.end type="italics"></emph.end>; hereby denoting the Sun; in which the verbal ſenſe of <lb></lb>Scripture agreeth with the Truth of the Thing; For that the Sun <lb></lb>is the Greateſt of all Luminaries, and Globes. </s> <s>But that which <lb></lb>followeth immediately after, <emph type="italics"></emph>And the leſſer Light to rule the <lb></lb>Night,<emph.end type="italics"></emph.end> meaning the Moon, cannot be taken in the true and real <lb></lb>ſenſe of the words: For the Moon is not the leſſer Light, but <lb></lb><emph type="italics"></emph>Mercury<emph.end type="italics"></emph.end>; which is not only much leſſer than the Moon, but alſo <lb></lb>than any other Star. </s> <s>And if, again, it be ſaid, That the Holy <lb></lb>Text doth not ſpeak of the Stars, but onely of the Luminaries, <lb></lb>for that preſently after they are mentioned apart, <emph type="italics"></emph>And the Stars<emph.end type="italics"></emph.end>; <lb></lb>and that what we ſay is true touching the compariſon of the Stars <lb></lb>amongſt themſelves, but not in reſpect of the Luminaries, name<lb></lb>ly, the Sun and Moon: This reply doth diſcover a man to be <lb></lb>utterly ignorant in theſe Studies, and ſuch who having not the <lb></lb>leaſt ſmattering in them, doth conceive an abſurd and erroneous <lb></lb>Opinion of the Cœleſtial Bodies. </s> <s>For the Moon and Sun, con<lb></lb>ſidered in themſelves, and as they appear to us, if they ſhould <lb></lb>be a far greater diſtance from us, than indeed they are, would be <lb></lb>no other, nor would appear to us otherwiſe than Stars, as the <lb></lb>reſt do in the Firmament. </s> <s>But Great Luminaries they neither <lb></lb><arrow.to.target n="marg890"></arrow.to.target><lb></lb>are, nor ſeem to be, ſave only <emph type="italics"></emph>in reſpect of us:<emph.end type="italics"></emph.end> And ſo, on <lb></lb>the other ſide, the Stars, as to themſelves, are no other than ſo <lb></lb>many Suns and ſo many Moons; yet are ſo far remote from us, <lb></lb>that by reaſon of their diſtance they appear thus ſmall, and dim <lb></lb>of light, as we behold them. </s> <s>For the greater and leſſer diſtance <lb></lb>of heavenly Bodies <emph type="italics"></emph>(cæteris paribus)<emph.end type="italics"></emph.end> doth augment and diminiſh <lb></lb>their appearance both as to Magnitude and Light. </s> <s>And there<lb></lb>fore the words which follow in that place of <emph type="italics"></emph>Geneſis, And the <lb></lb>Stars<emph.end type="italics"></emph.end> (as diſtinguiſhing the Stars from the Sun and Moon) are <lb></lb>to be taken in no other acceptation than that which we have ſpo<lb></lb>ken of, namely, <emph type="italics"></emph>according to the ſenſe of the Vulgar, and the <lb></lb>common manner of ſpeech.<emph.end type="italics"></emph.end> For indeed, according to the truth <lb></lb>of the matter, all Cœleſtial Bodies, being ſhining Globes, are of <lb></lb>a vaſt bigneſs, to which if we ſhould be ſo neer as we are to the <lb></lb>Moon, they would ſeem to us of as great, yea a greater magni<lb></lb>tude than the Moon: As likewiſe on the contrary, if we were as <lb></lb>far diſtant from the Sun and Moon, as we are from them, both <lb></lb>Moon and Sun would ſhew but as ſtars to us. </s> <s>And yet the <lb></lb>ſplendor of the Sun would doubtleſs be greater <emph type="italics"></emph>intenſivè<emph.end type="italics"></emph.end> than <lb></lb>that of any other ſtar. </s> <s>For, although it ſhould be granted that <lb></lb>ſome ſtars (as thoſe of the Fixed that twinkle) do ſhine of them <pb xlink:href="040/01/510.jpg" pagenum="486"></pb>ſelves, aud by their own nature, as the Sun, that derives not its <lb></lb>light from others (which yet remains undecided and doubtful) <lb></lb>and borrow not their light from the Sun; Nevertheleſs ſince the <lb></lb>brightneſs of none of the ſtars may be compared with the Suns <lb></lb>ſplendour, which was created by God firſt, and before all other <lb></lb>Luminaries, in the higheſt kind of Light, it would therefore <lb></lb>notwithſtanding follow, that none of thoſe ſtars, although pla<lb></lb>ced in the ſame proximity to us with the Sun, and therefore ap<lb></lb>pearing to us of the ſame Magnitude as the Sun, can beſtow up<lb></lb>on us ſo much Light as we receive from the Sun: As on the <lb></lb>contrary, the Sun, at the ſame remoteneſſe from us as they are, <lb></lb>would indeed, as to its Magnitude, appear to us as one of thoſe <lb></lb>ſtars, but of a ſplendour much more <emph type="italics"></emph>intenſe<emph.end type="italics"></emph.end> than that of theirs. <lb></lb><arrow.to.target n="marg891"></arrow.to.target><lb></lb>So that, now, the Earth is nothing elſe but another Moon or ſtar, <lb></lb>and ſo would it appear to us, if we ſhould behold it from a con<lb></lb>venient diſtance <emph type="italics"></emph>on high.<emph.end type="italics"></emph.end> And in it might be obſerved (in that <lb></lb>variety of Light and Darkneſs which the Sun produceth in it by <lb></lb>making Day and Night) the ſame difference of Aſpects that are <lb></lb>ſeen in the Moon, and ſuch as are obſerved in tricorporate <emph type="italics"></emph>Ve<lb></lb>nus<emph.end type="italics"></emph.end>; in like manner alſo 'tis very probable that the ſame might <lb></lb>be diſcerned in other Planets, which ſhine by no light of their <lb></lb>own, but by one borrowed from the Sun. </s> <s>What ever there<lb></lb>fore may touching theſe matters be delivered in the ſacred Leaves <lb></lb>or the common ſpeech of men, diſſenting from the real truth, it <lb></lb>ought (as we have ſaid before) abſolutely to be received and un<lb></lb>derſtood <emph type="italics"></emph>ſecundum vulgi ſententiam, & communem loquendi & <lb></lb>concipiendi ſtylum.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg889"></margin.target><emph type="italics"></emph>Which are really <lb></lb>the great Lights <lb></lb>in Heaven.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg890"></margin.target><emph type="italics"></emph>The Sun, Moon, <lb></lb>and Stars are one <lb></lb>& the ſame thing.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg891"></margin.target><emph type="italics"></emph>The Earth is a<lb></lb>nother Moon or <lb></lb>Star.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And ſo, to return to our purpoſe, if, all this conſidered, the <lb></lb><emph type="italics"></emph>Pythagorian<emph.end type="italics"></emph.end> opinion be true, it will be eaſie, according to the <lb></lb>ſame Rule, to reconcile the authority of ſacred Scriptures with <lb></lb>it, however they ſeem to oppoſe it, and in particular thoſe of the <lb></lb>firſt and ſecond Claſſis, <emph type="italics"></emph>ſcilicet<emph.end type="italics"></emph.end> by my firſt <emph type="italics"></emph>Maxime:<emph.end type="italics"></emph.end> For that in <lb></lb>thoſe places the holy Records ſpeak according to our manner of <lb></lb>underſtanding, and according to that which appeareth in reſpect <lb></lb>of us; <emph type="italics"></emph>For thus it is with thoſe Bodies, in compariſon of us, and<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg892"></arrow.to.target><lb></lb><emph type="italics"></emph>as they are deſcribed by the vulgar and commune way of humane <lb></lb>Diſcourſe; So that the Earth appears as if it were ſtanding ſtill <lb></lb>and immoveable, and the Sun, as if it were circumambient about <lb></lb>her.<emph.end type="italics"></emph.end> And ſo the Holy Scripture is uſed in the Commune and <lb></lb>Vulgar way of ſpeaking; becauſe in reſpect of our ſight, the <lb></lb>Earth ſeems rather to ſtand fixed in the Centre, and the Sun to <lb></lb>circumvolve about it, than otherwiſe: as it happens to thoſe that <lb></lb>are putting off from the Banks of a River to whom the ſhose <lb></lb>ſeems to move backwards, and go from them: but they do not <lb></lb>perceive (which yet is the truth) that they themſelves go forwards. <pb xlink:href="040/01/511.jpg" pagenum="487"></pb>Which fallacy of our ſight is noted, and the Reaſon thereof aſ<lb></lb>ſigned by the Opticks; upon wich, as being ſtrange to, and be<lb></lb>ſides my purpoſe, I will not ſtay) and on this account is <emph type="italics"></emph>Æneas<emph.end type="italics"></emph.end><lb></lb>brought in by <emph type="italics"></emph>Virgil,<emph.end type="italics"></emph.end> ſaying;<lb></lb><arrow.to.target n="marg893"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg892"></margin.target><emph type="italics"></emph>Why the Sunne <lb></lb>ſeemeth to us to <lb></lb>move, & not the <lb></lb>Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg893"></margin.target><emph type="italics"></emph>Æneid.<emph.end type="italics"></emph.end> 3.</s></p><p type="head"> <s><emph type="italics"></emph>Provehimur portu, terræque urbeſque recedunt.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>But it will not be amiſs to conſider why the ſacred Scripture <lb></lb>doth ſo ſtudiouſly comply with the opinions of the Vulgar, and <lb></lb>why it doth not rather accurately inſtruct men in the truth of the <lb></lb>matters, and the ſecrets of Nature. </s> <s>The Reaſon is, firſt, the be<lb></lb>nignity of Divine Wiſdome, whereby it ſweetly accomodates it <lb></lb>ſelf to all things, in proportion to their Capacity and Nature. <lb></lb></s> <s>Whence in Natural Sciences, it uſeth natural and neceſſary cau<lb></lb>ſes, but in Liberal Arts it worketh liberally, upon Generous <lb></lb>Perſons after a ſublime and lofty manner; upon the Common <lb></lb>People, familiarly and humbly; upon the Skilful, learnedly; <lb></lb>upon the Simple, vulgarly; and ſo on every one, according to <lb></lb>his condition and quality. </s> <s>Secondly, becauſe it is not its In<lb></lb>tention to fill our mindes in this life with vain and various curi<lb></lb>oſities, which might occaſion our doubt and ſuſpenſe. </s> <s>For the <lb></lb><arrow.to.target n="marg894"></arrow.to.target><lb></lb>truth is, <emph type="italics"></emph>(a) He that increaſeth knowledge, increaſeth ſorrow.<emph.end type="italics"></emph.end><lb></lb>Moreover it did not only permit, but even decree, thatth e <lb></lb>World ſhould be very much buſied in Controverſies and Diſpu<lb></lb>tations, and that it ſhould be imployed about the uncertainty of <lb></lb><arrow.to.target n="marg895"></arrow.to.target><lb></lb>things; according to that ſaying of <emph type="italics"></emph>Eccleſiaſtes<emph.end type="italics"></emph.end> <emph type="italics"></emph>(b) He hath <lb></lb>ſet the World in their heart; ſo that no man can find out the work <lb></lb>that God maketh from the beginning unto the end.<emph.end type="italics"></emph.end> And touching <lb></lb>thoſe doubts, God will not permit that they ſhall be diſcovered <lb></lb><arrow.to.target n="marg896"></arrow.to.target><lb></lb>to us before the end of the World: <emph type="italics"></emph>(c) At which time he will <lb></lb>bring to light the hidden things of darkneſſe:<emph.end type="italics"></emph.end> But Gods onely <lb></lb>ſcope in the ſacred Scripture is to teach men thoſe things which <lb></lb>conduce to the attainment of Eternal Life; which having ob<lb></lb><arrow.to.target n="marg897"></arrow.to.target><lb></lb>tained, <emph type="italics"></emph>(d) We ſhall ſee him face to face: (e) and ſhall be<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg898"></arrow.to.target><lb></lb><emph type="italics"></emph>like him, for we ſhall ſee him as he is.<emph.end type="italics"></emph.end> Then ſhall he clearly <emph type="italics"></emph>à <lb></lb>Priori<emph.end type="italics"></emph.end> make known unto us all thoſe Curioſities, and Dogmati<lb></lb>cal Queſtions, which in this life, <emph type="italics"></emph>(f) in which we ſee through a<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg899"></arrow.to.target><lb></lb><emph type="italics"></emph>Glaſſe darkly,<emph.end type="italics"></emph.end> could be known by us but imperfectly and <emph type="italics"></emph>à poſte<lb></lb>riori,<emph.end type="italics"></emph.end> and that not without much pains and ſtudy. </s> <s>For this <lb></lb>cauſe the Wiſdome of God, revealed to us in the ſacred Leaves, <lb></lb>is not ſtiled Wiſdome abſolutely, but <emph type="italics"></emph>(g) Saving Wiſdome<emph.end type="italics"></emph.end>; <lb></lb><arrow.to.target n="marg900"></arrow.to.target><lb></lb>Its onely end being to lead us to ſalvation. </s> <s>And S. <emph type="italics"></emph>Paul<emph.end type="italics"></emph.end> preach<lb></lb>ing to the <emph type="italics"></emph>Corinthians,<emph.end type="italics"></emph.end> ſaith; <emph type="italics"></emph>(h) I determined to know nothing<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg901"></arrow.to.target><lb></lb><emph type="italics"></emph>among you, ſave Jeſus Chriſt, and him crucified:<emph.end type="italics"></emph.end> whereas not<lb></lb>withſtanding he was thorowly inſtructed, and profoundly learned <pb xlink:href="040/01/512.jpg" pagenum="488"></pb>in all humane Sciences; but making no account of theſe things <lb></lb>he profeſſeth that it was his deſire to teach them no more but the <lb></lb>way to Heaven. </s> <s>Hence is that which God ſpeaketh to us by <lb></lb><arrow.to.target n="marg902"></arrow.to.target><lb></lb><emph type="italics"></emph>Iſaiah,<emph.end type="italics"></emph.end> <emph type="italics"></emph>(i) Ego Dominus Deus, docens te utilia<emph.end type="italics"></emph.end> [<emph type="italics"></emph>I am the Lord <lb></lb>thy God which teacheth thee profitable things:<emph.end type="italics"></emph.end>] Where the <emph type="italics"></emph>Gloſ<lb></lb>ſary<emph.end type="italics"></emph.end> addeth, <emph type="italics"></emph>non ſubtilia<emph.end type="italics"></emph.end> [not ſubtilties.] For God neither taught <lb></lb>us, Whether the <emph type="italics"></emph>Materia Prima<emph.end type="italics"></emph.end> of Heaven, and the Elements <lb></lb>be the ſame; nor Whether <emph type="italics"></emph>Cominual<emph.end type="italics"></emph.end> be compoſed of Indiviſi<lb></lb>bles, or whether it be diviſible <emph type="italics"></emph>in infinitum<emph.end type="italics"></emph.end>; nor, whether the <lb></lb>Elements are formally <emph type="italics"></emph>mixt<emph.end type="italics"></emph.end>; nor how many the Cœleſtial <lb></lb>Spheres, and their Orbs are; Whether there be Epicycles or <lb></lb>Eccentricks; nor the Vertues of Plants and Stones; nor the Na<lb></lb>ture of Animals; nor the Motion and Influence of the Planets; <lb></lb>nor the Order of the Univerſe; nor the Wonders of Minerals, <lb></lb>and univerſal Nature: but only [<emph type="italics"></emph>utilia:<emph.end type="italics"></emph.end>] things profitable, to <lb></lb>wit, his Holy Law ordained to the end, that we being put into <lb></lb>poſſeſſion of Bleſſedneſs, might at length be made capable of all <lb></lb>perfect knowledge, and the viſion of the whole Order and ad<lb></lb>mirable Harmony, as alſo the Sympathy and Antipathy of the <lb></lb>Univerſe and its parts, <emph type="italics"></emph>in his Word,<emph.end type="italics"></emph.end> wherein all thoſe <lb></lb>things ſhall moſt clearly and diſtinctly, then, appear to us, which <lb></lb>mean while, in this life, he hath remitted (as far as its ability <lb></lb>reacheth) to humane ſearch and enquiry: But it was not his <lb></lb>purpoſe to determine any thing, directly or indirectly, touching <lb></lb>the truth of them. </s> <s>Becauſe as the knowledge thereof would lit<lb></lb>tle or nothing profit Us, but might in ſome caſes prove prejudi<lb></lb>cial; ſo the ignorance thereof can doubtleſs be no detriment, <lb></lb>but may in ſome caſes be very beneficial to us. </s> <s>And therefore <lb></lb>by his moſt admirable Wiſdome it comes to paſs, that though all <lb></lb>things in this World are dubious, uncertain, wavering, and per<lb></lb>plexed; yet his Holy Faith alone is moſt certain; and although <lb></lb>the opinions about Philoſophical and Doctrinal points be divers, <lb></lb>there is in the Church but one Truth of Faith and Salvation. <lb></lb></s> <s>Which Faith, as neceſsary to Salvation, is ſo ordered by Divine <lb></lb>Providence, that it might not only be indubitable, but alſo un<lb></lb>ſhaken, ſure, immutable, and manifeſt to all men: the infallible <lb></lb>Rule of which he hath appointed the Holy Church, that is waſh<lb></lb>ed with his precious Blood, and governed by his Holy Spirit, to <lb></lb>whom belongs our Sanctification, as being his work. </s> <s>This there<lb></lb><arrow.to.target n="marg903"></arrow.to.target><lb></lb>fore is the Reaſon why God would have Speculative Queſtions, <lb></lb>which nothing conduce to our Salvation and Edification, and why <lb></lb>the Holy Ghoſt hath very often condeſcended to Vulgar Opini<lb></lb>ons and Capacities, and hath diſcovered nothing that is ſingular <lb></lb>or hidden to us, beſides thoſe things that pertain to Salvation. <lb></lb></s> <s>So that conſequently it is clear by what hath been ſaid, how and <pb xlink:href="040/01/513.jpg" pagenum="489"></pb>why nothing of certainty can be evinced from the foreſaid Au<lb></lb>thorities to the determining of Controverſies of this Nature; as <lb></lb>alſo with what Reaſon from this firſt <emph type="italics"></emph>Axiome<emph.end type="italics"></emph.end> the Objections of <lb></lb>the firſt and ſecond Claſſe are eaſily anſwered, as alſo any other <lb></lb>Authority of ſacred Scripture produced againſt the <emph type="italics"></emph>Pythagorian<emph.end type="italics"></emph.end><lb></lb>and <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Syſteme ſo long as by other proofs it is true.</s></p><p type="margin"> <s><margin.target id="marg894"></margin.target><emph type="italics"></emph>(a)<emph.end type="italics"></emph.end> Eccleſ. <emph type="italics"></emph>c. </s> <s>1. v. <lb></lb></s> <s>ult.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg895"></margin.target><emph type="italics"></emph>(b) Chap. </s> <s>3. v.<emph.end type="italics"></emph.end> 11.</s></p><p type="margin"> <s><margin.target id="marg896"></margin.target><emph type="italics"></emph>(c)<emph.end type="italics"></emph.end> 1 Cor. <emph type="italics"></emph>c. </s> <s>4. v.<emph.end type="italics"></emph.end> 5</s></p><p type="margin"> <s><margin.target id="marg897"></margin.target><emph type="italics"></emph>(d)<emph.end type="italics"></emph.end> 1 Cor. <emph type="italics"></emph>c. </s> <s>13. v.<emph.end type="italics"></emph.end><lb></lb>12.</s></p><p type="margin"> <s><margin.target id="marg898"></margin.target><emph type="italics"></emph>(e)<emph.end type="italics"></emph.end> 1 John <emph type="italics"></emph>c. </s> <s>3. v.<emph.end type="italics"></emph.end><lb></lb>2.</s></p><p type="margin"> <s><margin.target id="marg899"></margin.target><emph type="italics"></emph>(f)<emph.end type="italics"></emph.end> 1 Cor. <emph type="italics"></emph>c. </s> <s>13. v.<emph.end type="italics"></emph.end><lb></lb>12.</s></p><p type="margin"> <s><margin.target id="marg900"></margin.target><emph type="italics"></emph>(g)<emph.end type="italics"></emph.end> Eccleſiaſt. </s> <s>15. 3</s></p><p type="margin"> <s><margin.target id="marg901"></margin.target><emph type="italics"></emph>(h)<emph.end type="italics"></emph.end> 1 Cor. <emph type="italics"></emph>c. </s> <s>2. v.<emph.end type="italics"></emph.end> 2</s></p><p type="margin"> <s><margin.target id="marg902"></margin.target><emph type="italics"></emph>(i)<emph.end type="italics"></emph.end> Iſa. <emph type="italics"></emph>c. </s> <s>48. v.<emph.end type="italics"></emph.end> 17.</s></p><p type="margin"> <s><margin.target id="marg903"></margin.target>1 Theſſ. </s> <s>4.</s></p><p type="main"> <s>And the Authorities of the ſecond Claſſe in particular by <lb></lb>this ſame Maxime, <emph type="italics"></emph>Of the ordinary manner of apprehending <lb></lb>things as they appear to us, and after the common way of ſpeak<lb></lb>ing,<emph.end type="italics"></emph.end> may be thus reconciled and expounded; namely, Oftentimes <lb></lb>an Agent is commonly, and not improperly ſaid to move, (though <lb></lb>it have no motion) not becauſe it doth indeed move, but <emph type="italics"></emph>by ex<lb></lb>trinſick denomination,<emph.end type="italics"></emph.end> becauſe receiving its influence and action at <lb></lb>the motion of the Subject; the Form and Quality infuſed to <lb></lb>the Subject by the ſaid Agent doth likewiſe move. </s> <s>As for ex<lb></lb>ample, a Fire burning in a Chimney is an immoveable Agent, <lb></lb>before which a man oppreſt with cold ſits to warm himſelf who <lb></lb>being warmed on one ſide, turns the other to the Fire, that he <lb></lb>may be warmed on that ſide alſo, and ſo in like manner he holds <lb></lb>every part to the Fire ſucceſſively, till his whole body be warm<lb></lb>ed. 'Tis clear, that although the Fire do not move, yet at the <lb></lb>Motion of the Subject, to wit the Man, who receiveth the heat <lb></lb>and action of the Fire, the Form and Quality of its Heat doth <lb></lb>move <emph type="italics"></emph>ſingulatim, & per partes,<emph.end type="italics"></emph.end> round about the mans body, and <lb></lb>alwayes ſeeketh out a new place: and ſo, though the Fire do <lb></lb>not move, yet by reaſon of its effect, it is ſaid to go round all <lb></lb>the parts of the Mans body, and to warm it, not indeed by a <lb></lb>true and real motion of the Fire it ſelf, ſince it is ſuppoſed (and <lb></lb>that not untruly) not to move, but by the motion to which the <lb></lb>Body is excited, out of a deſire of receiving the heat of the Fire <lb></lb>in each of its parts. </s> <s>The ſame may be applied to the Illumina<lb></lb>tion impreſſed ſucceſſively on the parts of any Globe, which <lb></lb>moves Orbicularly at the aſpect of a ſhining immoveable <lb></lb>Light. </s> <s>And in the ſame manner may the Sun be ſaid to riſe and <lb></lb>ſet, and to move above the Earth, although in reality he doth <lb></lb>not move, nor ſuffer any mutation; that is to ſay, Inaſmuch as <lb></lb>his Light (which effect is the Form and Quality proceeding from <lb></lb>him, as the Agent, to the Earth as the Subject) doth ſenſibly <lb></lb>glide forwards, by reaſon of the Orbicular motion of the Earth; <lb></lb>and doth alwayes be take it ſelf to ſome new place of her ſurface; <lb></lb>upon which ground he is truly ſaid <emph type="italics"></emph>(ſecundum vnlgarem ſermo<lb></lb>nem)<emph.end type="italics"></emph.end> to move above, and revolve about the Earth: Not that the <lb></lb>Sun doth move, (for by this Opinion we affirm the Earth to <lb></lb>move, that it may receive the Sun one while in one, another <lb></lb>while in another part of it) but that at the motion of the Earth <pb xlink:href="040/01/514.jpg" pagenum="490"></pb>her ſelf a contrary way, the Quality diffuſed into her, and im<lb></lb>preſſed upon her by the Sun, namely the Light of the Day is <lb></lb>moved, which riſeth in one part of her, and ſets in another con<lb></lb>trary to that, according to the nature and condition of her motion; <lb></lb>And for this reaſon the Sun it ſelf by conſequence is ſaid to riſe <lb></lb>and ſet, (which notwithſtanding <emph type="italics"></emph>ex Hypotheſi<emph.end type="italics"></emph.end> ſtands immovea<lb></lb>ble) and that no otherwiſe then <emph type="italics"></emph>per donominationem extrinſecam,<emph.end type="italics"></emph.end><lb></lb>as hath been ſaid.</s></p><p type="main"> <s>After this manner the command of <emph type="italics"></emph>Joſhuah, Sun ſtand thou<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg904"></arrow.to.target><lb></lb><emph type="italics"></emph>ſtill,<emph.end type="italics"></emph.end> and the Miracle of the Suns ceſſation of Motion wrought <lb></lb>by him, may be ſo underſtood, as that not the Solar Body pro<lb></lb>perly, but the Suns ſplendour upon the Earth ſtood ſtill; ſo that <lb></lb>not the Sun it ſelf, (being of it ſelf before that time immovea<lb></lb>ble) but the Earth that receiveth its ſplendour, ſtayed her Mo<lb></lb>tion; which, as ſhe inceſſantly purſuing her ordinary Motion to<lb></lb><arrow.to.target n="marg905"></arrow.to.target><lb></lb>wards the Eaſt, ^{*} called up the Light of the Sun in the Weſt, ſo <lb></lb>ſtanding ſtill, the Suns light impreſt upon it likewiſe ſtood ſtill. <lb></lb><arrow.to.target n="marg906"></arrow.to.target><lb></lb>After the ſame manuer pioportionally is that Text of <emph type="italics"></emph>Iſaiah<emph.end type="italics"></emph.end> ex<lb></lb>plained, touching the Suns going ten degrees back ward upon the <lb></lb>Dial of <emph type="italics"></emph>Ahaz.<emph.end type="italics"></emph.end> So (which may ſerve for another Example) the <lb></lb>Hand being moved about the flame of a burning Candle that <lb></lb>ſtands ſtill, the Light moveth on the Hand, that is to ſay, the <lb></lb>ſaid Hand is illuſtrated now in one part, anon in another, when <lb></lb>as the Candle it ſelf all the while removes not out of its place: <lb></lb>whereupon <emph type="italics"></emph>per denominationem extrinſecam,<emph.end type="italics"></emph.end> the ſaid Light may <lb></lb>be affirmed to riſe and ſet upon the Hand, namely, by the ſole <lb></lb>motion of the ſaid Hand, the Candle it ſelf never moving all the <lb></lb>while. </s> <s>And let this ſuffice for the explanation of my firſt Prin<lb></lb>ciple or <emph type="italics"></emph>Maxime,<emph.end type="italics"></emph.end> which by reaſon of its difficulty and extraordi<lb></lb>nary weight required ſome prolixity in the handling of it.</s></p><p type="margin"> <s><margin.target id="marg904"></margin.target>Joſhua <emph type="italics"></emph>c. </s> <s>10. <lb></lb>ver.<emph.end type="italics"></emph.end> 12.</s></p><p type="margin"> <s><margin.target id="marg905"></margin.target><emph type="italics"></emph>* expected.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg906"></margin.target>Iſa. <emph type="italics"></emph>c. </s> <s>38. v.<emph.end type="italics"></emph.end> 8.</s></p><p type="main"> <s>My ſecond Maxime is this, Things both Spiritual and Cor<lb></lb>poreal, Durable and Corruptible, Moveable and Immoveable, <lb></lb>have received from God a perpetual, unchangeable, and inviola<lb></lb>ble Law, conſtituting the Eſſence and Nature of every one of <lb></lb>them: according to which Law all of them in their own Na<lb></lb>ture perſiſting in a certain Order and Conſtancy, and obſerving <lb></lb>the ſame perpetual Courſe, may deſervedly be ſtiled moſt Stable <lb></lb>and Determinate. </s> <s>Thus Fortune (than which there is nothing <lb></lb>in the World more inconſtant or fickle) is ſaid to be conſtant <lb></lb>and unalterable in her continual volubility, viciſſitude, and in<lb></lb>conſtancy, which was the occaſion of that Verſe,</s></p><p type="head"> <s><emph type="italics"></emph>Et ſemper conſtans in levitate ſua eſt.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And thus the motion of Heaven (which by the conſtan Law <pb xlink:href="040/01/515.jpg" pagenum="491"></pb>of Nature ought to be perpetual) may be ſaid to be immutable <lb></lb>and immoveable, and the Heavens themſelves to be immovea<lb></lb>bly moved, and Terrene things to be immutably changed, be<lb></lb>cauſe thoſe never ceaſe moving, nor theſe changing. </s> <s>By this Prin<lb></lb>ciple or Maxime all difficulties belonging to the firſt Claſſis are <lb></lb>cleared, by which the Earth is ſaid to be ſtable and immoveable, <lb></lb>that is, by underſtanding this one thing, That the Earth, as to its <lb></lb>own Nature, though it include in it ſelf a local Motion, and that <lb></lb>threefold, according to the opinion of <emph type="italics"></emph>Copernicus (ſcilicet<emph.end type="italics"></emph.end> Diur<lb></lb><arrow.to.target n="marg907"></arrow.to.target><lb></lb>nal, with which it revolveth about its own Centre; Annual, <lb></lb>by which it moveth through the twelve Signes of the Zodiack, <lb></lb>and the motion of Inclination, by which its Axis is alwayes op<lb></lb>poſed to the ſame part of the World) as alſo other Species of <lb></lb>Mutation, ſuch as Generation and Corruption, Accretion and <lb></lb>Diminution, and Alteration of divers kinds; yet in all theſe ſhe <lb></lb>is ſtable & conſtant, never deviating from that Order which God <lb></lb>hath appointed her, but moveth continually, conſtantly and im<lb></lb>mutably, according to the ſix before named Species of Motion.</s></p><p type="margin"> <s><margin.target id="marg907"></margin.target><emph type="italics"></emph>Several Motions <lb></lb>of the Earth ac<lb></lb>cording to<emph.end type="italics"></emph.end> Coper<lb></lb>nicus.</s></p><p type="main"> <s>My third Maxime ſhall be this; When a thing is moved ac<lb></lb>cording to ſome part of it, and not according to its whole, it <lb></lb>cannot be ſaid to be <emph type="italics"></emph>ſimply & abſolutely<emph.end type="italics"></emph.end> moved, but only <emph type="italics"></emph>per acci<lb></lb>dens,<emph.end type="italics"></emph.end> for that ſtability taken ſimply & abſolutly do rather accord <lb></lb>with the ſame. </s> <s>As for example, if a Barrel or other meaſure of <lb></lb>Water be taken out of the Sea, and transferred to another place, <lb></lb>the Sea may not therefore <emph type="italics"></emph>abſolutely & ſimply<emph.end type="italics"></emph.end> be ſaid to be remo<lb></lb>ved from place to place; but only <emph type="italics"></emph>per accidens,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>ſecundum <lb></lb>quid,<emph.end type="italics"></emph.end> that is, according to a part of it, but rather (to ſpeak ſim<lb></lb>ply) we ſhould ſay that the Sea cannot be carried or moved out of <lb></lb>its proper place,, though as to its parts it be moved, and transfer<lb></lb>red to & again. </s> <s>This Maxime is manifeſt of it ſelf, and by it may <lb></lb>the Authorities be explained which ſeem to make for the immo<lb></lb>bility of the Earth in this manner; namely, The Earth <emph type="italics"></emph>per ſe & <lb></lb>abſolutè<emph.end type="italics"></emph.end> conſidered as to its <emph type="italics"></emph>Whole,<emph.end type="italics"></emph.end> is not mutable, ſeeing it is <lb></lb>neither generated nor corrupted neither increaſed nor diminiſhed; <lb></lb>neither is it altered <emph type="italics"></emph>ſecundum totum,<emph.end type="italics"></emph.end> but only <emph type="italics"></emph>ſecundum partes.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg908"></arrow.to.target><lb></lb>Now it plainly appears, that this is the genuine and true Senſe of <lb></lb>what is aſcribed to it out of <emph type="italics"></emph>Eccleſiaſtes, cap. 1. v. </s> <s>4. One Generation <lb></lb>paſſeth away, and another Generation cometh, but the Earth abideth <lb></lb>for ever<emph.end type="italics"></emph.end>: as if he ſhould ſay; although the Earth, according to its <lb></lb>parts, doth generate and corrupt, and is liable to the viciſſitudes of <lb></lb>Generation and corruption, yet in reference to its Whole it never <lb></lb>generateth nor Corrupteth, but abideth immutable for ever: <lb></lb>Like as a Ship, which though it be mended one while in the Sail<lb></lb>yard, another while in the Stern, and afterwards in other parts <lb></lb>it yet remains the ſame Ship as it was at firſt. </s> <s>But tis to be ad <pb xlink:href="040/01/516.jpg" pagenum="492"></pb>vertized, that that Scripture doth not ſpeak of a Local Motion, <lb></lb>but of Mutations of another nature; as in the very ſubſtance, <lb></lb>quantity or quality of the Earth it ſelf. </s> <s>But if it be ſaid, that <lb></lb>it is to be underſtood of a Local Motion, then it may be ex<lb></lb>plained by the inſuing Maxime, that is to ſay, a reſpect being had <lb></lb>to the natural Place aſſigned it in the Univerſe, as ſhall be ſhewed <lb></lb>by and by.</s></p><p type="margin"> <s><margin.target id="marg908"></margin.target><emph type="italics"></emph>The Earth Se-<emph.end type="italics"></emph.end><lb></lb>cundum Totum <emph type="italics"></emph>is <lb></lb>Immutable, <lb></lb>though not Immo<lb></lb>vable.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The fourth Axiome is this; That every Corporeal thing, mo<lb></lb>veable or immoveable from its very firſt Creation, is alotted its <lb></lb>proper and natural place; and being drawn or removed from <lb></lb>thence, its motion is violent, and it hath a natural tendency to <lb></lb>move back thither again: alſo that nothing can be moved from <lb></lb>its natural place, <emph type="italics"></emph>ſecundum Totum<emph.end type="italics"></emph.end>; For moſt great and dreadſul <lb></lb>miſchiefs would follow from that perturbation of things in the <lb></lb>Univerſe. </s> <s>Therefore neither the whole Earth, nor the whole <lb></lb><arrow.to.target n="marg909"></arrow.to.target><lb></lb>Water, nor the whole Air can <emph type="italics"></emph>ſecundum totum<emph.end type="italics"></emph.end> be driuen or for<lb></lb>ced out of their proper place, ſite, or Syſteme in the Univerſe, <lb></lb>in reſpect of the order and diſpoſition of other mundane Bodies. <lb></lb></s> <s>And thus there is no Star (though Erratick) Orb or Sphere that <lb></lb>can deſert its natural place, although it may otherwiſe have ſome <lb></lb>kind of motion. </s> <s>Therefore all things, how moveable ſoever, <lb></lb>are notwithſtanding ſaid to be ſtable and immoveable in their <lb></lb>proper place, according to the foreſaid ſenſe, <emph type="italics"></emph>i.e. </s> <s>ſecundum to<lb></lb>tum<emph.end type="italics"></emph.end>; For nothing hinders, but that <emph type="italics"></emph>ſecundum partes<emph.end type="italics"></emph.end> they may <lb></lb>ſome waymove; which motion ſhall not be natural, but violent. <lb></lb></s> <s>Therefore the Earth, although it ſhould be moveable, yet it <lb></lb>might be ſaid to be immoveable, according to the precedent <lb></lb>Maxime, for that its neither moved in a right Motion nor out of <lb></lb>the Courſe aſſigned it in its Creation for the ſtanding Rule of its <lb></lb>motion; but keep within its own ſite, being placed in that <lb></lb>which is called the Grand Orb, above <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> and beneath <emph type="italics"></emph>Mars,<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg910"></arrow.to.target><lb></lb>and being in the middle betwixt theſe (which according to the <lb></lb>common opinion is the Suns place) it equally and continually <lb></lb>moveth about the Sun, and the two other intermediate Planets, <lb></lb>namely <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Mercury,<emph.end type="italics"></emph.end> and hath the Moon (which is another <lb></lb>Earth, but Ætherial, as <emph type="italics"></emph>Macrobius<emph.end type="italics"></emph.end> after ſome of the ancient Phi<lb></lb><arrow.to.target n="marg911"></arrow.to.target><lb></lb>loſophers, will have it) about it ſelf. </s> <s>From whence, inaſmuch as <lb></lb>ſhe perſiſteth uniformly in her Courſe, and never at any time <lb></lb>departeth from it, ſhe may be ſaid to be ſtable and immoveable: <lb></lb>and in the ſame ſenſe Heaven likewiſe, with all the Elements, <lb></lb>may be ſaid to be immoveable.</s></p><p type="margin"> <s><margin.target id="marg909"></margin.target><emph type="italics"></emph>The Earth can<lb></lb>not<emph.end type="italics"></emph.end> Secundum To<lb></lb>tum, <emph type="italics"></emph>remove out of <lb></lb>its Natural Place.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg910"></margin.target><emph type="italics"></emph>The Natural <lb></lb>Place of the Earth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg911"></margin.target><emph type="italics"></emph>The Moon is an <lb></lb>Ætherial Body.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The fifth Maxime followeth, being little different from the <lb></lb>former. </s> <s>Amongſt the things created by God, ſome are of ſuch a <lb></lb>nature, that their parts may be <emph type="italics"></emph>ab invicem,<emph.end type="italics"></emph.end> or by turns, ſe<lb></lb>parated from themſelves, and diſ-joyned from their Whole; <pb xlink:href="040/01/517.jpg" pagenum="493"></pb>others may not, at leaſt, taken <emph type="italics"></emph>collectively<emph.end type="italics"></emph.end>: now thoſe are pe<lb></lb>riſhable, but theſe perpetual. </s> <s>The Earth therefore ſince it <lb></lb>is reckoned amongſt thoſe things that are permanent, as hath <lb></lb><arrow.to.target n="marg912"></arrow.to.target><lb></lb>been ſaid already, hath its parts, not diſſipable, nor <emph type="italics"></emph>ab invicem,<emph.end type="italics"></emph.end><lb></lb>ſeparable from its Centre (whereby its true and proper place is <lb></lb>aſſigned it) and from its whole, taken collectively: becauſe ac<lb></lb>cording to its whole it is always preſerved, compact, united, and <lb></lb>cohærent in it ſelf, nor can its parts be ſeperated from the Cen<lb></lb>tre, or from one another, unleſs it may ſo fall out <emph type="italics"></emph>per accidens,<emph.end type="italics"></emph.end><lb></lb>and violently in ſome of its parts; which afterwards, the obſtacle <lb></lb>being removed, return to their Natural Station ſpontaneouſly, <lb></lb>and without any impulſe. </s> <s>In this Senſe therefore the Earth is <lb></lb>ſaid to be Immoveable, and Immutable: yea even the Sea, Aire, <lb></lb>Heaven, and any other thing (although otherwiſe moveable) ſo <lb></lb>long as its parts are not diſſipable and ſeperable, may be ſaid to <lb></lb>be Immoveable, at leaſt taken <emph type="italics"></emph>collectively.<emph.end type="italics"></emph.end> This Principle <lb></lb>or Maxim differeth from the precedent only in that this referrs <lb></lb>to the parts in order to <emph type="italics"></emph>Place,<emph.end type="italics"></emph.end> and this, in order to the Whole.</s></p><p type="margin"> <s><margin.target id="marg912"></margin.target><emph type="italics"></emph>The Earths Cen<lb></lb>tre keepeth it in <lb></lb>its Natural Place.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>From this Speculation another Secret is diſcovered. </s> <s>For hence <lb></lb><arrow.to.target n="marg913"></arrow.to.target><lb></lb>it is manifeſt wherein the proper and genuine formality of the <lb></lb>Gravity aad Levity of Bodyes conſiſteth; a point which is not ſo <lb></lb>clearly held forth, nor ſo undeniably explained by the Peripate<lb></lb>tick Phyloſophy. <emph type="italics"></emph>Gravity<emph.end type="italics"></emph.end> therefore is nothing elſe according to <lb></lb>the Principles of this new Opinion, than a certain power and ap<lb></lb>petite of the Parts to rejoyn with their Whole, and there to reſt <lb></lb>as in their proper place. </s> <s>Which Faculty or Diſpoſition is by <lb></lb>Divine Providence beſtowed not only on the Earth, and Ter<lb></lb>rene Bodies, but, as is believed, on Cœleſtial Bodies alſo, name<lb></lb><arrow.to.target n="marg914"></arrow.to.target><lb></lb>ly the Sun, Moon, and Starrs; all whoſe parts are by this Impul<lb></lb>ſion connected, and conſerved together, cleaving cloſely to each <lb></lb>other, and on all ſides preſſing towards their Centre, until they <lb></lb>come to reſt there. </s> <s>From which Concourſe and Compreſſion a <lb></lb>Sphærical and Orbicular Figure of the Cæleſtial Orbes is produ<lb></lb>ced, wherein by this occult Quality naturally incident to <lb></lb>each of them they of themſelves ſubſiſt, and are alwayes preſer<lb></lb>ved. </s> <s>But <emph type="italics"></emph>Levity<emph.end type="italics"></emph.end> is the Extruſion and Excluſion of a more te<lb></lb>nuoſe and thin Body from the Commerce of one more Solid and <lb></lb><arrow.to.target n="marg915"></arrow.to.target><lb></lb>denſe, that is Heterogeneal to it, by vertue of Heat. </s> <s>Where<lb></lb>upon, as the Motion of Grave Bodies is <emph type="italics"></emph>Compreſſive,<emph.end type="italics"></emph.end> ſo the Mo<lb></lb>tion of Light Bodies is <emph type="italics"></emph>Extenſive:<emph.end type="italics"></emph.end> For its the propperty of Heat <lb></lb>to dilate and rarify thoſe things to which it doth apply, conjoine <lb></lb>and communicate it ſelf. </s> <s>And for this reaſon we find Levity <lb></lb>and Gravity not only in reſpect of this our Tereſtrial Globe, and <lb></lb>the Bodies adjacent to it, but alſo in reſpect of thoſe Bodies <lb></lb>which are ſaid to be in the Heavens, in which thoſe parts which <pb xlink:href="040/01/518.jpg" pagenum="494"></pb>by reaſon of their proclivity make towards their Centre are <lb></lb>Grave, and thoſe that incline to the Circumference Light. </s> <s>And <lb></lb>ſo in the Sun, Moon, and Starrs, there are parts as well Grave as <lb></lb><arrow.to.target n="marg916"></arrow.to.target><lb></lb>Light. </s> <s>And conſequently Heaven it ſelf that ſo Noble Body, <lb></lb>and of a fifth Eſſence, ſhall not be conſtituted of a Matter diffe<lb></lb>rent from that of the Elements, being free from all Mutation in <lb></lb>it's Subſtance, Quantity, and Quality: Nor ſo admirable and <lb></lb><arrow.to.target n="marg917"></arrow.to.target><lb></lb>excellent as <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> would make us to believe; nor yet a ſolid <lb></lb>Body, and impermeable; and much leſſe (as the generality of <lb></lb>men verily believe) of an impenetrable and moſt obdurate Den<lb></lb>ſity: but in it (as this Opinion will have it) Comets may be ge<lb></lb>nerated; and the Sun it ſelf, as tis probable, exhaling or attract<lb></lb>ing ſundry vapours to the ſurface of its Body, may perhaps pro<lb></lb>duce thoſe Spots which were obſerved to be ſo various, and irre<lb></lb><arrow.to.target n="marg918"></arrow.to.target><lb></lb>gular in its <emph type="italics"></emph>Diſcus<emph.end type="italics"></emph.end>: of which <emph type="italics"></emph>Galilæus<emph.end type="italics"></emph.end> in a perticular ^{*} Treatiſe <lb></lb>hath moſt excellently and moſt accurately ſpoken; inſomuch, <lb></lb>that though it were not beſides my preſent purpoſe, yet it is con<lb></lb>venient that I forbear to ſpeak any thing touching thoſe matters, <lb></lb>leaſt I ſhould ſeem to do that which he hath done before me: But <lb></lb>now if there be found in the Sacred Scriptures any Authority <lb></lb>contrary to theſe things, it may be ſalved by the foreſaid Argu<lb></lb>ments Analogically applyed. </s> <s>And further more it may be ſaid, <lb></lb>that that Solidity is to be ſo underſtood, <emph type="italics"></emph>as that it admits of no <lb></lb>vacuum, cleft, or penetration from whence the leaſt vacuity might <lb></lb>proceed<emph.end type="italics"></emph.end> For the truth is, as that cannot be admitted in bodily <lb></lb>Creatures, ſo it is likewiſe repugnant to Heaven it ſelf, being <lb></lb>indeed a Body of its own Nature the moſt Rare of all o<lb></lb><arrow.to.target n="marg919"></arrow.to.target><lb></lb>thers, and tenuoſe beyond all Humane Conception, and happly <lb></lb>hath the ſame proportion to the Aire, as the Aire to the <lb></lb>Water.</s></p><p type="margin"> <s><margin.target id="marg913"></margin.target><emph type="italics"></emph>Gravity and Le<lb></lb>vity of Bodies, <lb></lb>what it is.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg914"></margin.target><emph type="italics"></emph>All Cœleſtial Bo<lb></lb>dies have Gravity <lb></lb>and Levety.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg915"></margin.target><emph type="italics"></emph>Compreſſive Ma<lb></lb>tion, proper to <lb></lb>Gravity; the Ex<lb></lb>tenſive, to Levity.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg916"></margin.target><emph type="italics"></emph>Heaven is not <lb></lb>compoſed of a fift <lb></lb>Eſſence differing <lb></lb>from the matter of <lb></lb>inferior Bodies.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg917"></margin.target><emph type="italics"></emph>Nor yet a Solid <lb></lb>or denſe Body but <lb></lb>Rare.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg918"></margin.target>* Delle Macchie <lb></lb>ſolarj.</s></p><p type="margin"> <s><margin.target id="marg919"></margin.target>* <emph type="italics"></emph>Vnius Corporis <lb></lb>fimplicis, unus eſt <lb></lb>motus ſimplex, et <lb></lb>huic duæ ſpecies, <lb></lb>Rectus & Circu<lb></lb>laris: Rectus du<lb></lb>plex à medio, & <lb></lb>ad medium; pri<lb></lb>mus levium, ut A<lb></lb>eris & Ignis: ſe<lb></lb>cundus gravium, <lb></lb>ut Aquæ & Ter<lb></lb>ræ: Circularis, <lb></lb>quieſt circa medi<lb></lb>um competit Cœlo, <lb></lb>quod neque eſt <lb></lb>grave, neque leve.<emph.end type="italics"></emph.end><lb></lb>Ariſt. <emph type="italics"></emph>de Cœlo.<emph.end type="italics"></emph.end><lb></lb>Lib. 1.</s></p><p type="main"> <s>It is clear alſo from theſe Principles how falſe theſe words of <lb></lb><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> are, that: <emph type="italics"></emph>Of one ſimple Body, there is one ſimple Motion<emph.end type="italics"></emph.end>; <lb></lb><emph type="italics"></emph>and this is of two kindes, Right and Circular: the Right is two<lb></lb>fold, from the medium, and to the medium; the firſt of Light Bo<lb></lb>dyes, as the Aire and Fire: the ſecond of Grave Bodyes, as the <lb></lb>Water and Earth: the Circular, which is about the medium, be<lb></lb>longeth to Heaven, which is neither Grave nor Light<emph.end type="italics"></emph.end>: For all this <lb></lb>Philoſophy is now forſaken, and of it ſelf grown into diſ-eſteem; <lb></lb>for though it be received for an unqueſtionable truth in this new <lb></lb>Opinion, that to a ſimple body appertains one only ſimple Moti<lb></lb><arrow.to.target n="marg920"></arrow.to.target><lb></lb>on, yet it granteth no Motion but what is Circular, by which alone <lb></lb>aſimple body is conſerved in its naturall Place, and ſubſiſts in its <lb></lb>Unity, and is properly ſaid to move <emph type="italics"></emph>in loco<emph.end type="italics"></emph.end> [<emph type="italics"></emph>in a place<emph.end type="italics"></emph.end>:] whereby <lb></lb><arrow.to.target n="marg921"></arrow.to.target><lb></lb>it comes to paſs that a Body for this reaſon doth continue to move <lb></lb>in it ſelf, [<emph type="italics"></emph>or about its own axis<emph.end type="italics"></emph.end>;] and although it have a Motion, <pb xlink:href="040/01/519.jpg" pagenum="495"></pb>yet it abideth ſtill in the ſame place, as if it were perpetually im<lb></lb>moveable. </s> <s>But right Motion, which is properly <emph type="italics"></emph>ad locum, [to a <lb></lb>place]<emph.end type="italics"></emph.end> can be aſcribed only to thoſe things which are out of their <lb></lb>naturall place, being far from union with one another, and from <lb></lb>unity with their whole, yea that are ſeperated and divided from <lb></lb>it: Which being that it is contrary to the Nature and forme of <lb></lb>the Univerſe, it neceſſarily followeth, that right Motion doth in <lb></lb><arrow.to.target n="marg922"></arrow.to.target><lb></lb>ſhort ſute with thoſe things which are deſtitute of that perfection, <lb></lb>that according to their proper Nature belongeth to them, and <lb></lb>which by this ſame right Motion they labour to obtaine, untill <lb></lb>they are redintigrated with their Whole, and with one another, <lb></lb>and reſtored to their Naturall place; in which at the length, <lb></lb>having obtained their perfection, they ſettle and remaine immove<lb></lb>able. </s> <s>Therefore in right Motions there can be no Uniformity, <lb></lb><arrow.to.target n="marg923"></arrow.to.target><lb></lb>nor ſimplicity; for that they vary by reaſon of the uncertaine <lb></lb>Levity or Gravity of their reſpective Bodyes: for which cauſe <lb></lb>they do not perſevere in the ſame Velocity or Tardity to the end <lb></lb>which they had in the beginning. </s> <s>Hence we ſee that thoſe things <lb></lb>whoſe weight maketh them tend downwards, do deſcend at firſt <lb></lb>with a ſlow Motion; but afterwards, as they approach neerer <lb></lb>and neerer to the Centre, they precipitate more and more ſwiftly. <lb></lb></s> <s>And on the otherſide, thoſe things which by reaſon of their light<lb></lb>neſs are carryed upwards (as this our Terreſtriall fire, which is no<lb></lb>thing elſe but a ſmoak that burneth, and is inkindled into a flame) <lb></lb>are no ſooner aſcended on high, but, in almoſt the ſelf-ſame mo<lb></lb>ment, they fly and vaniſh out of fight; by reaſon of the rare<lb></lb>faction and extenſion, that they as ſoon as they acquire, are freed <lb></lb>from thoſe bonds which violently and againſt their own Nature <lb></lb><arrow.to.target n="marg924"></arrow.to.target><lb></lb>kept them under, and deteined them here below. </s> <s>For which <lb></lb>reaſon, it is very apparent, that no Right Motion can be called <lb></lb>Simple, not only in regard that (as hath been ſaid) it is not <lb></lb>^{*} even and uniforme, but alſo becauſe it is mixt with the Circu<lb></lb><arrow.to.target n="marg925"></arrow.to.target><lb></lb>lar, which lurketh in the Right by an occult conſent, <emph type="italics"></emph>ſcilicet<emph.end type="italics"></emph.end> by <lb></lb>reaſon of the Natural affection of the Parts to conforme unto <lb></lb>their Whole. </s> <s>For when the Whole moveth Circularly, it is re<lb></lb>quiſite likewiſe that the Parts, to the end that they may be uni<lb></lb>ted to their Whole, (howbeit <emph type="italics"></emph>per accidens<emph.end type="italics"></emph.end> they are ſometimes <lb></lb>moved with a Right Motion) do move (though not ſo appa<lb></lb>rently) with a Circular Motion, as doth their Whole. </s> <s>And thus <lb></lb>at length we have evinced that Circular Motion only is Simple, <lb></lb><arrow.to.target n="marg926"></arrow.to.target><lb></lb>Uniform and ^{*} Æquable, and of the ſame tenor [<emph type="italics"></emph>or rate<emph.end type="italics"></emph.end>] for that <lb></lb><arrow.to.target n="marg927"></arrow.to.target><lb></lb>it is never deſtitute of its interne Cauſe: whereas on the contra<lb></lb>ry, Right Motion, (which pertains to things both Heavy and <lb></lb>Light) hath a Cauſe that is imperfect and deficient, yea that ari<lb></lb>ſeth from Defect it ſelf, and that tendeth to, and ſeeketh after <pb xlink:href="040/01/520.jpg" pagenum="496"></pb>nothing elſe but the end and termination of it ſelf: in regard <lb></lb>that Grave and Light Bodies, when once they have attained their <lb></lb>proper and Natural Place, do deſiſt from that Motion to which <lb></lb>they were incited by Levity and Gravity. </s> <s>Therefore: ſince Cir<lb></lb><arrow.to.target n="marg928"></arrow.to.target><lb></lb>cular Motion is proper <emph type="italics"></emph>to the Whole,<emph.end type="italics"></emph.end> and Right Motion <emph type="italics"></emph>to the <lb></lb>Parts,<emph.end type="italics"></emph.end> theſe differences are not rightly referred to Motion, ſo as <lb></lb>to call one Motion Right, another Circular, as if they were not <lb></lb>conſiſtent with one another: For they may be both together, and <lb></lb><arrow.to.target n="marg929"></arrow.to.target><lb></lb>that Naturally, in the ſame Body; no leſſe than it is equally <lb></lb>Natural for a Man to participate of Senſe and Reaſon, ſeeing <lb></lb>that theſe differences are not directly oppoſite to one another. <lb></lb></s> <s>Hereupon Reſt and Immobility only are oppoſed to Motion; <lb></lb>and not one Species of Motion to another. </s> <s>And for the other <lb></lb>differences <emph type="italics"></emph>à medio, ad medium,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>circa medium,<emph.end type="italics"></emph.end> they are di<lb></lb>ſtinguiſhed not <emph type="italics"></emph>really,<emph.end type="italics"></emph.end> but only <emph type="italics"></emph>formally,<emph.end type="italics"></emph.end> as the Point, Line and <lb></lb>Superficies, none of which can be without the other two, or <lb></lb>without a Body. </s> <s>Hence it appears, that in as much as this Phy<lb></lb>loſophy differs from that of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> ſo in like manner doth this <lb></lb>New Coſmographical Syſtem vary from the Common one, that <lb></lb>hath been hitherto received. </s> <s>But this by the way, upon occaſion <lb></lb>of explaining the Fifth Maxim: For as to the truth or falſhood <lb></lb>of theſe foregoing Poſitions (although I conceive them very pro<lb></lb>bable) I am reſolved to determine nothing at preſent, neither <lb></lb>ſhall I make any farther enquiry into them.</s></p><p type="margin"> <s><margin.target id="marg920"></margin.target>* <emph type="italics"></emph>Vide Coperni<lb></lb>cum de Revolutio<lb></lb>nibus Cœleſt.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg921"></margin.target><emph type="italics"></emph>Simple Motion <lb></lb>peculiar to only <lb></lb>Simple Bodies.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg922"></margin.target><emph type="italics"></emph>Right Motion <lb></lb>belongeth to Im<lb></lb>perfect Bodies, and <lb></lb>that are out of <lb></lb>their natural Pla<lb></lb>ces.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg923"></margin.target><emph type="italics"></emph>Right Motion <lb></lb>cannot be Simple.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg924"></margin.target><emph type="italics"></emph>Right Motion is <lb></lb>ever mixt with <lb></lb>the Circular.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg925"></margin.target>* <emph type="italics"></emph>æquabilis.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg926"></margin.target>* <emph type="italics"></emph>Even.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg927"></margin.target><emph type="italics"></emph>Circular Mo<lb></lb>tion is truly Sim<lb></lb>ple and Perpetual.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg928"></margin.target><emph type="italics"></emph>Circular Mo<lb></lb>tion belongeth to <lb></lb>the Whole Body, <lb></lb>and the Right to <lb></lb>its parts.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg929"></margin.target><emph type="italics"></emph>Circular and <lb></lb>Right Motion co<lb></lb>incedent, and may <lb></lb>conſiſt together in <lb></lb>the ſame Body.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The Sixth and Laſt Maxim is this. </s> <s>Every thing is Simply deno<lb></lb>minated ſuch as it is in compariſon of all things, or of many <lb></lb>things which make the greater number of that kinde, but not in <lb></lb>reſpect of a few which make but the leſſer part of them. </s> <s>As, <lb></lb>for inſtance, a Veſſel ſhall not be called abſolutely Great be<lb></lb>cauſe it is ſo whilſt it is compared with two or three others: but <lb></lb>it ſhall be ſaid to be great abſolutely, and will be ſo, if it ex<lb></lb>ceed in magnitude all indivials, or the greater part of them. </s> <s>Nor <lb></lb>again ſhall a Man be ſaid to be abſolutely Big, becauſe he is big<lb></lb>ger than a Pigmey; nor yet abſolutely Little, becauſe leſſe than <lb></lb>a Gyant: but he ſhall be termed abſolutely Big or Little in com<lb></lb>pariſon of the ordinary Stature of the greater part of Men. </s> <s>Thus <lb></lb>the Earth cannot abſolutely be ſaid to be High or Low for that it <lb></lb>is found to be ſo in reſpect of ſome ſmall part of the Univerſe; nor <lb></lb>again ſhall it be abſolutely affirmed to be High, being compared <lb></lb>to the Centre of the World, or ſome few parts of the Univerſe, <lb></lb>more near to the ſaid Centre, as is the <emph type="italics"></emph>Sun, Mercury<emph.end type="italics"></emph.end> or <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end>: <lb></lb><arrow.to.target n="marg930"></arrow.to.target><lb></lb>but it ſhall receive its abſolute denomination according as it ſhall <lb></lb>be found to be in compariſon of the greater number of the <lb></lb>Spheres and Bodies of the Univerſe. </s> <s>The Earth therefore, in <lb></lb>compariſon of the whole Circuit of the Eighth Sphære which in <pb xlink:href="040/01/521.jpg" pagenum="497"></pb>cludeth all Corporeal Creatures, and in compariſon of <emph type="italics"></emph>Jupiter, <lb></lb>Mars,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> together with the <emph type="italics"></emph>Moon,<emph.end type="italics"></emph.end> and much more in <lb></lb>compariſon of other Bodies, (if any ſuch there be) above the <lb></lb>Eighth Sphere and eſpecially the Empyrial Heaven, may be truly <lb></lb>ſaid to be in the loweſt place of the World, and almoſt in the <lb></lb>Centre of it; nor can it he ſaid to be above any of them, except <lb></lb>the <emph type="italics"></emph>Sun, Mercury<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end>: So that one may apply unto it the <lb></lb>name of an Infime and Low, but not a Supreme or Middle Body. <lb></lb></s> <s>And ſo to come down from Heaven, eſpecially the Empyrian, to it <lb></lb>(as it is accepted in the Deſcent of Chriſt from Heaven to his Holy <lb></lb>Incarnation) and from it to go up to Heaven (as in Chriſts return <lb></lb><arrow.to.target n="marg931"></arrow.to.target><lb></lb>to Heaven in his Glorious Aſcention) is truly and properly to <lb></lb><emph type="italics"></emph>Deſcend<emph.end type="italics"></emph.end> from the Circumference to the Centre, and to <emph type="italics"></emph>aſcend<emph.end type="italics"></emph.end><lb></lb>from the parts which are neareſt to the Centre of the World <lb></lb>to its utmoſt Circumference. </s> <s>This Maxim therefore may eaſily <lb></lb>and according to truth explain Theologicall Propoſitions: and <lb></lb>this is ſo much the more confirmed, in that (as I have obſerved) <lb></lb>almoſt all Texts of Sacred Scripture which oppoſe the Earth to <lb></lb>Heaven, are moſt conveniently and aptly underſtood of the Em<lb></lb>pyrial Heaven (being the Higheſt of all the Heavens, and Spiritual <lb></lb>in reſpect of its end) but not of the inferiour or intermediate Hea<lb></lb>vens, which are a Corporeal, and were framed for the benefit of <lb></lb>Corporeal Creatures: and thus when in the Plural Number <lb></lb>Heavens are mentioned, then all the Heavens promiſcuouſly and <lb></lb>without diſtinction are to be underſtood, as well the Empyrian <lb></lb>it ſelf as the Inferiour Heavens. </s> <s>And this Expoſition indeed any <lb></lb>man (that doth but take notice of it) may find to be moſt true. <lb></lb></s> <s>And ſo for this Reaſon the Third Heaveu into which St. <emph type="italics"></emph>Paul<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg932"></arrow.to.target><lb></lb>was wrapt up, by this Maxim may be taken for the Empyrean: <lb></lb>if for the the Firſt Heaven we underſtand that immenſe Space of <lb></lb>Erratick and Moveable Bodies illuminated by the Sun, in which <lb></lb>are comprehended the Planets, as alſo the Earth moveable, and <lb></lb>the Sun immoveable, Who like a King upon his Auguſt Tribu<lb></lb>nal, ſits with venerable Majeſty immoveable and conſtant in <lb></lb>Centre of all the Sphæres, and, with his Divine Beames, doth <lb></lb>bountifully exhilerate all Cœleſtial Bodies that ſtand in need of <lb></lb>his vital Light, for which they cravingly wander about him; and <lb></lb>doth liberally and on every ſide comfort and illuſtrate the Thea<lb></lb>tre of the whole World, and all its parts, even the very leaſt, like <lb></lb>an immortal and perpetual Lamp of high and unſpeakable va<lb></lb>lue. </s> <s>The Second Heaven ſhall be the Starry Heaven, common<lb></lb>ly called the Eighth Sphære, or the Firmament, wherein are all <lb></lb>the Fixed Starrs, which according to this Opinion of <emph type="italics"></emph>Pythagoras,<emph.end type="italics"></emph.end><lb></lb>is (like as the Sun and Centre) void of all Motion, the Centre <lb></lb>and utmoſt Circumference mutually agreeing with each other in <pb xlink:href="040/01/522.jpg" pagenum="498"></pb>Immobility. </s> <s>And the Third ſhall be the Empyrean Heaven, that <lb></lb>is the Seat of the Bleſſed. </s> <s>And in this manner we may come to <lb></lb>explain and underſtand that admirable Secret, and profound My<lb></lb><arrow.to.target n="marg933"></arrow.to.target><lb></lb>ſtery ænigmatically revealed by <emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> to <emph type="italics"></emph>Dionyſius<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Syracuſe<emph.end type="italics"></emph.end>: <lb></lb><arrow.to.target n="marg934"></arrow.to.target><lb></lb><emph type="italics"></emph>(a) All things are about the King of all things, Second things <lb></lb>about the ſecond, and Third things about the Third<emph.end type="italics"></emph.end>: For that <lb></lb>God being the Centre of Spiritual things, the Sun, of Cor<lb></lb>poreal, Chriſt, of thoſe that are Mixt, or made up of both, things <lb></lb>do doubtleſſe depend of that of theſe three Centres that is moſt <lb></lb>correſpondent and proportionable to them, and the Centre is <lb></lb>ever adjudged to be the nobler and worthier place: and therefore <lb></lb>in Animals the Heart, in Vegitables the Pith or Kernell wherein <lb></lb>the Seed lyeth that conſerveth their perpetuity, and virtually in<lb></lb>cludes the whole Plant, are in the Midſt, and in the Centre: and <lb></lb>thus much ſhall ſuffice to have hinted at, ſince there may another <lb></lb>occaſion offer it ſelf for a larger Explication of theſe things. </s> <s>By <lb></lb>this Maxim the Authorities and Arguments of the Third Fourth <lb></lb>and Fifth Claſſes are reſolved.</s></p><p type="margin"> <s><margin.target id="marg930"></margin.target><emph type="italics"></emph>The Earth in <lb></lb>what ſenſe it may <lb></lb>abſolutely be ſaid <lb></lb>to be in the loweſt <lb></lb>part of the World.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg931"></margin.target><emph type="italics"></emph>Chriſt in his <lb></lb>Incarnation tru<lb></lb>ly deſcended from <lb></lb>Heaven, and in <lb></lb>his Aſcenſion tru<lb></lb>ly aſcended into <lb></lb>Heaven.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg932"></margin.target>2 Cor. </s> <s>c. </s> <s>12. v. <lb></lb></s> <s>3. <emph type="italics"></emph>Whether in the <lb></lb>body or out of the <lb></lb>body, I cannot tell, <lb></lb>The Sun is King, <lb></lb>Heart and Lamp <lb></lb>of the World him<lb></lb>ſelf being<emph.end type="italics"></emph.end> <foreign lang="grc">αυταρκης</foreign><lb></lb><emph type="italics"></emph>abſolutely indepen<lb></lb>dent.<emph.end type="italics"></emph.end>)</s></p><p type="margin"> <s><margin.target id="marg933"></margin.target><emph type="italics"></emph>The Ænignsa of <lb></lb>Plato.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg934"></margin.target><emph type="italics"></emph>(a) Circa omni<lb></lb>um Regem ſunt <lb></lb>omnia. </s> <s>& Secun<lb></lb>da circa Secun<lb></lb>dum, et Tertia <lb></lb>circa Tertium: <lb></lb>Vide<emph.end type="italics"></emph.end> Theodo. </s> <s>de <lb></lb>Græc. </s> <s>affect. </s> <s>curat. <lb></lb></s> <s>lib. 2. Steuch. </s> <s>lib. <lb></lb></s> <s>de Parennj. </s> <s>Phi<lb></lb>loſo.</s></p><p type="main"> <s>It may be added withall, that even the <emph type="italics"></emph>Sun, Mercury<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ve<lb></lb>nus<emph.end type="italics"></emph.end> (that is to ſay in reſpect of the Earth) are to be thought <lb></lb><emph type="italics"></emph>aboue,<emph.end type="italics"></emph.end> and not <emph type="italics"></emph>beneath<emph.end type="italics"></emph.end> the Earth it ſelf, although in reſpect of <lb></lb>the Univerſe, yea and alſo abſolutely, they are <emph type="italics"></emph>below.<emph.end type="italics"></emph.end> The rea<lb></lb>ſon is, becauſe in reſpect of the Earth they alwayes appear above <lb></lb>its Surface: and although they do not environe it, yet by the <lb></lb>Motion of the ſaid Earth they behold one while one part, another <lb></lb>while another part of its Circumference. </s> <s>Since therefore thoſe <lb></lb>things which in a Sphærical Body are nearer to the Circumfe<lb></lb>rence and more remote from the Cenrre are ſaid to be <emph type="italics"></emph>above,<emph.end type="italics"></emph.end> but <lb></lb>thoſe that are next adjoyning to the Centre are ſaid to be <emph type="italics"></emph>below<emph.end type="italics"></emph.end>; <lb></lb>it clearly followeth that whilſt the <emph type="italics"></emph>Sun, Mercury<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> are <lb></lb>not only turned towards the Surface and Circumference of the <lb></lb>ſaid Earth, but are at a very great diſtance without it, ſucceſſively <lb></lb>turned about it, and every way have a view of it, and are very <lb></lb>far remote from its Centre, they may, in reſpect of the ſaid Earth, <lb></lb>be ſaid to be <emph type="italics"></emph>above<emph.end type="italics"></emph.end> it; as alſo on the other ſide, the Earth in <lb></lb>reſpect of them may be ſaid to be <emph type="italics"></emph>beneath<emph.end type="italics"></emph.end>: howbeit on the con<lb></lb>trary, in reſpect of the Univerſe, the Earth in reality is much <lb></lb>higher than they. </s> <s>And thus is ſalved the Authority of <emph type="italics"></emph>Eccleſi-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg935"></arrow.to.target><lb></lb><emph type="italics"></emph>aſtes<emph.end type="italics"></emph.end> in many places, expreſſing thoſe things that are, or are done <lb></lb>on the Eeath in theſe words, <emph type="italics"></emph>Which are done, or which are under<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg936"></arrow.to.target><lb></lb><emph type="italics"></emph>the Sun,<emph.end type="italics"></emph.end> And in the ſame manner thoſe words are reduced to their <lb></lb>true Senſe wherein it is ſaid, That we are <emph type="italics"></emph>under the Sun,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>un<lb></lb>der the Moon,<emph.end type="italics"></emph.end> whereupon Terrene things are expreſſed by the <lb></lb>name of <emph type="italics"></emph>Sublunary.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg935"></margin.target>Eccleſ. </s> <s>c. </s> <s>1. 2. 3. <lb></lb><emph type="italics"></emph>and almoſt tho<lb></lb>out.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg936"></margin.target>* <emph type="italics"></emph>Quod fiunt, vel <lb></lb>ſunt ſub ſole.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The Sixth Claſſis threatneth a difficulty which is common as <pb xlink:href="040/01/523.jpg" pagenum="499"></pb>well to this of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> as to the Vulgar Opinion; ſo that they <lb></lb>are both alike concerned in the ſolution of it: But ſo far as it <lb></lb>oppoſeth that of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> its anſwer is eaſy from the Firſt <lb></lb>Maxim.</s></p><p type="main"> <s>But that which is added in the Fourth Claſſe, That it follow<lb></lb>eth from this Opinion, that Hell (for that it is included by the <lb></lb>Earth, as is commonly held) doth move circularly about the <lb></lb>Sun, and in Heaven, and that ſo Hell it ſelf will be found to be <lb></lb>in Heaven; diſcovers, in my judgment, nothing but Ignorance <lb></lb>and Calumny, that inſinuate the belief of their Arguments ra<lb></lb>ther by a corrupt ſenſe of the Words, than by ſolid Reaſons <lb></lb>taken from the boſome of the Nature of things. </s> <s>For in this <lb></lb>place Heaven is no wiſe to be taken for Paradice, nor according <lb></lb>to the Senſe of Common Opinion, but (as hath been ſaid above) <lb></lb><arrow.to.target n="marg937"></arrow.to.target><lb></lb>according to the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Hypotheſis, for the ſubtileſt and <lb></lb>Pureſt Aire, far more tenuous and rare than this of ours; where<lb></lb>upon the Solid Bodies of the Stars, Moon, and Earth, in their <lb></lb>Circular and Ordinary Motions, do paſſe thorow it, (the Sphære <lb></lb>of Fire being by this Opinion taken away.) And as according <lb></lb>to the Common Opinion it was no abſurdity to ſay, That Hell <lb></lb>being demerged in the Centre of the Earth and of the World it <lb></lb>ſelf, hath Heaven and Paradice above and below it, yea and on <lb></lb>all ſides of it, and that it is in the middle of all the Cœleſtial <lb></lb>Bodies (as if it were poſited in a more unworthy place) ſo, nei<lb></lb>ther in this will it be deemed an Error, if from the other Syſtem, <lb></lb>which differeth not much from the Vulgar one, thoſe or the like <lb></lb>things follow as do in that. </s> <s>For both in that of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> and <lb></lb>the Vulgar Hypotheſis, Hell is ſuppoſed to be placed amongſt the <lb></lb>very dreggs of the Elements, and in the Centre of the Earth it <lb></lb>ſelf, for the confinement and puniſhment of the damned. </s> <s>There<lb></lb>fore we ought not for want of Reaſons to trifle away time in <lb></lb>vain and impertinent ſtrife about words, ſince their true Senſe <lb></lb>is clouded then with no obſcurity, and in regard that it is very <lb></lb>clear to any man indued with a refined Intellect, and that hath <lb></lb>but an indifferent judgment in the Liberal Arts, and eſpecially <lb></lb>in the Mathematicks, that the ſame, or not very different Gon<lb></lb>ſequences do flow from both theſe Opinions.</s></p><p type="margin"> <s><margin.target id="marg937"></margin.target><emph type="italics"></emph>Heaven accord<lb></lb>ing to Copernicus <lb></lb>is the ſame with <lb></lb>the moſt tenuous <lb></lb>Æther; but dif<lb></lb>ferent from Para<lb></lb>dice, which ſar<lb></lb>paſſeth all the <lb></lb>Heavens.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>By theſe Maxims and their Interpretations it appears, that <lb></lb>the <emph type="italics"></emph>Pythagorick<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Opinion is ſo probable, that its <lb></lb>poſſible it may exceed even the <emph type="italics"></emph>Ptolemaick<emph.end type="italics"></emph.end> in probability; and <lb></lb>ſince there may be deduced from it a moſt ordinate Syſteme, and <lb></lb>a mroe admirable and myſterious Hypotheſis of the World <lb></lb>than from that of <emph type="italics"></emph>Ptolomy:<emph.end type="italics"></emph.end> the Authorities of Sacred Scripture <lb></lb>and Theological Tenents in the mean while not oppoſing it, be<lb></lb>ing opportunely and appoſitely (as I have ſhown how they may <pb xlink:href="040/01/524.jpg" pagenum="500"></pb>be) reconciled with it: And ſince that by it not only the Phœ<lb></lb>nomena of all the Cœleſtial Bodies are moſt readily ſalved, but <lb></lb>alſo many Natural Reaſons are diſcovered, which could not o<lb></lb>therwiſe, (but with extream difficulty) have been found out: <lb></lb>And ſince it, laſt of all, doth open a more eaſy way into Aſtro<lb></lb>nomy and Phyloſophy, and rejecteth all thoſe ſuperfluous and <lb></lb>imaginary inventions produced by Aſtronomers to the end only, <lb></lb>that they might be able by them to render a reaſon of the ſo ma<lb></lb>ny and ſo various Motions of the Cœleſtial Orbs.</s></p><p type="main"> <s>And who knows, but that in that admirable compoſure of the <lb></lb>Candleſtick which was to be placed in the Tabernacle of God, he <lb></lb>might out of his extraordinary love to us have been pleaſed to <lb></lb>ſhaddow forth unto us the Syſteme of the Univerſe, and more <lb></lb><arrow.to.target n="marg938"></arrow.to.target><lb></lb>eſpecially of the Planets? <emph type="italics"></emph>(a) Thou ſhalt make a Candleſtick of<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg939"></arrow.to.target><lb></lb><emph type="italics"></emph>pure Gold,<emph.end type="italics"></emph.end> (ſaith the Text;) <emph type="italics"></emph>of beaten work ſhall it be made: <lb></lb>his Shaft, and his Branches, his Bowls, his Knops, and his <lb></lb>Flowers (b) ſhall be of the ſame.<emph.end type="italics"></emph.end> Here are five things deſcribed, the <lb></lb>Shaft of the Candleſtick in the midle, the Branches on the ſides, <lb></lb>the Bowls, the Knops and the Flowers. </s> <s>And ſince there can be no <lb></lb>more Shafts but one, the Branches are immediatly deſcribed in <lb></lb>theſe <emph type="italics"></emph>(c)<emph.end type="italics"></emph.end> words: <emph type="italics"></emph>Six Branches ſhall come out of the ſides of it: <lb></lb>three Branches out of the one ſide, and three Branches out of the <lb></lb>other ſide:<emph.end type="italics"></emph.end> Happly theſe fix Branches may point out to us ſix <lb></lb><emph type="italics"></emph>(d)<emph.end type="italics"></emph.end> Heavens, which are moved about the Sun in this order; <emph type="italics"></emph>Saturn,<emph.end type="italics"></emph.end><lb></lb>the ſloweſt and moſt remote of all, finiſheth his courſe about the <lb></lb><arrow.to.target n="marg940"></arrow.to.target><lb></lb>Sun thorrow all the twelve Signes of the Zodiack in thirty Years: <lb></lb><arrow.to.target n="marg941"></arrow.to.target><lb></lb><emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> being nearer than he, in twelve Years: <emph type="italics"></emph>Mars,<emph.end type="italics"></emph.end> being yet <lb></lb><arrow.to.target n="marg942"></arrow.to.target><lb></lb>nearer than him, in two Years: The <emph type="italics"></emph>Earth,<emph.end type="italics"></emph.end> which is ſtill nearer <lb></lb>than he, doth perform the ſame Revolution, together with <lb></lb>the Orbe of the <emph type="italics"></emph>Moon,<emph.end type="italics"></emph.end> in the ſpace of a Year, that is in Twelve <lb></lb>Months: <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> which is yet nearer than all theſe, in <emph type="italics"></emph>(e)<emph.end type="italics"></emph.end> 9 Months: <lb></lb>And laſt of all <emph type="italics"></emph>Mercury,<emph.end type="italics"></emph.end> whoſe vicinity to the Sun is the greateſt <lb></lb>of all, accompliſheth its whole converſion about the Sun in eighty <lb></lb>Dayes. </s> <s>After the deſcription of the ſix Branches, the ſacred <lb></lb>Text proceeds to the deſcription of the Bowls, the Knops, and <lb></lb>the Flowers, ſaying, <emph type="italics"></emph>(f) Three Bowls made like unto Almonds, <lb></lb>with a Knop and a Flower in one Branch; and three Bowls made <lb></lb>like Almonds in the other Branch, with a Knop and a Flower: this <lb></lb>ſhall be the work of the ſix Branches that come out of the Shaft. <lb></lb></s> <s>And in the Candleſtick ſhall be four Bowls made like unto Al<lb></lb>monds, with their Knops and their Flowers: there ſhall be a knop <lb></lb>under two branches of the ſame, and a Knop under two Branches <lb></lb>of the ſame, and a Knop under two Branches of the ſame; which <lb></lb>together are ſix Branches, proceeding from one Shaft.<emph.end type="italics"></emph.end> The truth <lb></lb><arrow.to.target n="marg943"></arrow.to.target><lb></lb>is, the ſhallowneſſe of my underſtanding cannot fathome the <pb xlink:href="040/01/525.jpg" pagenum="501"></pb>depth of all the Myſteries that are couched in this moſt wiſe <lb></lb>diſpoſure of things: nevertheleſſe being amazed, and tranſported <lb></lb>with admiration, I will ſay; Who knows but that thoſe three <lb></lb>Bowls like unto Almonds to be repreſented on each of the <lb></lb>Branches of the Candleſtick may ſignifie thoſe Globes which are <lb></lb>apter (as is this our Earth) for the receiving than emitting of Influ<lb></lb>ences? </s> <s>Perhaps alſo they denote thoſe Globes of late diſcovered <lb></lb>by the help of the Optick Teleſcope, which participate with <lb></lb><emph type="italics"></emph>Saturn, Jupiter, Venus,<emph.end type="italics"></emph.end> and poſſibly alſo with the other Planets? <lb></lb></s> <s>Who knows likewiſe, but that there may be ſome occult propor<lb></lb>tion between theſe Globes and thoſe Myſterious Knops and <lb></lb>Lilies inſinuated unto us in the ſacred Scriptures? </s> <s>But this <lb></lb>ſhall here ſuffice to bound humane Preſumption, and to teach us <lb></lb>to exſpect with an Harpocratick ſilence from Time, the Indice of <lb></lb>Truth, a diſcovery of theſe Myſteries: <emph type="italics"></emph>(g) Solomon<emph.end type="italics"></emph.end> made ten <lb></lb><arrow.to.target n="marg944"></arrow.to.target><lb></lb>Candleſticks by the ſame Patern of <emph type="italics"></emph>Moſes,<emph.end type="italics"></emph.end> which he placed, five <lb></lb>on one hand and five on another, in the Temple erected by him <lb></lb>in honour of the moſt High God; which very thing doth alſo, <lb></lb>without all queſtion, contain moſt abſtruſe ſigniſications. </s> <s>More<lb></lb>over, that Apple of the Knowledg of Good and Evil prohibited <lb></lb>our firſt Parents by God is not without a Myſtery; which ſome <lb></lb>ſay was an Indian Figg. </s> <s>In which theſe things are to be obſerv<lb></lb>ed: Firſt, That it is replete with many Kernels, every one of <lb></lb>which hath a particular Centre. </s> <s>Secondly, Though of it ſelf it <lb></lb>be hard and ſolid, yet about its Circumference it is of a more rare <lb></lb>and tenuouſe ſubſtance; herein reſembling the Earth, which <lb></lb>though in its Centre, and thoſe parts which are neareſt to it, it <lb></lb>be ſtony, Metallick, and compact, yet the nearer one approacheth <lb></lb>to the Circumference, its parts are ſeen to be the more rare and <lb></lb>tenuouſe: and withall it hath another body, more rare than its <lb></lb>own, namely the Water, above which there is yet another, more <lb></lb>ſubtil than all the reſt of inferiour Bodyes, that is to ſay, <lb></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"></emph>My Authour <lb></lb>following the vul<lb></lb>gar Tranſlation, <lb></lb>which hath an E<lb></lb>ligance in ſome <lb></lb>things beyond ours, <lb></lb>cites the words <lb></lb>thus,<emph.end type="italics"></emph.end> Facies Can<lb></lb>delabrum ducti<lb></lb>le de auro mun<lb></lb>diſſimo, Haſtile <lb></lb>ejus, & Calamos, <lb></lb>& Sphærulas, ac <lb></lb>Lilia, ex ipſo pro<lb></lb>cedentia.</s></p><p type="margin"> <s><margin.target id="marg940"></margin.target>(c) <emph type="italics"></emph>verſe<emph.end type="italics"></emph.end> 12.</s></p><p type="margin"> <s><margin.target id="marg941"></margin.target>(d) <emph type="italics"></emph>or Spheres.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg942"></margin.target>(e) <emph type="italics"></emph>Though our <lb></lb>Authour ſpeaketh <lb></lb>here poſitively of <lb></lb>nine Months,<emph.end type="italics"></emph.end> &c. <lb></lb><emph type="italics"></emph>Fathers are not a<lb></lb>greed about the pe<lb></lb>riod of this planet, <lb></lb>nor that of<emph.end type="italics"></emph.end> Mercu<lb></lb>ry, <emph type="italics"></emph>as you may ſee <lb></lb>at large in<emph.end type="italics"></emph.end> Riccio<lb></lb>lus, Almageſt. </s> <s>nov. <lb></lb><emph type="italics"></emph>Tom. </s> <s>1. part 1. l. <lb></lb></s> <s>7. ſect. </s> <s>3. cha. </s> <s>11. <lb></lb>num. </s> <s>11. page 627. <lb></lb>where he maketh<emph.end type="italics"></emph.end><lb></lb>Venus <emph type="italics"></emph>to conſum<lb></lb>mate her Revolu<lb></lb>tion in neer 225 <lb></lb>dayes, or 7 1/2 Mon. <lb></lb></s> <s>and<emph.end type="italics"></emph.end> Mecury <emph type="italics"></emph>in a<lb></lb>bout 88 dayes, or 3 <lb></lb>Months: in which <lb></lb>he followeth<emph.end type="italics"></emph.end> Kepl. <lb></lb><emph type="italics"></emph>in Epitome Aſtro<lb></lb>nom. </s> <s>p.<emph.end type="italics"></emph.end> 760.</s></p><p type="margin"> <s><margin.target id="marg943"></margin.target>(f) <emph type="italics"></emph>verſ.<emph.end type="italics"></emph.end> 33, 34.</s></p><p type="margin"> <s><margin.target id="marg944"></margin.target>(g) 1 Kings <emph type="italics"></emph>c.<emph.end type="italics"></emph.end> 7. <lb></lb><emph type="italics"></emph>v.<emph.end type="italics"></emph.end> 49. 2 Chron. <emph type="italics"></emph>c.<emph.end type="italics"></emph.end><lb></lb>4. <emph type="italics"></emph>verſ.<emph.end type="italics"></emph.end> 7.</s></p><p type="main"> <s>The ſame Repreſentation with that of the Indian Figg is held <lb></lb>forth to us by the <emph type="italics"></emph>Malum Punicum,<emph.end type="italics"></emph.end> or Pomegranate, with its <lb></lb>innumerable poly centrick Stones or Kernels, all which in the parts <lb></lb>more remote from their Centre, and nearer approaching towards <lb></lb>the Circumference, are of a ſubſtance ſo ſubtil and rare, that being <lb></lb>but lightly compreſſed, they in a manner wholly convert into a <lb></lb>moſt tenuoſe Liquor or juice: Of which fruit it pleaſed Divine <lb></lb>Wiſdom to make mention, and ordained that its Figure ſhould be <lb></lb>imbroidered and wrought with a needle in the <emph type="italics"></emph>ſacerdotal<emph.end type="italics"></emph.end> Garment <lb></lb>of <emph type="italics"></emph>Aaron: (h) Beneath<emph.end type="italics"></emph.end> (ſaith God) <emph type="italics"></emph>upon the hem of it thou<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg945"></arrow.to.target><lb></lb><emph type="italics"></emph>ſhalt make Pomegranates of blew, and of purple, and of ſcarlet, <lb></lb>round about the border thereof; and Bells of gold between them<emph.end type="italics"></emph.end> <pb xlink:href="040/01/526.jpg" pagenum="502"></pb><emph type="italics"></emph>round about: a golden bell and a pomegranate, a golden bell and a <lb></lb>pomegranate, upon the hem of the Robe round about.<emph.end type="italics"></emph.end> And that this <lb></lb>was a Myſtical Repreſentation of the Worlds Effigies, is averred <lb></lb><arrow.to.target n="marg946"></arrow.to.target><lb></lb>by <emph type="italics"></emph>Solomon,<emph.end type="italics"></emph.end> ſaying; <emph type="italics"></emph>(i) For in the long (k) Garment that be <lb></lb>had on was the (l) whole World; and in the foure rows of the ſtones<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg947"></arrow.to.target><lb></lb><emph type="italics"></emph>was the Glory of the Fathers graven, and thy Majeſty in the Di-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg948"></arrow.to.target><lb></lb><emph type="italics"></emph>adem of his Head.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg945"></margin.target>(h) Exod. </s> <s>28. 33, <lb></lb>34, & 39. v. </s> <s>24, <lb></lb>25, 26.</s></p><p type="margin"> <s><margin.target id="marg946"></margin.target><emph type="italics"></emph>(i)<emph.end type="italics"></emph.end> Sap. </s> <s>c. </s> <s>18. v. <lb></lb></s> <s>24.</s></p><p type="margin"> <s><margin.target id="marg947"></margin.target><emph type="italics"></emph>(k)<emph.end type="italics"></emph.end> Exod. </s> <s>c. </s> <s>28. <lb></lb>v. </s> <s>6, 9. 17, 36.</s></p><p type="margin"> <s><margin.target id="marg948"></margin.target><emph type="italics"></emph>(l)<emph.end type="italics"></emph.end> Or, <emph type="italics"></emph>totus Or<lb></lb>bis Terrarum,<emph.end type="italics"></emph.end> as <lb></lb>the vulgar Tranſ<lb></lb>lation hath it.</s></p><p type="main"> <s>The ſame likewiſe is ſignified to us by the Grape, and in like <lb></lb>manner by all other Fruits; but eſpecially the Figg, Grape, and <lb></lb>Pomegranate: whence theſe three are almoſt alwayes placed to<lb></lb>gether in the Sacred Scriptures. </s> <s>So <emph type="italics"></emph>Numb.<emph.end type="italics"></emph.end> 20. the People of Iſra<lb></lb>el complain againſt <emph type="italics"></emph>Moſes<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Aaron: (m) Wherefore have you<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg949"></arrow.to.target><lb></lb><emph type="italics"></emph>made us to come up out of Egypt, to bring us into this evil place, <lb></lb>where there can grow no Seed, neither is there either Figgs, or <lb></lb>Vines, or Pomegranates<emph.end type="italics"></emph.end>? </s> <s>Intimating that theſe kinds of Fruits <lb></lb>were preferred by them for their excellency before all others. <lb></lb></s> <s>And in <emph type="italics"></emph>Joel (n) The Vine is dryed up, and the Figg-tree languiſh-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg950"></arrow.to.target><lb></lb><emph type="italics"></emph>eth, the Pomegranate-trce, the Palm-tree alſo, and the Apple-tree, <lb></lb>even all the Trees of the field are withered; becauſe joy is wither<lb></lb>ed away from the Sons of Men.<emph.end type="italics"></emph.end> Likewiſe in <emph type="italics"></emph>Haggai: (o) Is the<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg951"></arrow.to.target><lb></lb><emph type="italics"></emph>ſeed yet in the Bud? </s> <s>and hath as yet the Vine and the Fig-tree, <lb></lb>and the Pomegranate, and the Olive-tree brought forth<emph.end type="italics"></emph.end>? </s> <s>In like <lb></lb>manner in <emph type="italics"></emph>Deuteronomie<emph.end type="italics"></emph.end> the Land of Promiſe is commended to <lb></lb>be <emph type="italics"></emph>(p) A Land of Wheat, and Barly, and Vines in which grow,<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg952"></arrow.to.target><lb></lb><emph type="italics"></emph>Figg-trees, and Pomegranates, and Olive-trees,<emph.end type="italics"></emph.end> &c. </s> <s>And in the <lb></lb>Structure of the Temple undertaken by <emph type="italics"></emph>Solomon<emph.end type="italics"></emph.end> upon Divine In<lb></lb><arrow.to.target n="marg953"></arrow.to.target><lb></lb>ſpiration the <emph type="italics"></emph>(q)<emph.end type="italics"></emph.end> Chapiters of the Pillars were adorned with ſeve<lb></lb>ral rowes of Pomegranates: which particular is mentioned, not <lb></lb>in one but many places of Holy Writ. </s> <s>Yea and ſometimes acci<lb></lb>dentally and occaſionally the Holy hath Ghoſt ænigmatically re<lb></lb>preſented this moſt admirable and Moſt Wiſe Sructure of the <lb></lb>World, the Order of the Heavens, and the diſpoſure of Crea<lb></lb>tures Spiritual and Corporeal by Emblems, Parables, and Figures, <lb></lb>leaſt they ſhould be as it were dazled and blinded, by the reful<lb></lb>gent ſplendor of ſo excellent an Object. </s> <s>Hence we ſee, that in <lb></lb>theſe Doctrinal & Dubious Points we may diſcourſe in ſuch man<lb></lb>ner by help of the Holy Scripture as is meet for the underſtanding <lb></lb>of the Prophets; which ſeeing they are very obſcure, they ſhall be <lb></lb>fully underſtood, and may be aptly applyed only then when they <lb></lb>ſhall be fulfilled, and not before: So alſo when once the true <lb></lb>Syſteme of the Univerſe is found out, then, and not till then, the <lb></lb>meaning of theſe Figures, and Ænigma's ſhall be made known <lb></lb>unto us: Thus before the coming of the Son of God had diſco<lb></lb>vered unto us the Myſtery of the Holy Trinity, none were able <lb></lb>to comprehend or imagine what was concealed under thoſe <pb xlink:href="040/01/527.jpg" pagenum="503"></pb>words; <emph type="italics"></emph>(r) In Principio creavit Elohim Cœlum & Terram:<emph.end type="italics"></emph.end> for <lb></lb><arrow.to.target n="marg954"></arrow.to.target><lb></lb>that they did not ſee how the Noun Plural <emph type="italics"></emph>Elohim<emph.end type="italics"></emph.end> (which is as much <lb></lb>as to ſay <emph type="italics"></emph>Dij,<emph.end type="italics"></emph.end> [Gods] ſhould be joyned with the Verb Singular, <lb></lb><emph type="italics"></emph>Creavit<emph.end type="italics"></emph.end>: But the Myſtery of the Unity of Eſſence and Trinity <lb></lb>of Perſons in God being revealed, it was preſently known, that <lb></lb>the Singular Number, <emph type="italics"></emph>Creavit,<emph.end type="italics"></emph.end> had reference to the Unity of Eſ<lb></lb>ſence, (in regard that the Works of the Trinity <emph type="italics"></emph>ad extra<emph.end type="italics"></emph.end> are in<lb></lb>diviſible) and the Plural, <emph type="italics"></emph>Elohim,<emph.end type="italics"></emph.end> to the Perſons. </s> <s>Who, I pray, <lb></lb>in elder times could have found out this Myſtery? </s> <s>And thus the <lb></lb>Name of God is thrice repeated in <emph type="italics"></emph>Pſal. </s> <s>67. (s) God, even our<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg955"></arrow.to.target><lb></lb><emph type="italics"></emph>God ſhall bleſſe us, God ſhall bleſſe us, &c.<emph.end type="italics"></emph.end> Which at firſt might <lb></lb>ſeem a Pleonaſme, and ſuperfluous repetition; but afterwards it <lb></lb>was evident that <emph type="italics"></emph>David<emph.end type="italics"></emph.end> did there ſet out the Benedictions of ſe<lb></lb>veral Perſons implyed, to wit, the Father, Son, and Holy Ghoſt. <lb></lb></s> <s>Innumerable Examples of the like kind may be found in the Sa<lb></lb>cred Leaves. </s> <s>Therefore, to conclude, I will ſay with ^{*}<emph type="italics"></emph>David,<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg956"></arrow.to.target><lb></lb><emph type="italics"></emph>Pſal.<emph.end type="italics"></emph.end> 92. <emph type="italics"></emph>Oh Lord how glorious are thy Works! thy thoughts <lb></lb>are very deep: an unwiſeman knoweth not, and a fool doth not <lb></lb>underſtand theſe things.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg949"></margin.target><emph type="italics"></emph>(m)<emph.end type="italics"></emph.end> Numb. c. >20. <lb></lb>v. 5.</s></p><p type="margin"> <s><margin.target id="marg950"></margin.target><emph type="italics"></emph>(n)<emph.end type="italics"></emph.end> Joel c. </s> <s>1. v. </s> <s>12.</s></p><p type="margin"> <s><margin.target id="marg951"></margin.target><emph type="italics"></emph>(o)<emph.end type="italics"></emph.end> Hagg. c. 2. <lb></lb>v. 19.</s></p><p type="margin"> <s><margin.target id="marg952"></margin.target><emph type="italics"></emph>(p)<emph.end type="italics"></emph.end> Deut. c. 8. v. 8.</s></p><p type="margin"> <s><margin.target id="marg953"></margin.target><emph type="italics"></emph>(q)<emph.end type="italics"></emph.end> 1 Kings c 7. <lb></lb>v. 20. & 2 Kings <lb></lb>c. 25. v. 17. & <lb></lb>2 Chro. c. 3. v. 15, <lb></lb>16. & c. 4. v. 12. <lb></lb>13. & Jerem. c. <lb></lb>52. v. 21, 22.</s></p><p type="margin"> <s><margin.target id="marg954"></margin.target><emph type="italics"></emph>(r)<emph.end type="italics"></emph.end> Gen. c. 1. v. 1</s></p><p type="margin"> <s><margin.target id="marg955"></margin.target><emph type="italics"></emph>(s) P<emph.end type="italics"></emph.end>ſal. 67. v. 6 <lb></lb>7.</s></p><p type="margin"> <s><margin.target id="marg956"></margin.target>* Pſal. 92 v. 536.</s></p><p type="main"> <s>Theſe are the particulars that I have thought fit to offer, as <lb></lb>a Divine, concerning the not-improbable Opinion of the Mobili<lb></lb>ty of the Earth and Stability of the Sun: which I hope will be <lb></lb>acceptable to you, Reverend Sir, out of the love and diligence <lb></lb>wherewith you perſue Virtue and Learning. </s> <s>But (to the end <lb></lb>that you may alſo receive an account of my other Studies) I <lb></lb>hope very ſhortly to publiſh in Print my Second Tome ^{*}<emph type="italics"></emph>Of the In-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg957"></arrow.to.target><lb></lb><emph type="italics"></emph>ſtitutions of all Learnings,<emph.end type="italics"></emph.end> which ſhall containe all the Liberall <lb></lb>Arts, as I have already ſignified in that <emph type="italics"></emph>Syntax,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Spicimen<emph.end type="italics"></emph.end> by <lb></lb>me heretofore put forth, and publiſhed under your Name. </s> <s>The <lb></lb>other five following Tomes by me promiſed (which ſhall treat of <lb></lb>Phyloſophy and Theology) are not altogether ſo forward, ne<lb></lb>vertheleſs they will be ſpeedily finiſhed. </s> <s>In the mean time there <lb></lb>will come forth my Book <emph type="italics"></emph>Concerning ^{*} Oracles,<emph.end type="italics"></emph.end> now finiſhed, to<lb></lb><arrow.to.target n="marg958"></arrow.to.target><lb></lb>gether with a Treatiſe ^{*} <emph type="italics"></emph>Of Artificial Divination.<emph.end type="italics"></emph.end> And for a <lb></lb><arrow.to.target n="marg959"></arrow.to.target><lb></lb>pledge thereof, I ſend you at this time annexed to this Epiſtle a <lb></lb>Tract ^{*} <emph type="italics"></emph>Concerning Natural Coſmological Divination,<emph.end type="italics"></emph.end> or of Natu<lb></lb><arrow.to.target n="marg960"></arrow.to.target><lb></lb>ral Prognoſticks, and Preſages of the Changes oſ Weather, and <lb></lb>other things which fall within the compaſſe of Natue. </s> <s>God grant <lb></lb>you all Happineſſe.</s></p><p type="margin"> <s><margin.target id="marg957"></margin.target>* <emph type="italics"></emph>Inſtitutionum<lb></lb>omnium Doctri<lb></lb>narum.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg958"></margin.target>* <emph type="italics"></emph>De Oraculis.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg959"></margin.target>* <emph type="italics"></emph>De Divinatio<lb></lb>ne artificioſa.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg960"></margin.target>* <emph type="italics"></emph>De Divinatio<lb></lb>ne Naturali Coſ<lb></lb>mologica.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>Moſt Reverend Sir<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>NAPLES,<emph.end type="italics"></emph.end> from the Covent <lb></lb>of the <emph type="italics"></emph>Carmelites,<emph.end type="italics"></emph.end> Jan. <lb></lb></s> <s>6. 1615.</s></p><p type="main"> <s><emph type="italics"></emph>Your Moſt Humble Servant<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>PAOLO ANTONIO FOSCARINI.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>FINIS.</s></p><pb xlink:href="040/01/528.jpg"></pb><p type="head"> <s><emph type="italics"></emph>Imprimatur,<emph.end type="italics"></emph.end> P. ANT. GHIBERT, <emph type="italics"></emph>Vic. Gen.</s><emph.end type="italics"></emph.end><lb></lb><s>JOANNES LONGUS <emph type="italics"></emph>Can. & Cur. Archiep. <lb></lb>Neap.<emph.end type="italics"></emph.end> THEOL. <emph type="italics"></emph>Vidit.<emph.end type="italics"></emph.end></s></p> </chap> <pb xlink:href="040/01/529.jpg"></pb><chap><p type="head"> <s>A <lb></lb>TABLE <lb></lb>Of the moſt Obſervable <lb></lb>PERSONS and MATTERS <lb></lb>Mentioned in the FIRST PART Of <lb></lb>The Firſt Tome.<lb></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 ſame in <emph type="italics"></emph>Abstract,<emph.end type="italics"></emph.end> as in Concrete.</cell><cell>185</cell></row><row><cell>AIRE.</cell><cell></cell></row><row><cell>The part of the <emph type="italics"></emph>Aire<emph.end type="italics"></emph.end> 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"></emph>Aire<emph.end type="italics"></emph.end> apt to carry with it light things, but not heavy.</cell><cell>124</cell></row><row><cell> The <emph type="italics"></emph>Aire<emph.end type="italics"></emph.end> alwayes touching us with the ſame part of it, cannot make us feel it.</cell><cell>228</cell></row><row><cell> It is more reaſonable that the <emph type="italics"></emph>Aire<emph.end type="italics"></emph.end> be commoved by the rugged ſurface of the Earth, than by the Celeſtial Motion.</cell><cell>400</cell></row><row><cell> It is demonſtrated, inverting the Argument, that the perpetual Motion of the <emph type="italics"></emph>Aire<emph.end type="italics"></emph.end> from Eaſt to Weſt, commeth from the Motion of Heaven.</cell><cell>403</cell></row><row><cell>ANIMALS.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Animals, Vide,<emph.end type="italics"></emph.end> The Motion of <emph type="italics"></emph>Animals.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>The cauſe of the Wearineſſe that attends the Motion of <emph type="italics"></emph>Animals.<emph.end type="italics"></emph.end></cell><cell>244</cell></row><row><cell>APOLLONIUS.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Apollonius<emph.end type="italics"></emph.end> and Copernicus demonſtrate the Retrogradations of Venus and Mercury.</cell><cell>311</cell></row><row><cell><emph type="italics"></emph>Arguing, Arguments, & Argumentations<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>Somein <emph type="italics"></emph>Arguing<emph.end type="italics"></emph.end> fix in their minds the Concluſion believed by them, and then adapt their Reaſons to that.</cell><cell>250</cell></row><row><cell>One ſingle Experiment or ſound Demonſtration, overthroweth all <emph type="italics"></emph>Arguments<emph.end type="italics"></emph.end> meerly probable.</cell><cell>105</cell></row><row><cell>A pleaſant Example ſhewing the invalidity of ſome Phiſical <emph type="italics"></emph>Argumentations.<emph.end type="italics"></emph.end></cell><cell>363</cell></row><row><cell>ARISTARCHUS.</cell><cell></cell></row><row><cell>Reaſon and Diſcourſe in <emph type="italics"></emph>Ariſtarchus<emph.end type="italics"></emph.end> and Copernicus prevailed over manifeſt Senſe.</cell><cell>301</cell></row><row><cell>ARISTOTLE.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> maketh the World perfect, becauſeit hath the Threefold Dimenſion.</cell><cell>2</cell></row><row><cell><emph type="italics"></emph>Ariſt.<emph.end type="italics"></emph.end> his Demonſtrations to prove the Worlds Dimenſions to be three, and no more.</cell><cell>2</cell></row><row><cell><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> his Definition of Nature either imperfect or unſeaſonable.</cell><cell>7</cell></row><row><cell><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> 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"></emph>Ariſtotle<emph.end type="italics"></emph.end> cannot equivocate, being the Inventer oſ Logick.</cell><cell>23</cell></row><row><cell><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> his Paralogiſme in proving the Earth to be in the centre of the World.</cell><cell>24</cell></row><row><cell><emph type="italics"></emph>Ariſt.<emph.end type="italics"></emph.end> Paralogiſme another way diſcovered.</cell><cell>24</cell></row><row><cell><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> his Diſcourſe to prove the Incorruptibility of Heaven.</cell><cell>26</cell></row><row><cell><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> proveth that Circular Motion hath no Contrary.</cell><cell>26</cell></row><row><cell><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> defective in aſſigning the Cauſes, why the Elements are Generable and Corruptible.</cell><cell>31</cell></row><row><cell><emph type="italics"></emph>Ariſiotle<emph.end type="italics"></emph.end> would change his opinion, did he ſee the Novelties of our Age.</cell><cell>37</cell></row><pb xlink:href="040/01/530.jpg"></pb><row><cell><emph type="italics"></emph>Ariſt,<emph.end type="italics"></emph.end> preferres Senſe before Ratiocination.</cell><cell>42</cell></row><row><cell><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> affirmeth the Heavens alterable, rather then otherwiſe, by his Doctrine.</cell><cell>42</cell></row><row><cell>Requifites to fit a man to Philoſophate well in the way of <emph type="italics"></emph>Ariſtotle.<emph.end type="italics"></emph.end></cell><cell>92</cell></row><row><cell>Some of <emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> Sectators impaire his Reputation, in going about to enhanſe it.</cell><cell>93</cell></row><row><cell>The ſervile Spirit of ſome of <emph type="italics"></emph>Ariſt.<emph.end type="italics"></emph.end> followers.</cell><cell>95</cell></row><row><cell>Too cloſe an adherence to <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> is blameable.</cell><cell>95</cell></row><row><cell><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ptolomy<emph.end type="italics"></emph.end> argue againſt the Diurnal Motion aſcribed to the Earth.</cell><cell>97</cell></row><row><cell>A Propoſition that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> filched from the Ancients, and ſomewhat altered.</cell><cell>99</cell></row><row><cell><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> his Arguments for the Earths Quieſcence and Immobility.</cell><cell>107</cell></row><row><cell><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> were he alive, would either refute his Adverſaries Arguments, or elſe would alter his Opinion.</cell><cell>113</cell></row><row><cell><emph type="italics"></emph>Aristotles<emph.end type="italics"></emph.end> firſt Argument againſt the Earths Motion, is defective in two things.</cell><cell>121</cell></row><row><cell>The Paralogiſme of <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> and Ptolomy in ſuppoſing that for known, which is in queſtion.</cell><cell>121</cell></row><row><cell><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> admitteth that the Fire moveth directly upwards by Nature, and round about, by Participation.</cell><cell>122</cell></row><row><cell><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> and Ptolomy ſeem to confute the Earths Mobility againſt thoſe who think that it, having along time ſtood ſtill, began to move in the time of Pythagoras.</cell><cell>168</cell></row><row><cell><emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> 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"></emph>Ariſtotle<emph.end type="italics"></emph.end> his Demonſtrations 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"></emph>Aristotle<emph.end type="italics"></emph.end> maketh that Point to be the Centre of the Univerſe, about which all the Celeſtial Spheres do revolve</cell><cell>294</cell></row><row><cell>A queſtion is put, if <emph type="italics"></emph>Ariſt.<emph.end type="italics"></emph.end> were forced to receive one of two Propoſitions, that make againſt his Doctrine, which he would admit.</cell><cell>294</cell></row><row><cell><emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> his Argument againſt the Ancients, who held that the Earth was a Planet.</cell><cell>344</cell></row><row><cell><emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> taxeth Plato of being overſtudious of Geometry.</cell><cell>361</cell></row><row><cell><emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> holdeth thoſe Effects to be miraculous, of which the Cauſes are unknown.</cell><cell>384</cell></row><row><cell>ASTRONOMERS.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Aſtronomers<emph.end type="italics"></emph.end> confuted by AntiTycho.</cell><cell>38</cell></row><row><cell>The principal Scope of <emph type="italics"></emph>Aſtronomers<emph.end type="italics"></emph.end> is to give a reaſon of Appearances and Phænomena.</cell><cell>308</cell></row><row><cell><emph type="italics"></emph>Actronomers<emph.end type="italics"></emph.end> all agree that the greater Magnitudes of the Orbes is the cauſe of the tardity in their Converſions.</cell><cell>331</cell></row><row><cell><emph type="italics"></emph>Aſtronomers<emph.end type="italics"></emph.end> 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"></emph>Actronomers<emph.end type="italics"></emph.end> having omitted to inſtance what alterations thoſe are, that may be derived from the Annual Motion of the Earth, do thereby teſtifie that they never rightly underſtood the ſame.</cell><cell>343</cell></row><row><cell>ASTRONOMICAL.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Aſtronomical<emph.end type="italics"></emph.end> Obſervations wreſted by AntiTycho to his own purpoſe.</cell><cell>39</cell></row><row><cell><emph type="italics"></emph>Actronomical<emph.end type="italics"></emph.end> Inſtruments are very ſubject to errour.</cell><cell>262</cell></row><row><cell>ASTRONOMY.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Aſtronomy<emph.end type="italics"></emph.end> reſtored by Copernicus upon the Suppoſitions of Ptolomy</cell><cell>308</cell></row><row><cell>Many things may remain as yet unobſerved in <emph type="italics"></emph>Aſtronomy<emph.end type="italics"></emph.end></cell><cell>415</cell></row><row><cell>AUCUPATORIAN.</cell><cell></cell></row><row><cell>An <emph type="italics"></emph>Aucupatorian<emph.end type="italics"></emph.end> Problem for ſhooting of Birds flying.</cell><cell>157</cell></row><row><cell>AXIOME, or <emph type="italics"></emph>Axiomes.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>In the <emph type="italics"></emph>Axiome, Fruſtra fit per plura, &c.<emph.end type="italics"></emph.end> the addition of <emph type="italics"></emph>æquœ bene<emph.end type="italics"></emph.end> is ſuperfluous.</cell><cell>106</cell></row><row><cell>Three <emph type="italics"></emph>Axiomes<emph.end type="italics"></emph.end> that are ſuppoſed manifeſt.</cell><cell>230</cell></row><row><cell>Certain <emph type="italics"></emph>Axiomes<emph.end type="italics"></emph.end> commonly admitted by all Philoſophers.</cell><cell>361</cell></row><row><cell>B</cell><cell></cell></row><row><cell>BODY and <emph type="italics"></emph>Bodies.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>Contraries that corrupt, reſide not in the ſame <emph type="italics"></emph>Body<emph.end type="italics"></emph.end> that corrupteth.</cell><cell>30</cell></row><row><cell>GRAVE BODY; If the Celeſtial Globe were perforated, a <emph type="italics"></emph>Grave Body<emph.end type="italics"></emph.end> deſcending by that Bore, would paſſe and aſcend as far beyond the Centre, as it did deſcend.</cell><cell>203</cell></row><row><cell>The motion of <emph type="italics"></emph>Grave Bodies,<emph.end type="italics"></emph.end> Vide <emph type="italics"></emph>Motion.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>The Accelleration of <emph type="italics"></emph>Grave Bodies<emph.end type="italics"></emph.end> that deſcend naturally, increaſeth from moment to moment.</cell><cell>205</cell></row><row><cell>We know no more who moveth <emph type="italics"></emph>Grave Bodies<emph.end type="italics"></emph.end>downwards, than who moveth the Stars round; nor know we any thing of theſe <pb xlink:href="040/01/531.jpg"></pb>Courſes, more than the Names impoſed on them by our ſelves.</cell><cell>210</cell></row><row><cell>The great Maſſe of <emph type="italics"></emph>Grave Bodies<emph.end type="italics"></emph.end> being tranſferred out of their Place, the ſeperated parts would follow that Maſſe.</cell><cell>221</cell></row><row><cell>PENSILE BODY; Every <emph type="italics"></emph>Penſile Body<emph.end type="italics"></emph.end> carried round in the Circumference of a Circle, acquireth of it ſelf a Motion in it ſelf contrary to the ſame.</cell><cell>362</cell></row><row><cell>CBLESTIAL BODIES neither heavy nor light according to <emph type="italics"></emph>Ariſtoile.<emph.end type="italics"></emph.end></cell><cell>23</cell></row><row><cell><emph type="italics"></emph>Celeſtial Bodies<emph.end type="italics"></emph.end> are Generable and Corruptible becauſe they are Ingenerable aud Incorruptible.</cell><cell>29</cell></row><row><cell>Amongſt <emph type="italics"></emph>Celeſt. Bodies<emph.end type="italics"></emph.end> there is no contrariety.</cell><cell>29</cell></row><row><cell><emph type="italics"></emph>Celeſtial Bodies<emph.end type="italics"></emph.end> touch, but are not touched by the Elements.</cell><cell>30</cell></row><row><cell>Rarity and Denſity in <emph type="italics"></emph>Celectial Bodies,<emph.end type="italics"></emph.end> different from Rarity and Denſity in the Elements.</cell><cell>30</cell></row><row><cell><emph type="italics"></emph>Celeſtial Bodies<emph.end type="italics"></emph.end> deſigned to ſerve the Earth, need no more but Motion and Light.</cell><cell>45</cell></row><row><cell><emph type="italics"></emph>Celeſtial Bodies<emph.end type="italics"></emph.end> wantan interchangeable Operation on each other.</cell><cell>46</cell></row><row><cell><emph type="italics"></emph>Celeſtial Bodies<emph.end type="italics"></emph.end> alterable in their externe parts.</cell><cell>46</cell></row><row><cell>Perfect Sphericity why aſcribed to <emph type="italics"></emph>Celeſtial Bodies<emph.end type="italics"></emph.end> by Peripateticks.</cell><cell>69</cell></row><row><cell>All <emph type="italics"></emph>Celectial Bodies<emph.end type="italics"></emph.end> have Gravity and Levity.</cell><cell>493</cell></row><row><cell>ELEMENTARY BODIES; Their propenſion to follow the Earth, hath a limited Sphere of Activity.</cell><cell>213</cell></row><row><cell>LIGHT BODIES eaſier to be moved than heavy, but leſſe apt to conſerve the Motion.</cell><cell>400</cell></row><row><cell>LUMINOUS BODIES; <emph type="italics"></emph>Bodies<emph.end type="italics"></emph.end> naturally <emph type="italics"></emph>Luminous<emph.end type="italics"></emph.end> are different from thoſe that are by nature Obſcure.</cell><cell>34</cell></row><row><cell>The reaſon why <emph type="italics"></emph>Luminous Bodies<emph.end type="italics"></emph.end> appear ſo much the more enlarged, by how much they are leſſer.</cell><cell>304</cell></row><row><cell>Manifeſt Experience ſhews that the more <emph type="italics"></emph>Luminous Bodies<emph.end type="italics"></emph.end> do much more irradiate than the leſſe 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"></emph>Spherical Bodies Deorſum<emph.end type="italics"></emph.end> is the Centre, and <emph type="italics"></emph>Surſum<emph.end type="italics"></emph.end> the Cirference.</cell><cell>479</cell></row><row><cell>BONES.</cell><cell></cell></row><row><cell>The ends of the <emph type="italics"></emph>Bones<emph.end type="italics"></emph.end> are rotund, and why.</cell><cell>232</cell></row><row><cell>BUONARRUOTTI.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Buonarruotti<emph.end type="italics"></emph.end> 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 ſhameful Errour in the Argument taken from the <emph type="italics"></emph>Canon<emph.end type="italics"></emph.end>Bullets falling from the Moons Concave.</cell><cell>197</cell></row><row><cell>An exact Computation of the fall of the <emph type="italics"></emph>Canon<emph.end type="italics"></emph.end>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"></emph>Celeſtial<emph.end type="italics"></emph.end> Subſtances that be Unalterable, and Elementary that be Alterable, neceſſary in the opinion of <emph type="italics"></emph>Ariſtotle.<emph.end type="italics"></emph.end></cell><cell>2</cell></row><row><cell>CENTRE.</cell><cell></cell></row><row><cell>The Sun more probably in the <emph type="italics"></emph>Centre<emph.end type="italics"></emph.end> of the Univerſe, 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"></emph>Centre.<emph.end type="italics"></emph.end></cell><cell>22</cell></row><row><cell>Grave Bodies may more rationally be affirmed to tend towards the <emph type="italics"></emph>Centre<emph.end type="italics"></emph.end> of the Earth, than of the Univerſe.</cell><cell>25</cell></row><row><cell>CHYMISTS.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Chymiſts<emph.end type="italics"></emph.end> interpret the Fables of Poets to be Secrets for making of Gold.</cell><cell>93</cell></row><row><cell>CIRCLE, and <emph type="italics"></emph>Circular.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>It is not impoſſible with the Circumference of a ſmall <emph type="italics"></emph>Circle<emph.end type="italics"></emph.end> few times revolved, to meaſure and deſcribe a line bigger than any great <emph type="italics"></emph>Circle<emph.end type="italics"></emph.end> whatſoever.</cell><cell>222</cell></row><row><cell>The <emph type="italics"></emph>Circular Line<emph.end type="italics"></emph.end> perfect, according to <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end>and the Right imperfect, and why.</cell><cell>9</cell></row><row><cell>CLARAMONTIUS.</cell><cell></cell></row><row><cell>The Paralogiſme of <emph type="italics"></emph>Claramontius.<emph.end type="italics"></emph.end></cell><cell>241</cell></row><row><cell>The Argument of <emph type="italics"></emph>Claramontius<emph.end type="italics"></emph.end> recoileth upon himſelf.</cell><cell>245</cell></row><row><cell>The Method obſerved by <emph type="italics"></emph>Claramontius<emph.end type="italics"></emph.end> in confuting Aſtronomers, and by Salviatus in refuting him.</cell><cell>253</cell></row><row><cell>CLOUDS.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Clouds<emph.end type="italics"></emph.end> no leſſe apt than the Moon to be illuminated by the Sun.</cell><cell>73</cell></row><pb xlink:href="040/01/532.jpg"></pb><row><cell>CONCLUSION and <emph type="italics"></emph>Concluſions.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>The certainty of the <emph type="italics"></emph>Concluſion<emph.end type="italics"></emph.end> helpeth by a reſolutive Method to finde the Demonſtration.</cell><cell>37</cell></row><row><cell>The Book of <emph type="italics"></emph>Concluſio s,<emph.end type="italics"></emph.end> frequently mentioned, was writ by Chriſtopher Scheiner a Jeſuit.</cell><cell>195, & 323.</cell></row><row><cell>CONTRARIES.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Contraries<emph.end type="italics"></emph.end> that corrupt, reſide not in the ſame Body that corrupteth.</cell><cell>30</cell></row><row><cell>COPERNICAN.</cell><cell></cell></row><row><cell>Anſwers to the three firſt Objections againſt the <emph type="italics"></emph>Copernican Syſtem.<emph.end type="italics"></emph.end></cell><cell>303</cell></row><row><cell>The <emph type="italics"></emph>Copernican Syſtem<emph.end type="italics"></emph.end> difficul to be underſtood, but eaſie to be effected.</cell><cell>354</cell></row><row><cell>A plain Scheme repreſenting the <emph type="italics"></emph>Copernican Sycteme<emph.end type="italics"></emph.end> and its conſequences.</cell><cell>354</cell></row><row><cell>The proſcribing of the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Doctrine, after ſo long a Tolleration, and now that it is more than ever followed, ſtudied and confirmed, would be an affront to Truth.</cell><cell>444</cell></row><row><cell>The <emph type="italics"></emph>Copern.<emph.end type="italics"></emph.end> Syſtem admirably agreeth with the Miracle of <emph type="italics"></emph>Joſhuah<emph.end type="italics"></emph.end> in the Literal Senſe.</cell><cell>456</cell></row><row><cell>If Divines would admit of the <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Syſtem, they might ſoon find out Expoſitions for all Scriptures that ſeem to make againſt it.</cell><cell>459</cell></row><row><cell>The <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Syſtem rejected by many, out of a devout reſpect to Scripture Authorities.</cell><cell>461</cell></row><row><cell>The <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> Syſtem more plainly aſſerted in Scripture than the <emph type="italics"></emph>Ptolomaick.<emph.end type="italics"></emph.end></cell><cell>469</cell></row><row><cell>COPERNICANS.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Copernicans<emph.end type="italics"></emph.end> are not moved through ignorance of the Arguments on the Adverſe part.</cell><cell>110</cell></row><row><cell><emph type="italics"></emph>Copernicans<emph.end type="italics"></emph.end> were all firſt againſt that Opinion, but the Peripateticks were never on the other ſide.</cell><cell>110</cell></row><row><cell><emph type="italics"></emph>Copernicans<emph.end type="italics"></emph.end> too freely admit certain Propoſitions for true, which are doubtful.</cell><cell>159</cell></row><row><cell>He that will be a <emph type="italics"></emph>Copernican<emph.end type="italics"></emph.end> muſt deny his Senſes.</cell><cell>228</cell></row><row><cell>A Great Mathematician made a <emph type="italics"></emph>Copernican,<emph.end type="italics"></emph.end> by looking into that Doctrine, with a purpoſe to confute it.</cell><cell>443</cell></row><row><cell>COPERNICUS.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> eſteemeth the Earth a Globe, like to a Planet.</cell><cell>1</cell></row><row><cell>Objections of two Moderne Authours [Scheiner and Claramontius] againſt <emph type="italics"></emph>Copernicus.<emph.end type="italics"></emph.end></cell><cell>195</cell></row><row><cell><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> his Opinion overthrows the <emph type="italics"></emph>Criterium<emph.end type="italics"></emph.end>of Phyloſophers.</cell><cell>223</cell></row><row><cell>A groſle Errour in the Oppoſer of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end>and wherein it appears.</cell><cell>234, 235, & 236</cell></row><row><cell>A ſubtle and withal ſimple Argument againſt <emph type="italics"></emph>Copernicus.<emph.end type="italics"></emph.end></cell><cell>234</cell></row><row><cell><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> his Opponent had but little ſtudied him, as appears by another groſſe Errour.</cell><cell>235</cell></row><row><cell>Its queſtioned whither he underſtood the third Motion aſſigned to the Earth by <emph type="italics"></emph>Copern.<emph.end type="italics"></emph.end></cell><cell>236</cell></row><row><cell><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> erroneouſly aſſignes the ſame Operations to different Natures.</cell><cell>238</cell></row><row><cell>A declaration of the improbability of <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end>his Opinion.</cell><cell>301</cell></row><row><cell>Reaſon and Diſcourſe in <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> and Ariſtarchus prevailed over Senſe.</cell><cell>301</cell></row><row><cell><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> ſpeaketh nothing of the ſmall Variation of Bigneſſe in Venus and Mars.</cell><cell>302</cell></row><row><cell><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> perſwaded by Reaſons contrary to Senſible Experiments.</cell><cell>306</cell></row><row><cell><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> reſtored Aſtronomy upon the Suppoſitions of Ptolomy.</cell><cell>308</cell></row><row><cell>What moved <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> to eſtabliſh his Syſteme.</cell><cell>308</cell></row><row><cell>Its a great argument in favour of <emph type="italics"></emph>Copernicus,<emph.end type="italics"></emph.end> that he obviates the Stations and Retrogradations of the Motions of the Planets.</cell><cell>309</cell></row><row><cell>Inſtances Ironically propounded by Scheiner againſt <emph type="italics"></emph>Copernicus.<emph.end type="italics"></emph.end></cell><cell>323</cell></row><row><cell><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> underſtood not ſome things for want of Inſtruments.</cell><cell>338</cell></row><row><cell>The grand difficulty in <emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> his Doctrine, is that which concerns the Phænomena of the Sun and fixed Stars.</cell><cell>343</cell></row><row><cell><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> the Reſtorer of the Pythagorean Hypotheſis, and the Occaſion of it.</cell><cell>429</cell></row><row><cell><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> founded not his Doctrine on Reaſons depending on Scripture, wherein he might have miſtaken their Senſe, but upon Natural Concluſions and Aſtronomical and Geometrical Demonſtrations.</cell><cell>431</cell></row><row><cell>CORRUPTIBLE, and <emph type="italics"></emph>Corruptibility.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>The perfection of Figure operates in <emph type="italics"></emph>Corruptible Bodies,<emph.end type="italics"></emph.end> but not in Eternal.</cell><cell>69</cell></row><row><cell>The Diſparagers of <emph type="italics"></emph>Corruptibility<emph.end type="italics"></emph.end> ought to be turned into Statua's.</cell><cell>37</cell></row><row><cell><emph type="italics"></emph>Corruptibility<emph.end type="italics"></emph.end> admits of more and leſſe, ſo doth not Incorruptibility.</cell><cell>69</cell></row><row><cell>COUNCILS.</cell><cell></cell></row><row><cell>The <emph type="italics"></emph>Councils<emph.end type="italics"></emph.end> refuſe to impoſe Natural Concluſions as matters of Faith.</cell><cell>450</cell></row><pb xlink:href="040/01/533.jpg"></pb><row><cell>D</cell><cell></cell></row><row><cell>DIAMONDS.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Diamonds<emph.end type="italics"></emph.end> ground to divers ſides, and why.</cell><cell>63</cell></row><row><cell>DIDACUS.</cell><cell></cell></row><row><cell><emph type="italics"></emph> Didacus à Stunica<emph.end type="italics"></emph.end> reconcileth Texts of Scripture with the Copernican Hypotheſis.</cell><cell>468</cell></row><row><cell>DEFINITIONS.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Definitions<emph.end type="italics"></emph.end> contain virtually all the Paſſions 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"></emph>Earth<emph.end type="italics"></emph.end> Spherical by the Conſpiration of its parts to go to its Centre.</cell><cell>21</cell></row><row><cell>Itis eaſier to prove the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> to move, than that Corruptibility is made by Contraries.</cell><cell>27</cell></row><row><cell>The <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> very Noble, by reaſon of the Mutations made therein.</cell><cell>45</cell></row><row><cell>The <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> unprofitable and full of Idleneſſe, its Alterations being taken away.</cell><cell>45</cell></row><row><cell>The <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> more Noble than Gold and Jewels.</cell><cell>45</cell></row><row><cell>The Celeſtial Bodies deſigned to ſerve the <emph type="italics"></emph>Earth,<emph.end type="italics"></emph.end>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"></emph>Earth,<emph.end type="italics"></emph.end> are all for the Good of Man.</cell><cell>47</cell></row><row><cell>From the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> we ſee more than half the Lunar Globe.</cell><cell>51</cell></row><row><cell>Seven Reſemblances between the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> and Moon.</cell><cell>48 to 53</cell></row><row><cell>The <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> unable to reflect the Suns Rays.</cell><cell>54</cell></row><row><cell>The <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> may reciprocally operate on Celeſtial Bodies with its Light.</cell><cell>80</cell></row><row><cell>Affinity between the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> and Moon, by reaſon of their Vicinity.</cell><cell>81</cell></row><row><cell>The Motions of the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> imperceptible to its Inhabitants.</cell><cell>97</cell></row><row><cell>The <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> can have no other Motions than thoſe which to us appear commune to all the reſt of the Univerſe, the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> excepted.</cell><cell>97</cell></row><row><cell>The Diurnal Motion ſeemeth commune to all the Univerſe, the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> onely excepted.</cell><cell>97</cell></row><row><cell>Ariſtotle and Ptolomy argue againſt the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end>Diurnal Motion.</cell><cell>97</cell></row><row><cell>The Diurnal Motion of the <emph type="italics"></emph>Earth.<emph.end type="italics"></emph.end> Vide <emph type="italics"></emph>Diurnal Motion.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>Seven Arguments to prove the Diurnal Motion to belong to the <emph type="italics"></emph>Earth.<emph.end type="italics"></emph.end></cell><cell>99 to 103</cell></row><row><cell>The <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> a pendent Body, and equilibrated in a fluid Medium, ſeems unable to reſiſt the Rapture of the Diurnal Motion.</cell><cell>103</cell></row><row><cell>Two kinds of Arguments againſt the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end>Motion.</cell><cell>108</cell></row><row><cell>Arguments of Ariſtotle, Ptolomy, Tycho, and other perſons, againſt the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Motion.</cell><cell>107 & 108</cell></row><row><cell>The firſt Argument againſt the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Motion taken from Grave Bodies falling from on high to the Ground.</cell><cell>108</cell></row><row><cell>Which Argument is conſirmed by the Experiment of a Body let fall from the Roundtop of a Ships Maſt.</cell><cell>108</cell></row><row><cell>The ſecond Argument taken from a Project ſhot very high.</cell><cell>108</cell></row><row><cell>The third Argument taken from the Shot of a Canon towards the Eaſt, and towards the Weſt.</cell><cell>108</cell></row><row><cell>This Argument is conſirmed by two Shots towards the North and South, and two others towards the Eaſt and Weſt.</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 Horſe at full ſpeed.</cell><cell>114</cell></row><row><cell>A ſixth Argument taken from the whirling of Circular Bodies, which hath a faculty to extrude and diſſipate.</cell><cell>114</cell></row><row><cell>The Anſwer to Ariſtotles firſt Argument.</cell><cell>115</cell></row><row><cell>The Anſwer to the ſecond Argument.</cell><cell>117</cell></row><row><cell>The Anſwer to the third Argument.</cell><cell>120 to 150</cell></row><row><cell>An Inſtance of the Diurnal Motion of the <emph type="italics"></emph>Earth,<emph.end type="italics"></emph.end>taken from the Shot of a Piece of Ordinance perpendicularly, and the Anſwers to the ſame, ſhewing the Equivoke.</cell><cell>153, 154</cell></row><row><cell>The Anſwer to the Argument of the Shots of Canons made towards the North and South.</cell><cell>158</cell></row><row><cell>The Anſwer to the Argument taken from the Shots at point blank towards the Eaſt and Weſt.</cell><cell>159</cell></row><row><cell>The Anſwer to the Argument of the flying of Birds contrary to the Motion of the <emph type="italics"></emph>Earth.<emph.end type="italics"></emph.end></cell><cell>165</cell></row><row><cell>An Experiment by which alone is ſhewn the Nullity of all the Arguments produced againſt the Motion of the <emph type="italics"></emph>Earth.<emph.end type="italics"></emph.end></cell><cell>165</cell></row><row><cell>The Stupidity of ſome that think the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> began to move, when Pythagoras began to affirme that it did ſo.</cell><cell>167</cell></row><row><cell>A Geometrical Demonſtration to prove the Impoſſibility of Extruſion, by means of the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Vertigo, in Anſwer to the ſixth <pb xlink:href="040/01/534.jpg"></pb>Argument.</cell><cell>176</cell></row><row><cell>Granting the Diurnal Vertigo of the <emph type="italics"></emph>Earth,<emph.end type="italics"></emph.end> and that by ſome ſudden Stop or Obſtacle it were Arreſted, Houſes, Mountains themſelves, and perhaps the whole Globe, would be ſhaken in pieces.</cell><cell>190</cell></row><row><cell>Other Arguments of two Modern Authours [Scheiner and. Claramontius] againſt the Copernican Hypotheſis of the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Motion.</cell><cell>195</cell></row><row><cell>The firſt Objection of the Modern Authour [Scheiner] in his Book of Concluſions.</cell><cell>195</cell></row><row><cell>The Argument of [Claramontius] againſt the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Motion, taken from things falling perpendicularly, another way anſwered.</cell><cell>223</cell></row><row><cell>The <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Motion collected from the Stars.</cell><cell>229</cell></row><row><cell>Argumeuts againſt the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Motion, taken <emph type="italics"></emph>ex rerum natura.<emph.end type="italics"></emph.end></cell><cell>230</cell></row><row><cell>A Simple Body as the <emph type="italics"></emph>Earth,<emph.end type="italics"></emph.end> cannot move with three ſeveral Motions.</cell><cell>231</cell></row><row><cell>The <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> cannot move with any of the Motions aſſigned it by Copernicus.</cell><cell>231</cell></row><row><cell>Anſwers to the Arguments againſt the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end>Motion, token <emph type="italics"></emph>ex rerum natnra.<emph.end type="italics"></emph.end></cell><cell>231</cell></row><row><cell>Four Axiomes againſt the Motion of the <emph type="italics"></emph>Earth.<emph.end type="italics"></emph.end></cell><cell>230 to 232</cell></row><row><cell>One onely Principle might cauſe a Plurality of Motions in the <emph type="italics"></emph>Earth.<emph.end type="italics"></emph.end></cell><cell>233</cell></row><row><cell>The ſame Argument againſt the Plurality of Motions in the <emph type="italics"></emph>Earth,<emph.end type="italics"></emph.end> anſwered by Examples of the like Motions in other Celeſtial Bodies.</cell><cell>236</cell></row><row><cell>A fourth Argument [of Claramontius] againſt the Copernican Hypotheſis of the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end>Mobility.</cell><cell>239</cell></row><row><cell>From the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> obſcurity, and the ſplendor 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] againſt the Copernican Hypotheſis of the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end>Mobility.</cell><cell>240</cell></row><row><cell>Another difference between the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> and Celeſtial Bodies, taken from Purity and impurity.</cell><cell>240</cell></row><row><cell>It ſeems a Soleciſme, to affirme that the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end>is not in Heaven.</cell><cell>241</cell></row><row><cell>Granting to the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> the Annual, it muſt of neceſſity alſo have the Diurnal Motion aſſigned to it.</cell><cell>300</cell></row><row><cell>Diſcourſes more than childiſh, that ſerve to keep Fools in the Opinion of the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Stability.</cell><cell>301</cell></row><row><cell>The Difficulties removed that ariſe from the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> moving about the Sun, not ſolitarily, but in conſort with the Moon.</cell><cell>307</cell></row><row><cell>The Axis of the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> continueth alwayes parallel to it ſelf, and deſcribeth a Cylindraical Superficies, inclining to the Orb.</cell><cell>344</cell></row><row><cell>The Orb of the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> never incllneth, but is immutably the ſame.</cell><cell>345</cell></row><row><cell>The <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> 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 ſhould diſcover any Mutation, the Motion of the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> would be undeniable.</cell><cell>351</cell></row><row><cell>Neceſſary Propoſitions for the better conceiving of the Conſequences of the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Motion.</cell><cell>354</cell></row><row><cell>An admirable Accident depending on the notinclining of the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Axis.</cell><cell>358</cell></row><row><cell>Four ſeveral Motions aſſigned to the <emph type="italics"></emph>Earth.<emph.end type="italics"></emph.end></cell><cell>362</cell></row><row><cell>The third Motion aſcribed to the <emph type="italics"></emph>Earth,<emph.end type="italics"></emph.end> is rather a reſting immoveable.</cell><cell>363</cell></row><row><cell>An admirable interne vertue [or faculty] of the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Globe, to behold alwayes the ſame part of Heaven.</cell><cell>363</cell></row><row><cell>Nature, as iu ſport, maketh the Ebbing and Flowing of the Sea to prove the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Mobility.</cell><cell>379</cell></row><row><cell>All Terrene Effects indifferently confirm the Motion or Reſt of the <emph type="italics"></emph>Earth,<emph.end type="italics"></emph.end> except the Ebbing and Flowing of the Sea.</cell><cell>380</cell></row><row><cell>The Cavities of the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> cannot approach or recede from the Centre of the ſame.</cell><cell>387</cell></row><row><cell>The Hypotheſis of the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Mobility taken in favour of the Ebbing and Flowing oppoſed.</cell><cell>399</cell></row><row><cell>The Anſwers to thoſe Objections made againſt the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Motion.</cell><cell>399</cell></row><row><cell>The Revolution of the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> confirmed by a new Argument taken from the Aire.</cell><cell>400</cell></row><row><cell>The vaporous parts of the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> partake of its Motions.</cell><cell>400</cell></row><row><cell>Another obſervation taken from the Ayr, in confirmation of the motion of the <emph type="italics"></emph>Earth.<emph.end type="italics"></emph.end></cell><cell>402</cell></row><row><cell>A Reaſon of the continual Motion of the Air and Water may be given by making the <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> moveable, rather then by making it immoveable.</cell><cell>405</cell></row><row><cell>The <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Mobility held by ſundry great Philoſophers amongſt the Antients.</cell><cell>437 & 468</cell></row><row><cell>The Fathers agree not in expounding the Texts of Scripture that are alledged againſt the <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Mobility.</cell><cell>450</cell></row><row><cell>The <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> Mobility defended by many amongſt the Modern Writers.</cell><cell>478</cell></row><row><cell>The <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> ſhall ſtand ſtill after the Day of Judgement.</cell><cell>480</cell></row><row><cell>The <emph type="italics"></emph>Earth<emph.end type="italics"></emph.end> is another Moon or Star.</cell><cell>486</cell></row><row><cell>The <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> ſeveral Motions, according to Co<pb xlink:href="040/01/535.jpg"></pb>pernicus.</cell><cell>491</cell></row><row><cell>The <emph type="italics"></emph>Earth ſecundum totum<emph.end type="italics"></emph.end> is Immutable, though not Immoveable.</cell><cell>491</cell></row><row><cell>The <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Natural Place.</cell><cell>492</cell></row><row><cell>The <emph type="italics"></emph>Earths<emph.end type="italics"></emph.end> Centre keepeth her in her Natural Place.</cell><cell>493</cell></row><row><cell>The <emph type="italics"></emph>Earth,<emph.end type="italics"></emph.end> in what Senſe it may <emph type="italics"></emph>abſolutely<emph.end type="italics"></emph.end> be ſaid to be in the loweſt part of the World.</cell><cell>496</cell></row><row><cell>EBBING and <emph type="italics"></emph>Ebbings.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>The firſt general Concluſion of the impoſſibility of <emph type="italics"></emph>Ebbing<emph.end type="italics"></emph.end> and Flowing the Immobility of the Terreſtrial Globe being granted.</cell><cell>380</cell></row><row><cell>The Periods of <emph type="italics"></emph>Ebbings<emph.end type="italics"></emph.end> 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"></emph>Ebbings<emph.end type="italics"></emph.end> and Flowings.</cell><cell>382</cell></row><row><cell>The Cauſes of <emph type="italics"></emph>Ebbings<emph.end type="italics"></emph.end> and Flowings alledged by a Modern Phyloſopher.</cell><cell>382</cell></row><row><cell>The Cauſe of the <emph type="italics"></emph>Ebbing<emph.end type="italics"></emph.end> and Flowing aſeribed to the Moon by a certain Prelate.</cell><cell>383</cell></row><row><cell>The Cauſe of the <emph type="italics"></emph>Ebbing, &c.<emph.end type="italics"></emph.end> referred by Hyeronimus Borrius and other Peripateticks, to the temperate heat of the Moon.</cell><cell>383</cell></row><row><cell>Anſwersto the Vanities alledged as Cauſes of the <emph type="italics"></emph>Ebbing<emph.end type="italics"></emph.end> and Flowing.</cell><cell>383</cell></row><row><cell>Its proved impoſſible that there ſhould naturally be any <emph type="italics"></emph>Ebbing<emph.end type="italics"></emph.end> and Flowing, the Earth being immoveable.</cell><cell>386</cell></row><row><cell>The moſt potent and primary Cauſe of the <emph type="italics"></emph>Ebbing<emph.end type="italics"></emph.end> and Flowing.</cell><cell>390</cell></row><row><cell>Sundry accidents that happen in the <emph type="italics"></emph>Ebbings<emph.end type="italics"></emph.end>and Flowings.</cell><cell>391</cell></row><row><cell>Reaſons renewed of the particular Accidents obſerved in the <emph type="italics"></emph>Ebbings<emph.end type="italics"></emph.end> and Flowings.</cell><cell>393</cell></row><row><cell>Second Cauſes why in ſeveral Seas and Lakes there are no <emph type="italics"></emph>Ebbings<emph.end type="italics"></emph.end> and Flowings.</cell><cell>394</cell></row><row><cell>The Reaſon why the <emph type="italics"></emph>Ebbings<emph.end type="italics"></emph.end> and Flowings for the moſt part, are every Six Hours.</cell><cell>395</cell></row><row><cell>The Cauſe why ſome Seas though very long, ſuffer no <emph type="italics"></emph>Ebbing<emph.end type="italics"></emph.end> and Flowing.</cell><cell>395</cell></row><row><cell><emph type="italics"></emph>Ebbings<emph.end type="italics"></emph.end> and Flowings, why greateſt in the Extremities of Gulphs, and leaſt in the middle parts.</cell><cell>396</cell></row><row><cell>A Diſcuſſion of ſome more Abſtruce Accidents obſerved in the <emph type="italics"></emph>Ebbing<emph.end type="italics"></emph.end> and Flowing.</cell><cell>396</cell></row><row><cell>The <emph type="italics"></emph>Ebbing<emph.end type="italics"></emph.end> and Flowing may depend on the Diurnal Motion of Heaven.</cell><cell>404</cell></row><row><cell>The <emph type="italics"></emph>Ebbing<emph.end type="italics"></emph.end> and Flowing cannot depend on the Motion of Heaven.</cell><cell>405</cell></row><row><cell>The Cauſes of the Periods of the <emph type="italics"></emph>Ebbings<emph.end type="italics"></emph.end> and Flowings Monethly and Annual, at large aſſigned</cell><cell>407</cell></row><row><cell>The Monethly and Annual alterations of the <emph type="italics"></emph>Ebbings<emph.end type="italics"></emph.end> and Flowings, can depend on nothing, ſave 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"></emph>Ebbing<emph.end type="italics"></emph.end> and Flowing.</cell><cell>409</cell></row><row><cell><emph type="italics"></emph>Ebbings<emph.end type="italics"></emph.end> and Flowings are petty things, in compariſon of the vaſtneſſe of the Seas, and the Velocity of the Motion of the Terreſtrial Globe.</cell><cell>417</cell></row><row><cell>EFFECT and <emph type="italics"></emph>Effects.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>Of anew <emph type="italics"></emph>Effect<emph.end type="italics"></emph.end> its neceſſary that the Cauſe be likewiſe new.</cell><cell>370</cell></row><row><cell>The Knowledge of the <emph type="italics"></emph>Effects<emph.end type="italics"></emph.end> contribute to the inveſtigation of the Cauſes.</cell><cell>380</cell></row><row><cell>True and Natural <emph type="italics"></emph>Effects<emph.end type="italics"></emph.end> follow without difficulty.</cell><cell>387</cell></row><row><cell>Alterations in the <emph type="italics"></emph>Effects<emph.end type="italics"></emph.end> argue alteration in the Cauſe.</cell><cell>407</cell></row><row><cell>ELEMENTS, <emph type="italics"></emph>and their Motions,<emph.end type="italics"></emph.end> Vide MOTION.</cell><cell></cell></row><row><cell>ENCYCLOPEDIA.</cell><cell></cell></row><row><cell>Subtilties fufficiently inſipid, ironically ſpoken, and taken from a certain <emph type="italics"></emph>Encyclopedia.<emph.end type="italics"></emph.end></cell><cell>153</cell></row><row><cell>EXPERIMENTS.</cell><cell></cell></row><row><cell>Senſible <emph type="italics"></emph>Experiments<emph.end type="italics"></emph.end> 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"></emph>Experiments<emph.end type="italics"></emph.end> for true, to thoſe that never tryed them.</cell><cell>162</cell></row><row><cell><emph type="italics"></emph>Experiments<emph.end type="italics"></emph.end> and Arguments againſt the Earths Motion, ſeem ſo far concluding, as they lye under Equivokes</cell><cell>162</cell></row><row><cell>The Authority of Senſible <emph type="italics"></emph>Experiments<emph.end type="italics"></emph.end> and neceſſary Demonſtrations in deciding of Phyſical Controverſies.</cell><cell>436</cell></row><row><cell>EYE.</cell><cell></cell></row><row><cell>The Circle of the Pupil of the <emph type="italics"></emph>Eye<emph.end type="italics"></emph.end> contracteth and enlargeth.</cell><cell>329</cell></row><row><cell>How to finde the diſtance of the Rays Concourſe from the Pupil of the <emph type="italics"></emph>Eye.<emph.end type="italics"></emph.end></cell><cell>329</cell></row><row><cell>F</cell><cell></cell></row><row><cell>FAITH.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Faith<emph.end type="italics"></emph.end> more infallible than either Senſe of <pb xlink:href="040/01/536.jpg"></pb>Reaſon.</cell><cell>475</cell></row><row><cell>FIRE.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Fire<emph.end type="italics"></emph.end> moveth directly upwards by Nature, and round about by Participation, according to Ariſtotle.</cell><cell>122</cell></row><row><cell>It is improbable that the Element of <emph type="italics"></emph>Fire<emph.end type="italics"></emph.end> ſhould be carried round by the Concave of the Moon.</cell><cell>405</cell></row><row><cell>FIGURE and <emph type="italics"></emph>Figures.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Figure<emph.end type="italics"></emph.end> is not the Cauſe of Incorruptibility, but of Longer Duration.</cell><cell>66</cell></row><row><cell>The perfection of <emph type="italics"></emph>Figure<emph.end type="italics"></emph.end> appeareth in Corruptible Bodies, but not in the Eternal.</cell><cell>69</cell></row><row><cell>If the Spherical <emph type="italics"></emph>Figure<emph.end type="italics"></emph.end> conferred Eternity, all things would be Eternal.</cell><cell>69</cell></row><row><cell>It is more difficult to finde <emph type="italics"></emph>Figures<emph.end type="italics"></emph.end> that touch in a part of their Surface, then in one ſole point.</cell><cell>185</cell></row><row><cell>The Circular <emph type="italics"></emph>Figure<emph.end type="italics"></emph.end> placed amongſt the <emph type="italics"></emph>Postulata<emph.end type="italics"></emph.end> of Mathematicians.</cell><cell>186</cell></row><row><cell>Irregular <emph type="italics"></emph>Figure<emph.end type="italics"></emph.end> and Formes difficult to be introduced.</cell><cell>187</cell></row><row><cell>Superficial figures increaſe in proportion double to their Lines.</cell><cell>304</cell></row><row><cell>FLFXURES.</cell><cell></cell></row><row><cell>The neceſſity and uſe of <emph type="italics"></emph>Flexures<emph.end type="italics"></emph.end> in Animals, for varying of their Motions.</cell><cell>232</cell></row><row><cell>FOSCARINI.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Foſcarini<emph.end type="italics"></emph.end> his Reconciling of Scripture Texts with the Copernican <emph type="italics"></emph>Hypotheſis.<emph.end type="italics"></emph.end></cell><cell>473</cell></row><row><cell>G</cell><cell></cell></row><row><cell>GENERABILITY.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Generability<emph.end type="italics"></emph.end> and Corruptibility are onely amongſt Contraries, according to Ariſt.</cell><cell>26</cell></row><row><cell><emph type="italics"></emph>Generability<emph.end type="italics"></emph.end> and Alterability are greater perfections in Mundane Bodies, then the Contrary Qualities.</cell><cell>44</cell></row><row><cell>GEOMETRICAL, and <emph type="italics"></emph>Geometry.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Geometrical<emph.end type="italics"></emph.end> Demonſtrations of the Triple Dimenſion.</cell><cell>4</cell></row><row><cell><emph type="italics"></emph>Geometrical<emph.end type="italics"></emph.end> Exactneſſe needleſſe in Phyſical Proofs.</cell><cell>6</cell></row><row><cell>Ariſtotle taxeth Plato for being too ſtudious of <emph type="italics"></emph>Geometry.<emph.end type="italics"></emph.end></cell><cell>334</cell></row><row><cell>Peripatetick Phyloſophers condemne the Study of <emph type="italics"></emph>Geometry,<emph.end type="italics"></emph.end> and why.</cell><cell>461</cell></row><row><cell>GILBERT.</cell><cell></cell></row><row><cell>The Magnetick Phyloſophy of <emph type="italics"></emph>Will. Gilbert.<emph.end type="italics"></emph.end></cell><cell>364</cell></row><row><cell>The Method of <emph type="italics"></emph>Gilbert<emph.end type="italics"></emph.end> in his Philoſophy.</cell><cell>367</cell></row><row><cell>GLOBE.</cell><cell></cell></row><row><cell>Our <emph type="italics"></emph>Globe<emph.end type="italics"></emph.end> would have been called Stone, inſtead 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"></emph>God<emph.end type="italics"></emph.end> and Nature do employ themſelves in caring for Men, as if they minded nothing elſe.</cell><cell>333</cell></row><row><cell>An Example of <emph type="italics"></emph>Gods<emph.end type="italics"></emph.end> care of Mankind, taken from the Sun.</cell><cell>333</cell></row><row><cell><emph type="italics"></emph>God<emph.end type="italics"></emph.end> hath given all things an inviolable Law to obſerve.</cell><cell>4..</cell></row><row><cell>GREAT.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Great<emph.end type="italics"></emph.end> and Small, Immenſe, &c. are Relative Terms.</cell><cell>334</cell></row><row><cell>GRAVITY.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Grave<emph.end type="italics"></emph.end>; Vide <emph type="italics"></emph>Body.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Gravity<emph.end type="italics"></emph.end> and Levity, Rarity and Denſity, are contrary qualities.</cell><cell>30</cell></row><row><cell>Things Grave had being before the Common Centre of <emph type="italics"></emph>Gravity.<emph.end type="italics"></emph.end></cell><cell>221</cell></row><row><cell><emph type="italics"></emph>Gravity<emph.end type="italics"></emph.end> and Levity of Bodies defined.</cell><cell>493</cell></row><row><cell>GUN and <emph type="italics"></emph>Gunnery.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>The Reaſon why a <emph type="italics"></emph>Gun<emph.end type="italics"></emph.end> ſhould ſeem to carry farther towards the Weſt than towards the Eaſt.</cell><cell>148</cell></row><row><cell>The Revolution of the Earth ſuppoſed, the Ball in the <emph type="italics"></emph>Gun<emph.end type="italics"></emph.end> erected perpendicularly, doth not move by a perpendicular, but an inclined Line.</cell><cell>155</cell></row><row><cell>It is ingenuouſly demonſtrated, that, the Earths Motion ſuppoſed, the Shot of Great <emph type="italics"></emph>Guns<emph.end type="italics"></emph.end>ought to vary no more than in its Reſt.</cell><cell>161</cell></row><row><cell>The Experiment of a Running Chariot to find out the difference of Ranges in <emph type="italics"></emph>Gunnery.<emph.end type="italics"></emph.end></cell><cell>148</cell></row><row><cell>A Computation in <emph type="italics"></emph>Gunnery,<emph.end type="italics"></emph.end> 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"></pb><row><cell>H</cell><cell></cell></row><row><cell>HEAVEN.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Heaven<emph.end type="italics"></emph.end> an Habitation for the Immortal Gods.</cell><cell>26</cell></row><row><cell><emph type="italics"></emph>Heavens<emph.end type="italics"></emph.end> Immutability evident to Senſe.</cell><cell>26</cell></row><row><cell><emph type="italics"></emph>Heaven<emph.end type="italics"></emph.end> Immutable, becauſe there never was any Mutation ſeen in it.</cell><cell>34</cell></row><row><cell>One cannot (ſaith <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end>) ſpeak confidently of <emph type="italics"></emph>Heaven,<emph.end type="italics"></emph.end> by reaſon of its great diſtance.</cell><cell>42</cell></row><row><cell>The ſubſtance of the <emph type="italics"></emph>Heavens<emph.end type="italics"></emph.end> impenetrable, according to <emph type="italics"></emph>Ariſtotle.<emph.end type="italics"></emph.end></cell><cell>54</cell></row><row><cell>The Subſtance of <emph type="italics"></emph>Heaven<emph.end type="italics"></emph.end> Intangible.</cell><cell>55</cell></row><row><cell> Many things may be in <emph type="italics"></emph>Heaven,<emph.end type="italics"></emph.end> that are Inviſible to us.</cell><cell>334</cell></row><row><cell>There are more Documents in the Open Book of <emph type="italics"></emph>Heaven,<emph.end type="italics"></emph.end> than Vulgar Wits are able to Penetrate.</cell><cell>444</cell></row><row><cell><emph type="italics"></emph>Heaven<emph.end type="italics"></emph.end> and Earth ever mutually oppoſed to each other.</cell><cell>480</cell></row><row><cell>Which are really the Greater Lights in <emph type="italics"></emph>Heaven,<emph.end type="italics"></emph.end>and which the leſſer.</cell><cell>484</cell></row><row><cell><emph type="italics"></emph>Heaven<emph.end type="italics"></emph.end> is not compoſed of a fifth Eſſence, differing from the Matter of inferiour Bodies.</cell><cell>494</cell></row><row><cell><emph type="italics"></emph>Heaven<emph.end type="italics"></emph.end> is no Solid or Denſe Body, but Rare.</cell><cell>494</cell></row><row><cell>Chriſt at his Incarnatiou truly deſcended from <emph type="italics"></emph>Heaven,<emph.end type="italics"></emph.end> and at his Aſcenſion truly aſcended into <emph type="italics"></emph>Heaven.<emph.end type="italics"></emph.end></cell><cell>496</cell></row><row><cell>Of the Firſt, Second and Third <emph type="italics"></emph>Heaven.<emph.end type="italics"></emph.end></cell><cell>497</cell></row><row><cell><emph type="italics"></emph>Heaven<emph.end type="italics"></emph.end> in the Senſe of Copernicus, is the ſame with the moſt tenuous Æther, but different from Paradice, which excells all the <emph type="italics"></emph>Heavens.<emph.end type="italics"></emph.end></cell><cell>499</cell></row><row><cell>HELL.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Hell<emph.end type="italics"></emph.end> 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"></emph>Helix<emph.end type="italics"></emph.end> about the Cylinder may be ſaid to be a Simple Line.</cell><cell>7</cell></row><row><cell>HYPOTHESIS.</cell><cell></cell></row><row><cell>The true <emph type="italics"></emph>Hypotheſis<emph.end type="italics"></emph.end> may diſpatch its Revolutions in a ſhorter time in leſſer 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"></emph>Jeſt<emph.end type="italics"></emph.end> put upon one that offered to ſell a certain Secret of holding Correſpondence at a Thouſand Miles diſtance.</cell><cell>79</cell></row><row><cell>A <emph type="italics"></emph>Jest<emph.end type="italics"></emph.end> of a certain Statuary.</cell><cell>94</cell></row><row><cell>IMPOSSIBILITY and <emph type="italics"></emph>Impoſſibilities.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>Nature attempts not <emph type="italics"></emph>Impoſſibilities.<emph.end type="italics"></emph.end></cell><cell>10</cell></row><row><cell>To ſeek what would follow upon an <emph type="italics"></emph>Impoſſibility<emph.end type="italics"></emph.end> is Folly.</cell><cell>22</cell></row><row><cell>INCORRUPTIBILITY.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Incorruptibility<emph.end type="italics"></emph.end> eſteemed 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"></emph>Infinity<emph.end type="italics"></emph.end> 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"></emph>Inſtruments.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Inſtruments<emph.end type="italics"></emph.end> Aſtronomical very ſubject to Errour.</cell><cell>262</cell></row><row><cell>Copernicus underſtood not ſome things for want of <emph type="italics"></emph>Instruments.<emph.end type="italics"></emph.end></cell><cell>338</cell></row><row><cell>A proof of the ſmall credit that is to be given to Aſtronomical <emph type="italics"></emph>Instruments<emph.end type="italics"></emph.end> in Minute Obſervations.</cell><cell>351</cell></row><row><cell>Ptolomy did not confide in an <emph type="italics"></emph>Instruments<emph.end type="italics"></emph.end> made by Archimedes.</cell><cell>352</cell></row><row><cell><emph type="italics"></emph>Inſtruments<emph.end type="italics"></emph.end> of Tycho made with great Expence.</cell><cell>352</cell></row><row><cell>What <emph type="italics"></emph>Inſtruments<emph.end type="italics"></emph.end> are moſt apt for exact Obſervations.</cell><cell>352</cell></row><row><cell>INVENTORS.</cell><cell></cell></row><row><cell>The Firſt <emph type="italics"></emph>Inventors<emph.end type="italics"></emph.end> and Obſervers 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"></emph>Joſhuah<emph.end type="italics"></emph.end> in commanding the Sun to ſtand ſtill, contradicts the Ptolomaick Syſtem.</cell><cell>456</cell></row><row><cell><emph type="italics"></emph>Joſhuahs<emph.end type="italics"></emph.end> Miracle admirably agreeth with the Pythagorick Syſteme.</cell><cell>457</cell></row><pb xlink:href="040/01/538.jpg"></pb><row><cell>IRON.</cell><cell></cell></row><row><cell>Its proved that <emph type="italics"></emph>Iron<emph.end type="italics"></emph.end> conſiſts of parts more ſubtil, pure and compact than the Magner.</cell><cell>370</cell></row><row><cell>JUPITER.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> and Saturn do encompaſſe the Earth, and the Sun.</cell><cell>258</cell></row><row><cell><emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end> augments leſſe 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"></emph>Kepler<emph.end type="italics"></emph.end> in favour of Copernicus.</cell><cell>242</cell></row><row><cell>An Explanation of the true Senſe of <emph type="italics"></emph>Kepler,<emph.end type="italics"></emph.end> and his Defence.</cell><cell>243</cell></row><row><cell>The feigned Anſwer of <emph type="italics"></emph>Kepler<emph.end type="italics"></emph.end> couched in an Artificial Irony.</cell><cell>244</cell></row><row><cell><emph type="italics"></emph>Kepler<emph.end type="italics"></emph.end> is, with reſpect, blamed.</cell><cell>422</cell></row><row><cell><emph type="italics"></emph>Keplers<emph.end type="italics"></emph.end> reconciling of Scripture Texts whith the Copernican Hypotheſis.</cell><cell>461</cell></row><row><cell>KNOW, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>The having a perfect <emph type="italics"></emph>Knowledge<emph.end type="italics"></emph.end> of nothing, maketh ſome beleeve they underſtand all things.</cell><cell>84</cell></row><row><cell>Gods manner of <emph type="italics"></emph>Knowing<emph.end type="italics"></emph.end> different from that of Man.</cell><cell>87</cell></row><row><cell>The great Felicity for which they are to be envied, who perſwade themſelves that they <emph type="italics"></emph>Know<emph.end type="italics"></emph.end> every thing.</cell><cell>164</cell></row><row><cell>Our <emph type="italics"></emph>Knowledge<emph.end type="italics"></emph.end> is a kind of Reminiſcence, 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"></emph>Light<emph.end type="italics"></emph.end> reflected from the Earth into the Moon.</cell><cell>52</cell></row><row><cell>The Reflex <emph type="italics"></emph>Light<emph.end type="italics"></emph.end> of uneven Bodies is more univerſal than that of the ſmooth, and why.</cell><cell>62</cell></row><row><cell>The more rough Superficies make greater Reflection of <emph type="italics"></emph>Light<emph.end type="italics"></emph.end> than the leſſe rough</cell><cell>65</cell></row><row><cell>Perpendicular Rays of <emph type="italics"></emph>Light<emph.end type="italics"></emph.end> illuminate more than the Oblique, and why.</cell><cell>65</cell></row><row><cell>The more Oblique Rays of <emph type="italics"></emph>Light<emph.end type="italics"></emph.end> illuminate leſſe, and why,</cell><cell>65</cell></row><row><cell><emph type="italics"></emph>Light<emph.end type="italics"></emph.end> or Luminous Bodies appear the brighter in an Obſcure Ambient.</cell><cell>74</cell></row><row><cell>LINE.</cell><cell></cell></row><row><cell>The <emph type="italics"></emph>Right Line<emph.end type="italics"></emph.end> and Circumference of an infinite Circle are the ſame thing.</cell><cell>342</cell></row><row><cell>LAWYERS.</cell><cell></cell></row><row><cell>Contentious <emph type="italics"></emph>Lawyers<emph.end type="italics"></emph.end> that are retained in an ill Cauſe, keep cloſe to ſome expreſſion fallen from the adverſe party at unawares.</cell><cell>324</cell></row><row><cell>LOOKINGGLASSES.</cell><cell></cell></row><row><cell>Flat <emph type="italics"></emph>LookingGlaſſes<emph.end type="italics"></emph.end> caſt 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"></emph>Lyncean<emph.end type="italics"></emph.end> Academick the firſt Diſcoverer of the Solar ſpots, and all the other Celeſtial Novelties.</cell><cell>312</cell></row><row><cell>The Hiſtory of his proceedings for a long time, about the Obſervation 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"></emph>Magnet.<emph.end type="italics"></emph.end></cell><cell>367</cell></row><row><cell>The <emph type="italics"></emph>Magnet<emph.end type="italics"></emph.end> armed takes up more Iron, than when unarmed.</cell><cell>369</cell></row><row><cell>The true cauſe of the Multiplication of Vertue in the <emph type="italics"></emph>Magnet,<emph.end type="italics"></emph.end> by means of the Arming.</cell><cell>370</cell></row><row><cell>A ſenſible proof of the Impurity of the <emph type="italics"></emph>Magnet.<emph.end type="italics"></emph.end></cell><cell>371</cell></row><row><cell>The ſeveral Natural Motions of the <emph type="italics"></emph>Magnet.<emph.end type="italics"></emph.end></cell><cell>374</cell></row><row><cell>Philoſophers are forced to confeſſe that the <emph type="italics"></emph>Magnet<emph.end type="italics"></emph.end> is compounded of Celeſtial Subſtances, and of Elementary.</cell><cell>375</cell></row><row><cell>The Error of thoſe who call the <emph type="italics"></emph>Magnet<emph.end type="italics"></emph.end> a mixt Body, and the Terreſtrial Globe, a ſimple Body.</cell><cell>375</cell></row><row><cell>An improbable Effect admired by Gilbertus in the <emph type="italics"></emph>Magnet.<emph.end type="italics"></emph.end></cell><cell>376</cell></row><row><cell>MAGNETICK <emph type="italics"></emph>Philoſophy.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>The <emph type="italics"></emph>Magnetick Philoſophy<emph.end type="italics"></emph.end> of William Gilbert.</cell><cell>364</cell></row><row><cell>MAGNITUDE.</cell><cell></cell></row><row><cell>The <emph type="italics"></emph>Magnitude<emph.end type="italics"></emph.end> of the Orbs and the Velocity of the Motions of Planets anſwer proporti<pb xlink:href="040/01/539.jpg"></pb>onably, as if deſcended from the ſame place.</cell><cell>19</cell></row><row><cell>Immenſe <emph type="italics"></emph>Magnitudes<emph.end type="italics"></emph.end> and Numbers are incomprehenſible by our Underſtandings.</cell><cell>332</cell></row><row><cell>MARS.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> neceſſarily includeth within its Orb the Earth, and alſo the Sun.</cell><cell>298</cell></row><row><cell><emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> at its Oppoſition to the Sun, ſeems ſixty times bigger than towards the Conjunction.</cell><cell>298</cell></row><row><cell><emph type="italics"></emph>Mars<emph.end type="italics"></emph.end> makes an hot aſſault upon the Copernican Syſteme.</cell><cell>302</cell></row><row><cell>MARSILIUS.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Signor Cæſar Marſilius<emph.end type="italics"></emph.end> obſerveth 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"></emph>Medicean<emph.end type="italics"></emph.end> Planets converſions.</cell><cell>101</cell></row><row><cell>The <emph type="italics"></emph>Medicean<emph.end type="italics"></emph.end> Planets are as it were four Moons about <emph type="italics"></emph>Jupiter.<emph.end type="italics"></emph.end></cell><cell>307</cell></row><row><cell>MEDITERRAN.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Mediterranean<emph.end type="italics"></emph.end> Sea made by the Seperation of Abila and Calpen.</cell><cell>35</cell></row><row><cell>The Voyages in the <emph type="italics"></emph>Mediterran<emph.end type="italics"></emph.end> from Eaſt to Weſt are made in ſhorter times than from Weſt to Eaſt.</cell><cell>403</cell></row><row><cell>MERCURY.</cell><cell></cell></row><row><cell>The Revolution of <emph type="italics"></emph>Mercury<emph.end type="italics"></emph.end> concluded to be about the Sun, within the Orb of Venus.</cell><cell>298</cell></row><row><cell><emph type="italics"></emph>Mercury<emph.end type="italics"></emph.end> admitteth not of clear Obſervations.</cell><cell>307</cell></row><row><cell>MOON.</cell><cell></cell></row><row><cell>The <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> 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"></emph>Moon<emph.end type="italics"></emph.end> may be a Generation of things different from ours.</cell><cell>47</cell></row><row><cell>There may be Subſtances in the <emph type="italics"></emph>Moon,<emph.end type="italics"></emph.end> very different from ours.</cell><cell>48</cell></row><row><cell>The firſt reſemblance between the <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> 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 ſecond reſemblance is the <emph type="italics"></emph>Moons<emph.end type="italics"></emph.end> being Opacous, as the Earth.</cell><cell>48</cell></row><row><cell>The third reſemblance is the <emph type="italics"></emph>Moons<emph.end type="italics"></emph.end> being Denſe and Mountainous as the Earth.</cell><cell>49</cell></row><row><cell>The fourth reſemblance is the <emph type="italics"></emph>Moons<emph.end type="italics"></emph.end> being diſtinguiſhed into two different parts for Clarity and Obſcurity, as the Terreſtrial Globe into Sea and Land.</cell><cell>49</cell></row><row><cell>The fifth reſemblance is Mutation of Figures in the Earth, like thoſe of the <emph type="italics"></emph>Moon,<emph.end type="italics"></emph.end> and made with the ſame Periods.</cell><cell>49</cell></row><row><cell>All the Earth ſeeth halfe onely of the <emph type="italics"></emph>Moon,<emph.end type="italics"></emph.end>and halfe onely of the <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> ſeeth all the Earth</cell><cell>51</cell></row><row><cell>Two Spots in the <emph type="italics"></emph>Moon,<emph.end type="italics"></emph.end> by which it is perceived that She hath reſpect 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"></emph>Moon.<emph.end type="italics"></emph.end></cell><cell>52</cell></row><row><cell>The ſixth reſemblance is that the Earth and <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> interchangeably illuminate.</cell><cell>53</cell></row><row><cell>The ſeventh reſemblance is that the Earth and <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> interchangeably Ecclipſe.</cell><cell>53</cell></row><row><cell>The Secondary Clarity of the <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> eſteemed to be its Native Light.</cell><cell>54</cell></row><row><cell>The Surface of the <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> more ſleek then any LookingGlaſſe.</cell><cell>55</cell></row><row><cell>The eminencies and Cavities in the <emph type="italics"></emph>Moon,<emph.end type="italics"></emph.end> are illuſions of its Opacous and Perſpicuous parts.</cell><cell>55</cell></row><row><cell>The <emph type="italics"></emph>Moons<emph.end type="italics"></emph.end> Surface is ſharp, as is largely proved.</cell><cell>57</cell></row><row><cell>The <emph type="italics"></emph>Moon,<emph.end type="italics"></emph.end> if it it were ſleek like a Spherical LookingGlaſſe, would be inviſible.</cell><cell>60 & 62</cell></row><row><cell>The apparent Unevenneſſes of the <emph type="italics"></emph>Moons<emph.end type="italics"></emph.end> Surface aptly repreſented by Mother of Pearl.</cell><cell>70</cell></row><row><cell>The apparent Unevenneſſes of the <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> cannot be imitated by way of more and leſſe Opacity, and Perſpicuity</cell><cell>71</cell></row><row><cell>The various Aſpects of the <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> imitable by any Opacous matter.</cell><cell>71</cell></row><row><cell>Sundry Phænomena from whence the <emph type="italics"></emph>Moons<emph.end type="italics"></emph.end>Montuoſity is argued.</cell><cell>71</cell></row><row><cell>The <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> appears brighter by night, than by day.</cell><cell>72</cell></row><row><cell>The <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> beheld in the day time, is like to a little Cloud.</cell><cell>72</cell></row><row><cell>Clouds are no leſſe apt than the <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> 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"></emph>Moon,<emph.end type="italics"></emph.end> ſhines no leſſe than it.</cell><cell>73</cell></row><row><cell>The third reflection of a Wall illuminates more than the firſt of the <emph type="italics"></emph>Moon.<emph.end type="italics"></emph.end></cell><cell>74</cell></row><row><cell>The Light of the <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> weaker than that of the Twylight.</cell><cell>74</cell></row><row><cell>The ſecondary Light of the <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> cauſed by the Sun, according to ſome.</cell><cell>76</cell></row><pb xlink:href="040/01/540.jpg"></pb><row><cell>The ſecondary Light of the <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> appears in form of a Ring, <emph type="italics"></emph>i. e.<emph.end type="italics"></emph.end> bright in the extreme Circumference, and not in the midſt, and why.</cell><cell>77</cell></row><row><cell>The ſecondary Light of the <emph type="italics"></emph>Moon,<emph.end type="italics"></emph.end> how it is to be obſerved.</cell><cell>78</cell></row><row><cell>The <emph type="italics"></emph>Moons<emph.end type="italics"></emph.end> Diſcus in a Solar Eclipſe can be ſeen onely by Privation.</cell><cell>78</cell></row><row><cell>Solidity of the <emph type="italics"></emph>Moons<emph.end type="italics"></emph.end> Globe argued from its being Mountainous.</cell><cell>81</cell></row><row><cell>The ſecondary Light of the <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> clearer before the Conjunction than after.</cell><cell>82</cell></row><row><cell>The obſcurer parts of the <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> 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"></emph>Moon.<emph.end type="italics"></emph.end></cell><cell>83</cell></row><row><cell>There are not generated in the <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> 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"></emph>Moon<emph.end type="italics"></emph.end> not compoſed of Water and Earth.</cell><cell>83</cell></row><row><cell>Thoſe Aſpects of the Sun neceſſary for our Productions, are not ſo in the <emph type="italics"></emph>Moon.<emph.end type="italics"></emph.end></cell><cell>83</cell></row><row><cell>Natural Dayes in the <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> are of a Moneth long.</cell><cell>84</cell></row><row><cell>To the <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> the Sun declineth with a difference of ten Degrees, and to the Earth of Forty ſeven Degrees.</cell><cell>84</cell></row><row><cell>There are no Rains in the <emph type="italics"></emph>Moon.<emph.end type="italics"></emph.end></cell><cell>84</cell></row><row><cell>The <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> cannot ſeperate from the Earth.</cell><cell>295</cell></row><row><cell>The <emph type="italics"></emph>Moons<emph.end type="italics"></emph.end> Orbe environeth the Earth, but not the Sun.</cell><cell>299</cell></row><row><cell>The <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> much diſturbeth the Order of the other Planets.</cell><cell>362</cell></row><row><cell>The <emph type="italics"></emph>Moons<emph.end type="italics"></emph.end> Motion principally ſought in the Account of Eclipſes.</cell><cell>416</cell></row><row><cell>The <emph type="italics"></emph>Moon<emph.end type="italics"></emph.end> is an Æthereal Earth.</cell><cell>492</cell></row><row><cell>MOTION and <emph type="italics"></emph>Motions.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of Projects. Vide <emph type="italics"></emph>Projects.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>The Conditions and Attributes which differ the Celeſtial and Elementary Bodies depend on the <emph type="italics"></emph>Motions<emph.end type="italics"></emph.end> aſſigned them by Ariſtotle.</cell><cell>25</cell></row><row><cell>Peripateticks improperly aſſign thoſe <emph type="italics"></emph>Motions<emph.end type="italics"></emph.end> to the Elements for Natural with which they never were moved, and thoſe for Preternatural with which they alwayes move.</cell><cell>33</cell></row><row><cell><emph type="italics"></emph>Motion,<emph.end type="italics"></emph.end> as to the things that move thereby, is as if it never were, and ſo farre operates, as it relates to things deprived of <emph type="italics"></emph>Motion.<emph.end type="italics"></emph.end></cell><cell>98</cell></row><row><cell><emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> cannot be made without its moveable Subject.</cell><cell>104</cell></row><row><cell><emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> and Reſt principal Accidents in Nature.</cell><cell>112</cell></row><row><cell>Two things neceſſary for the perpetuating of a <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end>; an unlimited Space, and an incorruptible Moveable.</cell><cell>117</cell></row><row><cell>Diſparity in the <emph type="italics"></emph>Motions<emph.end type="italics"></emph.end> 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"></emph>Motion<emph.end type="italics"></emph.end> of grave Pendula might be perpetuated, impediments being removed.</cell><cell>203</cell></row><row><cell>Whence the <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of a Cadent Body is collected.</cell><cell>224</cell></row><row><cell>The <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of the Eye argueth the <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of the Body looked on.</cell><cell>224</cell></row><row><cell>Different <emph type="italics"></emph>Motions<emph.end type="italics"></emph.end> depending on the Fluctuation of the Ship.</cell><cell>226</cell></row><row><cell>Our <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> may be either interne, or externe, and yet we never perceive or feelit.</cell><cell>229</cell></row><row><cell>The <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of a Boat inſenſible to thoſe that are within it, as to the Senſe of Feeling.</cell><cell>229</cell></row><row><cell>The <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of a Boat ſenſible to Sight joyned with Reaſon.</cell><cell>229</cell></row><row><cell>A ſimple Body, as the Earth, cannot move with three ſeveral <emph type="italics"></emph>Motions.<emph.end type="italics"></emph.end></cell><cell>231</cell></row><row><cell><emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> and Reſt are more different than Right <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> and Circular.</cell><cell>237</cell></row><row><cell>One may more rationally aſcribe to the Earth two intern Principles to the Right and Circular <emph type="italics"></emph>Motion,<emph.end type="italics"></emph.end> than two to <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> and Reſt.</cell><cell>237</cell></row><row><cell>The diverſity of <emph type="italics"></emph>Motions<emph.end type="italics"></emph.end> helpeth us to know the Diverſity of Natures.</cell><cell>237</cell></row><row><cell>Bodies of the ſame kind, have <emph type="italics"></emph>Motions<emph.end type="italics"></emph.end> that agree in kinde.</cell><cell>239</cell></row><row><cell>The greatneſſe and ſmallneſſe of the Body make a difference in <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> and not in Reſt.</cell><cell>243</cell></row><row><cell>Every penſile and librated Body carried round in the Circumference of a Circle acquireth of it ſelf a <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> in it ſelf equal to the ſame.</cell><cell>362</cell></row><row><cell>Two ſorts of <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> in the containing Veſſel may make the containing Water to riſe and fall.</cell><cell>387</cell></row><row><cell>An Accident in the Earths <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> impoſſible to be imitated.</cell><cell>392</cell></row><row><cell>ABSOLUTE MOTION: Things ſaid to move according to certain of their parts, and not according to their whole, may not be ſaid to move with an Abſolute <emph type="italics"></emph>Motion,<emph.end type="italics"></emph.end> but <emph type="italics"></emph>per accidens.<emph.end type="italics"></emph.end></cell><cell>491</cell></row><row><cell>ANIMAL MOTION: The Diverſity of the <emph type="italics"></emph>Motions<emph.end type="italics"></emph.end> 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"></emph>Motions.<emph.end type="italics"></emph.end></cell><cell>232</cell></row><row><cell>The <emph type="italics"></emph>Motions<emph.end type="italics"></emph.end> of Animals are of oneſort.</cell><cell>232</cell></row><row><cell>The <emph type="italics"></emph>Motions<emph.end type="italics"></emph.end> of Animals are all Circular.</cell><cell>233</cell></row><row><cell>Secondary <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of Animals dependent on the firſt.</cell><cell>233</cell></row><pb xlink:href="040/01/541.jpg"></pb><row><cell>Animals would not grow weary of their <emph type="italics"></emph>Motion,<emph.end type="italics"></emph.end> proceeding as that which is aſſigned to the Terreſtrial Globe.</cell><cell>244</cell></row><row><cell>The Cauſe of the wearineſſe that attends the <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of Animals.</cell><cell>244</cell></row><row><cell>The <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> 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"></emph>Motion<emph.end type="italics"></emph.end>of the Earth muſt cauſe a conſtant and ſtrong Winde.</cell><cell>228</cell></row><row><cell>The Errour oſ the Antagoniſt of Copernicus is manifeſt, 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"></emph>Motion<emph.end type="italics"></emph.end> of the Earth mixing with the <emph type="italics"></emph>Motions<emph.end type="italics"></emph.end> of the other Planets, produce extravagant Appearances.</cell><cell>296</cell></row><row><cell>Reſt, Annual <emph type="italics"></emph>Motion,<emph.end type="italics"></emph.end> and the Diurnal, ought to be diſtributed betwixt the Sun, Earth, and Firmament.</cell><cell>300</cell></row><row><cell>Granting to the Earth the Annual, it muſt of heceſſity have the Diurnal <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> aſſigned to it.</cell><cell>300</cell></row><row><cell>The ſole Annual <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of the Earth, cauſeth great inequality in the <emph type="italics"></emph>Motions<emph.end type="italics"></emph.end> of the Planets.</cell><cell>310</cell></row><row><cell>A Demonſtration of the inequalities of the three ſuperiour Planets dependent on the Annual <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of the Earth.</cell><cell>310</cell></row><row><cell>The Annual <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of the Earth moſt apt to render a reaſon of the Exorbitance of the five Planets.</cell><cell>312</cell></row><row><cell>Argument of Tycho againſt the Annual <emph type="italics"></emph>Motion,<emph.end type="italics"></emph.end> from the invariable Elevation of the Pole.</cell><cell>338</cell></row><row><cell>Upon the Annual <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> oſ the Earth, alteration may enſue in ſome Fixed Stars, not in the Pole.</cell><cell>341</cell></row><row><cell>The Parallogiſme of thoſe who believe that in the Annual <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> 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 diſcovered by means of the Earths Annual <emph type="italics"></emph>Motion.<emph.end type="italics"></emph.end></cell><cell>342</cell></row><row><cell>Aſtronomers having omitted to inſtance what alterations thoſe are that may be derived from the Annual <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of the Earth, do thereby teſtifie that they never rightly underſtood the ſame.</cell><cell>343</cell></row><row><cell>The Anuual <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> made by the Centre of the Earth under the Ecliptick, and the Diurnal <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> made by the Earth about its own Centre.</cell><cell>344</cell></row><row><cell>Objections againſt the Earths Annual <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end>taken from the Fixed Stars placed in the Ecliptick.</cell><cell>345</cell></row><row><cell>An Indice or Obſervation in the Fixed Stars like to that which is ſeen in the Planets, is an Argument of the Earths Annual <emph type="italics"></emph>Motion.<emph.end type="italics"></emph.end></cell><cell>347</cell></row><row><cell>The Suns Annual <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> how it cometh to paſſe, according to Copernicus.</cell><cell>355</cell></row><row><cell>The Annual and Diurnal <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> are conſiſtent 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"></emph>Motion.<emph.end type="italics"></emph.end></cell><cell>409</cell></row><row><cell>The Earths Annual <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> thorow the Ecliptick unequal, by reaſon of the Moons <emph type="italics"></emph>Motion.<emph.end type="italics"></emph.end></cell><cell>413</cell></row><row><cell>The Cauſes of the inequality of the Additions and Subſtractions of the Diurnal Converſion from the Annual <emph type="italics"></emph>Motion.<emph.end type="italics"></emph.end></cell><cell>418</cell></row><row><cell>CIRCULAR MOTION: Circular and Right <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> are ſimple, as proceeding in ſimple Lines.</cell><cell>6</cell></row><row><cell>The Circular <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> is never acquired Naturally, unleſſe Right <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> precede it.</cell><cell>18</cell></row><row><cell>Circular <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> perpetually uniforme.</cell><cell>18</cell></row><row><cell>In the Circular <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> every point in the Circumference is the beginning and end.</cell><cell>20</cell></row><row><cell>Circular <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> onely is Uniforme.</cell><cell>20</cell></row><row><cell>Circular <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> may be continued pcrpetually.</cell><cell>20</cell></row><row><cell>Circular <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> onely and Reſt are apt to conſerve Order.</cell><cell>20</cell></row><row><cell>To the Circular <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> no other <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> is contrary.</cell><cell>26</cell></row><row><cell>Circular <emph type="italics"></emph>Motions<emph.end type="italics"></emph.end> are not contrary, according to Ariſtotle.</cell><cell>100</cell></row><row><cell>The <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> 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"></emph>Motion<emph.end type="italics"></emph.end> encreaſeth according to the encreaſe of the Diameter of the Circle.</cell><cell>242</cell></row><row><cell>Circular <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> is truly ſimple 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"></emph>Motion<emph.end type="italics"></emph.end> are coincident, and may conſiſt together in the ſame Body.</cell><cell>496</cell></row><row><cell>COMMON MOTION: A notable Inſtance of Sagredus, to ſhew the nonoperating of Common <emph type="italics"></emph>Motion.<emph.end type="italics"></emph.end></cell><cell>151</cell></row><row><cell>An Experiment that ſheweth how the Common <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> is imperceptible.</cell><cell>224</cell></row><row><cell>The concurrence of the Elements in a Common <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> imports no more than their concurrence in a Common Reſt.</cell><cell>239</cell></row><row><cell>Common <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> is as if it never were.</cell><cell>223, 340</cell></row><row><cell>COMPRESSIVE MOTION: Compreſſive <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> is proper to Gravity, Extenſive to Levity.</cell><cell>493</cell></row><pb xlink:href="040/01/542.jpg"></pb><row><cell>CONTRARY MOTIONS: An Experiment which plainly ſhews that two Contrary <emph type="italics"></emph>Motions<emph.end type="italics"></emph.end> may agree in the ſame Moveable.</cell><cell>363</cell></row><row><cell>The parts of a Circle regularly moved about its own Centre, move in diverſe times with Contrary <emph type="italics"></emph>Motions.<emph.end type="italics"></emph.end></cell><cell>389</cell></row><row><cell>DESCENDING MOTION: The Inclination of Grave Bodies to the <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of Deſcent, is equal to their reſiſtance to the <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of Aſcent.</cell><cell>191</cell></row><row><cell>The Spaces paſt in the Deſcending <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of the ſalling Grave Body, are as the Squares|of their times.</cell><cell>198</cell></row><row><cell>The <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of Deſcent belongs not to the Terreſtrial Globe, but to its parts.</cell><cell>362</cell></row><row><cell>DIVRNAL MOTION: The Diurnal <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end>ſeemeth Commune to all the Univerſe, the Earth onely excepted.</cell><cell>97</cell></row><row><cell>Diurnal <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> why it ſhould more probably belong to the Earth than to the Reſt of the Univerſe.</cell><cell>98</cell></row><row><cell>The firſt Diſcourſe to prove that the Diurnal <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> belongs to the Earth.</cell><cell>99</cell></row><row><cell>The Diurnal <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> cauſeth no Mutation among Celeſtial Bodies, but all changes have relation to the Earth.</cell><cell>100</cell></row><row><cell>A ſecond Confirmation that|the Diurnal <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> belongs to the Earth.</cell><cell>100</cell></row><row><cell>A third Confirmation that the Diurnal <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end>belongs to the Earth.</cell><cell>101</cell></row><row><cell>A fourth, fiſth, and ſixth Confirmation that the Diurnal <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> belongs to the Eatth.</cell><cell>102</cell></row><row><cell>Aſeventh Confirmation that the Diurnal <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> belongs to the Earth.</cell><cell>103</cell></row><row><cell>If the Diurnal <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> ſhould alter, the Annual Period would ceaſe.</cell><cell>409</cell></row><row><cell>LOCAL MOTION: Local <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> 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"></emph>Motion.<emph.end type="italics"></emph.end></cell><cell>198</cell></row><row><cell>MIXT MOTION: Of Mixt <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> we ſee not the part that is Circular, becauſe we pertake thereof.</cell><cell>218</cell></row><row><cell>Ariſtotle granteth a Mixt <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> to Mixt Bodies.</cell><cell>375</cell></row><row><cell>The <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of Mixt Bodies ought to be ſuch as may reſult from the Compoſition of the <emph type="italics"></emph>Motions<emph.end type="italics"></emph.end> of the ſimple Bodies compounding.</cell><cell>375</cell></row><row><cell>NATVRAL MOTION: Accelleration of the Natural <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of Graves is made according to the Odd Numbers beginning at Unity.</cell><cell>198</cell></row><row><cell>Natural <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> changeth into that which is PreterNatural and Violent.</cell><cell>212</cell></row><row><cell>PROGRESSIVE MOTION: The Progreſſive <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> may make the Water in a Veſſel to run to and fro.</cell><cell>387</cell></row><row><cell>RIGHT MOTION: Sometimes Simple, and ſometimes Mixt, according to Ariſtotle.</cell><cell>8</cell></row><row><cell>Right <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> impoſſible in the World exactly Ordinate.</cell><cell>10</cell></row><row><cell>Right <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> Naturally Infinite.</cell><cell>10</cell></row><row><cell>Right <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> Naturally Impoſſible.</cell><cell>10</cell></row><row><cell>Right <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> might poſſibly have been in the Firſt Chaos.</cell><cell>11</cell></row><row><cell>Right <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> is uſeful to reduce into Order things out of Order.</cell><cell>11</cell></row><row><cell>Right <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> cannot naturally be Perpetual.</cell><cell>20</cell></row><row><cell>Right <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> aſſigned 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"></emph>Motion<emph.end type="italics"></emph.end> of Grave Bodies manifeſt to Senſe.</cell><cell>22</cell></row><row><cell>Right <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> with more reaſon aſcribed to the Parts, than to the whole Elements.</cell><cell>33</cell></row><row><cell>Right <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> cannot be Eternal, and conſequently cannot be Natural to the Earth.</cell><cell>117</cell></row><row><cell>Right <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> ſeemeth to be wholly excluded in Nature.</cell><cell>147</cell></row><row><cell>With two Right <emph type="italics"></emph>Motions<emph.end type="italics"></emph.end> one cannot compoſe Circular <emph type="italics"></emph>Motions.<emph.end type="italics"></emph.end></cell><cell>375</cell></row><row><cell>Right <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> belongeth to imperfect Bodies, and that are out of their Natural Places.</cell><cell>495</cell></row><row><cell>Right <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> is not Simple.</cell><cell>495</cell></row><row><cell>Right <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> 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 Terreſtrial Globe accelerate and retard in their <emph type="italics"></emph>Motion.<emph.end type="italics"></emph.end></cell><cell>388</cell></row><row><cell>One ſingle Terreſtrial <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> ſufficeth not to produce the Ebbing and Flowing.</cell><cell>421</cell></row><row><cell>UNEVEN MOTION may make the Water in a Veſſel to Run to and fro.</cell><cell>387</cell></row><row><cell>The Mixture of the two <emph type="italics"></emph>Motions<emph.end type="italics"></emph.end> Annual and Diurnal, cauſeth the unevenneſſe in the <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> of the parts of the Terreſtrial Globe.</cell><cell>390</cell></row><row><cell>MOVE.</cell><cell></cell></row><row><cell>Its queſtionable whether deſcending Bodies <emph type="italics"></emph>Move<emph.end type="italics"></emph.end> in a Right Line.</cell><cell>21</cell></row><row><cell>Ariſtotles Argument to prove that Grave Bodies <emph type="italics"></emph>Move<emph.end type="italics"></emph.end> with an inclination to arrive at the Centre.</cell><cell>22</cell></row><row><cell>Grave Bodies <emph type="italics"></emph>Move<emph.end type="italics"></emph.end> towards the Centre of the Centre of the Earth <emph type="italics"></emph>per Accidens.<emph.end type="italics"></emph.end></cell><cell>22</cell></row><row><cell>Things forſaking the place which was natural ro them by Creation, are ſaid to <emph type="italics"></emph>Move<emph.end type="italics"></emph.end> violently, <pb xlink:href="040/01/543.jpg"></pb>and naturally tend to return back to the ſame.</cell><cell>492</cell></row><row><cell>MOVEABLE, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>A <emph type="italics"></emph>Moveable<emph.end type="italics"></emph.end> being in the ſtate of Reſt ſhall not move unleſſe it have an inclination to ſome particular Place.</cell><cell>11</cell></row><row><cell>The <emph type="italics"></emph>Moveable<emph.end type="italics"></emph.end> accellerates its Motion in going towards the Place whither it hath an inclination.</cell><cell>11</cell></row><row><cell>The <emph type="italics"></emph>Moveable<emph.end type="italics"></emph.end> departing from Reſt goeth thorow all the Degrees of Tardity.</cell><cell>11</cell></row><row><cell>The <emph type="italics"></emph>Moveable<emph.end type="italics"></emph.end> doth not accelerate ſave only as it approacheth near to its terme of Reſt.</cell><cell>12</cell></row><row><cell>To introduce in a <emph type="italics"></emph>Moveable<emph.end type="italics"></emph.end> 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"></emph>Moveable<emph.end type="italics"></emph.end> departing from Reſt paſſeth through all the Degrees of Velocity without ſtaying in any.</cell><cell>13</cell></row><row><cell>The Grave <emph type="italics"></emph>Moveable<emph.end type="italics"></emph.end> deſcending, acquireth Impetus ſufficient to recarry it to the like height.</cell><cell>13</cell></row><row><cell>The Impetus of <emph type="italics"></emph>Moveables<emph.end type="italics"></emph.end> equally approaching to the Centre are equal.</cell><cell>14</cell></row><row><cell>Upon an Horizontal Plane the <emph type="italics"></emph>Moveable<emph.end type="italics"></emph.end> lyeth ſtill.</cell><cell>14</cell></row><row><cell>A ſingle <emph type="italics"></emph>Moveable<emph.end type="italics"></emph.end> hath but one only Natural Motion, and all the reſt are by participation.</cell><cell>103</cell></row><row><cell>A Line deſcribed by a <emph type="italics"></emph>Moveable<emph.end type="italics"></emph.end> in its Natural Deſcent, the Motion of the Earth about its own Centre being preſuppoſed, would probably be the Circumference of a Circle.</cell><cell>145</cell></row><row><cell>A <emph type="italics"></emph>Moveable<emph.end type="italics"></emph.end> 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"></emph>Moveable<emph.end type="italics"></emph.end> falling from a Tower moveth neither more nor leſſe, then if it had ſtaid alwayes there.</cell><cell>146</cell></row><row><cell>A <emph type="italics"></emph>Moveable<emph.end type="italics"></emph.end> falling from a Tower moveth with an Uniforme not an Accelerate Motion.</cell><cell>146</cell></row><row><cell>The Cadent <emph type="italics"></emph>Moveable,<emph.end type="italics"></emph.end> if it fall with a Degree of Velocity acquired in a like time with an Uniform Motion, it ſhall paſſe a ſpace double to that paſſed with the Accelerate Motion.</cell><cell>202</cell></row><row><cell>Admirable Problems of <emph type="italics"></emph>Moveables<emph.end type="italics"></emph.end> deſcending by the Quadrant of a Circle, and thoſe deſcending 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"></emph>Mundane<emph.end type="italics"></emph.end> Bodies were moved in the beginning in a Right Line, and afterwards circularly, according to <emph type="italics"></emph>Plato.<emph.end type="italics"></emph.end></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"></emph>Natural.<emph.end type="italics"></emph.end></cell><cell>116</cell></row><row><cell>NATURE, and <emph type="italics"></emph>Natures.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Nature<emph.end type="italics"></emph.end> attempts not things impoſſible to be effected.</cell><cell>10</cell></row><row><cell><emph type="italics"></emph>Nature<emph.end type="italics"></emph.end> never doth that by many things which may be done by a few.</cell><cell>99</cell></row><row><cell><emph type="italics"></emph>Nature<emph.end type="italics"></emph.end> firſt made things as ſhe pleaſed, and afterwards capacitated Mans underſtanding for conceiving of them.</cell><cell>238</cell></row><row><cell>From Common Accidents one cannot know different <emph type="italics"></emph>Natures.<emph.end type="italics"></emph.end></cell><cell>238</cell></row><row><cell><emph type="italics"></emph>Natures<emph.end type="italics"></emph.end> Order is to make the leſſer Orbes to Circulate in ſhorter times, and the bigger in longer.</cell><cell>243</cell></row><row><cell>That which to us is hard to be underſtood, is with <emph type="italics"></emph>Nature<emph.end type="italics"></emph.end> caſie to be effected.</cell><cell>403</cell></row><row><cell><emph type="italics"></emph>Nature<emph.end type="italics"></emph.end> keeping within the bounds aſſigned 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"></emph>Natures<emph.end type="italics"></emph.end> Actions no leſs admirably diſcover 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"></emph>Nerves<emph.end type="italics"></emph.end> according to Ariſtotle, and according to Phyſitians.</cell><cell>91</cell></row><row><cell>The ridieulous Anſwer of a Phyloſopher determining the Original of the <emph type="italics"></emph>Nerves.<emph.end type="italics"></emph.end></cell><cell>91</cell></row><row><cell>O</cell><cell></cell></row><row><cell>OBJECTS.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Objects,<emph.end type="italics"></emph.end> the more Vigorous they are in Light, the more they do ſeem to encreaſe.</cell><cell>305</cell></row><row><cell>That Remote <emph type="italics"></emph>Objects<emph.end type="italics"></emph.end> appear ſo ſmall is the Defect of the Eye, as is demonſtrated.</cell><cell>337</cell></row><row><cell>In <emph type="italics"></emph>Objects<emph.end type="italics"></emph.end> far Remote and Luminous, a ſmall acceſſion or receſſion is imperceptible.</cell><cell>350</cell></row><row><cell>OPINIONS.</cell><cell></cell></row><row><cell>It's all one, whether <emph type="italics"></emph>Opinions<emph.end type="italics"></emph.end> are new to Men, or Men new to <emph type="italics"></emph>Opinions.<emph.end type="italics"></emph.end></cell><cell>77</cell></row><row><cell>ORBE, and <emph type="italics"></emph>Orbes.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>The greater <emph type="italics"></emph>Orbes<emph.end type="italics"></emph.end> make their Converſions in <pb xlink:href="040/01/544.jpg"></pb>greater times.</cell><cell>101 <emph type="italics"></emph>&<emph.end type="italics"></emph.end> 331</cell></row><row><cell>It's more rational, that the <emph type="italics"></emph>Orbe<emph.end type="italics"></emph.end> 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"></emph>Paſſions<emph.end type="italics"></emph.end> are perhaps but one onely.</cell><cell>87</cell></row><row><cell>PENDULUM, and <emph type="italics"></emph>Pendula.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Pendula<emph.end type="italics"></emph.end> might have a perpetual Motion, impediments being removed.</cell><cell>203</cell></row><row><cell>The <emph type="italics"></emph>Pendulum<emph.end type="italics"></emph.end> hanging at a longer thread maketh its Vibrations more ſeldome than the <emph type="italics"></emph>Pendulum<emph.end type="italics"></emph.end> hanging at a ſhorter.</cell><cell>206</cell></row><row><cell>The Vibrations of the ſame <emph type="italics"></emph>Pendulum<emph.end type="italics"></emph.end> are made with the ſame frequency, whether they be ſmall or great.</cell><cell>206</cell></row><row><cell>The cauſe which impedeth the <emph type="italics"></emph>Pendulum,<emph.end type="italics"></emph.end> and reduceth it to reſt.</cell><cell>206</cell></row><row><cell>The thread or Chain to which the <emph type="italics"></emph>Pendulum<emph.end type="italics"></emph.end> is faſtened maketh an Arch, and doth not ſtretch it ſelf ſtraight out in its Vibrations.</cell><cell>207</cell></row><row><cell>Two particular notable Accidents in the <emph type="italics"></emph>Pendula<emph.end type="italics"></emph.end>and their Vibrations.</cell><cell>411</cell></row><row><cell>PERIPATETICK, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> Phyloſophy unchangeable.</cell><cell>42</cell></row><row><cell>A brave reſolution of a certain <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end>Philoſopher to prove the Right Line to be the ſhorteſt of all Lines.</cell><cell>182</cell></row><row><cell>The Paralogiſme of the ſaid <emph type="italics"></emph>Peripatetick<emph.end type="italics"></emph.end> who proveth <emph type="italics"></emph>Ignotum per ignotius.<emph.end type="italics"></emph.end></cell><cell>183</cell></row><row><cell>The Diſcourſes of <emph type="italics"></emph>Peripateticks<emph.end type="italics"></emph.end> full of Errors and Contradictions.</cell><cell>376</cell></row><row><cell>The <emph type="italics"></emph>Peripateticks<emph.end type="italics"></emph.end> perſecuted Galileo out of envy to his happy Diſcoveries in Phyloſophy.</cell><cell>427</cell></row><row><cell>The <emph type="italics"></emph>Peripateticks<emph.end type="italics"></emph.end> in defect of Reaſons repair to Scripture for Arguments againſt their Adverſaries.</cell><cell>429</cell></row><row><cell>PHYLOSOPHERS.</cell><cell></cell></row><row><cell>It is not juſt, that thoſe who never. Phyloſophate, ſhould uſurp the title of <emph type="italics"></emph>Phyloſophers.<emph.end type="italics"></emph.end></cell><cell>96</cell></row><row><cell>PHYLOSOPHY.</cell><cell></cell></row><row><cell>The Diſputes and Contradictions of <emph type="italics"></emph>Phyloſophers<emph.end type="italics"></emph.end>may conduce to the benefit of <emph type="italics"></emph>Phyloſophy.<emph.end type="italics"></emph.end></cell><cell>25</cell></row><row><cell>A cunning way to gather <emph type="italics"></emph>Phyloſophy<emph.end type="italics"></emph.end> out of any Book whatſoever.</cell><cell>92</cell></row><row><cell>PLANETS.</cell><cell></cell></row><row><cell>The approximation and receſſion of the three ſuperiour <emph type="italics"></emph>Planets<emph.end type="italics"></emph.end> importeth double the Suns diſtance.</cell><cell>299</cell></row><row><cell>The difference of the <emph type="italics"></emph>Tlanets<emph.end type="italics"></emph.end> apparent Magnitude leſſe in Saturn than in Jupiter, and leſſe in Jupiter than in Mars, and why.</cell><cell>299</cell></row><row><cell>The Station, Direction, and Retrogradation of the <emph type="italics"></emph>Planets<emph.end type="italics"></emph.end> 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"></emph>Planets<emph.end type="italics"></emph.end> not yet well reſolved.</cell><cell>416</cell></row><row><cell>The <emph type="italics"></emph>Planets<emph.end type="italics"></emph.end> places may more certainly be aſſigred by this Doctrine, than by that of Ptolomies great Almageſt.</cell><cell>469</cell></row><row><cell>PLATO.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> held, that Humane underſtanding pertook of Divinity, becauſe it underſtood Numbers.</cell><cell>3</cell></row><row><cell><emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> 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"></emph>Pole<emph.end type="italics"></emph.end> urged as an Argument againſt the Annual Motion.</cell><cell>338</cell></row><row><cell>An Example to prove that the Altitude of the <emph type="italics"></emph>Pole<emph.end type="italics"></emph.end> 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"></emph>Power<emph.end type="italics"></emph.end> one would think a greater part ſhould rather be imployed than a leſſer.</cell><cell>105</cell></row><row><cell>PRINCIPLES.</cell><cell></cell></row><row><cell>By denying <emph type="italics"></emph>Principles<emph.end type="italics"></emph.end> in Sciences, any Paradox may be maintained.</cell><cell>28</cell></row><row><cell>Contrary <emph type="italics"></emph>Principles<emph.end type="italics"></emph.end> cannot naturally reſide in the ſame Subject.</cell><cell>211</cell></row><row><cell>PROJECT, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>The <emph type="italics"></emph>Project,<emph.end type="italics"></emph.end> according to Ariſtotle, is not moved by virtue impreſſed, but by the Medium.</cell><cell>130</cell></row><row><cell>Operation of the Medium in continuing the Motion of the <emph type="italics"></emph>Project.<emph.end type="italics"></emph.end></cell><cell>131</cell></row><row><cell>Many Experiments and Reaſons againſt the Motions of <emph type="italics"></emph>Projects<emph.end type="italics"></emph.end> aſſigned by Ariſtotle.</cell><cell>132</cell></row><row><cell>The Medium doth impede and not conferre the <pb xlink:href="040/01/545.jpg"></pb>Motion of <emph type="italics"></emph>Projests.<emph.end type="italics"></emph.end></cell><cell>134</cell></row><row><cell>An admirable accident in the Motion of <emph type="italics"></emph>Projects.<emph.end type="italics"></emph.end></cell><cell>135</cell></row><row><cell>Sundry curious Problems touching the Motion of <emph type="italics"></emph>Projects.<emph.end type="italics"></emph.end></cell><cell>137</cell></row><row><cell><emph type="italics"></emph>Projects<emph.end type="italics"></emph.end> continue their <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> by a Right Line that follows the direction of the Motion made together with the <emph type="italics"></emph>Projicient,<emph.end type="italics"></emph.end> whilſt they were conjoyned therewith.</cell><cell>154</cell></row><row><cell>The Motion impreſſed by the <emph type="italics"></emph>Projicient<emph.end type="italics"></emph.end> is onely in a Right Line.</cell><cell>170</cell></row><row><cell>The <emph type="italics"></emph>Project<emph.end type="italics"></emph.end> moveth by the Tangent of the Circle of the Motion preceeding in the inſtant of Seperation.</cell><cell>172</cell></row><row><cell>A Grave <emph type="italics"></emph>Project<emph.end type="italics"></emph.end> aſſoon as it is ſeperated from the <emph type="italics"></emph>Projicient,<emph.end type="italics"></emph.end> beginneth to decline.</cell><cell>173</cell></row><row><cell>The Cauſe of the <emph type="italics"></emph>Projection<emph.end type="italics"></emph.end> encreaſeth not according to the Proportion of Velocity encreaſed by making the Wheel bigger.</cell><cell>189</cell></row><row><cell>The Virtue which carrieth Grave <emph type="italics"></emph>Projects<emph.end type="italics"></emph.end> upwards, is no leſſe Natural to them than the Gravity which moveth them downwards.</cell><cell>211</cell></row><row><cell>PTOLOMY, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>Inconveniences that are in the Syſtem of <emph type="italics"></emph>Ptolomy.<emph.end type="italics"></emph.end></cell><cell>309</cell></row><row><cell><emph type="italics"></emph>Ptolomies<emph.end type="italics"></emph.end> Syſtem full of defects.</cell><cell>476</cell></row><row><cell>The Learned both of elder and later times diſſatisfied with the <emph type="italics"></emph>Ptolomaick<emph.end type="italics"></emph.end> Syſtem.</cell><cell>477</cell></row><row><cell>PYTHAGORAS, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Pythagorick<emph.end type="italics"></emph.end> Miſtery of Numbers fabulous.</cell><cell>3</cell></row><row><cell><emph type="italics"></emph>Pythagoras<emph.end type="italics"></emph.end> offered an Hecatombe for a Geometrical Demonſtration which he found.</cell><cell>38</cell></row><row><cell><emph type="italics"></emph>Pythagoras<emph.end type="italics"></emph.end> and many other Ancients enumerated, that held the Earths Mobility.</cell><cell>437 <emph type="italics"></emph>&<emph.end type="italics"></emph.end> 468</cell></row><row><cell>R</cell><cell></cell></row><row><cell>RAYS.</cell><cell></cell></row><row><cell>Shining Objects ſeem fringed and environed with adventitious <emph type="italics"></emph>Rays.<emph.end type="italics"></emph.end></cell><cell>304</cell></row><row><cell>RIST.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Reſt.<emph.end type="italics"></emph.end> Vide <emph type="italics"></emph>Motion.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Reſt<emph.end type="italics"></emph.end> the Infinite degree of Tardity.</cell><cell>11</cell></row><row><cell>RBTROGRADATIONS.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Retrogradations<emph.end type="italics"></emph.end> more frequent in Saturn, leſſe fre quent in Jupiter, and yet leſſe in Mars, and why.</cell><cell>311</cell></row><row><cell>The <emph type="italics"></emph>Retrogradations<emph.end type="italics"></emph.end> of Venus and Mercury demonſtrated 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"></emph>Saturn<emph.end type="italics"></emph.end> for its ſlowneſſe, and Mercury for its late appearing, were amongſt thoſe that were laſt obſerved.</cell><cell>416</cell></row><row><cell>SCARCITY.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Scarcity<emph.end type="italics"></emph.end> and Plenty enhanſe and debaſe the price of all things.</cell><cell>43</cell></row><row><cell>SCHEINER.</cell><cell></cell></row><row><cell>Chriſtopher <emph type="italics"></emph>Scheiner<emph.end type="italics"></emph.end> the Jefuit his Book of Concluſions confuted.</cell><cell>78 <emph type="italics"></emph>& 195, & <expan abbr="ſeq.">ſeque</expan> &<emph.end type="italics"></emph.end> 323</cell></row><row><cell>A Canon Bullet would ſpend more than ſix dayes in falling from the Concave of the Moon to the Center of the Earth, according to <emph type="italics"></emph>Scheiner.<emph.end type="italics"></emph.end></cell><cell>195</cell></row><row><cell>Chriſtopher <emph type="italics"></emph>Scheiner<emph.end type="italics"></emph.end> his Book entituled <emph type="italics"></emph>Apelles poſt Tabulam<emph.end type="italics"></emph.end> cenſured, and diſproved.</cell><cell>313</cell></row><row><cell>The Objections of <emph type="italics"></emph>Scheiner<emph.end type="italics"></emph.end> by way of Interrogation.</cell><cell>336</cell></row><row><cell>Anſwers to the Interrogations of <emph type="italics"></emph>Schtiner.<emph.end type="italics"></emph.end></cell><cell>336</cell></row><row><cell>Queſtions put to <emph type="italics"></emph>Scheiner,<emph.end type="italics"></emph.end> by which the weakneſle of his is made appear.</cell><cell>336</cell></row><row><cell>SCIENCES.</cell><cell></cell></row><row><cell>In Natural <emph type="italics"></emph>Sciences<emph.end type="italics"></emph.end> the Art of Oratory is of no uſe.</cell><cell>40</cell></row><row><cell>In Natural <emph type="italics"></emph>Sciences<emph.end type="italics"></emph.end> it is not neceſſary to ſeek Mathematical evidence.</cell><cell>206</cell></row><row><cell>SCRIPTURE, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>The Caution we are to uſe in determining the Senſe of <emph type="italics"></emph>Scripture<emph.end type="italics"></emph.end> in difficult points of Phyloſophy.</cell><cell>427</cell></row><row><cell><emph type="italics"></emph>Scripture<emph.end type="italics"></emph.end> ſtudiouſly condeſcendeth to the apprehenſion of the Vulgar.</cell><cell>432</cell></row><row><cell>In dicuſſing of Natural Queſtions, we ought not to begin at <emph type="italics"></emph>Scripture,<emph.end type="italics"></emph.end> but at Senſible Experiments and Neceſſary Demonſtrations.</cell><cell>433</cell></row><row><cell>The intent of <emph type="italics"></emph>Scripture<emph.end type="italics"></emph.end> is by its Authority to recommend thoſe 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"></pb><row><cell><emph type="italics"></emph>Scripture<emph.end type="italics"></emph.end> Authority to be preferred, even in Natural Controverſies to ſuch Sciences as are not confined to a Demonſtrative Method.</cell><cell>434</cell></row><row><cell>The Penmen of <emph type="italics"></emph>Scripture,<emph.end type="italics"></emph.end> though read in Aſtronomy, 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"></emph>Scripture,<emph.end type="italics"></emph.end> to teach us whether the Earth moveth or ſtandeth ſtill, as nothing concerning our Salvation.</cell><cell>436</cell></row><row><cell>Inconveniencies that ariſe from licentious uſurping of <emph type="italics"></emph>Scripture,<emph.end type="italics"></emph.end> to ſtuffe out Books that treat of Nat. Arguments.</cell><cell>438</cell></row><row><cell>The Literal Senſe of <emph type="italics"></emph>Scripture<emph.end type="italics"></emph.end> joyned with the univerſal conſent of the Fathers, is to be received without farther diſpute</cell><cell>444</cell></row><row><cell>A Text of <emph type="italics"></emph>Scripture<emph.end type="italics"></emph.end> ought no leſſe diligently to be reconciled with a Demonſtrated Propoſition in Philoſophy, than with another Text of <emph type="italics"></emph>Scripture<emph.end type="italics"></emph.end> ſounding to a contrary Senſe.</cell><cell>446</cell></row><row><cell>Demonſtrated Truth ought to aſſiſt the Commentator in finding the true Senſe of <emph type="italics"></emph>Scripture.<emph.end type="italics"></emph.end></cell><cell>446</cell></row><row><cell>It was neceſſary by way of condeſcenſion to Vulgar Capacities, that the <emph type="italics"></emph>Scripture<emph.end type="italics"></emph.end> ſhould ſpeak of the Reſt and Motion of the Sun and Earth in the ſame manner that it doth.</cell><cell>447</cell></row><row><cell>Not onely the Incapacity of the Vulgar, but the Current Opinion of thoſe times, made the Sacred Writers of the <emph type="italics"></emph>Scripture<emph.end type="italics"></emph.end> to accommodate themſelves to Popular Eſteem more than Truth.</cell><cell>447</cell></row><row><cell>The <emph type="italics"></emph>Scripture<emph.end type="italics"></emph.end> had much more reaſon to affirm the Sun Moveable, and the Earth Immoveable, than otherwiſe.</cell><cell>448</cell></row><row><cell>Circumſpection of the Fathers about impoſing poſitive Senſes on Doubtful Texts of <emph type="italics"></emph>Scripture.<emph.end type="italics"></emph.end></cell><cell>451</cell></row><row><cell>Tis Cowardice makes the AntiCopernican fly to Scripture Authorities, thinking thereby to affright their Adverſaries.</cell><cell>455</cell></row><row><cell><emph type="italics"></emph>Scripture<emph.end type="italics"></emph.end> ſpeaks in Vulgar and Common Points after the manner of Men.</cell><cell>462</cell></row><row><cell>The intent of <emph type="italics"></emph>Scripture<emph.end type="italics"></emph.end> is to be obſerved in Places that ſeem to affirme the Earths Stability.</cell><cell>464</cell></row><row><cell><emph type="italics"></emph>Scripture<emph.end type="italics"></emph.end> Authorities that ſeem to affirm the Motion of the Sun and Stability of the Earth, divided into ſix Claſſes.</cell><cell>478</cell></row><row><cell>Six Maximes to be obſerved in Expounding Dark Texts of <emph type="italics"></emph>Scripture.<emph.end type="italics"></emph.end></cell><cell>481</cell></row><row><cell><emph type="italics"></emph>Scripture<emph.end type="italics"></emph.end> Texts ſpeaking of things inconvenient to be underſtood in their Literal Senſe, are to be interpreted one of the four wayes named.</cell><cell>81</cell></row><row><cell>Why the Sacred <emph type="italics"></emph>Scripture<emph.end type="italics"></emph.end> accommodates it ſelf to the Senſe of the Vulgar.</cell><cell>487</cell></row><row><cell>SEA.</cell><cell></cell></row><row><cell>The <emph type="italics"></emph>Seas<emph.end type="italics"></emph.end> Surface would ſhew at a diſtance more obſcure than the Land.</cell><cell>49</cell></row><row><cell>The <emph type="italics"></emph>Seas<emph.end type="italics"></emph.end> Reflection of Light much weaker than that of the Earth.</cell><cell>81</cell></row><row><cell>The Iſles are tokens of the unevenneſſe of the Bottoms of <emph type="italics"></emph>Seas.<emph.end type="italics"></emph.end></cell><cell>383</cell></row><row><cell>SELEUCUS.</cell><cell></cell></row><row><cell>Opinion of <emph type="italics"></emph>Seleucus<emph.end type="italics"></emph.end> the Mathematician cenſured.</cell><cell>422</cell></row><row><cell>SENSE.</cell><cell></cell></row><row><cell>He who denieth <emph type="italics"></emph>Senſe,<emph.end type="italics"></emph.end> deſerves to be deprived of it.</cell><cell>21</cell></row><row><cell><emph type="italics"></emph>Senſe<emph.end type="italics"></emph.end> ſheweth that things Grave move <emph type="italics"></emph>ad Medium,<emph.end type="italics"></emph.end> 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"></emph>Senſes,<emph.end type="italics"></emph.end> would have us lay them aſide, and look for other Proofs for ſuch Natural Points as <emph type="italics"></emph>Senſe<emph.end type="italics"></emph.end> ſets before our Eyes.</cell><cell>434</cell></row><row><cell><emph type="italics"></emph>Senſe<emph.end type="italics"></emph.end> and Reaſon leſſe certain than Faith.</cell><cell>475</cell></row><row><cell>SILVER.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Silver<emph.end type="italics"></emph.end> burniſhed appears much more obſcure than the unburniſhed, and why.</cell><cell>64</cell></row><row><cell>SIMPLICIUS.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> his Declamation.</cell><cell>43</cell></row><row><cell>SOCRATES.</cell><cell></cell></row><row><cell>The Anſwer of the Oracle true in judging <emph type="italics"></emph>Socrates<emph.end type="italics"></emph.end> the Wiſeſt of his time.</cell><cell>85</cell></row><row><cell>SORITES.</cell><cell></cell></row><row><cell>The Forked Sylogiſme called <foreign lang="grc">Sοπειτες</foreign></cell><cell>29</cell></row><row><cell>SPEAKING.</cell><cell></cell></row><row><cell>We cannot abſtract our manner of <emph type="italics"></emph>Speaking<emph.end type="italics"></emph.end>from our Senſe of Seeing.</cell><cell>461</cell></row><row><cell>SPHERE.</cell><cell></cell></row><row><cell>The Motion of 24 hours aſcribed to the Higheſt <pb xlink:href="040/01/547.jpg"></pb><emph type="italics"></emph>Sphere,<emph.end type="italics"></emph.end> diſorders the Period of the Inferiour.</cell><cell>102</cell></row><row><cell>The <emph type="italics"></emph>Sphere<emph.end type="italics"></emph.end> 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"></emph>Sphere.<emph.end type="italics"></emph.end></cell><cell>182</cell></row><row><cell>A Demonſtration that the <emph type="italics"></emph>Sphere<emph.end type="italics"></emph.end> toucheth the Plane but in one point.</cell><cell>183</cell></row><row><cell>Why the <emph type="italics"></emph>Sphere<emph.end type="italics"></emph.end> in abſtract 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"></emph>Sphere<emph.end type="italics"></emph.end> onely, but belongeth to all Curved Figures.</cell><cell>185</cell></row><row><cell>In a Moveable <emph type="italics"></emph>Sphere<emph.end type="italics"></emph.end> it ſeemeth more reaſonable that its Centre be ſtable, than any of its parts.</cell><cell>300</cell></row><row><cell>SPHERE of <emph type="italics"></emph>Activity.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>The <emph type="italics"></emph>Sphere of Activity<emph.end type="italics"></emph.end> greater in Celeſtial Bodies than in Elimentary.</cell><cell>59</cell></row><row><cell>STARRY SPHERE.</cell><cell></cell></row><row><cell>Wearineſſe more to be feared in the <emph type="italics"></emph>Starry Sphere<emph.end type="italics"></emph.end>than in the Terreſtrial Globe.</cell><cell>245</cell></row><row><cell>By the proportion of Jupiter and of Mars, the <emph type="italics"></emph>Starry Sphere<emph.end type="italics"></emph.end> is found to be yet more remote.</cell><cell>331</cell></row><row><cell>Vanity of thoſe mens diſcourſe, who argue the <emph type="italics"></emph>Starry Sphere<emph.end type="italics"></emph.end> to be too vaſt in the Copernican Hypotheſis.</cell><cell>335</cell></row><row><cell>The whole <emph type="italics"></emph>Starry Sphere<emph.end type="italics"></emph.end> beheld from a great diſtance, might appear as ſmall as one ſingle Star.</cell><cell>335</cell></row><row><cell>SPHERICAL.</cell><cell></cell></row><row><cell>The <emph type="italics"></emph>Spherical<emph.end type="italics"></emph.end> Figure is eaſier to be made than any other.</cell><cell>186</cell></row><row><cell><emph type="italics"></emph>Spherical<emph.end type="italics"></emph.end> Figures of ſundry Magnitudes, may be made with one ſole Inſtrument.</cell><cell>187</cell></row><row><cell>SPIRIT.</cell><cell></cell></row><row><cell>The <emph type="italics"></emph>Spirit<emph.end type="italics"></emph.end> had no intent to teach us whether the Earth moveth or ſtandeth ſtill, as nothing concerning our Salvation.</cell><cell>436</cell></row><row><cell>SOLAR SPOTS.</cell><cell></cell></row><row><cell><emph type="italics"></emph>Spots<emph.end type="italics"></emph.end> generate and diſſolve in the face of the Sun.</cell><cell>38</cell></row><row><cell>Sundry Opinions touching the <emph type="italics"></emph>Solar Spots.<emph.end type="italics"></emph.end></cell><cell>39</cell></row><row><cell>An Argument that neceſſarily proveth the <emph type="italics"></emph>Solar Spots<emph.end type="italics"></emph.end> to generate and diſſolve.</cell><cell>40</cell></row><row><cell>A concluſive Demonſtration to prove that the <emph type="italics"></emph>Spots<emph.end type="italics"></emph.end> are contiguous to the Body of the Sun.</cell><cell>41</cell></row><row><cell>The Motion of the <emph type="italics"></emph>Spots<emph.end type="italics"></emph.end> towards the Circumcumference of the Sun appears ſlow.</cell><cell>41</cell></row><row><cell>The Figure of the <emph type="italics"></emph>Spots<emph.end type="italics"></emph.end> towards the Circumference of the Suns Diſcus, appear narrow, and why.</cell><cell>41</cell></row><row><cell>The <emph type="italics"></emph>Solar Spots<emph.end type="italics"></emph.end> are not Spherical, but flat, like thin plates.</cell><cell>41</cell></row><row><cell>The Hiſtory of the proceedings of the Academian for a long time about the Obſervation of the <emph type="italics"></emph>Solas Spots.<emph.end type="italics"></emph.end></cell><cell>312</cell></row><row><cell>A conceit that ſuddenly came into the mind of our Academian concerning the great conſequence that followeth upon the Motion of the <emph type="italics"></emph>Solar Spots.<emph.end type="italics"></emph.end></cell><cell>314</cell></row><row><cell>Extravagant Mutations to be obſerved in the Motions of the <emph type="italics"></emph>Solar Spots<emph.end type="italics"></emph.end> foreſeen by the Academick, in caſe the Earth had the Annual Motion.</cell><cell>314</cell></row><row><cell>The firſt Accident to be obſerved in the Motion of the <emph type="italics"></emph>Solar Spots,<emph.end type="italics"></emph.end> and conſequently all the reſt, explained.</cell><cell>315</cell></row><row><cell>The events being obſerved were anſwerable to the Predictions touching theſe <emph type="italics"></emph>Spots.<emph.end type="italics"></emph.end></cell><cell>318</cell></row><row><cell>Though the Annual Motion aſſigned to the Earth, anſwereth to the Phænomena of the <emph type="italics"></emph>Solar Spots,<emph.end type="italics"></emph.end> yet doth it not follow by converſion, that from the Phænomena of the <emph type="italics"></emph>Spots<emph.end type="italics"></emph.end>one may inferre the Annual Motion to belong to the Earth.</cell><cell>319</cell></row><row><cell>The Pure Peripatetick Philoſophers will laugh at the <emph type="italics"></emph>Spots<emph.end type="italics"></emph.end> and their Phænomena, as the Illuſions of the Chriſtals in the Teleſcope.</cell><cell>319</cell></row><row><cell>The <emph type="italics"></emph>Solar Spots<emph.end type="italics"></emph.end> of Galileo.</cell><cell>494</cell></row><row><cell>STAR and <emph type="italics"></emph>Stars.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>The <emph type="italics"></emph>Stars<emph.end type="italics"></emph.end> infinitely ſurpaſſe the reſt of Heaven in Denſity.</cell><cell>30</cell></row><row><cell>It is no leſſe impoſſible for a <emph type="italics"></emph>Star<emph.end type="italics"></emph.end> to corrupt, than the whole Terreſtrial Globe.</cell><cell>37</cell></row><row><cell>New <emph type="italics"></emph>Stars<emph.end type="italics"></emph.end> diſcovered in Heaven.</cell><cell>38</cell></row><row><cell>The ſmall Body of a <emph type="italics"></emph>Star<emph.end type="italics"></emph.end> fringed about with Rays, appeareth very much bigger than plain, naked, and in its native Clarity.</cell><cell>61</cell></row><row><cell>An eaſie Experiment that ſheweth the encreaſe in the <emph type="italics"></emph>Stars,<emph.end type="italics"></emph.end> by means of the Adventitious Rays.</cell><cell>305</cell></row><row><cell>A <emph type="italics"></emph>Star<emph.end type="italics"></emph.end> of the Sixth Magnitude ſuppoſed by Tycho and Scheiner an hundred and ſix Millions of times bigger than needs.</cell><cell>326</cell></row><row><cell>A common errour of all Aſtronomers touching the Magnitude of the <emph type="italics"></emph>Stars.<emph.end type="italics"></emph.end></cell><cell>326</cell></row><pb xlink:href="040/01/548.jpg"></pb><row><cell> <gap></gap>2 Full PAGES MISSING<pb xlink:href="040/01/549.jpg"></pb><pb xlink:href="040/01/550.jpg"></pb><gap></gap><pb xlink:href="040/01/551.jpg"></pb> a falſe one, none.</cell><cell>112. 245</cell></row><row><cell>TRUTH, and <emph type="italics"></emph>Truths.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>Untruths cannot be Demonſtrated as <emph type="italics"></emph>Truths<emph.end type="italics"></emph.end>are.</cell><cell>112</cell></row><row><cell>The <emph type="italics"></emph>Truth<emph.end type="italics"></emph.end> ſometimes gains ſtrength by Contradiction.</cell><cell>181</cell></row><row><cell><emph type="italics"></emph>Truth<emph.end type="italics"></emph.end> hath not ſo little light as not to be diſcovered amongſt the Umbrages of Falſhoods.</cell><cell>384</cell></row><row><cell>TYCHO.</cell><cell></cell></row><row><cell>The Argument of <emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end> grounded upon a falſe Hypotheſis.</cell><cell>324</cell></row><row><cell><emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end> and his Followers never attempted to ſee whether there were any Phænomena in the Firmament for or againſt the Annual Motion.</cell><cell>337</cell></row><row><cell><emph type="italics"></emph>Tycho<emph.end type="italics"></emph.end> and others argue againſt 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"></emph>Velocity<emph.end type="italics"></emph.end> ſutable with Circular Motion.</cell><cell>12</cell></row><row><cell>Nature doth not immediately conferre a determinate degree of <emph type="italics"></emph>Velocity,<emph.end type="italics"></emph.end> although She could.</cell><cell>12</cell></row><row><cell>The <emph type="italics"></emph>Velocity<emph.end type="italics"></emph.end> by the inclining plane equal to the <emph type="italics"></emph>Velocity<emph.end type="italics"></emph.end> by the Perpendicular, and the Motion by the Perpendicular ſwifter than by the inclining plane.</cell><cell>14</cell></row><row><cell><emph type="italics"></emph>Velocities<emph.end type="italics"></emph.end> are ſaid to be equal, when the Spaces paſſed are proportionate to their times.</cell><cell>15</cell></row><row><cell>The greater <emph type="italics"></emph>Velocity<emph.end type="italics"></emph.end> exactly compenſates 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"></emph>Venus<emph.end type="italics"></emph.end> argueth its Motion to be about the Sun.</cell><cell>295</cell></row><row><cell><emph type="italics"></emph>Veuus<emph.end type="italics"></emph.end> very great towards the Veſpertine Conjunction, and very ſmall towards the Macutine.</cell><cell>297</cell></row><row><cell><emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> neceſſarily proved to move about the Sun.</cell><cell>298</cell></row><row><cell>The Phænomena of <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> appear contrary to the Syſtem of Copernicus.</cell><cell>302</cell></row><row><cell>Another Difficulty raiſed by <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> againſt Copernicus.</cell><cell>302</cell></row><row><cell><emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> according to Copernicus either lucid in it ſelf, or a tranſparent ſubſtance.</cell><cell>302</cell></row><row><cell>The Reaſon why <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> and Mars do not appear to vary Magnitude ſo much as is requiſite.</cell><cell>303</cell></row><row><cell>A ſecond Reaſon of the ſmall apparent encreale of <emph type="italics"></emph>Venus.<emph.end type="italics"></emph.end></cell><cell>306</cell></row><row><cell><emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> renders the Errour of Aſtronomers in determining the Magnitude of Stars inexcuſeable.</cell><cell>327</cell></row><row><cell>VESSEL.</cell><cell></cell></row><row><cell>Of the Motion of Water in a <emph type="italics"></emph>Veſſel.<emph.end type="italics"></emph.end> Vide <emph type="italics"></emph>Water.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>UNDERSTAND, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>Man <emph type="italics"></emph>Underſtandeth<emph.end type="italics"></emph.end> very much <emph type="italics"></emph>intenſive,<emph.end type="italics"></emph.end> but little <emph type="italics"></emph>extenſive.<emph.end type="italics"></emph.end></cell><cell>86</cell></row><row><cell>Humane <emph type="italics"></emph>Uuderſtanding<emph.end type="italics"></emph.end> operates by Ratiocination.</cell><cell>87</cell></row><row><cell>UNIVERSE.</cell><cell></cell></row><row><cell>The Conſtitution of the <emph type="italics"></emph>Uuiverſe<emph.end type="italics"></emph.end> is one of the Nobleſt Problems a Man can ſtudy.</cell><cell>187</cell></row><row><cell>The Centre of the <emph type="italics"></emph>Univerſe<emph.end type="italics"></emph.end> according to Ariſtotle is that Polnt about which the Celeſtial Spheres do revolve.</cell><cell>294</cell></row><row><cell>Which ought to be accounted the Sphere of the <emph type="italics"></emph>Univerſe.<emph.end type="italics"></emph.end></cell><cell>299</cell></row><row><cell>It is a great raſhneſſe to cenſure that to be ſuperfluous in the <emph type="italics"></emph>Univerſe<emph.end type="italics"></emph.end> which we do not perceive to be made for us.</cell><cell>334</cell></row><row><cell>VURSTITIUS.</cell><cell></cell></row><row><cell>Chriſtianus <emph type="italics"></emph>Vurſtitius<emph.end type="italics"></emph.end> 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"></emph>Water,<emph.end type="italics"></emph.end>could never fancie to himſelf Ships and Fiſhes.</cell><cell>47</cell></row><row><cell>An Experiment to prove the Reflection of <emph type="italics"></emph>Water<emph.end type="italics"></emph.end> lefs bright than that of the Land.</cell><cell>81</cell></row><row><cell>The Motion of the <emph type="italics"></emph>Water<emph.end type="italics"></emph.end> in Ebbing and Flowing, not interrupted by Reſt.</cell><cell>251</cell></row><row><cell>The vain Argumentation of ſome, to prove the Element of <emph type="italics"></emph>Water<emph.end type="italics"></emph.end> to be of a Spherical Superficies.</cell><cell>377</cell></row><pb xlink:href="040/01/552.jpg"></pb><row><cell>The Progreſſive and uneven Motion makes the <emph type="italics"></emph>Water<emph.end type="italics"></emph.end> in a Veſſel to run to and fro.</cell><cell>387</cell></row><row><cell>The Several Motions in the conteining Veſſel, may make the conteined <emph type="italics"></emph>Water<emph.end type="italics"></emph.end> to riſe and fall.</cell><cell>387</cell></row><row><cell>The <emph type="italics"></emph>Water<emph.end type="italics"></emph.end> raiſed in one end of the Veſſel returneth it ſelf to <emph type="italics"></emph>Æquilibrium.<emph.end type="italics"></emph.end></cell><cell>391</cell></row><row><cell>In the ſhorter Veſſels the Undulations of <emph type="italics"></emph>Waters<emph.end type="italics"></emph.end> are more frequent.</cell><cell>391</cell></row><row><cell>The greater profundity maketh the Undulations of <emph type="italics"></emph>Water<emph.end type="italics"></emph.end> the more frequent.</cell><cell>391</cell></row><row><cell>Why in narrow places the Courſe of the <emph type="italics"></emph>Waters<emph.end type="italics"></emph.end> is ſwifter than in larger.</cell><cell>396</cell></row><row><cell>The cauſe why in ſome narrow Chanels, we ſee the Sea<emph type="italics"></emph>Waters<emph.end type="italics"></emph.end> run alwayes one way.</cell><cell>398</cell></row><row><cell>The <emph type="italics"></emph>Water<emph.end type="italics"></emph.end> more apt to conſerve an Impetus conceived than the Air.</cell><cell>400</cell></row><row><cell>The Motion of the <emph type="italics"></emph>Water<emph.end type="italics"></emph.end> dependeth on the Motion of Heaven.</cell><cell>404</cell></row><row><cell>WEIGHTS.</cell><cell></cell></row><row><cell>Its queſtionable whether Deſcending <emph type="italics"></emph>Weights<emph.end type="italics"></emph.end>move in a Right Line.</cell><cell>21</cell></row><row><cell>WEST.</cell><cell></cell></row><row><cell>The Courſe to the <emph type="italics"></emph>West<emph.end type="italics"></emph.end> India's eaſie, the return difficult.</cell><cell>402</cell></row><row><cell>WINDE.</cell><cell></cell></row><row><cell>Conſtant Gales of <emph type="italics"></emph>Winde<emph.end type="italics"></emph.end> within the Tropicks blow towards the Weſt.</cell><cell>402</cell></row><row><cell><emph type="italics"></emph>Windes<emph.end type="italics"></emph.end> from the Land, make rough the Seas.</cell><cell>402</cell></row><row><cell>WISDOME <emph type="italics"></emph>Divine.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Divine Wiſdome<emph.end type="italics"></emph.end> infinitely infinite.</cell><cell>85</cell></row><row><cell>The Diſcourſes which Humane Reaſon makes in time, the <emph type="italics"></emph>Divine Wiſdom<emph.end type="italics"></emph.end> reſolveth in a Moment, that is hath them alwayes preſent.</cell><cell>87</cell></row><row><cell>WIT.</cell><cell></cell></row><row><cell>The <emph type="italics"></emph>Wit<emph.end type="italics"></emph.end> of Man admirably acute.</cell><cell>87</cell></row><row><cell>The Puſilanimity of Popular <emph type="italics"></emph>Wits.<emph.end type="italics"></emph.end></cell><cell>364</cell></row><row><cell>Poctick <emph type="italics"></emph>Wits<emph.end type="italics"></emph.end> of two kinds.</cell><cell>384</cell></row><row><cell>WORLD.</cell><cell></cell></row><row><cell><emph type="italics"></emph>World.<emph.end type="italics"></emph.end> Vide <emph type="italics"></emph>Univerſe.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>The <emph type="italics"></emph>Worlds<emph.end type="italics"></emph.end> parts are according to Ariſtotle two, Celeſtial and Elementary, contrary to each other.</cell><cell>6</cell></row><row><cell>The <emph type="italics"></emph>World<emph.end type="italics"></emph.end> ſuppoſed by the Anthour [Galileo] to be perfectly Ordinate.</cell><cell>10</cell></row><row><cell>The Senſible <emph type="italics"></emph>World.<emph.end type="italics"></emph.end></cell><cell>96</cell></row><row><cell>It hath not been hitherto proved by any whether the <emph type="italics"></emph>World<emph.end type="italics"></emph.end> be finite or infinite.</cell><cell>293</cell></row><row><cell>If the Centre of the <emph type="italics"></emph>World<emph.end type="italics"></emph.end> be the ſame 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"></emph>Write<emph.end type="italics"></emph.end> what they underſtand not, and therefore underſtand not what they <emph type="italics"></emph>Write.<emph.end type="italics"></emph.end></cell><cell>63</cell></row><row><cell>The Invention of <emph type="italics"></emph>Writing<emph.end type="italics"></emph.end> 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"></emph>Years<emph.end type="italics"></emph.end> beginning and ending, which Ptolomy and his Followers could never poſitively aſſign, is exactly determined by the Copernican Hypotheſis.</cell><cell>469</cell></row></table><p type="head"> <s><emph type="italics"></emph>THE END OF THE TABLE.<emph.end type="italics"></emph.end></s></p></chap><pb xlink:href="040/01/553.jpg"></pb><pb xlink:href="040/01/554.jpg"></pb><chap><p type="head"> <s>The ERRATA of the <emph type="italics"></emph>firſt<emph.end type="italics"></emph.end> PART of the <emph type="italics"></emph>firſt<emph.end type="italics"></emph.end> TOME.</s></p><p type="main"> <s>line 31. <emph type="italics"></emph>for<emph.end type="italics"></emph.end> where leave, <emph type="italics"></emph>read<emph.end type="italics"></emph.end> why omit. </s> <s>p 3, l 32, only for. </s> <s>p 5, l 8, Dimenſions of a Superficies, </s> <s><emph type="italics"></emph>ibid.<emph.end type="italics"></emph.end> l 15, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> line <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> thread, </s> <s>l <emph type="italics"></emph>ult.<emph.end type="italics"></emph.end><lb></lb> <emph type="italics"></emph>for<emph.end type="italics"></emph.end> on all ſides, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> every way. </s> <s>p 6, l 41, by neceſſary. </s> <s>p 9, l 15, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> Medium, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Way. </s> <s>l 40. <emph type="italics"></emph>for<emph.end type="italics"></emph.end> ſome <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> ſave, <emph type="italics"></emph></s> <s>marg<emph.end type="italics"></emph.end> and the. </s> <s>p 10, l 1. farther be <lb></lb>l 28. intigrall, </s> <s>l 44, prefixed. </s> <s>p 11, 19, oppoſitely might have. </s> <s>l 10, conſtituted Bodie. </s> <s>l 11, ſo are. </s> <s>l 15, would only enſue. </s> <s>p 12, l 28, <lb></lb>doth, </s> <s>p 14, l 25. inclined plane. </s> <s>l 16. p 34, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> by <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> through. </s> <s>p 17, l 20, beyond T, p 19, l 3, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> of. </s> <s>l 6, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> of aſſigning, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> that he <lb></lb>aſſigned. </s> <s>l 9, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> and with the &c. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> and given them the intended inclinations of moving thence towards the Centre. </s> <s>l 15, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> Orbes, <lb></lb><emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Globes, l 38, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> truly <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> exactly. </s> <s>p 21, l 36, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> another, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> one. </s> <s>p 22, l 19, that <emph type="italics"></emph>contra,<emph.end type="italics"></emph.end></s> <s> l 20. <emph type="italics"></emph>for<emph.end type="italics"></emph.end> than contend with you, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> than as being. <lb></lb>convinced by the ſtrength of your Reaſons. </s> <s>p 23, 18. <emph type="italics"></emph>for<emph.end type="italics"></emph.end> to diſcover, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> to be ſhowne, </s> <s>l 17, ſuppoſing. </s> <s>l 22, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> follow, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> hit upon. </s> <s>l 52, as <lb></lb>you well underſtand. </s> <s>p 24, l 17, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> thither <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> there. </s> <s>l 33, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Earth aſcend and deſcend. </s> <s>p 25, l 7, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> quality <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> power. </s> <s>l <emph type="italics"></emph>ult.<emph.end type="italics"></emph.end> part. </s> <s>p 26, <lb></lb>l 9. contraries; But of contraries the motions are contrary, </s> <s>l 32, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> beſides <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> in caſe. </s> <s>p 27, l 2, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> repeat, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> go over. </s> <s>l 3. <emph type="italics"></emph>for<emph.end type="italics"></emph.end> reaſſume, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end><lb></lb>repeat. </s> <s> p 29, l <emph type="italics"></emph>ult. for<emph.end type="italics"></emph.end> ſay <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> mean. </s> <s>l 18, reſide. </s> <s>l 39, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> may. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> can. </s> <s>p 32, l 1, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> others, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> one. </s> <s>l 15, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> the beſt we can whether, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> whats to <lb></lb>be done with it in caſe that. </s> <s>l 37, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> they m<emph type="italics"></emph>u<emph.end type="italics"></emph.end>ſt grant us, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> let it be granted, p 32, l 5, what. </s> <s>l 12, unalterable. </s> <s>p 37, l 28, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> confront <emph type="italics"></emph>r.<emph.end type="italics"></emph.end><lb></lb> preferre. </s> <s>l 37, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> bethink, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> think, p 41. l 39, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> obſerve them to be hid, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> observe that he hath concealed from you thoſe that are <lb></lb>diſſolved. </s> <s>p 42, l 17. which experience and ſenſe. </s> <s>l 17, unalterable. </s> <s>p 43, l 15, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> more <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> leſſe. </s> <s>p 44. l 4, Globes? </s> <s>p 46, l 18, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> liquifie, <lb></lb><emph type="italics"></emph>for<emph.end type="italics"></emph.end> them <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> it, p 49. l 11, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> thing <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> thinke. </s> <s>p 50, l 19. <emph type="italics"></emph>and<emph.end type="italics"></emph.end> p 51, l 3, Superficies p 53, l 14, Truths. </s> <s>p 54, l 38, be ſolid. </s> <s>p 55, l 15, <lb></lb>ult. </s> <s>l 36, of the. </s> <s>l 40, <emph type="italics"></emph>omit<emph.end type="italics"></emph.end> ſo. </s> <s>p 57, l 44, maketh, p 59, l 1, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> that <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> the. </s> <s>p 61, l 5, thoſe. </s> <s>p 62, l 6, diſperſe. </s> <s>p 64, l 13, evene. </s> <s>l 26, <lb></lb>change. </s> <s>l 37, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> of, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> in. </s> <s>l 42, acquieſſe. </s> <s>p 65. l 20, happeneth. </s> <s>p 67, l 13, Solutions, l 15, viſive. </s> <s>p 69, l 18, wood?. l 31, wayes,. p 70, l 7, <lb></lb>concluſion is very good for, l 10, ſhould we, l 11, would alter. </s> <s>l 12, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> or, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> and, l 22, Propoſitions, l 29, Protubrances, l 41, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> their, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> its. </s> <s><lb></lb>p. 71, l 5, by one <emph type="italics"></emph>dele<emph.end type="italics"></emph.end>;. </s> <s>l 12, of the Moon, l 37, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> in youes, &c. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> with your Opacity and Perſpicuity. </s> <s>p 72, l 20, what time do. <lb></lb><emph type="italics"></emph>for<emph.end type="italics"></emph.end> p 74. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> 73. l 26, yea and more. </s> <s>p 76, l 18, <emph type="italics"></emph>Vitellio.<emph.end type="italics"></emph.end> p 81, l 6, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> more. </s> <s>p 81, l 25, of a fluid matter, l 29, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> ſentence <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Centre. <emph type="italics"></emph>for<emph.end type="italics"></emph.end> on <lb></lb><emph type="italics"></emph>r.<emph.end type="italics"></emph.end> one.</s> <s> p 85, l 39, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> make raiſins, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> make the kernels, p 86, l 29 <emph type="italics"></emph>intenſivè,<emph.end type="italics"></emph.end> p 87, l 17, the which, neither,. p. </s> <s>88. l. </s> <s>8. <emph type="italics"></emph>Raffaelio,<emph.end type="italics"></emph.end> or <emph type="italics"></emph>a Tiziano<emph.end type="italics"></emph.end>?<lb></lb></s> <s>p 90. l 20. <emph type="italics"></emph>for<emph.end type="italics"></emph.end> receſſe <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> remote. </s> <s>p 91. l 11, curioſity. </s> <s>p 94. l 41. reputation. </s> <s>p 101, l 18, altercations. </s> <s>p 107, l 29, ſtar. </s> <s>p 104, l 32, <lb></lb>naturally. </s> <s>p 107, l 26, <emph type="italics"></emph>accidens.<emph.end type="italics"></emph.end> p 111, l 24, ſelfe, l 18, third teime, p. </s> <s>113, l 21, Guns. </s> <s>p 111, l 3, tranſported, l. </s> <s>7, we paſſe. </s> <s>p 116, l 15, <lb></lb>otherwiſe <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> any wayes. </s> <s>p 118, <emph type="italics"></emph>Marg.<emph.end type="italics"></emph.end> rendred, p 128, 35, aſcending?. p 130, l 42, as being the. </s> <s>p 131, l 19, occaſion, l 30, ſeparated. <lb></lb></s> <s>3, l 11, <emph type="italics"></emph>pendula.<emph.end type="italics"></emph.end> p 134, ll 20, arows? </s> <s>p 135, l 12, time to prove it,. p 137, l 2, <emph type="italics"></emph>and<emph.end type="italics"></emph.end> 6, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> ball, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> bowl. </s> <s>p 142, l 17, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> very. </s> <s>p 143, l 3, <lb></lb>l, l 4, liberty. </s> <s>p 144, l 8, find out. </s> <s>p 145, l 21, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end>;. </s> <s>p 147, l 9, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> that. </s> <s>p 148, l 7, which ſo far exceeds their flight, l 33, is the. </s> <s>l <emph type="italics"></emph>ult.<emph.end type="italics"></emph.end><lb></lb>moment of. </s> <s>p 149, l 44, <emph type="italics"></emph>Tycho.<emph.end type="italics"></emph.end> p 153, l 21, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> that is <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> or. </s> <s>p 154. 3. <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> of. </s> <s>p 157, l 7, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> to the, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> by the. </s> <s>p 161, l 15, fifteen ſeconds: <lb></lb></s> <s> <emph type="italics"></emph>Marg<emph.end type="italics"></emph.end> in its reſt. </s> <s>p 162, l 13, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> motion <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Immobility. </s> <s>p. </s> <s>163, l 30, like. </s> <s>p 164, l 22, ſeeing. </s> <s>l 31, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> as great as, <emph type="italics"></emph>r<emph.end type="italics"></emph.end> no greater than. </s> <s>166, <lb></lb>l 24, poope, l 40, Aufractions. </s> <s>p 175, l 26, ſpeak. </s> <s>p 177, l 13, contraſt. </s> <s>p 184, l 15, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> becauſe it cannot, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> why may it not?. p 185, l 6, 7, is <lb></lb><emph type="italics"></emph>Marg<emph.end type="italics"></emph.end> Sphere. </s> <s>p 188. l 19 freind. </s> <s>p 190, l 28. <emph type="italics"></emph>for<emph.end type="italics"></emph.end> give leave, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> permit. </s> <s>p 191, l 17, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> on, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> one. </s> <s>l 31. ſee you. </s> <s>p 193, l 21, <emph type="italics"></emph>Vertigo?<emph.end type="italics"></emph.end> <lb></lb>p 197, l 1, ſubject. </s> <s>p 200, l 36, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> that, p 201, l 21, pace, l 35, will profeſſe, with. </s> <s>p 203, l 6, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> ſo, l 31, diminiſheth, l 33, degrees. </s> <s>p <lb></lb>104, l 14, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> and. </s> <s>p 206, l 19, and 44. <emph type="italics"></emph>Pendula,<emph.end type="italics"></emph.end> </s> <s>p 212, l 14, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> it. </s> <s>p 216, l <emph type="italics"></emph>ult. propieres.<emph.end type="italics"></emph.end></s> <s> p 219, 10, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> to theſe that, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> ſeeing that to theſe. <lb></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"></emph>for<emph.end type="italics"></emph.end> that to <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> that for. </s> <s>225, 25, invented it, </s> <s>227, 9, that the </s> <s>229, l 6, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end><lb></lb>either. </s> <s>l 18, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> and wee, </s> <s>l 45, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> From, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> 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"></emph>for<emph.end type="italics"></emph.end> were of, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end><lb></lb>were with. </s> <s>p 233, l 6, the error, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 14, revolve. </s> <s>p 240, l 40, virtue; amongſt. </s> <s>l 41, <emph type="italics"></emph>for Mars, &c. r. Mars.<emph.end type="italics"></emph.end> </s> <s>l 44, more ſuiting. </s> <s>p 224, l 44, <lb></lb> <emph type="italics"></emph>r.<emph.end type="italics"></emph.end>contrary. </s> <s>p 245, l 10, interfere. </s> <s>p 250, l 44, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> 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, ſelfe. </s> <s>p 259, l 9, <lb></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, ſame that you do, </s> <s><emph type="italics"></emph>line<emph.end type="italics"></emph.end> 18, rather than. </s> <s>p 266, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 8, I make. </s> <s>p 267, <lb></lb><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 24 <emph type="italics"></emph>Buſchins.<emph.end type="italics"></emph.end></s> <s> p 266, <emph type="italics"></emph>l 16, r. 40 min. </s> <s>pr.<emph.end type="italics"></emph.end> p 272, <emph type="italics"></emph>l 20, r.<emph.end type="italics"></emph.end> B G, is 42657. </s> <s>p 272. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 29, of the ^{*} 67^{d} 36. </s> <s>p 274, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 32, every. </s> <s>p 275. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 25, halfe ſo<lb></lb></s> <s>p 277, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 18, and 37, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> B.D. Chord. </s> <s>p 281, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 30. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> 540. 540 00. </s> <s>p. 285, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> 8. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> been the, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 38, ſay of: </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 39, <emph type="italics"></emph>circà.<emph.end type="italics"></emph.end> </s> <s>p 286, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 24, than: BP, PB. <lb></lb>being bigger than P D. </s> <s>p 287, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 4, ſee, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 33, 582 100000. </s> <s>p 288, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 21, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> 276, <expan abbr="q.">que</expan></s> <s>p 289 <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 32, ſpake. </s> <s>p, 290, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> p. 274. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> 290. </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 12. they kept. <lb></lb></s> <s>p 291, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 8, uncertain, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 37, Braces, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 42, breadth. </s> <s>p 292, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 6. <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> the other ar. </s> <s>p 244. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 23, Peripateticks , </s> <s>p 295. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 1. figure, and morning<lb></lb></s> <s>p 297, l 11, oppoſition, </s> <s><emph type="italics"></emph>marg r. veſpertine conjunction.<emph.end type="italics"></emph.end> </s> <s>p 298. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 23, argument and. </s> <s>p 301, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 1, your, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 30, are yet p. </s> <s>304, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 9, and allured, </s> <s><emph type="italics"></emph>marg<lb></lb> enlarged ſoe.<emph.end type="italics"></emph.end> p 305, l 27, we leave. </s> <s>p 306, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 25, it ought. </s> <s>p 307, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> 330, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> 307. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 10, digreſſions, </s> <s><emph type="italics"></emph>l 16, diſcus. </s> <s>l<emph.end type="italics"></emph.end> 32, years, together, with, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 34, <lb></lb>Jovial, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 41, alwayes all <emph type="italics"></emph>lucid.<emph.end type="italics"></emph.end> </s> <s>p 308, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> 394, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> 308. </s> <s>p 309, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> 395, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> 309. </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> in it. </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 34, ſole and ſingle </s> <s>p 310, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 11, CD. DE. EF. </s> <s>p 312. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 19, <lb></lb>shaking off,</s> <s> <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 19, matters that. </s> <s>p 314, <emph type="italics"></emph>l 8, &<emph.end type="italics"></emph.end> 10, Ecliptick. </s> <s>in 316, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 5, nor, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> FG: whereupon </s> <s>p 319, l 7, circuition, <lb></lb></s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 31, that he hath. </s> <s>p 220, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 31, extreme Terminator. </s> <s>p 124. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 30, Solar Globe,</s> <s> p 322. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 40. thoſe Phyſical and. </s> <s>p 324, l 20, ſaith that, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 29 <lb></lb><emph type="italics"></emph>Copernicus<emph.end type="italics"></emph.end> ſaith. </s> <s>p 329, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 39, this ſecond. </s> <s><emph type="italics"></emph>marg.<emph.end type="italics"></emph.end> to be the ſame. </s> <s>p. 332, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 24, below it. </s> <s>p 333, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 17, ſtar, that. </s> <s>p 335, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 24, ſtar now, <emph type="italics"></emph>marg. </s> <s>called <lb></lb>small in.<emph.end type="italics"></emph.end> </s> <s>p 338, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 41, Into this </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 24, now, no not for an.</s> <s> <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 28, follow thereupon,</s> <s> <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 31, point equidiſtant. </s> <s>p 341, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 10, out <lb></lb>till</s> <s> <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 18, yet the force (which. </s> <s>p 342, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 25, Orbe; ſo, </s> <s>p 343, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 21, be ſeen, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 33, Latitudes and, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 38, ours, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 91, greater varieth. </s> <s>p 344, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 39, and, <lb></lb>that. </s> <s>p 345. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 23. <emph type="italics"></emph>Cancer<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Capricorn,<emph.end type="italics"></emph.end> </s> <s>p 347, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 1, feinedly, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 30, Stars are. </s> <s>p 349, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 35, [in Fig. </s> <s>9.]. p 350, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 42, knew. </s> <s>p 355. <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 12, Weſt to <lb></lb>ſt. </s> <s>p 356, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 15, G N. </s> <s>p 360, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 38, circle l K. </s> <s>p 382, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 30, the propenſion. </s> <s><emph type="italics"></emph>marg.<emph.end type="italics"></emph.end> librated body. </s> <s>p 363, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 3, Experiment, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 7, baſon ſhall. </s> <s>p 364, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 2 of <emph type="italics"></emph>William, </s> <s>l<emph.end type="italics"></emph.end> 17, them as, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 38, that, think. </s> <s>p 366, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 14, <emph type="italics"></emph>and<emph.end type="italics"></emph.end> 39, ſtived. </s> <s>p 367, <emph type="italics"></emph>l.<emph.end type="italics"></emph.end> that this, </s> <s>p 370, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 3, do that for natural, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 12, appli<lb></lb>cation of a perſon to. </s> <s>p 372, <emph type="italics"></emph>l ult.<emph.end type="italics"></emph.end> thoſe. </s> <s>p 373, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 17, than if, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 39, Launes, Woods, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 43, whither, </s> <s>p 374, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 16, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> ſelfe. </s> <s>p 375, l 28. ſtreight <lb></lb>motion is peculiar, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 39, and an. </s> <s>p 376, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 5, (For, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 6, together, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 12, granted ought, </s> <s>p 380, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 1, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> hath. </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 5, a mutual, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 6, <emph type="italics"></emph>Indices<emph.end type="italics"></emph.end>, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 45, admit. <lb></lb></s> <s>p 381, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 36, which with, </s> <s><emph type="italics"></emph>ibid. dele<emph.end type="italics"></emph.end> with. </s> <s>p 382, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 3, place), </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 13, extremities. </s> <s>p 384, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 3. write of, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 29, SALU. </s> <s>p 385, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 18, more, in </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 13, againſt <lb></lb>the</s> <s> <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 24, ſwagg, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 37, reply, </s> <s>p 386, l 16, as if it. </s> <s>p. 387, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 33, Water, conteined. </s> <s>p 389, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 43, at the. </s> <s>p 290 <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 22, that the diurnall litle. </s> <s>p 391, <lb></lb>11, grow even, it, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 13, <emph type="italics"></emph>Æquilibrium,<emph.end type="italics"></emph.end> but. </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 392, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 35, unitedly, equally. </s> <s>p 394, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 16, velocity, when. </s> <s>p 396, l 11, <emph type="italics"></emph>Sardigna<emph.end type="italics"></emph.end> </s> <s>p 397, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 38, returns. <lb></lb></s> <s>p399, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 30, is free. </s> <s>p 401, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 10, pound you, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 13, and argument. </s> <s>p 402, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 25, alledged that,</s> <s> <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 37, interruptions for. </s> <s>p 405, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 19, contact, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 37, <lb></lb>at in a Sea only which, <emph type="italics"></emph>l penult.<emph.end type="italics"></emph.end> ordinate. </s> <s>p 205, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 38, concern. </s> <s>p 407, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 3, for ſpeculation and the, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 8, light, with, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 23, at thoſe, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 28, <lb></lb>showwings, conſiſteth, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 42, from the, </s> <s><emph type="italics"></emph>l penult,<emph.end type="italics"></emph.end> ſubſtractions that, </s> <s><emph type="italics"></emph>l ult.<emph.end type="italics"></emph.end> maketh to or from. </s> <s>p 48, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 4, proportion in,</s> <s> <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 14, leſſer, ſo as that, </s> <s>p <lb></lb>409, l 12, ſwift, </s> <s>p 411, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 24 circles </s> <s><emph type="italics"></emph>marg, pendula,<emph.end type="italics"></emph.end> </s> <s>p 412, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 27, ſubtend,</s> <s> p 413, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 14, projected, l 24, conſume, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 93, is, contracted, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 34, of in the <lb></lb></s> <s>p 441, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 3, differs, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 5, Moon about, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 21, Orb, by. </s> <s>p 415, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 4, do either with. </s> <s>p 416, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 8, ran, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 11, Excentricks, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 13, apparitions, how, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 33, <lb></lb>cliptick divided, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 44, on account. </s> <s>p 417, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 43, on which. </s> <s>p 418, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 4, inequalities. </s> <s>p 419, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 12, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> therefore. </s> <s>p 430, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 33, Anomalies, <lb></lb><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 45, tracts. </s> <s>p 421,, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 4, Weſtern. </s> <s>p 423, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 41, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> in. </s> <s>p 425, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 16, GALILEO GALILEI</s> <s> p 428, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 32, theſe. </s> <s>p 430, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 27, from its. </s> <s>p 431, <emph type="italics"></emph>marg. <lb></lb>parum, </s> <s>ibid. marg. de iis.<emph.end type="italics"></emph.end> </s> <s>p 432, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 39, corporeal. </s> <s>p 433, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 26, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> in, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 37, appearance and. </s> <s>p 435, <emph type="italics"></emph>marg. Cœli eſſe, </s> <s>l<emph.end type="italics"></emph.end> 27, Spirit of God who <lb></lb>pake by them. </s> <s>p 430, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 34, tatling </s> <s>p 440, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 40, propoſe.</s> <s> <emph type="italics"></emph>p<emph.end type="italics"></emph.end> 443, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 2, interfere. </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 445, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 34, <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> with. </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 448, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 14, but. </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 449, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 27, make reflection. <lb></lb></s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 450, <emph type="italics"></emph>marg. & Sanctœ, </s> <s>l<emph.end type="italics"></emph.end> 42, <emph type="italics"></emph>ſtood ſtill,. </s> <s>p<emph.end type="italics"></emph.end> 451, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 37, her curſes. </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 453, <emph type="italics"></emph>marg. l<emph.end type="italics"></emph.end> 13, <emph type="italics"></emph>evoluerit. </s> <s>p<emph.end type="italics"></emph.end> 454, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 29, Lap. Your. </s> <s><emph type="italics"></emph>marg. l<emph.end type="italics"></emph.end> 6, <emph type="italics"></emph>prœſumptores, <lb></lb>ſatis, </s> <s>l<emph.end type="italics"></emph.end> 14, <emph type="italics"></emph>auctoritate non tenentur, ad deſcendendum id, quod leviſſima temeritate, &. </s> <s>p<emph.end type="italics"></emph.end> 451, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 27, or at leaſt the. </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 456, l 47, in </s> <s><emph type="italics"></emph>marg In <lb></lb>Epist ad Polycarpum. </s> <s>p<emph.end type="italics"></emph.end> 463, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 17, Stabil try. </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 454, <emph type="italics"></emph>l ult.<emph.end type="italics"></emph.end> riſe, </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 468, l 25, motion. </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 467, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 26, Sacred, is the Inquiſition. </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 469, <lb></lb><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 4, Almageſt. </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 471, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 28, <emph type="italics"></emph>Si quis. </s> <s>p<emph.end type="italics"></emph.end> 475, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 12, <emph type="italics"></emph>Credit. </s> <s>l<emph.end type="italics"></emph.end> 19, Antlents. </s> <s>p 476, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 9, Deferents, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 33, and in a word. </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 477, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 10, <emph type="italics"></emph>Nicetas. </s> <s>p<emph.end type="italics"></emph.end> 478, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 1, <lb></lb>Hypotheſes), </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 5, <emph type="italics"></emph>dece<emph.end type="italics"></emph.end> of, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 19, <emph type="italics"></emph>Galileo Galilei, </s> <s>l<emph.end type="italics"></emph.end> 21, Invinſible, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 23, who. </s> <s>p 481, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 26, or thats incommenſurate, </s> <s><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 33, vulgar mode of, </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 482<lb></lb><emph type="italics"></emph>l<emph.end type="italics"></emph.end> 7, grieveth. </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 485, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 18, ſuch that having, </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 487, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 3, ſtay: and. </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 488, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 41, Edification, leſt undecided in Holy Scripture. </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 491, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 15, <lb></lb>Alterations. </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 492, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 30, keeps, </s> <s><emph type="italics"></emph>marg Æthereal Earth. </s> <s>p<emph.end type="italics"></emph.end> 493, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 17, that that. </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 495, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 27, frees them. </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 500, <emph type="italics"></emph>marg<emph.end type="italics"></emph.end> Authors are not agreed, <lb></lb> </s> <s><emph type="italics"></emph>p<emph.end type="italics"></emph.end> 582, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> 30, Holy Ghoſt hath.</s></p> </chap> <chap> <pb xlink:href="040/01/555.jpg"></pb><pb xlink:href="040/01/556.jpg"></pb><p type="head"> <s>MATHEMATICAL <lb></lb>COLLECTIONS <lb></lb>AND <lb></lb>TRANSLATIONS: <lb></lb>THE SECOND <lb></lb>TOME.</s></p><p type="head"> <s>THE SECOND PART, <lb></lb>Containing,</s></p><p type="main"> <s>D. BENEDICTUS CASTELLUS, <emph type="italics"></emph>his DISCOURSE <lb></lb>of the MENSURATION of RUN<lb></lb>NING WATERS.<emph.end type="italics"></emph.end></s></p> </chap> <chap> <p type="main"> <s><emph type="italics"></emph>His Geometrical DEMONSTRATIONS of <lb></lb>the Meaſure of RUNNING WATERS.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>I. </s> <s>His LETTERS and CONSIDERATIONS <lb></lb>touching the Draining of FENNS, Diverſions of <lb></lb>RIVERS, &c.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>V.<emph.end type="italics"></emph.end> D. CORSINUS, <emph type="italics"></emph>His RELATION of the ſtate of the <lb></lb>Inundations, &c. </s> <s>in the Territories of BOLOGNA, <lb></lb>and FERRARA.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>By <emph type="italics"></emph>THOMAS SALUSBURY, <expan abbr="Eſq.">Eſque</expan><emph.end type="italics"></emph.end></s></p><p type="head"> <s>LONDON, <lb></lb>Printed by WILLIAM LEYBOURNE, MDCLXI.</s></p> <pb xlink:href="040/01/557.jpg"></pb><pb xlink:href="040/01/558.jpg"></pb><p type="head"> <s>OF THE <lb></lb>MENSURATION <lb></lb>OF <lb></lb>RUNNING WATERS.</s></p><p type="head"> <s>An Excellent Piece <lb></lb><emph type="italics"></emph>Written in ITALIAN<emph.end type="italics"></emph.end><lb></lb>BY</s></p><p type="head"> <s>DON BENEDETTO CASTELLI, <lb></lb>Abbot of St. <emph type="italics"></emph>BENEDETTO ALOYSIO,<emph.end type="italics"></emph.end><lb></lb>and Profeſſour of the Mathematicks to <lb></lb>Pope <emph type="italics"></emph>URBAN VIII.<emph.end type="italics"></emph.end> in <emph type="italics"></emph>ROME.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>Engliſhed from the Third and beſt Edition, with <lb></lb>the addition of a Second Book not before extant:</s></p><p type="head"> <s>By <emph type="italics"></emph>THOMAS SALUSBURY.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>LONDON,<emph.end type="italics"></emph.end><lb></lb>Printed by WILLIAM LEYBOURN, 1661.</s></p><pb xlink:href="040/01/559.jpg"></pb><pb xlink:href="040/01/560.jpg"></pb><p type="head"> <s>THE <lb></lb>AUTHOURS EPISTLE <lb></lb>TO <lb></lb>Pope VRBAN VIII.</s></p><p type="main"> <s>I lay at the Feet of your Ho<lb></lb>lineſſe theſe my Conſide<lb></lb>rations concerning the <lb></lb>MENSURATION OF <lb></lb>RUNNING WATERS: <lb></lb>Wherein if I ſhall have ſucceeded, being a <lb></lb>matter ſo difficult and unhandled by Wri<lb></lb>ters both Ancient Modern, the diſcovery of <lb></lb>any thing of truth hath been the Effect of <lb></lb>Your Holineſſes Command; and if through <lb></lb>inability I have miſſed the Mark, the ſame <pb xlink:href="040/01/561.jpg"></pb>Command will ſerve me for an Excuſe with <lb></lb>Men of better Judgment, and more eſpeci<lb></lb>ally with Your Holineſſe, to whom I humbly <lb></lb>proſtrate my ſelf, and kiſſe Your Sacred <lb></lb>Feet.</s></p><p type="main"> <s><emph type="italics"></emph>From ROME.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Your Holineſſes</s></p><p type="main"> <s><emph type="italics"></emph>Moſt humble Servant<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>BENEDETTO.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>A Monk of <emph type="italics"></emph>Caſſino.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/562.jpg"></pb><p type="head"> <s>AN <lb></lb>ACCOUNT <lb></lb>OF THE <lb></lb>Authour and Work.</s></p><p type="main"> <s>DON BENEDETTO CASTELLI, <lb></lb><emph type="italics"></emph>the famous Authour of theſe enſuing <lb></lb>Diſcourſes of the<emph.end type="italics"></emph.end> Menſuration of <lb></lb>Running Waters, <emph type="italics"></emph>is deſcended from <lb></lb>the Worſhipful FAMILY of the<emph.end type="italics"></emph.end><lb></lb>GASTELLII, <emph type="italics"></emph>and took his <lb></lb>firſt breath near to the lake THR A<lb></lb>SIMENVS, (where<emph.end type="italics"></emph.end> Hanibal <emph type="italics"></emph>gave <lb></lb>a fatal overthrow to the<emph.end type="italics"></emph.end> Roman <lb></lb><emph type="italics"></emph>Legions) in that ſweet and fertile part <lb></lb>of happy<emph.end type="italics"></emph.end> ITALY, <emph type="italics"></emph>called the<emph.end type="italics"></emph.end> Territory <lb></lb><emph type="italics"></emph>of<emph.end type="italics"></emph.end> PERUGIA, <emph type="italics"></emph>a branch of the Dukedome of<emph.end type="italics"></emph.end> TUSCANY, <emph type="italics"></emph>which <lb></lb>at preſent ſubmitteth to the Juriſdiction of the Church, as being a <lb></lb>part of<emph.end type="italics"></emph.end> St. </s> <s>PETER'S Patrimony. <emph type="italics"></emph>His Parents, who were more <lb></lb>zealous of the good of his Soul than obſervant of the Propenſion of <lb></lb>his Genius, dedicated him (according to the Devotion of that Coun<lb></lb>try) to the Service of the Church; and entered him into the Flou<lb></lb>riſhing Order of Black-Friers, called from the place Moncks <lb></lb>of<emph.end type="italics"></emph.end> Monte Caſino, <emph type="italics"></emph>and from the Founder<emph.end type="italics"></emph.end> Benedictines. <emph type="italics"></emph>Na<lb></lb>ture, that She might conſummate the Profuſion of her Fa<lb></lb>vours upon him, ſent him into the World in an Age that was ſo <lb></lb>ennobled and illuminated with Eminent Scholars in all Kinds of <lb></lb>Literature, that hardly any Century ſince the Creation can boaſt <lb></lb>the like.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/563.jpg"></pb><p type="main"> <s>§. <emph type="italics"></emph>In particular, the<emph.end type="italics"></emph.end> SCIENCES MATHEMATI<lb></lb>CAL <emph type="italics"></emph>had then got that Fame and Eſteem in the Learned World, <lb></lb>that all men of Spirit or Quality became either Students in, or <lb></lb>Patrons of thoſe Sublime Knowledges. </s> <s>On this occaſion the Curi<lb></lb>oſity of our<emph.end type="italics"></emph.end> AUTHOUR <emph type="italics"></emph>being awakened, his Active Wit <lb></lb>could not endure to be any longer confined to the Slaviſh Tuition <lb></lb>of Hermetical Pedagogues; but in concurrence with the Genius <lb></lb>of the Age, he alſo betook himſelf to thoſe moſt Generous and <lb></lb>Liberal Studies. </s> <s>His helps in this his deſign were ſo many, and <lb></lb>ſo extraordinary, that had his Inclination been weaker, or his <lb></lb>Apprehenſion leſſer, he could hardly have failed attaining more <lb></lb>than a Common Eminency in theſe Sciences. </s> <s>For beſides the De<lb></lb>luge of Learned and Vſeful Books, which the Preſſe at that <lb></lb>time ſent forth from all parts of<emph.end type="italics"></emph.end> EUROPE, <emph type="italics"></emph>he had the good <lb></lb>Fortune to fall into the Acquaintance, and under the Inſtruction <lb></lb>of the moſt Demonſtrative and moſt Familiar Man in the World, <lb></lb>the Famous<emph.end type="italics"></emph.end> GALILEO<emph type="italics"></emph>: whoſe ſucceſſe being no leſſe upon <lb></lb>this his<emph.end type="italics"></emph.end> Pupil <emph type="italics"></emph>than upon the reſt of thoſe Illuſtrious and Ingeni<lb></lb>ous Perſons that reſorted from all parts to ſit under his Admi<lb></lb>rable Lectures, he in a ſhort time attained to that Name in the <lb></lb>Mathematicks, that he was invited to<emph.end type="italics"></emph.end> ROME, <emph type="italics"></emph>Complemen<lb></lb>ted, and Preferred by his then Holineſſe the Eighth<emph.end type="italics"></emph.end> URBAN, <lb></lb><emph type="italics"></emph>upon his very firſt Acceſſion to the<emph.end type="italics"></emph.end> Papacy, <emph type="italics"></emph>which was in the <lb></lb>Year<emph.end type="italics"></emph.end> 1623.</s></p><p type="main"> <s>§. <emph type="italics"></emph>This Pope being moved with a Paternal Providence for the <lb></lb>Concerns of his Subjects in that part of<emph.end type="italics"></emph.end> ITALY <emph type="italics"></emph>about<emph.end type="italics"></emph.end> BO<lb></lb>LOGNA, FERRARA, <emph type="italics"></emph>and<emph.end type="italics"></emph.end> COMMACHIO, <emph type="italics"></emph>ly<lb></lb>ing between the Rivers of<emph.end type="italics"></emph.end> PO <emph type="italics"></emph>and<emph.end type="italics"></emph.end> RENO, <emph type="italics"></emph>which is part of<emph.end type="italics"></emph.end><lb></lb>Lo Stato della Chieſa, <emph type="italics"></emph>or the Church Patrimony, appoints this <lb></lb>our<emph.end type="italics"></emph.end> CASTELLI <emph type="italics"></emph>in the Year 1625, to accompany the Right <lb></lb>Honourable<emph.end type="italics"></emph.end> Monſignore GORSINI <emph type="italics"></emph>(a moſt obſervant and <lb></lb>intelligent perſon in theſe affaires, and at that time Superinten<lb></lb>dent of the General Draines, and Preſident of<emph.end type="italics"></emph.end> ROMAGNA) <lb></lb><emph type="italics"></emph>in the Grand Viſitation which he was then ordered to make con<lb></lb>cerning the diſorders occaſioned by the Waters of thoſe parts.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. </s> <s>CASTELLI, <emph type="italics"></emph>having now an Opportunity to employ, <lb></lb>yea more, to improve ſuch Notions as he had imbued from the <lb></lb>Lectures of his Excellent<emph.end type="italics"></emph.end> MASTER, <emph type="italics"></emph>falls to his work with <lb></lb>all induſtry: and in the time that his Occaſions detained him in<emph.end type="italics"></emph.end><lb></lb>ROMAGNA <emph type="italics"></emph>he perfected the Firſt Book of this his Diſ<lb></lb>courſe concerning the<emph.end type="italics"></emph.end> Menſuration of Running Waters. <emph type="italics"></emph>He con<lb></lb>feſſeth that he had ſome years before applyed himſelf to this part <lb></lb>of Practical Geometry, and from ſeveral Obſervations collected <lb></lb>part of that Doctrine which at this time he put into Method, and <lb></lb>which had procured him the Repute of ſo much Skill that he began<emph.end type="italics"></emph.end><pb xlink:href="040/01/564.jpg"></pb><emph type="italics"></emph>to be Courted by ſundry Princes, and great Prelates. </s> <s>In particu<lb></lb>lar about the beginning of the Year 1623. and before his Invita<lb></lb>tion to<emph.end type="italics"></emph.end> ROME <emph type="italics"></emph>he was employed by Prince<emph.end type="italics"></emph.end> Ferdinando I, <emph type="italics"></emph>Grand <lb></lb>Duke of<emph.end type="italics"></emph.end> TUSCANY, <emph type="italics"></emph>to remedy the Diſorders which at that <lb></lb>time happened in the Valley of<emph.end type="italics"></emph.end> PISA <emph type="italics"></emph>in the Meadows that lye <lb></lb>upon the Banks of<emph.end type="italics"></emph.end> Serchio <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Fiume Morto: <emph type="italics"></emph>and in the pre<lb></lb>ſence of the Grand Duke, Grand Dutcheſſe Mother, the Commiſ<lb></lb>ſioners of Sewers, and ſundry other Perſons in a few hours he <lb></lb>made ſo great a progreſſe in that affair, as gave his Moſt Serene <lb></lb>Highneſſe high ſatisfaction, and gained himſelf much Honour.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. <emph type="italics"></emph>No ſooner had he in his fore-mentioned Voiage to<emph.end type="italics"></emph.end> RO<lb></lb>MAGNA <emph type="italics"></emph>(which was but few Moneths after, in the ſame <lb></lb>Year) committed his Conceptions to paper, but he communicated <lb></lb>them to certain of his Friends. </s> <s>In which number we finde<emph.end type="italics"></emph.end> Signo<lb></lb>re Ciampoli <emph type="italics"></emph>Secretary of the Popes Private Affaires; whom in <lb></lb>the beginning of the Firſt Book he gratefully acknowledgeth to <lb></lb>have been contributary, in his Purſe, towards defraying the <lb></lb>charge of Experiments, and in his Perſon, towards the debating <lb></lb>and compleating of Arguments upon this Subject. </s> <s>Some few years <lb></lb>after the Importunity of Friends, and the Zeal he had for the <lb></lb>Publique Good prevailed with him to preſent the World with his <lb></lb>Firſt Diſcourſe, accompanied with a Treatiſe of the Geometrical <lb></lb>Demonſtrations of his whole Doctrine. </s> <s>What Reception it found <lb></lb>with the Judicious muſt needs be imagined by any one that hath <lb></lb>obſerved how<emph.end type="italics"></emph.end> Novelty <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Facility <emph type="italics"></emph>in conjunction with<emph.end type="italics"></emph.end> Verity <lb></lb><emph type="italics"></emph>make a Charm of irreſiſtable Operation.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. </s> <s>New <emph type="italics"></emph>it was, for that no man before him had ever attemp<lb></lb>ted to Demonſtrate all the three Dimenſions, to wit, the Length, <lb></lb>Breadth and Profundity, of this Fluid and Current Ele<lb></lb>ment. </s> <s>And he detecteth ſuch groſſe Errours in thoſe few that <lb></lb>had untertook to write upon the Subject (of which he inſtan<lb></lb>ceth in<emph.end type="italics"></emph.end> Frontinus <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Fontana, <emph type="italics"></emph>as thoſe that include the rest) <lb></lb>and delivereth ſuch ſingular and unheard-of Paradoxes (for ſo <lb></lb>they ſound in Vulgar Eares) as cannot but procure unſpeakable <lb></lb>delight to his Reader.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. </s> <s>Eafie <emph type="italics"></emph>it is likewiſe and<emph.end type="italics"></emph.end> True; <emph type="italics"></emph>and that upon ſo Familiar <lb></lb>Experiments and Manifeſt Demonſtrations, that I have oft que<lb></lb>ſtioned with my ſelf which merited the greater wonder, he, for <lb></lb>diſcovering, or all men that handled the Argument before him <lb></lb>for not diſcovering a Doctrine of ſuch ſtrange Facility and Infal<lb></lb>libility. </s> <s>But yet as if our Authour deſigned to oblige the whole <lb></lb>World to him by ſo excellent a<emph.end type="italics"></emph.end> Preſent, <emph type="italics"></emph>he ſelects a Subject that <lb></lb>he knew would be carreſſed by all perſons of Nobler Souls, upon <lb></lb>the accounts afore-named, and by all Mankind in General, as <lb></lb>gratifying them in their much adored Idol<emph.end type="italics"></emph.end> Utility. <emph type="italics"></emph>And to ren-<emph.end type="italics"></emph.end><pb xlink:href="040/01/565.jpg"></pb><emph type="italics"></emph>der his Art the more profitable, he reduceth the lofty, and eaſie-to<lb></lb>be-miſtaken Speculations of the Theory, into certain and facile <lb></lb>Directions for Practice; teaching us how to prevent and repaire <lb></lb>the Breaches of Seas, and Inundations of Rivers; to draine <lb></lb>and recover Fenns and Marches; to divert, conveigh and di<lb></lb>ſtribute Waters for the Flowing and Stercoration of Grounds, <lb></lb>ſtrengthening of Fortifications, ſerving of Aquaducts, preſer<lb></lb>ving of Health (by cleanſing Streets, and ſcowring Sewers) and <lb></lb>maintaining of Commerſe (by defending Bridges, cleering Ri<lb></lb>vers, and opening Ports and Channels) with innumerable other <lb></lb>Benefits of the like nature. </s> <s>And, that I may omit no circumſtance <lb></lb>that may recommend my Authour, the Fortune of this his Trea<lb></lb>tiſe hath been ſuch, that as if he intended a<emph.end type="italics"></emph.end> Plus ultra <emph type="italics"></emph>by it, <lb></lb>or as if all men deſpaired to out-do it, or laſtly, as if<emph.end type="italics"></emph.end> CA<lb></lb>STELLI <emph type="italics"></emph>hath been ſo great a<emph.end type="italics"></emph.end> Maſter <emph type="italics"></emph>that none have preſu<lb></lb>med to take Pencil in hand for the finiſhing of what he<emph.end type="italics"></emph.end> Pour<lb></lb>foild, <emph type="italics"></emph>this ſmall Tract like the Arabian Phœnix (of which it is <lb></lb>ſaid<emph.end type="italics"></emph.end> Unica ſemper Avis) <emph type="italics"></emph>did for ſeveral years together continue <lb></lb>ſingle in the World, till that to verifie it to be truly<emph.end type="italics"></emph.end> Phœnician, <lb></lb><emph type="italics"></emph>it renewed its Age by undergoing a ſecond Impreſſion. </s> <s>And as if <lb></lb>this did not make out the Immortal vertue of it, it hath had<emph.end type="italics"></emph.end><lb></lb>Anno 1660 <emph type="italics"></emph>a third Circulation, and riſen in this laſt Edition as <lb></lb>it were from the Vrne of its Authour; and that ſo improved by <lb></lb>the Addition of a ſecond part, that it promiſeth to perpetuate <lb></lb>his Merits to all Poſterity. </s> <s>To be brief, the meer Fame of this <lb></lb>Work reſounded the Honourable Name of<emph.end type="italics"></emph.end> CASTELLI <emph type="italics"></emph>in<lb></lb>to all the Corners of<emph.end type="italics"></emph.end> Italy, <emph type="italics"></emph>I may ſay of<emph.end type="italics"></emph.end> Europe; <emph type="italics"></emph>inſomuch, <lb></lb>that, in hopes to reap great benefit by his Art, the reſpective <lb></lb>Grandees of the adjacent Countries courted his Judgment and <lb></lb>Advice about their Draining of Fenns, Diverſion of Rivers, <lb></lb>Evacuation of Ports, Preventing of Inundations, &c. </s> <s>So that <lb></lb>every Summer he made one or more of theſe Journies or Viſitati<lb></lb>ons. </s> <s>Particularly, the Senate of<emph.end type="italics"></emph.end> Venice <emph type="italics"></emph>conſulted him about their <lb></lb>Lake; to whom he delivered his Opinion in<emph.end type="italics"></emph.end> May 1641. <emph type="italics"></emph>and up<lb></lb>on farther thoughts he preſented them with another Paper of Con<lb></lb>ſiderations the<emph.end type="italics"></emph.end> 20 December <emph type="italics"></emph>following. </s> <s>Prince<emph.end type="italics"></emph.end> LEOPOLDO <lb></lb><emph type="italics"></emph>of<emph.end type="italics"></emph.end> TUSCANY <emph type="italics"></emph>likewiſe requeſted his Advice in the begin<lb></lb>ning of the enſuing year 1642, which occaſioned his Letter to <lb></lb>Father<emph.end type="italics"></emph.end> Franceſco di San Giuſeppe, <emph type="italics"></emph>bearing date<emph.end type="italics"></emph.end> February 1, <lb></lb><emph type="italics"></emph>To which<emph.end type="italics"></emph.end> Signore Bartolotti <emph type="italics"></emph>oppoſing, he writes a ſecond Let<lb></lb>ter, directed to one of the Commiſſioners of Sewers, vindicating <lb></lb>his former, and refuting<emph.end type="italics"></emph.end> Bartolotti, <emph type="italics"></emph>both which I here give <lb></lb>you.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. <emph type="italics"></emph>The Preferments which his Merits recommended him unto, <lb></lb>were firſt to be Abbot of<emph.end type="italics"></emph.end> Caſſino, <emph type="italics"></emph>from which he was removed<emph.end type="italics"></emph.end><pb xlink:href="040/01/566.jpg"></pb>Anno 1640, <emph type="italics"></emph>or thereabouts, unto the Abbey of<emph.end type="italics"></emph.end> Santo Benedet<lb></lb>to Aloyſio; <emph type="italics"></emph>and much about the ſame time preferred to the Dig<lb></lb>nity of Chief Mathematician to his grand Patron Pope<emph.end type="italics"></emph.end> URBAN <lb></lb>VIII. <emph type="italics"></emph>and Publique Profeſſour of Mathematicks in the Vni<lb></lb>verſity of<emph.end type="italics"></emph.end> ROME.</s></p><p type="main"> <s>§. <emph type="italics"></emph>Here a Stop was put to the Carier of his Fortunes, and be<lb></lb>ing fuller of Honour than of Years, was by Death, the Importu<lb></lb>nate Intrerupter of Generous Deſigns, prevented in doing that <lb></lb>farther Good which the World had good reaſon to promiſe it ſelf <lb></lb>from ſo Profound and Induſtrious a Perſonage, leaving many <lb></lb>Friends and Diſciples of all Degrees and Qualities to lament <lb></lb>his loſſe, and honour his Memory.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. <emph type="italics"></emph>His ſingular Virtues and Abilities had gained him the <lb></lb>Friendſhip of very many; as to inſtance in ſome, he had con<lb></lb>racted ſtrict Amity with<emph.end type="italics"></emph.end> Monſignore Maffei Barberino <emph type="italics"></emph>a Floren<lb></lb>tine, Præfect of the Publique Wayes, and afterwards Pope with <lb></lb>the Name of<emph.end type="italics"></emph.end> URBAN VIII. <emph type="italics"></emph>as was ſaid before; with the <lb></lb>above-named<emph.end type="italics"></emph.end> Monſignore Corſini <emph type="italics"></emph>Superintendant of the General <lb></lb>Draines: with<emph.end type="italics"></emph.end> Monſignore Piccolomini <emph type="italics"></emph>Arch-Biſhop of<emph.end type="italics"></emph.end> Siena<emph type="italics"></emph>: <lb></lb>with Cardinal<emph.end type="italics"></emph.end> Serra: <emph type="italics"></emph>with Cardinal<emph.end type="italics"></emph.end> Caponi, <emph type="italics"></emph>who hath ſtudied <lb></lb>much and writ well upon this Subject; and with Cardinal<emph.end type="italics"></emph.end> Gae<lb></lb>tano <emph type="italics"></emph>who frequently conſulted with him in his deſign of Drain<lb></lb>ing the Fenns of<emph.end type="italics"></emph.end> ROMAGNA. <emph type="italics"></emph>Moreover Prince<emph.end type="italics"></emph.end> LEO<lb></lb>POLDO, <emph type="italics"></emph>and his Brother the Grand Duke had very great <lb></lb>kindneſſe for him; which ſpeaks no ſmall attractions in him, <lb></lb>conſidering him as a favourite of the Family of<emph.end type="italics"></emph.end> Barberini, <emph type="italics"></emph>be<lb></lb>tween whom and the Houſe of<emph.end type="italics"></emph.end> Medeci <emph type="italics"></emph>there is an inveterate <lb></lb>Fewd. </s> <s>Amongſt perſons of a lower Quality he acknowledgeth<emph.end type="italics"></emph.end><lb></lb>Signore Ciampoli <emph type="italics"></emph>the Popes Secretary,<emph.end type="italics"></emph.end> Sig. </s> <s>Ferrante Ceſarini, <lb></lb>Sig. </s> <s>Giovanni Baſadonna <emph type="italics"></emph>Senator of<emph.end type="italics"></emph.end> Venice; <emph type="italics"></emph>and I find menti<lb></lb>oned<emph.end type="italics"></emph.end> Sig. </s> <s>Lana, Sig. </s> <s>Albano, Padre Serafino, Pad. </s> <s>Franceſco <lb></lb>de San. </s> <s>Giuſeppe, <emph type="italics"></emph>and many others.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. <emph type="italics"></emph>The Works in which he will ſurvive to all ſucceeding Ages <lb></lb>are firſt His ſolid and ſober Confutation of the Arguments of<emph.end type="italics"></emph.end><lb></lb>Signore Lodovico dell Columbo, <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Signore Vincentio di <lb></lb>Gratia <emph type="italics"></emph>againſt the Tract of<emph.end type="italics"></emph.end> Galileo Delle coſe che ſtanno ſopra <lb></lb>Aqua, <emph type="italics"></emph>wherein he vindicates bis ſaid<emph.end type="italics"></emph.end> Maſter <emph type="italics"></emph>with a Gratitude <lb></lb>that Tutors very rarely reap from the pains they take in Culti<lb></lb>vating their Pupils. </s> <s>This Apology was firſt Printed<emph.end type="italics"></emph.end> Anno 1615. <lb></lb><emph type="italics"></emph>and was a ſecond time publiſhed, as alſo thoſe of his Antago<lb></lb>niſts, amongſt the Works of<emph.end type="italics"></emph.end> GALILEO, <emph type="italics"></emph>ſet forth by the <lb></lb>Learned<emph.end type="italics"></emph.end> Viviani 1656. <emph type="italics"></emph>He hath likewiſe writ ſeveral other <lb></lb>curious Pieces, as I am informed by the moſt Courteous<emph.end type="italics"></emph.end> Carolo <lb></lb>Manoleſſi <emph type="italics"></emph>of<emph.end type="italics"></emph.end> Bologna; <emph type="italics"></emph>amongſt others an excellent Treatiſe <lb></lb>concerning<emph.end type="italics"></emph.end> Colours, <emph type="italics"></emph>which he putteth me in hopes to ſee printed<emph.end type="italics"></emph.end><pb xlink:href="040/01/567.jpg"></pb><emph type="italics"></emph>very ſpeedily. </s> <s>And laſt of all theſe Diſcourſes and Reflections <lb></lb>upon the<emph.end type="italics"></emph.end> Menſuration of Running Waters, <emph type="italics"></emph>with the addition of <lb></lb>a Second Book, three Epiſtles, and four Conſiderations upon <lb></lb>the ſame Argument, which conduce much to Illuſtrate his Do<lb></lb>ctrine and Facilitate the Practice of it; and which with a Rela<lb></lb>tion of<emph.end type="italics"></emph.end> Monſignore Corſini, <emph type="italics"></emph>make the ſecond part of my Firſt <lb></lb>Tome.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. <emph type="italics"></emph>I might here ſally forth into the Citation of ſundry Au<lb></lb>thours of Good Account, that have tranſmitted his Character <lb></lb>to Poſterity, but ſhall confine my ſelf to onely two; the one is <lb></lb>of his<emph.end type="italics"></emph.end> Maſter, <emph type="italics"></emph>the other of his<emph.end type="italics"></emph.end> Scholar; <emph type="italics"></emph>than whom there can<lb></lb>not be two more competent Judges of his Accompliſhments. </s> <s>To <lb></lb>begin with his<emph.end type="italics"></emph.end> Maſter, <emph type="italics"></emph>the Quick-ſighted, and truly Lyncean<emph.end type="italics"></emph.end><lb></lb>GALILEO, <emph type="italics"></emph>who ſpeaking of his Abilities in Aſtronomy ſaith<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg961"></arrow.to.target><lb></lb><emph type="italics"></emph>(a)<emph.end type="italics"></emph.end> Che la felicità del ſuo ingegno non la fà biſognoſa dell' o<lb></lb>pera ſuo. <emph type="italics"></emph>And again, ſubmitting a certain Demonſtration, <lb></lb>which he intended to divulge, to the Judgment of this our Abbot, he<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg962"></arrow.to.target><lb></lb><emph type="italics"></emph>writes to him in this manner: (b)<emph.end type="italics"></emph.end> Queſto lo comunico a V. S. <lb></lb>per lettera prima che ad alcun altro, con attenderne principal<lb></lb>mente il parer ſuo, e doppo quello de' noſtri Amici diſcoſti, <lb></lb>conpenſiero d' inviarne poi altre Copie ad altri Amici d' Italia, <lb></lb>e di Francia, quando io ne venga da lei conſigliato: e qui pre<lb></lb>gandola a farci parte d' alcuna delle ſue peregrine ſpeculationi; <lb></lb>con ſinceriſſimo affetto, &c. <emph type="italics"></emph>And the moſt acute Mathematician<emph.end type="italics"></emph.end><lb></lb>Signore Evangeliſta Terricelli, <emph type="italics"></emph>late Profeſſour to the Grand <lb></lb>Duke in immediate Succeſſion after<emph.end type="italics"></emph.end> GALILEO, <emph type="italics"></emph>maketh this<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg963"></arrow.to.target><lb></lb><emph type="italics"></emph>Honourable and Grateful Mention of him, and his Book: (c)<emph.end type="italics"></emph.end> O<lb></lb>mitto magnum illum nutantis Maris motum; Prætereo etiam <lb></lb>omnem Fluminum, Aquarumque Currentium tum menſurum, <lb></lb>tum uſum, quarum omnis doctrina reperta primum fuit ab <lb></lb>Abbate BENEDICTO CASTELLIO Preceptore <lb></lb>meo. </s> <s>Scripſit ille Scientiam ſuam, & illam non ſolum demonſtra<lb></lb>tione, verum etiam opere confirmavit, maxima cum Princi<lb></lb>pum & populorum utilitatate, majore cum admiratione Phylo<lb></lb>ſophorum. </s> <s>Extat illius Liber, vere aureus.</s></p><p type="margin"> <s><margin.target id="marg961"></margin.target><emph type="italics"></emph>(a)<emph.end type="italics"></emph.end>Nella continu<lb></lb>atione dell Nun<lb></lb>tio ſiderio.</s></p><p type="margin"> <s><margin.target id="marg962"></margin.target><emph type="italics"></emph>(b)<emph.end type="italics"></emph.end> Lettera al P. <lb></lb></s> <s>Abbate D. B. </s> <s>Ca<lb></lb>ſtelli D'Arcetro; <lb></lb>li. </s> <s>3. Decemb. <lb></lb></s> <s>1639.</s></p><p type="margin"> <s><margin.target id="marg963"></margin.target><emph type="italics"></emph>(c)<emph.end type="italics"></emph.end> De Motu A<lb></lb>quarum. </s> <s>Lib. 2. <lb></lb>Prop. </s> <s>37. p. </s> <s>191.</s></p><p type="main"> <s>§. <emph type="italics"></emph>I have onely two particulars more to offer the Engliſh Rea<lb></lb>der: The one concerns the Book, and it is this, That after the <lb></lb>general Aprobation it hath had in<emph.end type="italics"></emph.end> Italy, <emph type="italics"></emph>I cannot but think it <lb></lb>deſerveth the ſame Civil Entertainment with us, in regard that <lb></lb>it cometh with no leſſe<emph.end type="italics"></emph.end> Novelty, Facility, Verity, and Utility <emph type="italics"></emph>to <lb></lb>us than to thoſe whom the Authour favoured with the Original. <lb></lb></s> <s>Our Rivers and Sewers through Publique Diſtractions and Pri<lb></lb>vate Incroachments are in great diſorder, as thoſe Channels for <lb></lb>iuſtance which formerly were Navigable unto the very Walls of<emph.end type="italics"></emph.end><pb xlink:href="040/01/568.jpg"></pb>York <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Salisbury, <emph type="italics"></emph>&c: Our Ports are choaked and obſtructed <lb></lb>by Shelfes and Setlements: Our Fenns do in a great part lie waſte <lb></lb>and unimproved: Now all theſe may be (and, as I find by the <lb></lb>Confeſſion of ſome whoſe Practiſes upon the Copy of the Firſt <lb></lb>Book onely of our Authour hath got them both Money and Repu<lb></lb>tation, in part have been) remedied by the Ways and Means he <lb></lb>here ſets down. </s> <s>The truth is the Argument hath been paſt over <lb></lb>with an Vniverſal Silence; ſo that to this day I have not ſeen <lb></lb>any thing that hath been written Demonſtratively and with Ma<lb></lb>thematical Certainty concerning the ſame, ſave onely what this <lb></lb>Learned Prelate hath delivered of his Own Invention in theſe <lb></lb>Treatiſes: who yet hath ſo fully and plainly handled the Whole <lb></lb>Doctrine, that I may affirm his Work to be every way abſolute. </s> <s>It <lb></lb>muſt be confeſt the Demonſtration of the Second Propoſition of the <lb></lb>Second Book did not well pleaſe the Authour, and had he lived <lb></lb>he would have ſupplyed that defect, but being prevented by <lb></lb>Death, the Reader muſt content himſelf with the Mechanical <lb></lb>Proof that he giveth you of the truth of ſo Excellent a Con<lb></lb>cluſion.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>§. <emph type="italics"></emph>The other particular that I am to offer is, that out of my de<lb></lb>ſire to contribute what lyeth in me to the compleating of this Piece <lb></lb>for Engliſh Practice, I have exeeded my promiſe not onely in gi<lb></lb>ving you the Second and following Books which were not extant at <lb></lb>the time of tendring my Overtures, but alſo in that I have added <lb></lb>a Map or Plat of all the Rivers, Lakes, Fenns, &c. </s> <s>mentioned <lb></lb>thorow out the Work. </s> <s>And if I have not kept touch in point of <lb></lb>Time, let it be conſidered that I am the Tranſlator and not the <lb></lb>Printer. </s> <s>To conclude, according to your acceptance of theſe my <lb></lb>endeavours, you may expect ſome other Tracts of no leſſe Profit <lb></lb>and Delight.<emph.end type="italics"></emph.end> Farewell.</s></p><p type="head"> <s><emph type="italics"></emph>T. S.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/569.jpg"></pb><p type="head"> <s>ERRATA of the <emph type="italics"></emph>ſecond<emph.end type="italics"></emph.end> PART of the <emph type="italics"></emph>firſt<emph.end type="italics"></emph.end> TOME.</s></p><p type="main"> <s>In PREFACE, I cad <emph type="italics"></emph>Ferdinando II.<emph.end type="italics"></emph.end> ibid. <emph type="italics"></emph>l' Aqua.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>PAGE 2. LINE 26, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> muſt <emph type="italics"></emph>read<emph.end type="italics"></emph.end> much. </s> <s>P. 3. l. </s> <s>22, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> and let. </s> <s>l. </s> <s>25. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> water, from l. </s> <s>41. <lb></lb><emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Tappe, (<emph type="italics"></emph>as every where elſe).<emph.end type="italics"></emph.end> Page 4. l. </s> <s>18. <emph type="italics"></emph>r<emph.end type="italics"></emph.end> cords. </s> <s>Page 6. l. </s> <s>9. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> acquire, or. <lb></lb></s> <s>Page 9. l. </s> <s>1. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> irreperable. </s> <s>P. 10. l. </s> <s>13. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> diſſimboguement. <emph type="italics"></emph>For<emph.end type="italics"></emph.end> Page 17. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> P. 15. <lb></lb>P. 15. l. </s> <s>27, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> in. </s> <s>l. </s> <s>36, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> is as. </s> <s>l. </s> <s>38, <emph type="italics"></emph>r. </s> <s>Panaro.<emph.end type="italics"></emph.end> P. 17. l. </s> <s>12, <emph type="italics"></emph>Giulio.<emph.end type="italics"></emph.end> l. </s> <s>17. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Meaſurers. </s> <s>l. <lb></lb></s> <s>25, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> meaſured it,. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> neceſſarily. </s> <s>P. 23. l. </s> <s>19. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> for help. <emph type="italics"></emph>for<emph.end type="italics"></emph.end> Page 31. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> P. 32. P. 24. <lb></lb>l. </s> <s>14, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> to. </s> <s>l. </s> <s>17, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> namly, of the. </s> <s>l. </s> <s>23, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> eaſie. </s> <s>P. 25. l. </s> <s>38. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Cock. </s> <s>p. </s> <s>29. l. </s> <s>7. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> laſted,. <lb></lb>p. </s> <s>31. l. </s> <s>32. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Soe. </s> <s>p. </s> <s>41. l. </s> <s>20. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> to the line. </s> <s>p. </s> <s>48. l. </s> <s>19. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> us the ^{*}. id. <emph type="italics"></emph>Figure falſe<emph.end type="italics"></emph.end> p. </s> <s>52. <lb></lb>l. </s> <s>30, and 31. <emph type="italics"></emph>for<emph.end type="italics"></emph.end> Theorem <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Propoſition. </s> <s>p. </s> <s>53. l. </s> <s>29. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> again. </s> <s>p. </s> <s>57. l. </s> <s>19, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> ſame if. <lb></lb></s> <s>l. </s> <s>44. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> bodily. </s> <s>p. </s> <s>58. l. </s> <s>9, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> gathering. </s> <s>l. </s> <s>40. <emph type="italics"></emph>omit<emph.end type="italics"></emph.end>;. </s> <s>p. </s> <s>60. l. </s> <s>2. <emph type="italics"></emph>omit,<emph.end type="italics"></emph.end> if. </s> <s>p. </s> <s>65. l. </s> <s>1. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> tide <lb></lb><emph type="italics"></emph>dele<emph.end type="italics"></emph.end>;. </s> <s>p. </s> <s>66. l. </s> <s>35. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Stoppage of. </s> <s>p. </s> <s>68. l. </s> <s>12, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> Lords the <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Lords. </s> <s>l. <emph type="italics"></emph>ult. </s> <s>for<emph.end type="italics"></emph.end> they <lb></lb><emph type="italics"></emph>r.<emph.end type="italics"></emph.end> it. </s> <s>p. </s> <s>69. l. </s> <s>14. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> to one. <emph type="italics"></emph>id.<emph.end type="italics"></emph.end> carried <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> to. </s> <s>p. </s> <s>71. l. </s> <s>20, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> and that. </s> <s>l. </s> <s>25, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Braces; it. </s> <s>l. <lb></lb></s> <s>29. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Braces. </s> <s>l. </s> <s>44, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> the <emph type="italics"></emph>Brent.<emph.end type="italics"></emph.end> p. </s> <s>72. l. </s> <s>23. <emph type="italics"></emph>r. </s> <s>Serene Highneſſe.<emph.end type="italics"></emph.end> p. </s> <s>73. l. </s> <s>24, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> deliberation:. <lb></lb>l. </s> <s>26, <emph type="italics"></emph>for<emph.end type="italics"></emph.end> ſumme <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Moddel. </s> <s>l. </s> <s>40. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Months. </s> <s>p. </s> <s>79. l. </s> <s>18. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> that into. </s> <s>p. </s> <s>82. l. </s> <s>22. <emph type="italics"></emph>dele<emph.end type="italics"></emph.end>;. </s> <s>p. <lb></lb></s> <s>85. l. </s> <s>9, 10. <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> a free drame. </s> <s>p. </s> <s>88. l. </s> <s>5. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Palmes. </s> <s>p. </s> <s>89. l. </s> <s>8. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Princes. </s> <s>p. </s> <s>92. l. </s> <s>3. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Diſ<lb></lb>courſes. </s> <s>p. </s> <s>93. l. </s> <s>31. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Tautologie. </s> <s>p. </s> <s>94. l. </s> <s>9. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> miracle;. </s> <s>p. </s> <s>97. l. </s> <s>13. <emph type="italics"></emph>r,<emph.end type="italics"></emph.end> weighty. </s> <s>p. </s> <s>101. <lb></lb>l. </s> <s>21. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Marrara. </s> <s>p. </s> <s>107. l. </s> <s>28, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Patrimony. </s> <s>l. </s> <s>40, <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> above. </s> <s>p. </s> <s>111. l. </s> <s>16. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> ſaid. <emph type="italics"></emph>For<emph.end type="italics"></emph.end> p. </s> <s>432. <lb></lb><emph type="italics"></emph>r.<emph.end type="italics"></emph.end> p. </s> <s>114. p. </s> <s>114. l. </s> <s>35. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> of 200, l. </s> <s>41. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> cloſed. </s> <s>p. </s> <s>115. l. </s> <s>29. <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> conſtant;.</s></p><pb xlink:href="040/01/570.jpg" pagenum="1"></pb><p type="head"> <s>OF THE <lb></lb>MENSURATION <lb></lb>OF <lb></lb>Running Waters.</s></p><p type="head"> <s><emph type="italics"></emph>LIB.<emph.end type="italics"></emph.end> I.</s></p><p type="main"> <s>What, and of how great moment the confi<lb></lb>deration of <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> is in natural things, <lb></lb>is ſo manifeſt, that the Prince of <emph type="italics"></emph>Peri<lb></lb>pateticks<emph.end type="italics"></emph.end> pronounced that in his Schools <lb></lb>now much uſed Sentence: <emph type="italics"></emph>Ignorato mo<lb></lb>tu, ignoratur natura.<emph.end type="italics"></emph.end> Thence it is that <lb></lb>true Philoſophers have ſo travailed in the <lb></lb>contemplation of the Celeſtial motions, <lb></lb>and in the ſpeculation of the motions of <lb></lb>Animals, that they have arrived to a wonderful height and ſub<lb></lb>limity of underſtanding. </s> <s>Under the ſame Science of <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end><lb></lb>is comprehended all that which is written by Mechanitians con<lb></lb>cerning Engines moving of themſelves, <emph type="italics"></emph>Machins<emph.end type="italics"></emph.end> moving by the <lb></lb>force of Air, and thoſe which ſerve to move weights and im<lb></lb>menſe magnitudes with ſmall force. </s> <s>There appertaineth to the <lb></lb>Science of <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> all that which hath been written of the <lb></lb>alteration not onely of Bodies, but of our Minds alſo; and <lb></lb>in ſum, this ample matter of <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end> is ſo extended and di<lb></lb>lated, that there are few things which fall under mans no<lb></lb>tice, which are not conjoyned with <emph type="italics"></emph>Motion,<emph.end type="italics"></emph.end> or at leaſt de<lb></lb>pending thereupon, or to the knowledge thereof directed; <lb></lb>and of almoſt every of them, there hath been written and <lb></lb>compoſed by ſublime wits, learned Treatiſes and Inſtructions. <pb xlink:href="040/01/571.jpg" pagenum="2"></pb>And becauſe that in the years paſt I had occaſion by Order of <lb></lb>our Lord Pope <emph type="italics"></emph>Vrban<emph.end type="italics"></emph.end> 8. to apply my thoughts to the motion of <lb></lb>the Waters of Rivers, (a matter difficult, moſt important, and <lb></lb>little handled by others) having concerning the ſame obſerved <lb></lb>ſome particulars not well obſerved, or conſidered till now, but of <lb></lb>great moment both in publick and private affairs; I have thought <lb></lb>good to publiſh them, to the end that ingenious ſpirits might <lb></lb>have occaſion to diſcuſſe more exactly then hitherto hath been <lb></lb>done, ſo neceſſary and profitable a matter, and to ſupply alſo my <lb></lb>defects in this ſhort and difficult Tractate. </s> <s>Difficult I ſay, for <lb></lb>the truth is, theſe knowledges, though of things next our ſenſes, <lb></lb>are ſometimes more abſtruce and hidden, then the knowledge of <lb></lb>things more remote; and much better, and with greater exquiſit<lb></lb>neſs are known the motions of the Planets, and Periods of the <lb></lb>Stars, than thoſe of Rivers and Seas: As that ſingular light of <lb></lb>Philoſophie of our times, and my Maſter <emph type="italics"></emph>Signore Galileo Galilei<emph.end type="italics"></emph.end><lb></lb>wiſely obſerveth in his Book concerning the Solar ſpots. </s> <s>And <lb></lb>to proceed with a due order in Sciences, I will take ſome ſuppo<lb></lb>ſitions and cognitions ſufficiently clear; from which I will after<lb></lb>wards proceed to the deducing of the principal concluſions. </s> <s>But <lb></lb>to the end that what I have written at the end of this diſcourſe in <lb></lb>a demonſtrative and Geometrical method, may alſo be under<lb></lb>ſtood of thoſe which never have applyed their thoughts to the <lb></lb>ſtudy of Geometry; I have endeavoured to explain my conceit <lb></lb>by an example, and with the conſideration of the natural things <lb></lb>themſelves, muſt after the ſame order in which I began to doubt <lb></lb>in this matter; and have placed this particular Treatiſe here in <lb></lb>the beginning, adverting nevertheleſs, that he who deſires more <lb></lb>full and abſolute ſolidity of Reaſons, may overpaſs this prefatory <lb></lb>diſcourſe, and onely conſider what is treated of in the demonſtra<lb></lb>tions placed towards the end, and return afterwards to the conſi<lb></lb>deration of the things collected in the <emph type="italics"></emph>Corollaries<emph.end type="italics"></emph.end> and Appendices; <lb></lb>which demonſtrations notwithſtanding, may be pretermitted by <lb></lb>him that hath not ſeen at leaſt the firſt ſix Books of the Elements <lb></lb>of Euclid; ſo that he diligently obſerveth that which fol<lb></lb>loweth.</s></p><p type="main"> <s>I ſay therefore, that having in times paſt, on divers occaſi<lb></lb>ons heard ſpeak of the meaſures of the waters of Rivers, and <lb></lb>Fountains, ſaying, ſuch a River is two or three thouſand feet of <lb></lb>water; ſuch a ſpring-water is twenty, thirty, or forty inches, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end><lb></lb>Although in ſuch manner I have found all to treat thereof in <lb></lb>word and writing, without variety, and as we are wont to ſay, <lb></lb><emph type="italics"></emph>conſtanti ſermone,<emph.end type="italics"></emph.end> yea even Artiſts and Ingeneers, as if it were <lb></lb>a thing that admitted not of any doubt, yet howſoever I re<lb></lb>mained ſtill infolded in ſuch an obſcurity, that I well knew I un<pb xlink:href="040/01/572.jpg" pagenum="3"></pb>derſtood nothing at all, of that which others pretended full and <lb></lb>clearly to underſtand. </s> <s>And my doubt aroſe from my frequent <lb></lb>obſervation of many Trenches and Channels, which carry <lb></lb>water to turn Mills, in which Trenches, and Channels, the <lb></lb>water being meaſured, was found pretty deep; but if afterwards <lb></lb>the ſame water was meaſured in the fall it made to turn the <lb></lb>Wheel of the Mill, it was much leſſe, not amounting often to the <lb></lb>tenth part, nor ſometimes to the twentieth, inſomuch, that the <lb></lb>ſame running water came to be one while more, another while leſs <lb></lb>in meaſure, in divers parts of its Channel; and for that reaſon this <lb></lb>vulgar manner of meaſuring running Waters, as indeterminate and <lb></lb>uncertain, was by me juſtly ſuſpected, the meaſure being to be de<lb></lb>terminate, and the ſame. </s> <s>And here I freely confeſſe that I had fin<lb></lb>gular help to reſolve this difficulty from the excellent & accurate <lb></lb>way of diſcourſing, as in allother matters, ſo alſo in this, of the <lb></lb>Right Honourable and Truly Noble Signior <emph type="italics"></emph>Ciampoli,<emph.end type="italics"></emph.end> Secretary <lb></lb>of the Popes ſecret affairs. </s> <s>Who moreover, not ſparing ſor the coſts <lb></lb>of the ſame, generouſly gave me occaſion a few years paſt to try by <lb></lb>exact experiments that which paſt concerning this particular. </s> <s>And <lb></lb>to explain all more clearly with an example; we ſuppoſe a Veſſel <lb></lb>filled with Water, as for inſtance a Butt, which is kept full, though <lb></lb>ſtill water runneth out, and the Water run out by two Taps equal <lb></lb>of bigneſſe, one put in the bottom of the Veſſel, and the other in <lb></lb>the upper part; it is manifeſt that in the time wherein from the <lb></lb>upper part ſhall iſſue a determinate meaſure of water ſrom <lb></lb>the inferiour part there ſhall iſſue four, five, and many more of <lb></lb>the ſame meaſures, according to the difference of the height of <lb></lb>the Taps, and the diſtance of the upper Tap from the Superfici<lb></lb>es and level of the water of the Veſſel: and all this will alwayes <lb></lb>follow, though, as hath been ſaid, the Taps be equal, and the <lb></lb>water in diſcharging keep the ſaid Taps alwayes full. </s> <s>Where firſt <lb></lb>we note, that, although the meaſure of the Taps be equal, never<lb></lb>theleſſe there iſſueth from them in equal times unequal quantities <lb></lb>of water, And if we ſhould more attentively conſider this buſi<lb></lb>neſſe, we ſhould find, that the water by the lower Tap, run<lb></lb>neth and paſſeth with much greater velocity, then it doth by the <lb></lb>upper, whatever is the reaſon. </s> <s>If therefore we would have <lb></lb>ſuch a quantity of Water diſcharge from the upper tap, as <lb></lb>would diſcharge from the neather in the ſame time, it is plain, that <lb></lb>either the upper Taps muſt be multiplyed in ſuch ſort, that ſo <lb></lb>many more Taps in number be placed above than below, as the <lb></lb>neather tap ſhall be more ſwift than the upper, or the upper Tap <lb></lb>made ſo much bigger than the nether, by how much that be<lb></lb>neath ſhall be more ſwift than that above; and ſo then in equal <lb></lb>times, the ſame quantity of Water ſhall diſcharge from the upper, <lb></lb>as doth from the neather part.</s></p><pb xlink:href="040/01/573.jpg" pagenum="4"></pb><p type="main"> <s>I will declare my ſelf by another example. </s> <s>If we ſhould ima<lb></lb>gine, that two cords or lines of equal thickneſs, be drawn through <lb></lb>two holes of equal bore; but ſo that the firſt paſs with quadruple <lb></lb>velocity to the ſecond: It is manifeſt, that if in a determinate <lb></lb>time, we ſhall by the firſt bore have drawn four Ells of the line, <lb></lb>in the ſame time, by the ſecond hole we ſhall have drawn but one <lb></lb>Ell of cord onely; and if by the firſt there paſſe twelve Ells, then <lb></lb>through the ſecond there ſhall paſſe onely three Ells; and in <lb></lb>ſhort the quantity of cord ſhall have the ſame proportion to the <lb></lb>cord, that the volocity hath to the velocity. </s> <s>And therefore we <lb></lb>deſiring to compenſate the tardity of the ſecond cord, and main<lb></lb>taining the ſame tardity to draw through the ſecond hole as much <lb></lb>cord as through the firſt, it will be neceſſary to draw through the <lb></lb>ſecond bore four ends of cord; ſo that the thickneſs of all the <lb></lb>cords by the ſecond hole, have the ſame proportion to the thick<lb></lb>neſs of the cord which paſſeth onely by the firſt, as the velocity <lb></lb>of the cord by the firſt hole hath reciprocally to the velocity of <lb></lb>the codrs by the ſecond hole. </s> <s>And thus its clear, that when <lb></lb>there is drawn through two holes equal quantity of cords in <lb></lb>equal time, but with unequal velocity, it will be neceſſary, that <lb></lb>the thickneſs of all the four cords ſhall have the ſame reciprocal <lb></lb>proportion to the thickneſs of the ſwifter cord, that the velo<lb></lb>city of the ſwifter cord hath to the velocity of the ſlower. </s> <s>The <lb></lb>which is verified likewiſe in the fluid Element of Water.</s></p><p type="main"> <s>And to the end that this principal fundamental be well under<lb></lb>ſtood, I will alſo note a certain obſervation made my me in the <lb></lb>Art of Wyer-drawing, or ſpinning Gold, Silver, Braſs, and Iron, <lb></lb>and it is this; That ſuch Artificers deſiring more and more to <lb></lb>diſgroſſe and ſubtillize the ſaid Metals, having would about a <lb></lb><emph type="italics"></emph>R<emph.end type="italics"></emph.end>ocket or Barrel, the thread of the Metal, they place the Roc<lb></lb>ket in a frame upon a ſtedfaſt Axis, in ſuch ſort that the Rocket <lb></lb>may turn about in it ſelf; then making one end of the thread to <lb></lb>paſſe by force through a Plate of Steel pierced with divers holes, <lb></lb>greater and leſſer, as need requireth, faſtning the ſame end of the <lb></lb>thread to another Rocket, they wind up the thread, which paſ<lb></lb>ſing through a bore leſs than the thickneſſe of the thread, is of <lb></lb>force conſtrained to diſgroſſe and ſubtillize. </s> <s>Now that which is <lb></lb>intenſly to be obſerved in this buſineſs, is this, That the parts of <lb></lb>the thread before the hole, are of ſuch a thickneſſe, but the parts <lb></lb>of the ſame thread after it is paſſed the hole, are of a leſſer thick<lb></lb>neſſe: and yet nevertheleſſe the maſſe and weight of the thread <lb></lb>which is drawn forth, is ever equal to the maſſe and weight of the <lb></lb>thread which is winded up. </s> <s>But if we ſhould well conſider the mat<lb></lb>ter, we ſhould finde, that the thicker the thread before the hole is, <lb></lb>than the thread paſſed the hole, the greater reciprocally is the <pb xlink:href="040/01/574.jpg" pagenum="5"></pb>velocity of the parts of the thread paſſed the hole, than the volo<lb></lb>city of the parts before the hole: Inſomuch that if <emph type="italics"></emph>verbi gratia<emph.end type="italics"></emph.end><lb></lb>the thickneſſe of the thread before the hole, were double to the <lb></lb>thickneſſe after the hole, in ſuch caſe the velocity of the parts of <lb></lb>the thread paſſed the hole, ſhould be double to the velocity of the <lb></lb>parts of the thread before the hole; and thus the thickneſſe <lb></lb>compenſates the velocity, and the velocity compenſates the thick<lb></lb>neſſe. </s> <s>So that the ſame occurreth in the ſolid Metals of Gold, <lb></lb>Silver, Braſs, Iron, &c. </s> <s>that eveneth alſo in the fluid Element of <lb></lb>Water, and other liquids, namely, That the velocity beareth the <lb></lb>ſame proportion to the velocity, that the thickneſſe of the Me<lb></lb>tal, or Water, hath to the thickneſſe.</s></p><p type="main"> <s>And therefore granting this diſcourſe, we may ſay, that as of<lb></lb>ten as two Taps with different velocity diſcharge equal quanti<lb></lb>ties of Water in equal times, it will be neceſſary that the Tap <lb></lb>leſſe ſwift be ſo much greater, and larger, than the Tap more <lb></lb>ſwift, by how much the ſwifter ſuperates in velocity the ſlower; <lb></lb>and to pronounce the Propoſition in more proper terms, we ſay; <lb></lb>That if two Taps of unequal velocity, diſcharge in equal times <lb></lb>equal quantities of Water, the greatneſſe of the firſt ſhall be to <lb></lb>the greatneſſe of the ſecond, in reciprocal proportion, as the ve<lb></lb>locity of the ſecond to the velocity of the firſt. </s> <s>As for example, <lb></lb>if the firſt Tap ſhall be ten times ſwifter than the ſecond Tap, it <lb></lb>will be neceſſary, that the ſecond be ten times bigger and larger <lb></lb>than the firſt; and in ſuch caſe the Taps ſhall diſcharge equall <lb></lb>quantities of water in equal times; and this is the principal and <lb></lb>moſt important point, which ought to be kept alwayes in minde, <lb></lb>for that on it well underſtood depend many things profitable, <lb></lb>and worthy of our knowledge.</s></p><p type="main"> <s>Now applying all that hath been ſaid neerer to our purpoſe, I <lb></lb>conſider, that it being moſt true, that in divers parts of the ſame <lb></lb>River or Current of running water, there doth always paſſe equal <lb></lb>quantity of Water in equal time (which thing is alſo demon<lb></lb>ſtrated in out firſt Propoſition) and it being alſo true, that in di<lb></lb>vers parts the ſame River may have various and different veloci<lb></lb>ty; it follows of neceſſary conſequence, that where the River <lb></lb>hath leſſe velocity, it ſhall be of greater meaſure, and in thoſe <lb></lb>parts, in which it hath greater velocity, it ſhall be of leſſe mea<lb></lb>ſure; and in ſum, the velocity of ſeveral parts of the ſaid River, <lb></lb>ſhall have eternally reciprocall and like proportion with <lb></lb>their meaſures. </s> <s>This principle and fundamental well eſtabliſh<lb></lb>ed, that the ſame Current of Water changeth meaſure, accor<lb></lb>ding to its varying of velocity; that is, leſſening the meaſure, <lb></lb>when the velocity encreaſeth, and encreaſing the meaſure, when <lb></lb>the velocity decreaſeth; I paſſe to the conſideration of many <pb xlink:href="040/01/575.jpg" pagenum="6"></pb>particular accidents in this admirable matter, and all depending <lb></lb>on this ſole Propoſition, the ſenſe of which I have oft repeated, <lb></lb>that it might be well underſtood.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> I.</s></p><p type="main"> <s>And firſt, we hence conclude, that the ſame Streams of a <lb></lb>Torrent, namely, thoſe ſtreams which carry equal quantity of <lb></lb>Water in equal times, make not the ſame depths or meaſures in <lb></lb>the River, in which they enter, unleſſe when in the entrance in<lb></lb>to the River they acquire; or to ſay better, keep the ſame velo<lb></lb>city; becauſe if the velocicities acquired in the River ſhall be <lb></lb>different, alſo the meaſures ſhall be diverſe; and conſequently <lb></lb>the depths, as is demonſtrated.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> II.</s></p><p type="main"> <s>And becauſe ſucceſſively, as the River is more and more full, <lb></lb>it is conſtituted ordinarily in greater & greater velocity: hence <lb></lb>it is that the ſame ſtreams of the Torrent, that enter into the Ri<lb></lb>ver, make leſſe and leſſe depths, as the River grows more and <lb></lb>more full; ſince that alſo the Waters of the Torrent being en<lb></lb>tered into the River, go acquiring greater and greater velocities, <lb></lb>and therefore diminiſh in meaſure and height.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> III.</s></p><p type="main"> <s>We obſerve alſo, that while the main River is ſhallow, if there <lb></lb>fall but a gentle rain, it ſuddenly much increaſeth and riſeth; <lb></lb>but when the River is already ſwelled, though there fall again a<lb></lb>nother new violent ſhower, yet it increaſeth not at the ſame rate <lb></lb>as before, proportionably to the rain which fell: which thing <lb></lb>we may affirm particularly to depend on this, that in the firſt <lb></lb>caſe, while the River is low, it is found alſo very ſlow, and there<lb></lb>fore the little water which entereth into it, paſſeth and runs with <lb></lb>little velocity, and conſequently occupieth a great meaſure: <lb></lb>But when the River is once augmented, by new water being alſo <lb></lb>made more ſwift, it cauſeth the great Flood of water which fal<lb></lb>leth, to bear a leſſe meaſure, and not to make ſuch a depth.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> IV.</s></p><p type="main"> <s>From the things demonſtrated is manifeſt alſo, that whilſt a <lb></lb>Torrent entereth into a River, at the time of Ebbe, then the <lb></lb>Torrent moveth with ſuch a certain velocity, what ever it be, <pb xlink:href="040/01/576.jpg" pagenum="7"></pb>paſſing by its extreameſt parts, wherewith it communicateth with <lb></lb>the River; in which parts, the Torrent being meaſured, ſhall <lb></lb>have ſuch a certain meaſure: but the River ſwelling and riſing, <lb></lb>alſo thoſe parts of the Torrent augment in greatneſſe and mea<lb></lb>ſure, though the Torrent, in that inſtant, diſ-imbogue no more <lb></lb>water than it did before: ſo that the River being ſwelled, we <lb></lb>are to conſider two mouths of the ſame Torrent, one leſſe be<lb></lb>fore the riſing, the other greater after the riſing, which mouths <lb></lb>diſcharge equal quantities of water in equal times; therefore the <lb></lb>velocity by the leſſer mouth ſhall be greater than the velocity by <lb></lb>the greater mouth; and thus the Torrent ſhall be retarded from <lb></lb>its ordinary courſe.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> V.</s></p><p type="main"> <s>From which operation of Nature proceedeth another effect <lb></lb>worthy of conſideration; and it is, that the courſe of the water <lb></lb>retarding, as hath been ſaid in thoſe ultimate parts of the Tor<lb></lb>rent, if it ſhall happen that the Torrent grow torbid and mud<lb></lb>dy, and its ſtreame be retarded in ſuch a degree, that it is not <lb></lb>able to carry away thoſe minute grains of Earth, which com<lb></lb>poſe the muddineſſe; in this caſe the Torrent ſhall clear away <lb></lb>the mud, and carry away the Sand at the bottome of its own <lb></lb>Chanel, in the extream parts of its mouth, which raiſed and <lb></lb>voided Sand, ſhall again afterwards be carried away, when the <lb></lb>River abating, the Torrent ſhall return to move with its primitive <lb></lb>velocity.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> VI.</s></p><p type="main"> <s>Whilſt it is demonſtrated, that the ſame water hath different <lb></lb>meaſures in its Chanel or courſe, according as it varieth in <lb></lb>velocity; ſo that the meaſure of the water is alwayes greater, where <lb></lb>the velocity is leſſer; and on the contrary, the meaſure leſſer, <lb></lb>where the velocity is greater: from hence we may moſt ele<lb></lb>gantly render the reaſon of the uſual Proverb, <emph type="italics"></emph>Take heed of the <lb></lb>ſtill waters:<emph.end type="italics"></emph.end> For that if we conſider the ſelf ſame water of a <lb></lb>River in thoſe parts, wherein it is leſs ſwift, and thence called <emph type="italics"></emph>ſtill<emph.end type="italics"></emph.end><lb></lb>or <emph type="italics"></emph>ſmooth<emph.end type="italics"></emph.end> water, it ſhall be, of neceſſity, of greater meaſure <lb></lb>than in thoſe parts, in which it is more ſwift, and therefore ordi<lb></lb>narily ſhall be alſo more deep and dangerous for paſſengers; <lb></lb>whence it is well ſaid, <emph type="italics"></emph>Take heed of the ſtill Waters<emph.end type="italics"></emph.end>; and this <lb></lb>ſaying hath been ſince applied to things moral.</s></p><pb xlink:href="040/01/577.jpg" pagenum="8"></pb><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> VII.</s></p><p type="main"> <s>Likewiſe, from the things demonſtrated may be concluded, <lb></lb>that the windes, which ſtop a <emph type="italics"></emph>R<emph.end type="italics"></emph.end>iver, and blowing againſt the <lb></lb>Current, retard its courſe and ordinary velocity ſhall neceſſarily <lb></lb>amplifie the meaſure of the ſame River, and conſequently ſhall <lb></lb>be, in great part, cauſes; or we may ſay, potent con-cauſes of <lb></lb>making the extraordinary inundations which Rivers uſe to make. <lb></lb></s> <s>And its moſt certain, that as often as a ſtrong and continual wind <lb></lb>ſhall blow againſt the Current of a River, and ſhall reduce the <lb></lb>water of the River to ſuch tardity of motion, that in the time <lb></lb>wherein before it run five miles, it now moveth but one, ſuch a <lb></lb>River will increaſe to five times the meaſure, though there ſhould <lb></lb>not be added any other quantity of water; which thing indeed <lb></lb>hath in it ſomething of ſtrange, but it is moſt certain, for that <lb></lb>look what proportion the waters velocity before the winde, hath <lb></lb>to the velocity after the winde, and ſuch reciprocally is the mea<lb></lb>ſure of the ſame water after the winde, to the meaſure before <lb></lb>the winde; and becauſe it hath been ſuppoſed in our caſe that the <lb></lb>velocity is diminiſhed to a fifth part, therefore the meaſure ſhall <lb></lb>be increaſed five times more than that, which it was before.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> VIII.</s></p><p type="main"> <s>We have alſo probable the cauſe of the inundations of <emph type="italics"></emph>Tyber,<emph.end type="italics"></emph.end><lb></lb>which befel at <emph type="italics"></emph>Rome,<emph.end type="italics"></emph.end> in the time of <emph type="italics"></emph>Alexander<emph.end type="italics"></emph.end> the Sixth, & of <lb></lb><emph type="italics"></emph>Clement<emph.end type="italics"></emph.end> the Seventh; which innundations came in a ſerene time, <lb></lb>and without great thaws of the Snows; which therefore much <lb></lb>puzzled the wits of thoſe times. </s> <s>But we may with much pro<lb></lb>bability affirm, That the River roſe to ſuch a height and excreſ<lb></lb>cence, by the retardation of the Waters dependant on the <lb></lb>boiſtrous and conſtant Winds, that blew in thoſe times, as is no<lb></lb>red in the memorials.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE.<emph.end type="italics"></emph.end> IX.</s></p><p type="main"> <s>It being moſt manifeſt, that by the great abundance of Water <lb></lb>the Torrents may increaſe, and of themſelves alone exorbitantly <lb></lb>ſwell the River; and having demonſtrated that alſo without new <lb></lb>Water, but onely by the notable retardment the River riſeth and <lb></lb>increaſeth in meaſure, in proportion as the velocity decreaſeth: <lb></lb>hence it is apparent, that each of theſe cauſes being able of it ſelf, <lb></lb>and ſeparate from the other to ſwell the River; when it ſhall <lb></lb>happen that both theſe two cauſes conſpire the augmentation of <pb xlink:href="040/01/578.jpg" pagenum="9"></pb>the River, in ſuch a caſe there muſt follow very great and irre<lb></lb>pable innundations.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> X.</s></p><p type="main"> <s>From what hath been demonſtrated, we may with facility re<lb></lb>ſolve the doubt which hath troubled, and ſtill poſeth the moſt <lb></lb>diligent, but incautelous obſervers of Rivers, who meaſuring <lb></lb>the Streams and Torrents which fall into another River; as thoſe <lb></lb>for inſtance, which enter into the <emph type="italics"></emph>Po,<emph.end type="italics"></emph.end> or thoſe which fall into <emph type="italics"></emph>Ti<lb></lb>ber<emph.end type="italics"></emph.end>; and having ſummed the total of theſe meaſures, and con<lb></lb>ferring the meaſures of the Rivers and Brooks, which fall into <lb></lb><emph type="italics"></emph>Tiber,<emph.end type="italics"></emph.end> with the meaſure of <emph type="italics"></emph>Tiber,<emph.end type="italics"></emph.end> and the meaſures of thoſe which <lb></lb>diſimbogue into <emph type="italics"></emph>Po,<emph.end type="italics"></emph.end> with the meaſure of <emph type="italics"></emph>Po,<emph.end type="italics"></emph.end> they find them not <lb></lb>equal, as, it ſeems to them, they ought to be, and this is becauſe <lb></lb>they have not well noted the moſt important point of the varia<lb></lb>tion of velocity, and how that it is the moſt potent cauſe of won<lb></lb>derfully altering the meaſures of running Waters; but we moſt <lb></lb>facilly reſolving the doubt, may ſay that theſe Waters diminiſh <lb></lb>the meaſure, being once entered the principal Channel, becauſe <lb></lb>they increaſe in velocity.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> XI.</s></p><p type="main"> <s>Through the ignorance of the force of the velocity of the Wa<lb></lb>ter, in altering its meaſure, & augmenting it when the velocity <lb></lb>diminiſheth; and diminiſhing it when the velocity augmenteth: <lb></lb>The Architect <emph type="italics"></emph>Giovanni Fontana,<emph.end type="italics"></emph.end> endeavoured to meaſure, and <lb></lb>and to cauſe to be meaſured by his Nephew, all the Brooks and <lb></lb>Rivers which diſcharged their Waters into <emph type="italics"></emph>Tiber,<emph.end type="italics"></emph.end> at the time of <lb></lb>the Innundation; which happened at <emph type="italics"></emph>Rome<emph.end type="italics"></emph.end> in the year 1598, <lb></lb>and publiſhed a ſmall Treatiſe thereof, wherein he ſummeth up <lb></lb>the meaſures of the extraordinary Water which fell into <emph type="italics"></emph>Tiber,<emph.end type="italics"></emph.end><lb></lb>and made account that it was about five hundred Ells more than <lb></lb>ordinary; and in the end of that Treatiſe concludeth, that to re<lb></lb>move the Innundation wholly from <emph type="italics"></emph>Rome,<emph.end type="italics"></emph.end> it would be neceſſary <lb></lb>to make two other Channels, equal to that at preſent, and that <lb></lb>leſſe would not ſuffice; and finding afterwards that the whole <lb></lb>Stream paſſed under the Bridge <emph type="italics"></emph>Quattro-Capi,<emph.end type="italics"></emph.end> (the Arch where<lb></lb>of is of a far leſs meaſure then five hundred Ells) concludeth, <lb></lb>that under the ſaid Bridge paſt a hundred fifty one Ells of Water <lb></lb>compreſſed, (I have ſet down the preciſe term of compreſt Wa<lb></lb>ter, written by <emph type="italics"></emph>Fontana<emph.end type="italics"></emph.end>) wherein I finde many errors.</s></p><p type="main"> <s>The firſt of which is to think that the meaſures of theſe Wa<lb></lb>ters compreſſed in the Channels of thoſe Brooks and Rivers, <pb xlink:href="040/01/579.jpg" pagenum="10"></pb>ſhould maintain themſelves the ſame in <emph type="italics"></emph>Tiber,<emph.end type="italics"></emph.end> which by his leave, <lb></lb>is moſt falſe, when ever thoſe waters reduced into <emph type="italics"></emph>Tiber,<emph.end type="italics"></emph.end> retain <lb></lb>not the ſame velocity which they had in the place in which <emph type="italics"></emph>Fon<lb></lb>tana<emph.end type="italics"></emph.end> and his Nephew meaſured them: And all this is manifeſt <lb></lb>from the things which we have above explained; for, if the Wa<lb></lb>ters reduced into <emph type="italics"></emph>Tiber<emph.end type="italics"></emph.end> increaſe in velocity, they decreaſe in mea<lb></lb>ſure; and if they decreaſe in velocity, they increaſe in mea<lb></lb>ſure.</s></p><p type="main"> <s>Secondly, I conſider that the meaſures of thoſe Brooks and <lb></lb>Rivers, which enter into <emph type="italics"></emph>Tiber<emph.end type="italics"></emph.end> at the time of Innundation, are <lb></lb>not between themſelves really the ſame, when their velocities are <lb></lb>not equal, though they have the ſame names of Ells and Feet; <lb></lb>for that its poſſible that a diſinboguement of ten Ells requadrated <lb></lb>(to ſpeak in the phraſe of <emph type="italics"></emph>Fontana<emph.end type="italics"></emph.end>) of one of thoſe Brooks, <lb></lb>might diſcharge into <emph type="italics"></emph>Tiber<emph.end type="italics"></emph.end> at the time of Innundation, four, ten, <lb></lb>and twenty times leſs Water, than another mouth equal to the <lb></lb>firſt in greatneſs, as would occur when the firſt mouth were four, <lb></lb>ten, or twenty times leſs ſwift than the ſecond. </s> <s>Whereupon, <lb></lb>whilſt <emph type="italics"></emph>Fontana<emph.end type="italics"></emph.end> ſummes up the Ells and Feet of the meaſures of <lb></lb>thoſe Brooks and Rivers into a total aggregate, he commits the <lb></lb>ſame error with him, which would add into one ſumme diverſe <lb></lb>moneys of diverſe values, and diverſe places, but that had the <lb></lb>ſame name; as if one ſhould ſay ten Crowns of <emph type="italics"></emph>Roman<emph.end type="italics"></emph.end> money, <lb></lb>four Crowns of Gold, thirteen Crowns of <emph type="italics"></emph>Florence,<emph.end type="italics"></emph.end> five Growns <lb></lb>of <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> and eight Crowns of <emph type="italics"></emph>Mantua,<emph.end type="italics"></emph.end> ſhould make the ſame <lb></lb>ſumme with forty Crowns of Gold, or forty Crowns of <emph type="italics"></emph>Mantua.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Thirdly, It might happen that ſome River or Current in the <lb></lb>parts nearer <emph type="italics"></emph>Rome,<emph.end type="italics"></emph.end> in the time of its flowing, did not ſend forth <lb></lb>more Water than ordinary; and however, its a thing very clear, <lb></lb>that whilſt the ſtream came from the ſuperior parts, that ſame <lb></lb>Brook or River would be augmented in meaſure, as hath been <lb></lb>noted in the fourth <emph type="italics"></emph>Corollary<emph.end type="italics"></emph.end>; in ſuch ſort, that <emph type="italics"></emph>Fontana<emph.end type="italics"></emph.end> might <lb></lb>have inculcated, and noted that ſame River or Current as con<lb></lb>curring to the Innundation, although it were therein altogether <lb></lb>unconcerned.</s></p><p type="main"> <s>Moreover, in the fourth place we muſt note, That it might <lb></lb>ſo fall out, that ſuch a River not onely was unintereſſed in the <lb></lb>Innundation, though augmented in meaſure, but it might I ſay <lb></lb>happen, that it was inſtrumental to the aſſwaging the Innunda<lb></lb>tion, by augmenting in the meaſure of its own Channel; which <lb></lb>matter is ſufficiently evident; for if it be ſuppoſed that the Ri<lb></lb>ver in the time of flood, had not had of it ſelf, and from its pro<lb></lb>per ſprings more Water than ordinary, its a thing certain, that <lb></lb>the Water of <emph type="italics"></emph>Tiber<emph.end type="italics"></emph.end> riſing and increaſing; alſo that River, to le<lb></lb>vel it ſelf with the Water of <emph type="italics"></emph>Tiber,<emph.end type="italics"></emph.end> would have retained ſome of <pb xlink:href="040/01/580.jpg" pagenum="11"></pb>its Waters in its own Chanel, without diſcharging them into <emph type="italics"></emph>Ty<lb></lb>ber,<emph.end type="italics"></emph.end> or elſe would have ingorged and ſwallowed (if I may ſo ſay) <lb></lb>ſome of the water of <emph type="italics"></emph>Tyber<emph.end type="italics"></emph.end>; and in this caſe, at the time of In<lb></lb>undation, leſſe abundance of water would have come to <emph type="italics"></emph>Rome,<emph.end type="italics"></emph.end><lb></lb>and yet nevertheleſſe the meaſure of that River would have been <lb></lb>increaſed.</s></p><p type="main"> <s>Fifthly, <emph type="italics"></emph>Fontana<emph.end type="italics"></emph.end> deceiveth himſelf, when he concludeth, that <lb></lb>to remove the Inundation from <emph type="italics"></emph>Rome,<emph.end type="italics"></emph.end> it would be neceſſary to <lb></lb>make two other Chanels of Rivers, that were as large as that, <lb></lb>which is the preſent one, and that leſs would not ſuffice, which, <lb></lb>I ſay, is a fallacy: and to convince him eaſily of his errour, it <lb></lb>ſufficeth to ſay, that all the Streams being paſſed under the Bridge <lb></lb><emph type="italics"></emph>Quattro-Capi,<emph.end type="italics"></emph.end> as he himſelf atteſts, a Channel would ſuffice on<lb></lb>ly of the capacity of the ſaid Bridge, provided that the water <lb></lb>there might run with the ſame velocity, as it did under the Bridge <lb></lb>at the time of Inundation; and on the contrary, twenty Cur<lb></lb>rents of capacity equal to the preſent one, would not ſuffice, if <lb></lb>the water ſhould run with twenty times leſs velocity, than it made <lb></lb>at the time of the Inundation.</s></p><p type="main"> <s>Sixthly, to me it ſeemeth a great weakneſſe to ſay, that there <lb></lb>ſhould paſſe under the Bridge <emph type="italics"></emph>Quattro-Capi,<emph.end type="italics"></emph.end> an hundred fifty one <lb></lb>ells of water compreſſed; for that I do not underſtand that wa<lb></lb>ter is like Cotton or Wool, which matters may be preſt and trod, <lb></lb>as it happeneth alſo to the air, which receiveth compreſſion in <lb></lb>ſuch ſort, that after that in ſome certain place a quantity of air <lb></lb>ſhall be reduced to its natural conſtitution; and having taken up <lb></lb>all the ſaid place, yet nevertheleſſe compreſſing the firſt Air <lb></lb>with force and violence, it is reduced into far leſs room, and will <lb></lb>admit four or ſix times as much air, as before, as is experimen<lb></lb>tally ^{*} ſeen in the Wind-Gun, invented in our dayes by <emph type="italics"></emph>M. Vin,<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg964"></arrow.to.target><lb></lb><emph type="italics"></emph>cenzo Vincenti<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Vrbin,<emph.end type="italics"></emph.end> which property of the Air of admit<lb></lb>ting condenſation, is alſo ſeen in the portable Fountains of the <lb></lb>ſame <emph type="italics"></emph>M. Vincenzo:<emph.end type="italics"></emph.end> which Fountains ſpirt the Water on high, <lb></lb>by force of the Air compreſſed, which whilſt it ſeeks to reduce <lb></lb>its ſelf to its natural conſtitution, in the dilation cauſeth that vi<lb></lb>olence. </s> <s>But the water can never, for any thing I know, crowd, <lb></lb>or preſs ſo, as that if before the compreſſion it held or poſſeſt a <lb></lb>place, being in its natural conſtitution, I believe not, I ſay, that it <lb></lb>is poſſible, by preſſing and crowding to make it poſſeſs leſs room, <lb></lb>for if it were poſſible to compreſs the Water, and make it to oc<lb></lb>cupy a leſs place, it would thence follow, that two Veſſels of e<lb></lb>qual meaſure, but of unequal height, ſhould be of unequal capa<lb></lb>city, and that ſhould hold more water which was higher; alſo a <lb></lb>Cylinder, or other Veſſel more high than broad, would containe <lb></lb>more water erected, than being laid along; for that being erect<pb xlink:href="040/01/581.jpg" pagenum="12"></pb>ed, the water put therein would be more preſſed and crowded.</s></p><p type="margin"> <s><margin.target id="marg964"></margin.target>* And as is at <lb></lb>large demonſtrated <lb></lb>by that moſt excel<lb></lb>lent and lonour<lb></lb>able perſonage Mr. <lb></lb><emph type="italics"></emph>Botle<emph.end type="italics"></emph.end> in the indu<lb></lb>ſtrious experiment <lb></lb>of his Pneumatical <lb></lb>Engine.</s></p><p type="main"> <s>And therefore, in our caſe, according to our principles we will <lb></lb>ſay, that the water of that Stream paſseth all under the ſaid <lb></lb>Bridge <emph type="italics"></emph>Quattro-Capi,<emph.end type="italics"></emph.end> for that being there moſt ſwift, it ought of <lb></lb>conſequence to be leſs in meaſure.</s></p><p type="main"> <s>And here one may ſee, into how many errours a man may run <lb></lb>through ignorance of a true and real Principle, which once known <lb></lb>and well underſtood, takes away all miſts of doubting, and ea<lb></lb>ſily reſolveth all difficulties.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE.<emph.end type="italics"></emph.end> XII.</s></p><p type="main"> <s>Through the ſame inadvertency of not regarding the variation <lb></lb>of velocity in the ſame Current, therea re committed by Ingi<lb></lb>neers and Learned men, errours of very great moment (and I <lb></lb>could thereof produce examples, but for good reaſons I paſs <lb></lb>them over in ſilence) when they think, and propoſe, by deriving <lb></lb>new Channels from great Rivers, to diminiſh the meaſure of the <lb></lb>water in the River, and to diminiſh it proportionally, according <lb></lb>to the meaſure of the Water which they make to paſs through <lb></lb>the Channel, as making <emph type="italics"></emph>v.g<emph.end type="italics"></emph.end> a Channel fifty foot broad, in which <lb></lb>the derived water is to run waſte, ten foot deep, they think they <lb></lb>have diminiſhed the meaſure of the Water in the River five hun<lb></lb>dred feet, which thing doth not indeed ſo fall out; and the rea<lb></lb>ſon is plain; for that the Chanel being derived, the reſt of the <lb></lb>main River, diminiſheth in velocity, and therefore retains a grea<lb></lb>ter meaſure than it had at firſt before the derivation of the Cha<lb></lb>nel; and moreover, if the Chanel being derived, it ſhall not <lb></lb>conſerve the ſame velocity which it had at firſt in the main Ri<lb></lb>ver, but ſhall diminiſh it, it will be neceſſary, that it hath a grea<lb></lb>ter meaſure than it had before in the River; and therefore <lb></lb>to accompt aright, there ſhall not be ſo much water derived into <lb></lb>the Channel, as ſhall diminiſh the River, according to the quanti<lb></lb>ty of the water in the Channel, as is pretended.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> XIII.</s></p><p type="main"> <s>This ſame conſideration giveth me occaſion to diſcover a moſt <lb></lb>ordinary errour, obſerved by me in the buſineſſe of the wa<lb></lb>ter of <emph type="italics"></emph>Ferara,<emph.end type="italics"></emph.end> when I was in thoſe parts, in ſervice of the moſt <lb></lb>Reverend and Illuſtrious Monfignor <emph type="italics"></emph>Corſini<emph.end type="italics"></emph.end>; the ſublime wit of <lb></lb>whom hath been a very great help to me in theſe contemplations; <lb></lb>its very true, I have been much perplexed, whether I ſhould <lb></lb>commit this particular to paper, or paſſe it over in ſilence, for <lb></lb>that I have ever doubted, that the opinion ſo common and <pb xlink:href="040/01/582.jpg" pagenum="13"></pb>moreover confirmed with a moſt manifeſt experiment, may not <lb></lb>onely make this my conjecture to be eſteemed far from true, <lb></lb>but alſo to diſcredit with the World the reſt of this my Treatiſe: <lb></lb>Nevertheleſſe I have at laſt reſolved not to be wanting to my <lb></lb>ſelf, and to truth in a matter of it ſelf, and for other conſe<lb></lb>quences moſt important; nor doth it ſeem to me requiſite in <lb></lb>difficult matters, ſuch as theſe we have in hand, to refigne our <lb></lb>ſelves to the common opinion, ſince it would be very ſtrange if <lb></lb>the multitude in ſuch matters ſhould hit on the truth, nor ought <lb></lb>that to be held difficult, in which even the vulgar do know the <lb></lb>truth and right; beſides that I hope morever to prove all in ſuch <lb></lb>ſort, that perſons of ſolid judgment, ſhall reſt fully perſwaded, <lb></lb>ſo that they but keep in mind the principal ground and foundation <lb></lb>of all this Treatiſe; and though that which I will propoſe, be a par<lb></lb>ticular, as I have ſaid, pertaining onely to the intereſts of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end>; <lb></lb>yet nevertheleſſe from this particular Doctrine well underſtood, <lb></lb>good judgement may be made of other the like caſes in general.</s></p><p type="main"> <s>I ſay then, for greater perſpecuity, and better underſtanding <lb></lb>of the whole, That about thirteen miles above <emph type="italics"></emph>Ferara,<emph.end type="italics"></emph.end> near to <lb></lb><emph type="italics"></emph>Stellata,<emph.end type="italics"></emph.end> the main of P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> branching it ſelf into two parts, with one <lb></lb>of its Arms it cometh cloſe to <emph type="italics"></emph>Ferara,<emph.end type="italics"></emph.end> retaining the name of the <lb></lb>P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end>; and here again it divideth it ſelf into two other <lb></lb>branches, and that which continueth on the right hand, is called <lb></lb>the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Argenta,<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Primaro<emph.end type="italics"></emph.end>; and that on the left the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end><lb></lb>of <emph type="italics"></emph>Volana.<emph.end type="italics"></emph.end> But for that the bed of the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end> being here<lb></lb>tofore augmented and raiſed, it followeth that it reſteth wholly <lb></lb>deprived of the Water of the great P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> except in the time of its <lb></lb>greater ſwelling; for in that caſe, this P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end> being re<lb></lb>ſtrained with a Bank near to <emph type="italics"></emph>Bondeno,<emph.end type="italics"></emph.end> would come alſo in the <lb></lb>overflowings of the main P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> to be free from its Waters: But the <lb></lb>Lords of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end> are wont at ſuch time as the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> threateneth to <lb></lb>break out, to cut the bank; by which cutting, there diſ<lb></lb>gorgeth ſuch a Torrent of Water, that it is obſerved, that the <lb></lb>main P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> in the ſpace of ſome few hours abateth near a foot, and <lb></lb>all perſons that I have ſpoken with hitherto, moved by this ex<lb></lb>periment, think that it is of great profit and benefit to keep ready <lb></lb>this Vent, and to make uſe of it in the time of its fullneſſe. </s> <s>And <lb></lb>indeed, the thing conſidered ſimply, and at the firſt appearance, <lb></lb>it ſeemeth that none can think otherwiſe; the rather, for that <lb></lb>many examining the matter narrowly, meaſure that body of <lb></lb>Water which runneth by the Channel, or Bed of the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Fera<lb></lb>ra,<emph.end type="italics"></emph.end> and make account, that the body of the Water of the great <lb></lb>P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> is diminiſhed the quantity of the body of the Water which <lb></lb>runneth by the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara.<emph.end type="italics"></emph.end> But if we well remember what <lb></lb>hath been ſaid in the beginning of the Treatiſe, and how much <pb xlink:href="040/01/583.jpg" pagenum="14"></pb>the variety of the velocities of the ſaid Water importeth, and the <lb></lb>knowledge of them is neceſſary to conclude the true quantity of <lb></lb>the running Water, we ſhall finde it manifeſt, that the benefit of <lb></lb>this Vent is far leſſe than it is generally thought: And mereover, <lb></lb>we ſhall finde, if I deceive not my ſelf, that there follow from <lb></lb>thence ſo many miſchiefs, that I could greatly incline to believe, <lb></lb>that it were more to the purpoſe wholly to ſtop it up, than to <lb></lb>maintain it open: yet I am not ſo wedded to my opinion, but <lb></lb>that I am ready to change my judgement upon ſtrength of better <lb></lb>reaſons; eſpecially of one that ſhall have firſt well underſtood <lb></lb>the beginning of this my diſcourſe, which I frequently inculcate, <lb></lb>becauſe its abſolutely impoſſible without this advertiſement to <lb></lb>treat of theſe matters, and not commit very great errours.</s></p><p type="main"> <s>I propoſe therefore to conſideration, that although it be true, <lb></lb>that whilſt the water of the main P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> is at its greateſt height, the <lb></lb>Bank and Dam then cut of the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara,<emph.end type="italics"></emph.end> and the ſuperior <lb></lb>waters having a very great fall into the Channel of <emph type="italics"></emph>Ferara,<emph.end type="italics"></emph.end> they <lb></lb>precipitate into the ſame with great violence and velocity, and <lb></lb>with the ſame in the beginning, or little leſſe, they run towards <lb></lb>the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Volana,<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Argenta<emph.end type="italics"></emph.end> on the ſea coaſts; yet after the <lb></lb>ſpace of ſome few hours, the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end> being full, and the ſu<lb></lb>perior Waters not finding ſo great a diclivity there, as they had <lb></lb>at the beginning of the cutting, they fall not into the ſame with <lb></lb>the former velocity, but with far leſſe, and thereby a great deal <lb></lb>leſſe Water begins to iſſue from the great P<emph type="italics"></emph>o<emph.end type="italics"></emph.end>; and if we dili<lb></lb>gently compare the velocity at the firſt cutting, with the velocity <lb></lb>of the Water after the cutting made, and when the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end><lb></lb>ſhall be full of Water, we ſhall finde perhaps that to be fifteen or <lb></lb>twenty times greater than this, and conſequently the Water <lb></lb>which iſſues from the great P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> that firſt impetuoſity being paſt, <lb></lb>ſhall be onely the fifteenth or twentieth part of that which iſſued <lb></lb>at the beginning; and therefore the Waters of the main P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> will <lb></lb>return in a ſmall time almoſt to the firſt height. </s> <s>And here I will <lb></lb>pray thoſe who reſt not wholly ſatisfied with what hath been ſaid, <lb></lb>that for the love of truth, and the common good, they would <lb></lb>pleaſe to make diligent obſervation whether in the time of great <lb></lb>Floods, the ſaid Bank or Dam at <emph type="italics"></emph>Bondeno<emph.end type="italics"></emph.end> is cut, and that in few <lb></lb>hours the main P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> diminiſheth, as hath been ſaid about a foot in <lb></lb>its height; that they would obſerve I ſay, whether, a day or two <lb></lb>being paſt, the Waters of the main P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> return almoſt to their firſt <lb></lb>height; for if this ſhould follow, it would be very clear, that the <lb></lb>benefit which reſulteth from this diverſion or Vent, is not ſo great <lb></lb>as is univerſally preſumed; I ſay, it is not ſo great as is <lb></lb>preſumed; becauſe, though it be granted for true, that <lb></lb>the Waters of the main P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> abate at the beginning of <pb xlink:href="040/01/584.jpg" pagenum="17"></pb>the Vent, yet this benefit happens to be but temporary and for a <lb></lb>few hours: If the riſing of P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> and the dangers of breaking forth <lb></lb>were of ſhort duration, as it ordinarily befalleth in the overflow<lb></lb>ings of Torrents, in ſuch a caſe the profit of the Vent would be <lb></lb>of ſome eſteem: But becauſe the ſwellings of P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> continue for <lb></lb>thirty, or ſometimes for forty dayes, therefore the gain which <lb></lb>reſults from the Vent proveth to be inconſiderable. </s> <s>It remain<lb></lb>eth now to conſider the notable harms which follow the ſaid <lb></lb>Sluice or Vent, that ſo reflection being made, and the profit and <lb></lb>the detriment compared, one may rightly judge, and chooſe that <lb></lb>which ſhall be moſt convenient. </s> <s>The firſt prejudice therefore <lb></lb>which ariſeth from this Vent or Sluice, is; That the Channels of <lb></lb><emph type="italics"></emph>Ferara, Primaro,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Volana<emph.end type="italics"></emph.end> filling with Water, all thoſe parts <lb></lb>from <emph type="italics"></emph>Bondeno<emph.end type="italics"></emph.end> to the Sea ſide are allarmed and endangered <lb></lb>thereby. </s> <s>Secondly, The Waters of the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Primaro<emph.end type="italics"></emph.end> having <lb></lb>free ingreſſe into the upper Valleys, they fill them to the great <lb></lb>damage of the Fields adjacent, and obſtruct the courſe of the <lb></lb>ordinary Trenches in the ſame Valleys; inſomuch that all the <lb></lb>care, coſt, and labour about the draining, and freeing the upper <lb></lb>Valleys from Water, would alſo become vain and ineffectual. <lb></lb></s> <s>Thirdly, I conſider that theſe Waters of the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end> being <lb></lb>paſſed downwards towards the Sea, at the time that the main P<emph type="italics"></emph>o<emph.end type="italics"></emph.end><lb></lb>was in its greater excreſcences and heights, it is manifeſt by expe<lb></lb>rience, that when the great P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> diminiſheth, then theſe Waters <lb></lb>paſſed by the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferara<emph.end type="italics"></emph.end> begin to retard in their courſe, and <lb></lb>finally come to turn the current upwards towards <emph type="italics"></emph>Stellata,<emph.end type="italics"></emph.end> reſting <lb></lb>firſt iu the intermediate time, almoſt fixed and ſtanding, and <lb></lb>therefore depoſing the muddineſſe, they fill up the Channel of <lb></lb>the River or Current of <emph type="italics"></emph>Ferara.<emph.end type="italics"></emph.end> Fourthly and laſtly, There <lb></lb>followeth from this ſame diverſion another notable damage, and <lb></lb>it is like to that which followeth the breaches made by Rivers; <lb></lb>near to which breaches in the lower parts, namely below the <lb></lb>breach, there is begot in the Channel of the River, a certain ridge <lb></lb>or ſhelf, that is, the bottom of the River is raiſed, as if ſufficiently <lb></lb>manifeſt by experience; and thus juſt in the ſame manner cutting <lb></lb>the Bank at <emph type="italics"></emph>Bondeno,<emph.end type="italics"></emph.end> there is at it were a breach made, from which <lb></lb>followeth the riſing in the lower parts of the main P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> being paſt <lb></lb>the mouth of <emph type="italics"></emph>Pamaro<emph.end type="italics"></emph.end>; which thing, how pernitious it is, let any one <lb></lb>judge that underſtandeth theſe matters. </s> <s>And therefore both for <lb></lb>the ſmall benefit, and ſo many harms that enſue from maintain<lb></lb>ing this diverſion, I ſhould think it were more ſound advice to <lb></lb>keep that Bank alwaies whole at <emph type="italics"></emph>Bondeno,<emph.end type="italics"></emph.end> or in any other conve<lb></lb>nient place, and not to permit that the Water of the Grand P<emph type="italics"></emph>o<emph.end type="italics"></emph.end><lb></lb>ſhould ever come near to <emph type="italics"></emph>Ferara.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/585.jpg" pagenum="16"></pb><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> XIV.<lb></lb><arrow.to.target n="marg965"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg965"></margin.target>* <emph type="italics"></emph>Arteſia.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>In the Grand Rivers, which fall into the Sea, as here in <emph type="italics"></emph>Italy <lb></lb>Po, Adige,<emph.end type="italics"></emph.end>^{*} and <emph type="italics"></emph>Arno,<emph.end type="italics"></emph.end> which are armed with Banks againſt their <lb></lb>excreſcencies, its obſerved that far from the Sea, they need <lb></lb>Banks of a notable height; which height goeth afterwards by <lb></lb>degrees diminiſhing, the more it approacheth to the Sea-coaſts: <lb></lb>in ſuch ſort, that the P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> diſtant from the Sea about fifty or ſixty <lb></lb>miles at <emph type="italics"></emph>Ferara,<emph.end type="italics"></emph.end> ſhall have Banks that be above twenty feet <lb></lb>higher than the ordinary Water marks; but ten or twelve miles <lb></lb>from the Sea, the Banks are not twelve feet higher than the ſaid <lb></lb>ordinary Water-marks, though the breadth of the River be the <lb></lb>ſame, ſo that the excreſcence of the ſame Innundation happens <lb></lb>to be far greater in meaſure remote from the Sea, then near; and <lb></lb>yet it ſhould ſeem, that the ſame quantity of Water paſſing by <lb></lb>every piace, the River ſhould need to have the ſame altitude of <lb></lb>Banks in all places: But we by our Principles and fundamentals <lb></lb>may be able to render the reaſon of that effect, and ſay; That <lb></lb>that exceſſe of quantity of Water, above the ordinary Water, <lb></lb>goeth alwaies acquiring greater velocity; the nearer it approach<lb></lb>eth the Sea, and therefore decreaſeth in meaſure, and conſequenly <lb></lb>in height. </s> <s>And this perhaps might have been the cauſe in great <lb></lb>part, why the <emph type="italics"></emph>Tyber<emph.end type="italics"></emph.end> in the Innundation <emph type="italics"></emph>Anno<emph.end type="italics"></emph.end> 1578. iſſued not <lb></lb>forth of its Channel below <emph type="italics"></emph>Rome<emph.end type="italics"></emph.end> towards the Sea.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> XV.</s></p><p type="main"> <s>From the ſame Doctrine may be rendred a moſt manifeſt rea<lb></lb>ſon why the falling Waters go leſſening in their deſcent, ſo <lb></lb>that the ſame falling Water, meaſured at the beginning of <lb></lb>its fall, is greater, and bigger, and afterwards by degrees leſſeneth <lb></lb>in meaſure the more it is remote from the beginning of the fall. <lb></lb></s> <s>Which dependeth on no other, than on the acquiſition, which <lb></lb>it ſucceſſively makes of greater velocity; it being a moſt fami<lb></lb>liar concluſion among Philoſophers, that grave bodies falling, <lb></lb>the more they remove from the beginning of their motion, the <lb></lb>more they acquire of ſwiftneſſe; and therefore the Water, as a <lb></lb>grave body, falling, gradually velocitates, and therefore de<lb></lb>creaſeth in meaſure, and leſſeneth.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end> XVI.</s></p><p type="main"> <s>And on the contrary, the ſpirtings of a Fountain of Water, <lb></lb>which ſpring on high, work a contrary effect; namely <pb xlink:href="040/01/586.jpg" pagenum="17"></pb>in the beginning they are ſmall, and afterwards become greater <lb></lb>and bigge; and the reaſon is moſt manifeſt, becauſe in the be<lb></lb>ginning they are very ſwift, and afterwards gradually relent <lb></lb>their impetuoſity, and motion, ſo that in the beginning of the <lb></lb>excurſion that they make, they ought to be ſmall, and after<lb></lb>wards to grow bigger, as in the effect is ſeen.</s></p><p type="head"> <s>APPENDIX. I.</s></p><p type="main"> <s>Into the errour of not conſidering how much the different <lb></lb>velocities of the ſame running water in ſeveral places of <lb></lb>its current, are able to change the meaſure of the ſame <lb></lb>water, and to make it greater, or leſſe, I think, if I be not <lb></lb>deceived, that <emph type="italics"></emph>Ginlio Frontino<emph.end type="italics"></emph.end> a noble antient Writer, may <lb></lb>have faln in the Second Book which he writ, of the Aqueducts <lb></lb>of the City of <emph type="italics"></emph>Rome<emph.end type="italics"></emph.end>: Whilſt finding the meaſure of the Water <lb></lb>^{*}<emph type="italics"></emph>Commentaries<emph.end type="italics"></emph.end> leſſe than it was <emph type="italics"></emph>in erogatione 1263. Quinaries,<emph.end type="italics"></emph.end> he </s></p><p type="main"> <s><arrow.to.target n="marg966"></arrow.to.target><lb></lb>thought that ſo much difference might proceed from the negligence <lb></lb>of the Meaſures; and when afterwards with his own induſtry he <lb></lb>meaſured the ſame water at the beginnings of the Aqueducts, <lb></lb>finding it neer 10000. <emph type="italics"></emph>Quinaries<emph.end type="italics"></emph.end> bigger than it was <emph type="italics"></emph>in Commenta<lb></lb>riis<emph.end type="italics"></emph.end> he judged, that the overplus was imbeziled by Miniſters and <lb></lb>Partakers; which in part might be ſo, for it is but too true, that <lb></lb>the publique is almoſt alwayes defrauded; yet nevertheleſſe, I <lb></lb>verily believe withal, that beſides the frauds of theſe Officers, <lb></lb>the velocities of the water in the place wherein <emph type="italics"></emph>Frontino<emph.end type="italics"></emph.end> meaſu<lb></lb>red, it might be different from thoſe velocities, which are <lb></lb>found in other places before meaſured by others; and there<lb></lb>fore the meaſures of the waters might, yea ought necſſarily to <lb></lb>be diffcrent, it having been by us demonſtrated, that the mea<lb></lb>ſures of the ſame running water have reciprocal proportion to <lb></lb>their velocities. </s> <s>Which <emph type="italics"></emph>Frontino<emph.end type="italics"></emph.end> not well conſidering, and find<lb></lb>ing the water <emph type="italics"></emph>in Commentariis 12755. Quinaries in erogati<lb></lb>one<emph.end type="italics"></emph.end> 14018, and in his own meaſure <emph type="italics"></emph>ad capita ductuum,<emph.end type="italics"></emph.end> at the <lb></lb>head of the fountain 22755. <emph type="italics"></emph>Quinaries,<emph.end type="italics"></emph.end> or thereabouts, he <lb></lb>thought, that in all theſe places there paſt different quantities of <lb></lb>water; namely, greater at the fountain head then that which was <lb></lb><emph type="italics"></emph>in Erogatione,<emph.end type="italics"></emph.end> and this he judged greater than that which was <lb></lb><emph type="italics"></emph>in Commentariis.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg966"></margin.target>+ <emph type="italics"></emph>Commentarius<emph.end type="italics"></emph.end><lb></lb>beareth many ſen<lb></lb>ſes, but in this <lb></lb>place ſignifieth a <lb></lb>certain Regiſter of <lb></lb>the quantities of <lb></lb>the Waters in the <lb></lb>ſeveral publique A<lb></lb>qu ducts of <emph type="italics"></emph>Rome<emph.end type="italics"></emph.end>; <lb></lb>which word I find <lb></lb>frequently uſed in <lb></lb>the Law-books of <lb></lb>antient Civilians: <lb></lb>Andby errogation <lb></lb>we are to under<lb></lb>ſtand the diſtribu<lb></lb>tion or delivering <lb></lb>out of thoſe ſtores <lb></lb>of Water.</s></p><p type="head"> <s>APPENDIX II.</s></p><p type="main"> <s>Alike miſtake chanced lately in the Aqueduct of <emph type="italics"></emph>Acqua<lb></lb>Paola,<emph.end type="italics"></emph.end> which Water ſhould be 2000 Inches, and ſo many <lb></lb>effectively ought to be allowed; and it hath been given in <pb xlink:href="040/01/587.jpg" pagenum="18"></pb>ſo to be by the Signors of <emph type="italics"></emph>Bracciano<emph.end type="italics"></emph.end> to the <emph type="italics"></emph>Apoſtolick-Chamber<emph.end type="italics"></emph.end>; <lb></lb>and there was a meaſure thereof made at the beginning of the <lb></lb>Aqueduct; which meaſure proved afterwards much leſſe and <lb></lb>ſhort, conſidered and taken in <emph type="italics"></emph>Rome,<emph.end type="italics"></emph.end> and thence followed diſ<lb></lb>contents and great diſorders, and all becauſe this property of <lb></lb>Running-Waters, of increaſing in meaſure, where the velocity <lb></lb>decreaſed; and of diminiſhing in meaſure, where the velocity <lb></lb>augmented, was not lookt into.</s></p><p type="head"> <s>APPENDIX III.</s></p><p type="main"> <s>Alike errour, in my judgement, hath beeen committed by <lb></lb>all thoſe learned men, which to prevent the diverſion of <lb></lb>the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Bologna<emph.end type="italics"></emph.end> into P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> by the Channels, through <lb></lb>which it at preſent runneth, judged, that the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> being in its <lb></lb>greater excreſcence about 2000 feet, and the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> being near <lb></lb>1000 feet broad, they judged, I ſay, that letting the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> into <lb></lb>P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> it would have raiſed the Water of P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> two feet; from which <lb></lb>riſe, they concluded afterwards moſt exorbitant diſorders, either <lb></lb>of extraordinary Inundations, or elſe of immenſe and intolera<lb></lb>ble expences to the people in raiſing the Banks of P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end><lb></lb>and with ſuch like weakneſſes, often vainly diſturbed the minds <lb></lb>of the perſons concerned: But now from the things demonſtra<lb></lb>ted, it is manifeſt, That the meaſure of the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> would <lb></lb>be different from the meaſure of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> in P<emph type="italics"></emph>o<emph.end type="italics"></emph.end>; in caſe that the <lb></lb>velocity of the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> in P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> ſhould differ from the velocity <lb></lb>of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> as is more exactly determined in the fourth Pro<lb></lb>poſition.</s></p><p type="head"> <s>APPENDIX IV.</s></p><p type="main"> <s>No leſs likewiſe are thoſe Ingeneers and Artiſts deceived, <lb></lb>that have affirmed, That letting the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> into P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> there <lb></lb>would be no riſe at all in the Water of P<emph type="italics"></emph>o<emph.end type="italics"></emph.end>: For the truth <lb></lb>is, That letting <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> into P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> there would alwaies be a riſing; but <lb></lb>ſometimes greater, ſometimes leſſe, as the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> ſhall have a ſwifter <lb></lb>or ſlower Current; ſo that if the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> ſhall be conſtituted in a great <lb></lb>velocity, the riſe will be very ſmall; and if the ſaid P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> ſhall be <lb></lb>ſlow in its courſe, then the riſe will be notable.</s></p><p type="head"> <s>APPENDIX V.</s></p><p type="main"> <s>And here it will not be beſides the purpoſe to advertiſe, That <lb></lb>the meaſures, partments, and diſtributions of the Waters <lb></lb>of Fountains, cannot be made exactly, unleſs there be con<pb xlink:href="040/01/588.jpg" pagenum="19"></pb>fidered, beſides the meaſure, the velocity alſo of the Water; <lb></lb>which particular not being thorowly obſerved, is the cauſe of <lb></lb>continual miſcariages in ſuch like affairs.</s></p><p type="head"> <s>APPENDIX VI.</s></p><p type="main"> <s>Like conſideration ought to be had with the greater diligence, <lb></lb>for that an errour therein is more prejudicial; I ſay, ought to <lb></lb>be had by thoſe which part and divide Waters; for the <lb></lb>watering of fields, as is done in the Territories of <emph type="italics"></emph>Breſcia, Ber<lb></lb>gama, Crema, Pavia, Lodigiano, Cremona,<emph.end type="italics"></emph.end> and other places: <lb></lb>For if they have not regard to the moſt important point of the <lb></lb>variation of the velocity of the Water, but onely to the bare <lb></lb>Vulgar meaſure, there will alwaies very great diſorders and pre<lb></lb>judices enſue to the perſons concerned.</s></p><p type="head"> <s>APPENDIX VII.</s></p><p type="main"> <s>It ſeemeth that one may obſerve, that whilſt the Water run<lb></lb>neth along a Channel, Current, or Conduit, its velocity is <lb></lb>retarded, withheld, and impeded by its touching the Bank or <lb></lb>ſide of the ſaid Channel or Current; which, as immoveable, not <lb></lb>following the motion of the Water, interrupteth its velocity: <lb></lb>From which particular, being true, as I believe it to be moſt <lb></lb>true, and from our conſiderations, we have an occaſion of diſ<lb></lb>covering a very nice miſtake, into which thoſe commonly fall <lb></lb>who divide the Waters of Fountains. </s> <s>Which diviſion is wont <lb></lb>to be, by what I have ſeen here in <emph type="italics"></emph>Rome,<emph.end type="italics"></emph.end> performed two wayes; <lb></lb>The firſt of which is with the meaſures of like figures, as Cir<lb></lb>cles, or Squares, having cut through a Plate of metal ſeveral <lb></lb>Circles or Squares, one of half an inch, another of one inch, <lb></lb>another of two, of three, of four, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> with which they after<lb></lb>wards adjuſt the Cocks to diſpence the Waters. </s> <s>The other <lb></lb>manner of dividing the Waters of Fountains, is with rectangle <lb></lb>paralellograms, of the ſame height, but of different Baſes, in ſuch <lb></lb>ſort likewiſe, that one paralellogram be of half an inch, another <lb></lb>of one, two, three, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> In which manner of meaſuring and <lb></lb>dividing the Water, it ſhould ſeem that the Cocks being placed <lb></lb>in one and the ſame plain, equidiſtant from the level, or ſuperior <lb></lb>ſuperficies of the water of the Well; and the ſaid meaſures be<lb></lb>ing moſt exactly made, the Water ought conſequently alſo to <lb></lb>be equally divided, and parted according to the proportion of <lb></lb>the meaſures. </s> <s>But if we well conſider every particular, we ſhall <lb></lb>finde, that the Cocks, as they ſucceſſively are greater, diſcharge <lb></lb>alwaies more Water than the juſt quantity, in compariſon of <pb xlink:href="040/01/589.jpg" pagenum="20"></pb>the leſſer; that is, to ſpeak more properly, The Water which <lb></lb>paſſeth through the greater Cock, hath alwaies a greater pro<lb></lb>portion to that which paſſeth through the leſſer, than the greater <lb></lb>Cock hath to the leſſer. </s> <s>All which I will declare by an exam<lb></lb>ple.</s></p><p type="main"> <s>Let there be ſuppoſed for more plainneſs two Squares; (the <lb></lb>ſame may be underſtood of Circles, and other like Figures) The <lb></lb>firſt Square is, as we will ſuppoſe, quadruple to the other, and <lb></lb>theſe Squares are the mouths of two Cocks.; one of four inches, <lb></lb>the other of one: Now its manifeſt by what hath been ſaid, that <lb></lb>the Water which paſſeth by the leſs Cock, findeth its velocity <lb></lb>impeded in the circumference of the Cock; which impediment <lb></lb><figure id="id.040.01.589.1.jpg" xlink:href="040/01/589/1.jpg"></figure><lb></lb>is meaſured by the ſaid circumfe<lb></lb>rence. </s> <s>Now it is to be conſider<lb></lb>ed, that if we would have the Wa<lb></lb>ter which paſſeth through the <lb></lb>greater Cock, to be onely qua<lb></lb>druple to that which paſſeth <lb></lb>through the leſſe, in equal ſpaces of time, it would be neceſſary, <lb></lb>that not onely the capacity and the meaſure of the greater Cock <lb></lb>be quadruple to the leſſer Cock, but that alſo the impediment be <lb></lb>quadrupled. </s> <s>Now in our caſe it is true, That the belly and <lb></lb>mouth of the Cock is quadrupled, and yet the impediment is not <lb></lb>quadrupled, but is onely doubled; ſeeing that the circumference <lb></lb>of the greater Square, is onely double to the circumference of <lb></lb>the leſier Square; for the greater circumference containeth eight <lb></lb>of thoſe parts, of which the leſſer containeth but four, as is ma<lb></lb>nifeſt by the deſcribed Figure; and for that cauſe there ſhall <lb></lb>paſs by the greater Cock, above four times as much Water, as <lb></lb>ſhall paſs by the leſſer Cock.</s></p><p type="main"> <s>The like errour occurreth alſo in the other manner of meaſu<lb></lb>ring the Water of a Fountain, as may eaſily be collected from <lb></lb>what hath been ſaid and obſerved above.</s></p><p type="head"> <s>APPENDIX VIII.</s></p><p type="main"> <s>The ſame contemplation diſcovereth the errour of thoſe <lb></lb>Architects, who being to erect a Bridge of ſundry Arches <lb></lb>over a River, conſider the ordinary breadth of the River; <lb></lb>which being <emph type="italics"></emph>v. </s> <s>g.<emph.end type="italics"></emph.end> fourty fathom, and the Bridge being to conſiſt <lb></lb>of four Arches, it ſufficeth them, that the breadth of all the four <lb></lb>Arches taken together, be fourty fathom; not conſidering that <lb></lb>in the ordinary Channel of the River, the Water hath onely <lb></lb>two impediments which retard its velocity; namely, the touching <lb></lb>and gliding along the two ſides or ſhores of the River: but <pb xlink:href="040/01/590.jpg" pagenum="21"></pb>the ſame water in paſſing under the Bridge, in our caſe meeteth <lb></lb>with eight of the ſame impediments, bearing, and thruſting upon <lb></lb>two ſides of each Arch (to omit the impediment of the bottom, <lb></lb>for that it is the ſame in the River, and under the Bridge) from <lb></lb>which inadvertency ſometimes follow very great diſorders, as <lb></lb>quotidian practice ſhews us.</s></p><p type="head"> <s>APPENDIX IX.</s></p><p type="main"> <s>It is alſo worthy to conſider the great and admirable benefit <lb></lb>that thoſe fields receive, which are wont to drink up the Rain<lb></lb>water with difficulty, through the height of the water in the <lb></lb>principal Ditches; in which caſe the careful Husbandman cutteth <lb></lb>away the reeds and ruſhes in the Ditches, through which the <lb></lb>waters paſs; whereupon may be preſently ſeen, ſo ſoon as the <lb></lb>reeds and ruſhes are cut, a notable Ebb in the level of the water <lb></lb>in the Ditches; inſomuch that ſometimes it is obſerved, that the <lb></lb>water is abated after the ſaid cutting a third and more, of what it <lb></lb>was before the cutting. </s> <s>The which effect ſeemingly might de<lb></lb>pend on this, That, before thoſe weeds took up room in the <lb></lb>Ditch, and for that cauſe the water kept a higher level, and the <lb></lb>ſaid Plants being afterwards cut and removed, the water came to <lb></lb>abate, poſſeſſing the place that before was occupied by the <lb></lb>weeds: Which opinion, though probable, and at firſt ſight ſa<lb></lb>tisfactory, is nevertheleſs inſufficient to give the total reaſon of <lb></lb>that notable abatement which hath been ſpoken of: But it is ne<lb></lb>ceſſary to have recourſe to our confideration of the velocity in <lb></lb>the courſe of the water, the chiefeſt and true cauſe of the vari<lb></lb>ation of the meaſure of the ſame Running-Water; for, that <lb></lb>multitudes of reeds, weeds, and plants diſperſed through the cur<lb></lb>rent of the Ditch, do chance notably to retard the courſe of the <lb></lb>water, and therefore the meaſure of the water increaſeth; and <lb></lb>thoſe impediments removed, the ſame water gaineth velocity, <lb></lb>and therefore decreaſeth in meaſure, and conſequently in <lb></lb>height.</s></p><p type="main"> <s>And perhaps this point well underſtood, may be of great <lb></lb>profit to the fields adjacent to the <emph type="italics"></emph>Pontine<emph.end type="italics"></emph.end> Fens, and I doubt not <lb></lb>but if the River <emph type="italics"></emph>Ninfa,<emph.end type="italics"></emph.end> and the other principal Brooks of thoſe <lb></lb>Territories were kept well cleanſed from weeds, their waters <lb></lb>would be at a lower level, and conſequently the drains of the <lb></lb>fields would run into them more readily; it being alwayes to be <lb></lb>held for undoubted, that the meaſure of the water before the <lb></lb>cleanſing, hath the ſame proportion to the meaſure after clean<lb></lb>ſing, that the velocity after the cleanſing hath to the velocity <lb></lb>before the cleanſing: An dbecauſe thoſe weeds being cleanſed <pb xlink:href="040/01/591.jpg" pagenum="22"></pb>away, the courſe ef the water notably increaſeth, it is therefore <lb></lb>neceſſary that the ſaid water abate in meaſure, and become <lb></lb>lower.</s></p><p type="head"> <s>APPENDIX. X.</s></p><p type="main"> <s>We having above obſerved ſome errors that are commit<lb></lb>ted in diſtributing the waters of Fountains, and thoſe <lb></lb>that ſerve to water fields; it ſeemeth now fit, by way of <lb></lb>a cloſe to this diſcourſe, to advertiſe by what means theſe divi<lb></lb>ſions may be made juſtly and without error. </s> <s>I therefore think <lb></lb>that one might two ſeveral wayes exquiſitly divide the water of <lb></lb>Fountains; The firſt would be by diligently examining, Firſt, <lb></lb>how much water the whole Fountain diſchargeth in a determi<lb></lb>nate time, as for inſtance: How many Barrels, or Tuns it carri<lb></lb>eth in a ſet time; and in caſe you are afterwards to diſtribute <lb></lb>the water, diſtribute it at the rate of ſomany Barrels or Tuns, in <lb></lb>that ſame time; and in this caſe the participants would have <lb></lb>their punctual ſhares: Nor could it ever happen to ſend out more <lb></lb>water, than is reckoned to be in the principal Fountain; as befel <lb></lb><emph type="italics"></emph>Giulio Frontino,<emph.end type="italics"></emph.end> and as alſo it frequently happeneth in the Mo<lb></lb>dern Aqueducts, to the publick and private detriment.</s></p><p type="main"> <s>The other way of dividing the ſame waters of a Fountain, is <lb></lb>alſo ſufficiently exact and eaſie, and may be, by having one one<lb></lb>ly ſize for the Cock or Pipe, as ſuppoſe of an inch, or of half an <lb></lb>inch; and when the caſe requireth to diſpence two, three, and <lb></lb>more inches, take ſo many Cocks of the ſaid meaſure as do eva<lb></lb>cuate the water, which is to be emitted; and if we are to make <lb></lb>uſe onely of one greater Cock, we being to place one to diſ<lb></lb>charge for example four inches; and having the former ſole mea<lb></lb>ſure of an inch, we muſt make a Cock that is bigger, its true, than <lb></lb>the Cock of one inch; but not ſimply in a quadruple propor<lb></lb>tion, for that it would diſcharge more than juſt ſo much water, <lb></lb>as hath been ſaid above; but we ought to examine diligently <lb></lb>how much water the little Cock emitteth in an hour; and then <lb></lb>enlarge, and contract the greater Cock, ſo, that it may diſ<lb></lb>charge four times as much water as the leſſer in the ſame time; <lb></lb>and by this means we ſhall avoid the diſorder hinted in the <lb></lb>ſeventh Appendix. </s> <s>It would be neceſſary nevertheleſs, to ac<lb></lb>commodate the Cocks of the Ciſtern ſo, that the level of the <lb></lb>water in the Ciſtern may alwayes reſt at one determinate mark <lb></lb>above the Cock, otherwiſe the Cocks will emit ſometimes <lb></lb>greater, and ſometimes leſſe abundance of water: And becauſe <lb></lb>it may be that the ſame water of the Fountain may be ſometimes <lb></lb>more abundant, ſometimes leſs; in ſuch caſe it will be neceſſary <pb xlink:href="040/01/592.jpg" pagenum="23"></pb>to adjuſt the Ciſtern ſo, that the exceſs above the ordinary wa<lb></lb>ter, diſcharge into the publick Fountains, that ſo the particular <lb></lb>participants may have alwayes the ſame abundance of <lb></lb>water.</s></p><p type="head"> <s>APPENDIX XI.</s></p><p type="main"> <s>Much more difficult is the diviſion of the waters which <lb></lb>ſerve to water the fields, it not being poſſible to obſerve <lb></lb>ſo commodiouſly, what quantity of water the whole <lb></lb>Ditch ſends forth in one determinate time, as may be done in <lb></lb>Fountains: Yet nevertheleſs, if the ſecond propoſition by us a <lb></lb>little below demonſtrated, be well underſtood, there may be <lb></lb>thence taken a very ſafe and juſt way to diſtribute ſuch waters. <lb></lb></s> <s>The Propoſition therefore by us demonſtrated is this: If there <lb></lb>be two Sections, (namely two mouths of Rivers) the quantity of <lb></lb>the water which paſſeth by the firſt, hath a proportion to that <lb></lb>which paſſeth by the ſecond, compounded of the proportions of <lb></lb>the firſt Section to the ſecond, and of the velocity through <lb></lb>the firſt, to the velocity through the ſecond: As I will declare <lb></lb>for example by help of practice, that I may be underſtood by <lb></lb>all, in a matter ſo important. </s> <s>Let the two mouths of the <lb></lb>Rivers be A, and B, and let <lb></lb><figure id="id.040.01.592.1.jpg" xlink:href="040/01/592/1.jpg"></figure><lb></lb>the mouth A be in meaſure <lb></lb>and content thirty two feet, <lb></lb>and the mouth B, eight feet. <lb></lb></s> <s>Here you muſt take notice, <lb></lb>that it is not alwayes true, that <lb></lb>the Water which paſſeth by A, <lb></lb>hath the ſame proportion to that which paſſeth by B, that the <lb></lb>mouth A hath to the mouth B; but onely when the velocityes <lb></lb>by each of thoſe paſſages are equal: But if the velocityes ſhall <lb></lb>be unequal, it may be that the ſaid mouths may emit equal <lb></lb>quantity of Water in equal times, though their meaſure be un<lb></lb>equal; and it may be alſo, that the bigger doth diſcharge a great<lb></lb>er quantity of Water: And laſtly, it may be, that the leſs mouth <lb></lb>diſchargeth more Water than the greater; and all this is mani<lb></lb>feſt by the things noted in the beginning of this diſcourſe, and <lb></lb>by the ſaid ſecond Propoſition. </s> <s>Now to examine the propor<lb></lb>tion of the Water that paſſeth by one Ditch, to that which paſ<lb></lb>ſeth by another, that this being known, the ſame Waters and <lb></lb>mouths of Ditches may be then adjuſted; we are to keep ac<lb></lb>count not onely of the greatneſs of the mouths or paſſages of the <lb></lb>Water, but of the velocity alſo; which we will do, by firſt find<lb></lb>ing two numbers that have the ſame proportion between them<pb xlink:href="040/01/593.jpg" pagenum="24"></pb>ſelves, as have the mouths, which are the numbers 32 and 8 <lb></lb>in our example: Then this <lb></lb><figure id="id.040.01.593.1.jpg" xlink:href="040/01/593/1.jpg"></figure><lb></lb>being done, let the velocity <lb></lb>of the Water by the paſſa<lb></lb>ges A and B, be examined <lb></lb>(which may be done keeping <lb></lb>account what ſpace a piece <lb></lb>of Wood, or other body that <lb></lb>ſwimmeth, is carried by the ſtream in one determinate time; as <lb></lb>for inſtance in 50 pulſes) and then work by the golden Rule, as <lb></lb>the velocity by A, is to the velocity by B, ſo is the number 8, to <lb></lb>another number, which is 4. It is clear by what is demonſtra<lb></lb>ted in the ſaid ſecond Propoſition, that the quantity of water, <lb></lb>which paſſeth by the mouth A, ſhall have the ſame proportion of <lb></lb>that which paſſeth by the mouth B, that 8 hath to 1. Such pro<lb></lb>portion being compoſed of the proportions of 32 to 8, and of 8 to <lb></lb>4; namely, tothe greatneſs of the mouth A, to the greatneſs of the <lb></lb>mouth B, and of the velocity in A, to the velocity in B. </s> <s>This being <lb></lb>done, we muſt then contract the mouth which diſchargeth more <lb></lb>then its juſt quantity of water, or enlarge the other which diſchar<lb></lb>geth leſs, as ſhal be moſt commodious in practice, which to him that <lb></lb>hath underſtood this little that hath been delivered, will be very <lb></lb>afie.</s></p><p type="head"> <s>APPENDIX XII.</s></p><p type="main"> <s>Theſe opperations about Water, as I have hitherto on ſun<lb></lb>dry occaſions obſerved, are involved in ſo many difficul<lb></lb>ties, and ſuch a multiplicity of moſt extravagant accidents, <lb></lb>that it is no marvel if continually many, and very important er<lb></lb>rours be therein committed by many, and even by Ingeneers <lb></lb>themſelves, and Learned-men; and becauſe many times they <lb></lb>concern not onely the publique, but private intereſts: Hence it <lb></lb>is, that it not onely belongeth to Artiſts to treat thereof, but very <lb></lb>oft even the vulgar themſelves pretend to give their judgement <lb></lb>therein: And I have been troubled many times with a neceſſity <lb></lb>of treating, not onely with thoſe, which either by practice, or <lb></lb>particular ſtudy, underſtood ſomewhat in theſe matters; but alſo <lb></lb>with people wholly void of thoſe notions, which are neceſſary for <lb></lb>one that would on good grounds diſcourſe about this particular; <lb></lb>and thus many times have met with more difficulty in the thick <lb></lb>skulls of men, than in precipitous Torrents, and vaſt Fennes. <lb></lb></s> <s>And in particular, I had occafion ſome years paſt to go ſee the <lb></lb>Gave or Emiſſary of the Lake of <emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> made many years agon <lb></lb>by <emph type="italics"></emph>Braccio Fortobraccio,<emph.end type="italics"></emph.end> but for that it was with great ruines by <lb></lb>Time decayed, and rendred unuſeful, it was repaired with in<pb xlink:href="040/01/594.jpg" pagenum="25"></pb>duſtry truly heroicall and admirable, by Monſignor <emph type="italics"></emph>Maffei Bar<lb></lb>herino,<emph.end type="italics"></emph.end> then Prefect for the Wayes, and now Pope. </s> <s>And being <lb></lb>neceſſitated, that I might be able to walk in the Cave, and for <lb></lb>other cauſes, I let down the Sluices of the ſaid Cave, at the mouth <lb></lb>of the Lake: No ſooner were they ſtopt, but a great many of the <lb></lb>people of the Towns and Villages coaſting upon the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ake <lb></lb>flocking thither, began to make grievous complaints, that if thoſe <lb></lb>Sluices were kept ſhut, not onely the Lake would want its due <lb></lb>Vent, but alſo the parts adjacent to the Lake would be over <lb></lb>flown to their very great detriment. </s> <s>And becauſe at firſt appea<lb></lb>rance their motion ſeemed very reaſonable, I found my ſelf hard <lb></lb>put to it, ſeeing no way to perſwade ſuch a multitude, that the <lb></lb>prejudice which they pretended I ſhould do them by keeping <lb></lb>the Sluices ſhut for two dayes, was abſolutely inſenſible; and that <lb></lb>by keeping them open, the Lake did not ebb in the ſame time ſo <lb></lb>much as the thickneſs of a ſheet of Paper: And therefore I was <lb></lb>neceſſitated to make uſe of the authority I had, and ſo followed <lb></lb>my buſineſs as cauſe required, without any regard to that Rab<lb></lb>ble tumultuouſly aſſembled. </s> <s>Now when I am not working with <lb></lb>Mattock or Spade, but with the Pen and Diſcourſe, I intend to <lb></lb>demonſtrate clearly to thoſe that are capable of reaſon, and that <lb></lb>have well underſtood the ground of this my Treatiſe, that the <lb></lb>fear was altogether vain which thoſe people conceited. </s> <s>And <lb></lb>therefore I ſay, that the Emiſſary or Sluice of the Lake of <emph type="italics"></emph>Peru<lb></lb>gia,<emph.end type="italics"></emph.end> ſtanding in the ſame mannner as at preſent, and the water <lb></lb>paſſing thorow it with the ſame velocity as now; to examine <lb></lb>how much the Lake may abate in two days ſpace, we ought to <lb></lb>conſider, what proportion the ſuperficies of the whole Lake hath <lb></lb>to the meaſure of the Section of the Emiſſary, and afterwards to <lb></lb>infer, that the velocity of the water by the Emiſſary or Sluice, <lb></lb>ſhall have the ſame proportion to the abatement of the Lake, <lb></lb>and to prove thorowly and clearly this diſcourſe, I intend to <lb></lb>demonſtrate the following Propoſition.</s></p><p type="main"> <s>Suppoſe a Veſſel of any bigneſſe, and that it hath an Emiſſary <lb></lb>or Cock, by which it diſchargeth its water. </s> <s>And look what pro<lb></lb>portion the ſuperſicies of the <lb></lb>veſſel hath to the meaſure of <lb></lb><figure id="id.040.01.594.1.jpg" xlink:href="040/01/594/1.jpg"></figure><lb></lb>the ſection of the cock, ſuch pro<lb></lb>portion ſhall the velocity of the <lb></lb>Water in the Cock have to the <lb></lb>abatement of the Lake Let the <lb></lb>Veſſel be A B C D, H I L B, through which the Water runneth, <lb></lb>the ſuperficies of the Water in the Veſſel A D, and the ſection <lb></lb>of the Cock H L: and let the Water in the Veſſel <lb></lb>be ſuppoſed to have falne in one determinate time from A to F. <pb xlink:href="040/01/595.jpg" pagenum="26"></pb>I ſay that the proportion of the ſuperficies of the Veſſel A D is <lb></lb>in proportion to the meaſure of the ſection of the Emiſſary <lb></lb>H L, as the velocity of the Emiſſary or Cock to the line A F; <lb></lb>which is manifeſt, for that the Water in the Veſsel moving by <lb></lb>the line A F; as far as F, and the whole maſs of Water A G <lb></lb>diſcharging it ſelf, and in the ſame time the ſame quantity of <lb></lb>Water being diſcharged by the ſection of the Emiſſary H L; it <lb></lb>is neceſſary by what I have demonſtrated in the third Propoſition, <lb></lb>and alſo explained in the beginning of this Treatiſe, that the ve<lb></lb>locity by the Emiſſary or Cock be in proportion to the velocity <lb></lb>of the abatement, as the ſuperficies of the Veſſel to the mea<lb></lb>ſure of the ſection of the Emiſſary, which was to be demon<lb></lb>ſtrated.</s></p><p type="main"> <s>That which hath been demonſtrated in the Veſſel, falls out ex<lb></lb>actly alſo in our Lake of <emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> and its Emiſsary; and becauſe <lb></lb>the immenſity of the ſuperficies of the Lake is in proportion to <lb></lb>the ſuperficies of the Emiſsary or Sluice, as many millions to <lb></lb>one, as may be eaſily calculated; it is manifeſt, that ſuch abate<lb></lb>ment ſhall be imperceptible, and almoſt nothing, in two dayes <lb></lb>ſpace, nay in four or ſix: and all this will be true, when we <lb></lb>ſuppoſe that for that time there entreth no other Water into the <lb></lb>Lake from Ditches or Rivolets, which falling into the Lake would <lb></lb>render ſuch abatement yet leſs.</s></p><p type="main"> <s>Now we ſee, that it's neceſsary to examine ſuch abatements <lb></lb>and riſings, with excellent reaſons, or at leaſt, with accurate ex<lb></lb>periments, before we reſolve and conclude any thing; and how <lb></lb>farre the vulgar are diſtant from a right judgment in ſuch <lb></lb>matters.</s></p><p type="head"> <s>APPENDIX XIII.</s></p><p type="main"> <s>For greater confirmation of all this which I have ſaid, I <lb></lb>will inſtance in another like caſe, which alſo I met with here<lb></lb>tofore, wherein, for that the buſineſs was not rightly un<lb></lb>derſtood, many diſorders, vaſt expences, and conſiderable miſ<lb></lb>chiefs have followed. </s> <s>There was heretofore an Emiſsary or <lb></lb>Sluice made to drain the Waters, which from Rains, Springs, and <lb></lb>Rivolets fall into a Lake; to the end, the ſhores adjoyning on <lb></lb>the Lake, ſhould be free from the overflowing of the Waters; <lb></lb>but becauſe perhaps the enterprize was not well managed and <lb></lb>carried on, it fell out, that the Fields adjacent to the ſaid Chanel <lb></lb>could not drain, but continued under water; to which diſorders <lb></lb>a preſent remedy hath been uſed, namely, in a time convenient <lb></lb>to ſtop up the Sluice, by meanes of certain Floodgates kept on <lb></lb>purpoſe for that end; and thus abating the Level of the Water <pb xlink:href="040/01/596.jpg" pagenum="27"></pb>in the Emiſſary, in the ſpace of three or four dayes, the Fields <lb></lb>have been haply drained. </s> <s>But on the other part, the proprietors <lb></lb>bordering on the Lake oppoſed this, grievouſly complaining, that <lb></lb>whilſt the Floodgates are ſhut, and the courſe of the Water of <lb></lb>the Sluice hindered, the Lake overflowes the Lands adjacent, by <lb></lb>meanes of the Rivers that fell into it, to their very great damage; <lb></lb>and ſo continuing their ſuits, they got more of vexation than ſa<lb></lb>tisfaction. </s> <s>Now, being asked my opinion herein, I judged it <lb></lb>requiſite (ſince the point in controverſie was about the riſing <lb></lb>and falling of the Lake) that the ſaid abatement, when the <lb></lb>Floodgates are open, and increaſe when they are ſhut ſhould be <lb></lb>exactly meaſured, and told them, that it might be eaſily done at <lb></lb>a time when no extraordinary Waters fell into the Lake, neither <lb></lb>of Rain, or otherwiſe; and the Lake was undiſturbed by winds <lb></lb>that might drive the Water to any ſide, by planting neer to an <lb></lb>Iſlet, which is about the middle of the Lake, a thick poſt, on <lb></lb>which ſhould be made the marks of the Lakes riſing and falling <lb></lb>for two or three dayes. </s> <s>I would not, at that time, pawn, or re<lb></lb>ſolutely declare, my judgment, in regard I might be, by divers <lb></lb>accidents miſled. </s> <s>But this I told them, that (by what I have <lb></lb>demonſtrated, and particularly that which I have ſaid above <lb></lb>touching the Lake of <emph type="italics"></emph>Perugia<emph.end type="italics"></emph.end>) I inclined greatly to think, <lb></lb>that theſe riſings and fallings would prove imperceptible, and <lb></lb>inconſiderable; and therefore, that in caſe experience ſhould <lb></lb>make good my reaſon, it would be to no purpoſe for them to <lb></lb>continue diſputing and wrangling, which cauſeth, (according <lb></lb>to the Proverb) <emph type="italics"></emph>A great deal of cry,<emph.end type="italics"></emph.end> but produceth not much <lb></lb><emph type="italics"></emph>Wool.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Laſtly, it importing very much to know what a Rain conti<lb></lb>nued for many dayes can do in raiſing theſe Lakes, I will here in<lb></lb>ſert the Copy of a Letter, which I writ formerly to <emph type="italics"></emph>Signior Ga<lb></lb>lilæo Galilæi,<emph.end type="italics"></emph.end> chief Philoſopher to the Grand Duke of <emph type="italics"></emph>Tuſcany,<emph.end type="italics"></emph.end><lb></lb>wherein I have delivered one of my conceits in this buſineſſe, and <lb></lb>it may be, by this Letter, I may, more ſtrongly, confirm what I <lb></lb>have ſaid above.</s></p><pb xlink:href="040/01/597.jpg" pagenum="28"></pb><p type="main"> <s><emph type="italics"></emph>The Copy of a Letter to<emph.end type="italics"></emph.end> Signore GALILÆO <lb></lb>GALILÆI, <emph type="italics"></emph>Chief Philoſopher to the moſt Serene <lb></lb>Great Duke of TVSCANY.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Worthy and moſt Excellent<emph.end type="italics"></emph.end> SIR,</s></p><p type="main"> <s>In ſatisfaction of my promiſe, in my former Letters of <lb></lb>repreſenting unto you ſome of my Conſiderations <lb></lb>made upon the Lake <emph type="italics"></emph>Thraſimeno,<emph.end type="italics"></emph.end> I ſay, That in times <lb></lb>paſt, being in <emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> where we held our General <lb></lb>Convention, having underſtood that the Lake <emph type="italics"></emph>Thraſimeno,<emph.end type="italics"></emph.end> by <lb></lb>the great drought of many Moneths was much abated, It came <lb></lb>into my head, to go privately and ſee this novelty, both for my <lb></lb>particular ſatisfaction, as alſo that might I be able to relate the <lb></lb>whole to my Patrons, upon the certitude of my own ſight of the <lb></lb>place. </s> <s>And ſo being come to the Emiſſary of the Lake, I found <lb></lb>that the Level of the Lakes ſurface was ebbed about five Ro<lb></lb>man Palmes of its wonted watermark, inſomuch that it was lower <lb></lb>than the tranſome of the mouth of the Emiſſary, by the length <lb></lb>of ----------------------------this deſcribed line, and there<lb></lb>fore no Water iſſued out of the Lake, to the great prejudice of <lb></lb>all the places and villages circumjacent, in regard that the Wa<lb></lb>ter which uſed to run from the ſaid Lake turned 22 Mills, which <lb></lb>not going, neceſſitated the inhabitants of thoſe parts to go a <lb></lb>dayes journey and more, to grinde upon the <emph type="italics"></emph>Tiber.<emph.end type="italics"></emph.end> Being retur<lb></lb>ned to <emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> there followed a Rain, not very great, but con<lb></lb>ſtant, and even, which laſted for the ſpace of eight hours, or <lb></lb>thereabouts; and it came into my thoughts to examine, being <lb></lb>in <emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> how much the Lake was increaſed and railed by this <lb></lb>Rain, ſuppoſing (as it was probable enough) that the Rain had <lb></lb>been univerſal over all the Lake; and like to that which fell in <lb></lb><emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> and to this purpoſe I took a Glaſſe formed like a Cy<lb></lb>linder, about a palme high, and half a palme broad; and having <lb></lb>put in water ſnfficient to cover the bottome of the Glaſſe, I no<lb></lb>ted diligently the mark of the height of the Water in the Glaſſe, <lb></lb>and afterwards expoſed it to the open weather, to receive the <lb></lb>Raine-water, which fell into it; and I let it ſtand for the <lb></lb>ſpace of an hour; and having obſerved that in that time the Wa<lb></lb>ter was riſen in the Veſſel the height of the following line---, <lb></lb>I conſidered that if I had expoſed to the ſame rain ſuch other veſ<lb></lb>ſels equal to that, the Water would have riſen in them all accor<lb></lb>ding to that meaſure: And thereupon concluded, that alſo in all <pb xlink:href="040/01/598.jpg" pagenum="29"></pb>the whole extent of the Lake, it was neceſſary the Water ſhould <lb></lb>be raiſed in the ſpace of an hour the ſame meaſure. </s> <s>Yet here I <lb></lb>conſidered two difficulties that might diſtutb and altar ſuch an <lb></lb>effect, or at leaſt render it inobſerveable, which afterwards well <lb></lb>weighed, and reſolved, left me (as I will tell you anon) in the <lb></lb>concluſion the more confirmed; that the Lake ought to be in<lb></lb>creaſed in the ſpace of eight hours, that the rain laſted eight <lb></lb>times that meaſure. </s> <s>And whilſt I again expoſed the Glaſs to re<lb></lb>peat the experiment, there came unto me an Ingeneer to talk <lb></lb>with me touching certain affairs of our Monaſtary of <emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> and <lb></lb>diſcourſing with him, I ſhewed him the Glaſs out at my Cham<lb></lb>ber-window, expoſed in a Court-yard; and communicated to <lb></lb>him my fancy, relacing unto him all that I had done. </s> <s>But I <lb></lb>ſoon perceived that this brave fellow conceited me to be but of <lb></lb>a dull brain, for he ſmilling ſaid unto me; Sir, you deceive <lb></lb>your ſelf: I am of opinion that the Lake will not be increaſ<lb></lb>ed by this rain, ſo much as the thickneſſe of a ^{*} <emph type="italics"></emph>Julio.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg967"></arrow.to.target><lb></lb>Hearing him pronounce this his opinion with freeneſs and <lb></lb>confidence, I urged him to give me ſome reaſon for what he <lb></lb>ſaid, aſſuring him, that I would change my judgement, when I <lb></lb>ſaw the ſtrength of his Arguments: To which he anſwered, that <lb></lb>he had been very converſant about the Lake, and was every day <lb></lb>upon it, and was well aſſured that it was not at all increaſed. </s> <s>And <lb></lb>importuning him further, that he would give me ſome reaſon <lb></lb>for his ſo thinking, he propoſed to my conſideration the great <lb></lb>drought paſſed, and that that ſame rain was nothing for the <lb></lb>great parching: To which I anſwered, I believe Sir that the ſur<lb></lb>face of the Lake, on which the rain had fallen was moiſtned; and <lb></lb>therefore ſaw not how its drought, which was nothing at all, <lb></lb>could have drunk up any part of the rain. </s> <s>For all this he per<lb></lb>ſiſting in his conceit, without yielding in the leaſt to my allega<lb></lb>tion; he granted in the end (I believe in civility to me) that <lb></lb>my reaſon was plauſible and good, but that in practiſe it could <lb></lb>not hold. </s> <s>At laſt to clear up all, I made one be called, and <lb></lb>ſent him to the mouth of the Emiſſary of the Lake, with order <lb></lb>to bring me an exact account, how he found the water of the <lb></lb>Lake, in reſpect of the Tranſome of the Sluice. </s> <s>Now here, <lb></lb>Signore <emph type="italics"></emph>Galilo,<emph.end type="italics"></emph.end> I would not have you think that I had brought <lb></lb>the matter in hand to concern me in my honour; but believe me <lb></lb>(and there are witneſſes of the ſame ſtill living) that my meſſen<lb></lb>ger returning in the evening to <emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> he brought me word, <lb></lb>that the water of the Lake began to run through the Cave; and <lb></lb>that it was riſen almoſt a fingers breadth above the Tranſome: <lb></lb>Inſomuch, that adding this meaſure, to that of the lowneſs of <lb></lb>the ſurface of the Lake, beneath the Tranſome before the rain, <pb xlink:href="040/01/599.jpg" pagenum="30"></pb>it was manifeſt that the riſing of the Lake cauſed by the rain, was <lb></lb>to a hair thoſe four fingers breadth that I had judged it to be. <lb></lb></s> <s>Two dayes after I had another bout with the Ingeneer, and re<lb></lb>lated to him the whole buſineſs, to which he knew not what to <lb></lb>anſwer.</s></p><p type="margin"> <s><margin.target id="marg967"></margin.target>* A Coyn of Pope <lb></lb><emph type="italics"></emph>Julius<emph.end type="italics"></emph.end> worth ſix <lb></lb>pence.</s></p><p type="main"> <s>Now the two difficulties which I thought of, able to impede <lb></lb>my concluſion, were theſe following: Firſt, I conſidered that <lb></lb>it might be, that the Wind blowing from the ſide where the <lb></lb>Sluice ſtood, to the Lake-ward; the mole and maſs of the Wa<lb></lb>ter of the Lake might be driven to the contrary ſhore; on which <lb></lb>the Water riſing, it might be fallen at the mouth of the Emiſſa<lb></lb>ry, and ſo the obſervation might be much obſcured. </s> <s>But this <lb></lb>difficulty wholly vaniſhed by reaſon of the Aires great tranqui<lb></lb>lity; which it kept at that time, for no Wind was ſtirring on any <lb></lb>ſide, neither whilſt it rained, nor afterwards.</s></p><p type="main"> <s>The ſecond difficulty which put the riſing in doubt, was, That <lb></lb>having obſerved in <emph type="italics"></emph>Florence,<emph.end type="italics"></emph.end> and elſewhere, thoſe Ponds into <lb></lb>which the rain-water, falling from the houſe, is conveyed <lb></lb>through the Common-ſhores: And that they are not thereby <lb></lb>ever filled, but that they ſwallow all that abundance of water, <lb></lb>that runs into them by thoſe conveyances which ſerve them with <lb></lb>water; inſomuch that thoſe conveyances which in time of <lb></lb>drought maintain the Pond, when there comes new abundance <lb></lb>of water into the Pond, they drink it up, and ſwallow it: A like <lb></lb>effect might alſo fall out in the Lake, in which there being many <lb></lb>veins (as it is very likely) that maintain and feed the Lake; theſe <lb></lb>veins might imbibe the new addition of the Rain-water, and ſo <lb></lb>by that means annuall the riſing; or elſe diminiſh it in ſuch ſort, as <lb></lb>to render it inobſervable. </s> <s>But this difficulty was eaſily reſolved <lb></lb>by conſidering my Treatiſe of the meaſure of Running-Waters; <lb></lb>foraſmuch as having demonſtrated, that the abatement of a Lake <lb></lb>beareth the reciprocal proportion to the velocity of the Emiſſa<lb></lb>ry, which the meaſure of the Section of the Emiſſary of the Lake, <lb></lb>hath to the meaſure of the ſurface of the Lake: making the <lb></lb>calculation and account, though in groſs; by ſuppoſing that its <lb></lb>veins were ſufficiently large, and that the velocity in them were <lb></lb>notable in drinking up the water of the Lake; yet I found never<lb></lb>theleſs, that many weeks and moneths would be ſpent in drink<lb></lb>ing up the new-come abundance of water by the rain, ſo that <lb></lb>I reſted ſure, that the riſing would enſue, as in effect it did.</s></p><p type="main"> <s>And becauſe many of accurate judgement, have again cauſed <lb></lb>me to queſtion this riſing, ſetting before me, that the Earth be<lb></lb>ing parched by the great drought, that had ſo long continued, it <lb></lb>might be, that that Bank of Earth which environed the brink of <lb></lb>the Lake, being dry, and imbibing great abundance of Water <pb xlink:href="040/01/600.jpg" pagenum="31"></pb>from the increaſing Lake, would not ſuffer it to increaſe in <lb></lb>height: I ſay therefore, that if we would rightly conſider this <lb></lb>doubt here propoſed, we ſhould, in the very conſideration of it, <lb></lb>ſee it reſolved; for, it being ſuppoſed that that liſt or border of <lb></lb>Banks which was to be occupied by the increaſe of the Lake, be <lb></lb>a Brace in breadth quite round the Lake, and that by reaſon of <lb></lb>its dryneſs it ſucks in water, and that by that means this propor<lb></lb>tion of water co-operates not in raiſing of the Lake: It is abſo<lb></lb>lutely neceſſary on the other hand, that we conſider, That the <lb></lb>Circuit of the water of the Lake being thirty miles, as its com<lb></lb>monly held, that is to ſay, Ninety thouſand Braces of <emph type="italics"></emph>Florence<emph.end type="italics"></emph.end><lb></lb>in compaſs; and therefore admitting for true, that each Brace of <lb></lb>this Bank drink two quarts of water, and that for the ſpieading <lb></lb>it require three quarts more, we ſhall finde, that the whole agre<lb></lb>gate of this portion of water, which is not imployed in the raiſing <lb></lb>of the Lake, will be four hundred and fifty thouſand Quarts of <lb></lb>water; and ſuppoſing that the Lake be ſixty ſquare miles, three <lb></lb>thouſand Braces long, we ſhall finde, that to diſpence the water <lb></lb>poſſeſt by the Bank about the Lake, above the total ſurface of <lb></lb>the Lake, it ought to be ſpread ſo thin, that one ſole quart of <lb></lb>water may over-ſpread ten thouſand ſquare Braces of ſurface: <lb></lb>ſuch a thinneſs, as muſt much exceed that of a leaf of beaten <lb></lb>Gold, and alſo leſs than that skin of water which covers the Bub<lb></lb>bles of it: and ſuch would that be, which thoſe men would have <lb></lb>ſubſtracted from the riſing of the Lake: But again, in the ſpace <lb></lb>of a quarter of an hour at the beginning of the rain, all that <lb></lb>Bank is ſoaked by the ſaid rain, ſo that we need not for the <lb></lb>moiſtning of it, imploy a drop of that water which falleth into <lb></lb>the Lake. </s> <s>Beſides we have not brought to account that abun<lb></lb>dance of water which runs in time of rain into the Lake, from <lb></lb>the ſteepneſs of the adjacent Hills and Mountains; which would <lb></lb>be enough to ſupply all our occaſions: So that, neither ought <lb></lb>we for this reaſon to queſtion our pretended riſing. </s> <s>And this <lb></lb>is what hath fallen in my way touching the conſideration of the <lb></lb><emph type="italics"></emph>Thraſimenian<emph.end type="italics"></emph.end> Lake.</s></p><p type="main"> <s>After which, perhaps ſomewhat raſhly, wandring beyond my <lb></lb>bounds, I proceeded to another contemplation, which I will re<lb></lb>late to you, hoping that you will receive it, as collected with <lb></lb>theſe cautions requiſite in ſuch like affairs; wherein we ought <lb></lb>not too poſitively to affirm any thing of our own heads for cer<lb></lb>tain, but ought to ſubmit all to the ſound and ſecure delibera<lb></lb>tion of the Holy Mother-Church, as I do this of mine, and all <lb></lb>others; moſt ready to change my judgement, and conform my <lb></lb>ſelf alwaies to the deliberations of my Superiors. </s> <s>Continu<pb xlink:href="040/01/601.jpg" pagenum="32"></pb>ing therefore my above-ſaid conceit about the riſing of the wa<lb></lb>ter in the glaſs tried before, it came into my minde, that the <lb></lb>forementioned rain having been very gentle, it might well be, <lb></lb>that if there ſhould have faln a Rain fifty, an hundred, or a thou<lb></lb>ſand times greater than this, and much more intenſe (which <lb></lb>would inſue as oft as thoſe falling drops were four, ſive or ten <lb></lb>times bigger than thoſe of the above-mentioned rain, keeping <lb></lb>the ſame number) in ſuch a caſe its manifeſt, that in the ſpace <lb></lb>of an hour the Water would riſe in our Glaſs, two, three, and <lb></lb>perhaps more Yards or Braces; and conſequently, if ſuch a <lb></lb>Raine ſhould fall upon a Lake, that the ſaid Lake would <lb></lb>riſe, according to the ſame rate: And likewiſe, if ſuch a <lb></lb>Rain were univerſall, over the whole Terreſtriall Globe, it <lb></lb>would neceſſarily, in the ſpace of an hour, make a ri<lb></lb>ſing of two, or three braces round about the ſaid Globe, <lb></lb>And becauſe we have from Sacred Records, that in the <lb></lb>time of the Deluge, it rained fourty dayes and fourty nights; <lb></lb>namely, for the ſpace of 960 houres; its clear, that if the ſaid <lb></lb>Rain had been ten times bigger than ours at <emph type="italics"></emph>Perugia,<emph.end type="italics"></emph.end> the riſing <lb></lb>of the Waters above the Terreſtrial Globe would reach and paſs <lb></lb>a mile higher than the tops of the Hills and Mountains that are <lb></lb>upon the ſuperficies of the Earth; and they alſo would concur <lb></lb>to increaſe the riſe. </s> <s>And therefore I conclude, that the riſe of <lb></lb>the Waters of the Deluge have a rational congruity with natural <lb></lb>Diſcourſes, of which I know very well that the eternal truths of <lb></lb>the Divine leaves have no need; but however I think ſo clear an <lb></lb>agreement is worthy of our conſideration, which gives us occa<lb></lb>ſion to adore and admire the greatneſſe of God in his mighty <lb></lb>Works, in that we are ſometimes able, in ſome ſort, to meaſure <lb></lb>them by the ſhort Standard of our Reaſon.</s></p><p type="main"> <s>Many Leſſons alſo may be deduced from the ſame Doctrine, <lb></lb>which I paſſe by, for that every man of himſelf may eaſily know <lb></lb>them, having once ſtabliſhed this Maxime; That it is not poſſi<lb></lb>ble to pronounce any thing, of a certainty, touching the quantity <lb></lb>of Running Waters, by conſidering only the ſingle vulgar mea<lb></lb>ſure of the Water wichout the velocity; and ſo on the contrary, <lb></lb>he that computes only the velocity, without the meaſure, ſhall <lb></lb>commit very great errours; for treating of the meaſure of Run<lb></lb>ning Waters, it is neceſſary, the water being a body, in handling <lb></lb>its quantity, to conſider in it all the three dimenſions of breadth, <lb></lb>depth, and length: the two firſt dimenſions are obſerved by all <lb></lb>in the common manner, and ordinary way of meaſuring Running <lb></lb>Waters; but the third dimenſion of length is omitted; and hap<lb></lb>ly ſuch an overſight is committed, by reaſon the length of Run<pb xlink:href="040/01/602.jpg" pagenum="33"></pb>ning Water is reputed in ſome ſenſe infinite, in that it never cea<lb></lb>ſeth to move away, and as infinite is judged incomprehenſible; <lb></lb>and ſuch as that there is no exact knowledge to be had thereof; <lb></lb>& ſo there comes to be no account made thereof; but if we ſhould <lb></lb>make ſtrict reflection upon our conſideration of the velocity of <lb></lb>Water, we ſhould find, that keeping account of the ſame, there <lb></lb>is a reckoning alſo made of the length; foraſmuch as whilſt we <lb></lb>ſay, the Water of ſuch a Spring runs with the velocity of paſſing <lb></lb>a thouſand or two thouſand paces an hour: this in ſubſtance is <lb></lb>no other than if we had ſaid, ſuch a Fountain diſchargeth in an <lb></lb>hour a Water of a thouſand or two thouſand paces long. </s> <s>So <lb></lb>that, albeit the total length of Running water be incomprehen<lb></lb>ſible, as being infinite, yet nevertheleſſe its rendered intelligible <lb></lb>by parts in its velocity. </s> <s>And ſo much ſufficeth to have hinted <lb></lb>about this matter, hoping to impart on ſome other occaſion other <lb></lb>more accurate Obſervations in this affair.</s></p><p type="head"> <s><emph type="italics"></emph>LAVS DEO.<emph.end type="italics"></emph.end></s></p><figure id="id.040.01.602.1.jpg" xlink:href="040/01/602/1.jpg"></figure><pb xlink:href="040/01/603.jpg"></pb><p type="head"> <s>GEOMETRICAL <lb></lb>DEMONSTRATIONS <lb></lb>OF THE <lb></lb>MEASURE <lb></lb>OF <lb></lb>Running Waters.</s></p><p type="head"> <s>BY <lb></lb>D. BENEDETTO CASTELLI, <lb></lb>Abbot of CASSINA, and Mathematician to <lb></lb>P. <emph type="italics"></emph>VRBAN. VIII.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>DEDICATED <lb></lb><emph type="italics"></emph>To the moſt Illuſtrious, and moſt Excellent Prince<emph.end type="italics"></emph.end></s></p><p type="head"> <s>DON THADDEO BARBERINI, <lb></lb>PRINCE OF <lb></lb>PALESTRINA, <lb></lb>AND <lb></lb>GENERAL of the HOLY CHURCH.</s></p><p type="head"> <s><emph type="italics"></emph>LONDON,<emph.end type="italics"></emph.end><lb></lb>Printed <emph type="italics"></emph>Anno Domini,<emph.end type="italics"></emph.end> MDCLXI.</s></p><pb xlink:href="040/01/604.jpg" pagenum="37"></pb><p type="head"> <s>OF THE <lb></lb>MENSURATION <lb></lb>OF <lb></lb>Running Waters.</s></p><p type="head"> <s>SUPPOSITION I.</s></p><p type="main"> <s>Let it be ſuppoſed, that the banks of the Rivers of which <lb></lb>we ſpeak be erected perpendicular to the plane of the up<lb></lb>per ſuperficies of the River.</s></p><p type="head"> <s>SUPPOSITION II.</s></p><p type="main"> <s>We ſuppoſe that the plane of the bottome of the River, of <lb></lb>which we ſpeak is at right angles with the banks.</s></p><p type="head"> <s>SUPPOSITION III.</s></p><p type="main"> <s>It is to be ſuppoſed, that we ſpeak of Rivers, when they are at <lb></lb>ebbe, in that ſtate of ſhallowneſſe, or at flowing in that ſtate <lb></lb>of deepneſſe, and not in their tranſition from the ebbe to the <lb></lb>flowing, or fr m the flowing to the ebbe.</s></p><p type="head"> <s><emph type="italics"></emph>Declaration of Termes.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>FIRST.</s></p><p type="main"> <s>If a River ſhall be cut by a Plane at right angles to the ſurface <lb></lb>of the water of the River, and to the banks of the River, <lb></lb>that ſame dividing Plane we call the Section of the River; and <lb></lb>this Section, by the Suppoſitions above, ſhall be a right angled <lb></lb>Parallelogram.</s></p><p type="head"> <s>SECOND.</s></p><p type="main"> <s>We call thoſe Sections equally Swift, by which the water runs <lb></lb>with equal velocity; and more ſwift and leſs ſwift that <lb></lb>Section of another, by which the water runs with greater or leſſe <lb></lb>velocity.</s></p><pb xlink:href="040/01/605.jpg" pagenum="38"></pb><p type="head"> <s>AXIOME I.</s></p><p type="main"> <s>Sections equal, and equally ſwift, diſcharge equal quantities <lb></lb>of Water in equal times.</s></p><p type="head"> <s>AXIOME II.</s></p><p type="main"> <s>Sections equally ſwift, and that diſcharge equal quantity of <lb></lb>Water, in equal time, ſhall be equal.</s></p><p type="head"> <s>AXIOME III.</s></p><p type="main"> <s>Sections equal, and that diſcharge equal quantities of Water <lb></lb>in equal times, ſhall be equally ſwift.</s></p><p type="head"> <s>AXIOME IV.</s></p><p type="main"> <s>When Sections are unequal, but equally ſwift, the quanti<lb></lb>ty of the Water that paſſeth through the firſt Section, <lb></lb>ſhall have the ſame proportion to the quantity that paſ<lb></lb>ſeth through the Second, that the firſt Section hath to the ſecond <lb></lb>Section. </s> <s>Which is manifeſt, becauſe the velocity being the <lb></lb>ſame, the difference of the Water that paſſeth ſhall be according <lb></lb>to the difference of the Sections.</s></p><p type="head"> <s>AXIOME V.</s></p><p type="main"> <s>If the Sections ſhall be equal, and of unequal velocity, the <lb></lb>quantity of the Water that paſſeth through the firſt, ſhall <lb></lb>have the ſame proportion to that which paſſeth through the <lb></lb>ſecond, that the velocity of the firſt Section, ſhall have to the <lb></lb>velocity of the ſecond Section. </s> <s>Which alſo is manifeſt, becauſe <lb></lb>the Sections being equal, the difference of the Water which <lb></lb>paſſeth, dependeth on the velocity.</s></p><p type="head"> <s><emph type="italics"></emph>PETITION.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>A Section of a River being given, we may ſuppoſe another <lb></lb>equal to the given, of different breadth, heigth, and ve<lb></lb>locity.</s></p><pb xlink:href="040/01/606.jpg" pagenum="37"></pb><p type="head"> <s>PROPOSITION I.</s></p><p type="main"> <s><emph type="italics"></emph>The Sections of the ſame River diſcharge equal quan<lb></lb>tities of Water in equal times, although the Secti<lb></lb>ons themſelves he unequal.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the two Sections be A and B, in the River C, running <lb></lb>from A, towards B; I ſay, that they diſcharge equal quan<lb></lb>tity of Water in equal times; for if greater quantity of Wa<lb></lb>ter ſhould paſs through A, than paſſeth through B, it would <lb></lb><figure id="id.040.01.606.1.jpg" xlink:href="040/01/606/1.jpg"></figure><lb></lb>follow that the Water in the intermediate ſpace of the River C, <lb></lb>would increaſe continually, which is manifeſtly falſe, but if <lb></lb>more Water ſhould iſſue through the Section B, than entreth at <lb></lb>the Section A, the Water in the intermediate ſpace C, would <lb></lb>grow continually leſs, and alwaies ebb, which is likewiſe falſe; <lb></lb>therefore the quantity of Water that paſſeth through the Secti<lb></lb>on B, is equal to the quantity of Water which paſſeth through <lb></lb>the Section A, and therefore the Sections of the ſame River diſ<lb></lb>charge, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> Which w s to be demonſtrated.</s></p><p type="head"> <s>PROPOSITION II.</s></p><p type="main"> <s><emph type="italics"></emph>In two Sections of Rivers, the quantity of the Water <lb></lb>which paſſeth by one Section, is to that which paſ<lb></lb>ſeth by the ſecond, in a Proportion compounded of <lb></lb>the proportions of the firſt Section to the ſecond, and <lb></lb>of the velocitie through the first, to the velocitie <lb></lb>of the ſecond.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>I Et A, and B be two Sections of a River; I ſay, that the <lb></lb>quantity of Water which paſſeth through A, is to that which <lb></lb>paſſeth through B, in a proportion compounded of the pro<lb></lb>portions of the firſt Section A, to the Section B; and of the velo<lb></lb>city through A, to the velocity through B: Let a Section be <pb xlink:href="040/01/607.jpg" pagenum="40"></pb>ſuppoſed equal to the Section A, in magnitude; but of velocity <lb></lb>equal to the Section B, and let it be G, and as the Section A is <lb></lb><figure id="id.040.01.607.1.jpg" xlink:href="040/01/607/1.jpg"></figure><lb></lb>to the Section B, ſo let the line F be to the line D; and as the <lb></lb>velocity A, is to the velocity by B, ſo let the line D be to the <lb></lb>line R: Therefore the Water which paſſeth thorow A, ſhall be <lb></lb>to that which paſſeth through G (in regard the Sections A and <lb></lb>G are of equal bigneſs, but of unequal velocity) as the velocity <lb></lb>through A, to the velocity through G; But as the velocity <lb></lb>through A, is to the velocity through G, ſo is the velocity through <lb></lb>A, to the velocity through B; namely, as the line D, to the <lb></lb>line R: therefore the quantity of the Water which paſſe the <lb></lb>through A, ſhall be to the quantity which paſſeth through G, as <lb></lb>the line D is to the line R; but the quantity which paſſeth <lb></lb>through G, is to that which paſſeth through B, (in regard the <lb></lb>Sections G, and B, are equally ſwift) as the Section G to the Se<lb></lb>ction B; that is, as the Section A, to the Section B; that is, as <lb></lb>the line F, to the line D: Therefore by the equal and perturbed <lb></lb>proportionality, the quantity of the Water which paſſeth through <lb></lb>A, hath the ſame proportion to that which paſſeth through B, <lb></lb>that the line F hath to the line R; but F to R, hath a proportion <lb></lb>compounded of the proportions of F to D, and of D to R; that <lb></lb>is, of the Section A to the Section B; and of the velocity through <lb></lb>A, to the velocity through B. </s> <s>Therefore alſo the quantity of <lb></lb>Water which paſſeth through the Section A, ſhall have a propor<lb></lb>tion to that which paſſeth through the Section B, compounded of <lb></lb>the proportions of the Section A, to the Section B; and of <lb></lb>the velocity through A, to the velocity through B: And <lb></lb>therefore in two Sections of Rivers, the quantity of Water which <lb></lb>paſſeth by the firſt, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> which was to be demonſtrated.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The ſame followeth, though the quantity of the Water which <lb></lb>paſſeth through the Section A, be equal to the quantity of <lb></lb>Water which paſſeth through the Section B, as is manifeſt by the <lb></lb>ſame demonſtration.</s></p><pb xlink:href="040/01/608.jpg" pagenum="41"></pb><p type="head"> <s>PROPOSITION III.</s></p><p type="main"> <s><emph type="italics"></emph>In two Sections unequal, through which paſs equal <lb></lb>quantities of Water in equal times, the Sections <lb></lb>have to one another, reciprocal proportion to their <lb></lb>velocitie.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the two unequal Sections, by which paſs equal quantities <lb></lb>of Water in equal times be A, the greater; and B, the leſſer: <lb></lb>I ſay, that the Section A, ſhall have the ſame Proportion <lb></lb>to the Section B, that reciprocally the velocity through B, hath to <lb></lb>the velocity through A; for ſuppoſing that as the Water that <lb></lb>paſſeth through A, is to that which paſſeth through B, ſo is the <lb></lb><figure id="id.040.01.608.1.jpg" xlink:href="040/01/608/1.jpg"></figure><lb></lb>line E to the line F: therefore the quantity of water which paſ<lb></lb>ſeth through A, being equal to that which paſſeth through B, <lb></lb>the line E ſhall alſo be equal to the line F: Suppoſing moreover, <lb></lb>That as the Section A, is to the Section B, ſo is the line F, to the <lb></lb>line G; and becauſe the quantity of water which paſſeth <lb></lb>through the Section A, is to that which paſſeth through the <lb></lb>Section B, in a proportion compoſed of the proportions of the <lb></lb>Section A, to the Section B, and of the velocity through A, to the <lb></lb>velocity through B; therefore the line E, ſhall be the line to F, in <lb></lb>a proportion compounded of the ſame proportions; namely, of <lb></lb>the proportion of the Section A, to the Section B, and of the ve<lb></lb>locity through A, to the velocity through B; but the line E, hath <lb></lb>to the line G, the proportion of the Section A, to the Section B, <lb></lb>therefore the proportion remaining of the line G, to the line F, <lb></lb>ſhall be the proportion of the velocity through A, to the velocity <lb></lb>through B; therefore alſo the line G, ſhall be to the line E, as <lb></lb>the velocity by A, to the velocity by B: And converſly, the ve<lb></lb>locity through B, ſhall be to the velocity through A, as the line <lb></lb>E, to the line G; that is to ſay, as the Section A, to the Section B, <lb></lb>and therefore in two Sections, &c. </s> <s>which was to be demonſtrated.</s></p><pb xlink:href="040/01/609.jpg" pagenum="42"></pb><p type="head"> <s><emph type="italics"></emph>COROLLARIE.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Hence it is manifeſt, that Sections of the ſame River (which <lb></lb>are no other than the vulgar meaſures of the River) have <lb></lb>betwixt themſelves reciprocal proportions to their veloci<lb></lb>ties; for in the firſt Propoſition we have demonſtrated that the <lb></lb>Sections of the ſame River, diſcharge equal quantities of Water <lb></lb>in equal times; therefore, by what hath now been demonſtrated <lb></lb>the Sections of the ſame River ſhall have reciprocal proportion <lb></lb>to their velocities; And therefore the ſame running water chan<lb></lb>geth meaſure, when it changeth velocity; namely, increaſeth the <lb></lb>meaſure, when it decreaſeth the velocity, and decreaſeth the <lb></lb>meaſure, when it increaſeth the velocity.</s></p><p type="main"> <s>On which principally depends all that which hath been ſaid <lb></lb>above in the <emph type="italics"></emph>Diſcourſe,<emph.end type="italics"></emph.end> and obſerved in the <emph type="italics"></emph>Corollaries<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ap<lb></lb>pendixes<emph.end type="italics"></emph.end>; and therefore is worthy to be well underſtood and <lb></lb>heeded.</s></p><p type="head"> <s>PROPOSITION IV.</s></p><p type="main"> <s><emph type="italics"></emph>If a River fall into another River, the height of the <lb></lb>firſt in its own Chanel ſhall be to the height that it <lb></lb>ſhall make in the ſecond Chanel, in a proportion <lb></lb>compounded of the proportions of the breadth of <lb></lb>the Chanel of the ſecond, to the breadth of the <lb></lb>Chanel of the firſt, and of the velocitie acquired in <lb></lb>the Chanel of the ſecond, to that which it had in <lb></lb>its proper and first Chanel.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the River A B, whoſe height is A C, and breadth C B, <lb></lb>that is, whoſe Section is A C B; let it enter, I ſay, into a<lb></lb>nother River as broad as the line E F, and let it therein make <lb></lb>the riſe or height D E, that is to ſay, let it have its Section in <lb></lb>the River whereinto it falls D E F; I ſay, that the height A C <lb></lb>hath to the height D E the proportion compounded of the pro<lb></lb>portions of the breadth E F, to the breadth C B, and of the ve<lb></lb>locity through D F, to the velocity through A B. </s> <s>Let us ſup<lb></lb>poſe the Section G, equal in velocity to the Section A B, and in <lb></lb>breadth equal to E F, which carrieth a quantity of Water e<lb></lb>qual to that which the Section A B carrieth, in equal times, <lb></lb>and conſequently, equal to that which D F carrieth. </s> <s>Moreover, <lb></lb>as the breadth E F is to the breadth C B, ſo let the line H be to <pb xlink:href="040/01/610.jpg" pagenum="43"></pb>the line I; and as the velocity of D F is to the velocity of A B, <lb></lb>ſo let the line I be to the line L; becauſe therefore the two <lb></lb>Sections A B and G are equally ſwift, and diſcharge equal quan<lb></lb>tity of Water in equal times, they ſhall be equal Sections; and <lb></lb><figure id="id.040.01.610.1.jpg" xlink:href="040/01/610/1.jpg"></figure><lb></lb>therefore the height of A <emph type="italics"></emph>B<emph.end type="italics"></emph.end> to the height of G, ſhall be as the <lb></lb>breadth of G, to the breadth of A <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> that is, as E F to C <emph type="italics"></emph>B,<emph.end type="italics"></emph.end><lb></lb>that is, as the line H to the line I: but becauſe the Water which <lb></lb>paſſeth through G, is equal to that which paſſeth through D E F, <lb></lb>therefore the Section G, to the Section D E F, ſhall have the re<lb></lb>ciprocal proportion of the velocity through D E F, to the velo<lb></lb>city through G; but alſo the height of G, is to the height D E, <lb></lb>as the Section G, to the Section D E F: Therefore the height of <lb></lb>G, is to the height D E, as the velocity through D E F, is to the <lb></lb>velocity through G; that is, as the velocity through D E F, is to <lb></lb>the velocity through A <emph type="italics"></emph>B<emph.end type="italics"></emph.end>; That is, finally, as the line I, to the <lb></lb>line L; Therefore, by equal proportion, the height of <emph type="italics"></emph>A B,<emph.end type="italics"></emph.end> that <lb></lb>is, A C, ſhall be to the height D E; as H to L, that is, com<lb></lb>pounded of the proportions of the breadth E F, to the breadth <lb></lb>C <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> and of the velocity through D F, to the velocity through <lb></lb>A <emph type="italics"></emph>B<emph.end type="italics"></emph.end>: So that if a River fall into another River, &c. </s> <s>which was <lb></lb>to be demonſtrated.</s></p><pb xlink:href="040/01/611.jpg" pagenum="44"></pb><p type="head"> <s>PROPOSITION V.</s></p><p type="main"> <s><emph type="italics"></emph>If a River diſcharge a certain quantitie of Water <lb></lb>in a certain time; and after that there come into it <lb></lb>a Flood, the quantity of Water which is diſchar<lb></lb>ged in as much time at the Flood, is to that which <lb></lb>was diſcharged before, whilſt the River was low, <lb></lb>in a proportion compounded of the proportions of <lb></lb>the velocity of the Flood, to the velocity of the first <lb></lb>Water, and of the height of the Flood, to the <lb></lb>height of the first Water.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Suppoſe a River, which whilſt it is low, runs by the Section <lb></lb>AF; and after a Flood cometh into the ſame, and runneth <lb></lb>through the Section D F, I ſay, that the quantity of the Wa<lb></lb>ter which is diſcharged through D F, is to that which is diſcharged <lb></lb><figure id="id.040.01.611.1.jpg" xlink:href="040/01/611/1.jpg"></figure><lb></lb>through A F, in a proportion compounded of the proportions of <lb></lb>the velocity through D F, to the velocity through A F, and of <lb></lb>the height D <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> to the height A <emph type="italics"></emph>B<emph.end type="italics"></emph.end>; As the velocity through DF <lb></lb>is to the velocity through A F, ſo let the line R, to the line S; <lb></lb>and as the height D <emph type="italics"></emph>B<emph.end type="italics"></emph.end> is to the height A <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> ſo let the line S, to <lb></lb>the line T; and let us ſuppoſe a Section L M N, equal to D F <lb></lb>in height and breadth; that is L M equal to D <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> and M N equal <lb></lb>to <emph type="italics"></emph>B F<emph.end type="italics"></emph.end>; but let it be in velocity equal to the Section A F, there<lb></lb>fore the quantity of Water which runneth through D F, ſhall be <lb></lb>to that which runneth through LN, as the velocity through DF, <lb></lb>is to the velocity through L N, that is, to the velocity through <lb></lb><emph type="italics"></emph>A F<emph.end type="italics"></emph.end>; and the line R being to the line S, as the velocity through <lb></lb>D <emph type="italics"></emph>F,<emph.end type="italics"></emph.end> to the velocity through <emph type="italics"></emph>A F<emph.end type="italics"></emph.end>; therefore the quantity which <lb></lb>runneth through D <emph type="italics"></emph>F,<emph.end type="italics"></emph.end> to that which runneth through L N, ſhall <lb></lb>have the proportion of R to S; but the quantity which runneth <lb></lb>through L N, to that which runneth through <emph type="italics"></emph>A F,<emph.end type="italics"></emph.end> (the Sections <pb xlink:href="040/01/612.jpg" pagenum="45"></pb>being equally ſwift) ſhall be in proportion as the Section <emph type="italics"></emph>L<emph.end type="italics"></emph.end> N, to <lb></lb>the Section A F; that is, as D B, to A B; that is as the line S, to <lb></lb>the line T: Therefore by equal proportion, the quantity of the <lb></lb>water which runneth through D F, ſhall be in proportion to that <lb></lb>which runneth through A F, as R is to T; that is, compounded of <lb></lb>the proportions of the height D B, to the height A B, and of the <lb></lb>velocity through <emph type="italics"></emph>D F,<emph.end type="italics"></emph.end> to the velocity through <emph type="italics"></emph>A F<emph.end type="italics"></emph.end>; and therefore <lb></lb>if a River diſcharge a certain quantity, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> which was to be de<lb></lb>monſtrated.</s></p><p type="head"> <s>ANNOTATION.</s></p><p type="main"> <s>The ſame might have been demonſtrated by the ſecond <lb></lb>Propoſition above demonſtrated, as is manifeſt.</s></p><p type="head"> <s>PROPOSITION VI.</s></p><p type="main"> <s><emph type="italics"></emph>If two equal ſtreams of the ſame Torrent, fall into a <lb></lb>River at divers times, the heights made in the Ri<lb></lb>ver by the Torrent, ſhall have between them<lb></lb>ſelves the reciprocal proportion of the velocities <lb></lb>acquired in the River.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let A and B, be two equal ſtreams of the ſame Torrent, <lb></lb>which falling into a River at divers times, make the heights <lb></lb>C D, and F G; that is the ſtream A, maketh the height <lb></lb>C D, and the ſtream B, maketh the height F G; that is, Let <lb></lb>their Sections in the River, into which they are fallen, be C E, <lb></lb>and FH; I ſay, that the height C D, ſhall be to the height F G, <lb></lb>in reciprocal proportion, as the velocity through F H, to the ve<lb></lb>locity through C E; for the quantity of water which paſſeth <lb></lb>through A, being equal to the quantity which paſſeth through B, <lb></lb>in equal times; alſo the quantity which paſſeth through C E, ſhall <lb></lb><figure id="id.040.01.612.1.jpg" xlink:href="040/01/612/1.jpg"></figure><lb></lb>be equal to that which paſſeth through F H: And therefore the <lb></lb>proportion that the Section C E, hath to the Section F H; ſhall <lb></lb>be the ſame that the velocity through F H, hath to the velocity <lb></lb>through C E; But the Section C E, is to the Section F H, as <lb></lb>C D, to F G, by reaſon they are of the ſame breadth: Therefore <lb></lb>C D, ſhall be to F G, in reciprocal proportion, as the velocity <lb></lb>through F H, is to the velocity through C E, and therefore if two <lb></lb>equal ſtreams of the ſame Torrent, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> which was to be de<lb></lb>monſtrated.</s></p><pb xlink:href="040/01/613.jpg" pagenum="47"></pb><p type="head"> <s>OF THE <lb></lb>MENSURATION <lb></lb>OF <lb></lb>Running Waters.</s></p><p type="head"> <s><emph type="italics"></emph>Lib.<emph.end type="italics"></emph.end> II.</s></p><p type="main"> <s>Having, in the cloſe of my Treatiſe of the <lb></lb>Menſuration of Running Waters promiſed <lb></lb>to declare upon another occaſion other par<lb></lb>ticulars more obſcure, and of very great <lb></lb>concern upon the ſame argumement: I now <lb></lb>do perform my promiſe on the occaſion <lb></lb>that I had the paſt year 1641. to propound <lb></lb>my thoughts touching the ſtate of the Lake <lb></lb>of <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> a buſineſs certainly moſt important, as being the <lb></lb>concernment of that moſt noble and moſt admirable City; and <lb></lb>indeed of all <emph type="italics"></emph>Italy,<emph.end type="italics"></emph.end> yea of all <emph type="italics"></emph>Europe, Aſia, & Africa<emph.end type="italics"></emph.end>; & one may <lb></lb>truly ſay of all the whole World. </s> <s>And being to proceed according <lb></lb>to the method neceſſary in Sciences, I wil propoſe, in the firſt place <lb></lb>certain Definitions of thoſe Terms whereof we are to make uſe <lb></lb>in our Diſcourſe: and then, laying down certain Principles we <lb></lb>will demonſtrate ſome Problemes and Theoremes neceſſary for <lb></lb>the underſtanding of thoſe things which we are to deliver; and <lb></lb>moreover, recounting ſundry caſes that have happened, we will <lb></lb>prove by practice, of what utility this contemplation of the <lb></lb>Meaſure of Running Waters is in the more important affairs both <lb></lb>Publique and Private.</s></p><p type="head"> <s>DEFINITION I.</s></p><p type="main"> <s>Two Rivers are ſaid to move with equal velocity, when in e<lb></lb>qual times they paſſe ſpaces of equal length.</s></p><p type="head"> <s>DEFINITION II.</s></p><p type="main"> <s>Rivers are ſaid to move with like velocity, when their propor<lb></lb>tional parts do move alike, that is, the upper parts alike to <lb></lb>the upper, and the lower to the lower; ſo that if the upper <lb></lb>part of one River ſhall be more ſwift than the upper part of ano<lb></lb>ther; then alſo the lower part of the former ſhall be more ſwift <lb></lb>than the part correſpondent to it in the ſecond, proportionally.</s></p><pb xlink:href="040/01/614.jpg" pagenum="48"></pb><p type="head"> <s>DEFINITON III.</s></p><p type="main"> <s>To meaſure a River, or running Water, is in our ſenſe to finde <lb></lb>out how many determinate meaſures, or weights of Water <lb></lb>in a given time paſſeth through the River, or Channel of the <lb></lb>Water that is to be meaſured.</s></p><p type="head"> <s>DEFINITION IV.</s></p><p type="main"> <s>If a Machine be made either of Brick, or of Stone, or of <lb></lb>Wood, ſo compoſed that two ſides of the ſaid Machine be <lb></lb>placed at right angles upon the ends of a third ſide, that is <lb></lb>ſuppoſed to be placed in the bottom of a River, parallel to the <lb></lb>Horizon, in ſuch a manner, that all the water which runneth <lb></lb>through the ſaid River, paſſeth thorow the ſaid Machine: And <lb></lb>if all the water coming to be diverted <lb></lb><figure id="id.040.01.614.1.jpg" xlink:href="040/01/614/1.jpg"></figure><lb></lb>that runneth through the ſaid River, the <lb></lb>upper ſuperficies of that third ſide placed <lb></lb>in the bottom do remain uncovered <lb></lb>and dry, and that the dead water be not <lb></lb>above it; This ſame Machine ſhall be <lb></lb><arrow.to.target n="marg968"></arrow.to.target><lb></lb>called by us ^{*} REGULATOR: And that third ſide of the <lb></lb>Machine which ſtandeth Horizontally is called the bottom of <lb></lb>the Regulator; and the other two ſides, are called the banks of <lb></lb>the Regulator; as is ſeen in this firſt Figure: A B C D, ſhall be <lb></lb>the Regulator; B C the bottom; and the other two ſides A B, <lb></lb>and C D are its banks.</s></p><p type="margin"> <s><margin.target id="marg968"></margin.target>* Or Sluice.</s></p><p type="head"> <s>DEFINITION V.</s></p><p type="main"> <s>By the quick height, we mean the Perpendicular from the upper <lb></lb>ſuperficies of the River, unto the upper ſuperficies of the bot<lb></lb>tom of the Regulator; as in the foregoing Figure the line. </s> <s>G H.</s></p><p type="head"> <s>DEFINITION VI.</s></p><p type="main"> <s>If the water of a <emph type="italics"></emph>R<emph.end type="italics"></emph.end>iver be ſuppoſed to be marked by three <lb></lb>ſides of a Regulator, that Rightangled Parallelogram compre<lb></lb>hended between the banks of the Regulator, and the bottom, <lb></lb>and the ſuperficies of the Water is called a Section of the <lb></lb>River.</s></p><pb xlink:href="040/01/615.jpg" pagenum="49"></pb><p type="head"> <s>ANNOTATION.</s></p><p type="main"> <s>Here it is to be noted, that the River it ſelf may have ſundry <lb></lb>and divers heights, in ſeveral parts of its Chanel, by reaſon of <lb></lb>the various velocities of the water, and its meaſures; as hath <lb></lb>been demonſtrated in the firſt book.</s></p><p type="head"> <s>SUPPOSITION I.</s></p><p type="main"> <s>It is ſuppoſed, that the Rivers equal in breadth, and quick <lb></lb>height, that have the ſame inclination of bed or bottom, ought <lb></lb>alſo to have equal velocities, the accidental impediments being <lb></lb>removed that are diſperſed throughout the courſe of the water, <lb></lb>and abſtracting alſo from the external windes, which may velo<lb></lb>citate, and retard the courſe of the water of the River.</s></p><p type="head"> <s>SUPPOSITION II.</s></p><p type="main"> <s>Let us ſuppoſe alſo, that if there be two Rivers that are in <lb></lb>their beds of equal length, and of the ſame inclination, but of <lb></lb>quick heights unequal, they ought to move with like velocity, <lb></lb>according to the ſenſe explained in the ſecond definition.</s></p><p type="head"> <s>SUPPOSITION III.</s></p><p type="main"> <s>Becauſe it will often be requiſite to meaſure the time exactly <lb></lb>in the following Problems, we take that to be an excellent <lb></lb>way to meaſure the time, which was ſhewed me many years ſince <lb></lb>by <emph type="italics"></emph>Signore Galilæo Galilæi,<emph.end type="italics"></emph.end> which is as followeth.</s></p><p type="main"> <s>A ſtring is to be taken three Roman feet long, to the end of <lb></lb>which a Bullet of Lead is to be hanged, of about two or three <lb></lb>ounces; and holding it by the other end, the Plummet is to be <lb></lb>removed from its perpendicularity a Palm, more or leſs, and then <lb></lb>let go, which will make many ſwings to and again, paſſing and <lb></lb>repaſſing the Perpendicular, before that it ſtay in the ſame: Now <lb></lb>it being required to meaſure the time that is ſpent in any what<lb></lb>ſoever operation, thoſe vibrations are to be numbred, that are <lb></lb>made whilſt the work laſteth; and they ſhall be ſo many ſecond <lb></lb>minutes of an hour, if ſo be, that the ſtring be three Roman feet <lb></lb>long, but in ſhorter ſtrings, the vibrations are more frequent, and <lb></lb>in longer, leſs frequent; and all this ſtill followeth, whether the <lb></lb>Plummet be little or much removed from its Perpendicularity, or <lb></lb>whether the weight of the Lead be greater or leſſer.</s></p><p type="main"> <s>Theſe things being pre-ſuppoſed, we will lay down ſome fa<pb xlink:href="040/01/616.jpg" pagenum="50"></pb>miliar Problems, from which we ſhall paſs to the Notions and <lb></lb>queſtions more ſubtil and curious; which will alſo prove profi<lb></lb>table, and not to be ſleighted in this buſineſs of Waters.</s></p><p type="head"> <s>PROPOSITION I. PROBLEME I.</s></p><p type="main"> <s><emph type="italics"></emph>Achanel of Running-Water being given, the breadth <lb></lb>of which paſsing through a Regulator, is three <lb></lb>Palms; and the height one Palm, little more or <lb></lb>leſs, to meaſure what water paſſeth through the <lb></lb>Regulator in a time given.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Firſt, we are to dam up the Chanel; ſo that there paſs not any <lb></lb>water below the Dam; then we muſt place in the ſide of the <lb></lb>Chanel, in the parts above the Regulator three, or four, or five <lb></lb>Bent-pipes, or Syphons, according to the quantity of the water <lb></lb>that runneth along the Chanel; in ſuch ſort, as that they may <lb></lb>drink up, or draw out of the Chanel all the water that the Cha<lb></lb>nel beareth (and then ſhall we know that the Syphons drink up <lb></lb>all the water, when we ſee that the water at the Dam doth nei<lb></lb>ther riſe higher, nor abate, but alwaies keepeth in the ſame Le<lb></lb>vel.) Theſe things being prepared, taking the Inſtrument to <lb></lb>meaſure the time, we will examine the quantity of the water that <lb></lb>iſſueth by one of thoſe Syphons in the ſpace of twenty vibrations, <lb></lb>and the like will we do one by one with the other Syphons; and <lb></lb>then collecting the whole ſumme, we will ſay, that ſo much is <lb></lb>the water that paſſeth and runneth thorow the Regulator or <lb></lb>Chanel (the Dam being taken away) in the ſpace of twenty ſe<lb></lb>cond minutes of an hour; and calculating, we may eaſily reduce <lb></lb>it to hours, dayes, months, and years: And it hath fallen to my <lb></lb>turn to meaſure this way the waters of Mills and Fountains, and I <lb></lb>have been well aſſured of its exactneſs, by often repeating the <lb></lb>ſame work.</s></p><p type="head"> <s>CONSIDERATION.</s></p><p type="main"> <s>And this method muſt be made uſe of in meaſuring the waters, <lb></lb>that we are to bring into Conducts, and carry into Cities <lb></lb>and Caſtles, for Fountains; and that we may be able afterwards <lb></lb>to divide and ſhare them to particular perſons juſtly; which will <lb></lb>prevent infinite ſuits and controverſies that every day happen in <lb></lb>theſe matters..</s></p><pb xlink:href="040/01/617.jpg" pagenum="51"></pb><p type="head"> <s>PROPOSITION II. THEOREM I.</s></p><p type="main"> <s><emph type="italics"></emph>If a River moving with ſuch a certain velocitie <lb></lb>through its Regulator, ſhall have a given quick <lb></lb>height, and afterwards by new water ſhall increaſe <lb></lb>to be double, it ſhall alſo increaſe double in ve<lb></lb>locitie.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the quick height of a River in the Regulator A B C D, <lb></lb>be the perpendicular F B, and afterwards, by new water that <lb></lb>is added to the River, let the water be ſuppoſed to be raiſ<lb></lb>ed to G, ſo that G B may be double to E B. </s> <s>I ſay, that all the <lb></lb>water G C ſhall be double in velocity to <lb></lb><figure id="id.040.01.617.1.jpg" xlink:href="040/01/617/1.jpg"></figure><lb></lb>that of E C: For the water G F, having <lb></lb>for its bed the bottom E F, equally in<lb></lb>clined as the bed B C, and its quick <lb></lb>height G E being equal to the quick <lb></lb>height E C, and having the ſame breadth <lb></lb>B C, it ſhall have of it ſelf a velocity e<lb></lb>qual to the velocity of the firſt water <lb></lb>F C: but becauſe, beſides its own moti<lb></lb>on, which is imparted to it by the motion of the water E C, it <lb></lb>hath alſo over and above its own motion, the motion of E C. </s> <s>And <lb></lb>becauſe the two waters G C, and E C, are alike in velocity, by <lb></lb>the third Suppoſition; therefore the whole water G C ſhall be <lb></lb>double in velocity to the water E C; which was that which we <lb></lb>were to demonſtrate.</s></p><p type="main"> <s><emph type="italics"></emph>This demonſtration is not here inſerted, as perfect, the Authour ha<lb></lb>ving by ſeveral letters to his friends confeſſed himſelf unſatisfi<lb></lb>ed therewith; and that he intended not to publiſh the<emph.end type="italics"></emph.end> Theorem <lb></lb><emph type="italics"></emph>without a more ſolid demonſtration, which he was in hope to light <lb></lb>upon. </s> <s>But being overtaken by Death, he could not give the <lb></lb>finiſhing touch either to this, or to the rest of the ſecond Book. </s> <s>In <lb></lb>conſideration of which, it ſeemed good to the Publiſher of the <lb></lb>ſame, rather to omit it, than to do any thing contrary to the mind of <lb></lb>the Authour. </s> <s>And this he hints, by way of advertiſement, to <lb></lb>thoſe that have Manuſcript Copies of this Book, with the ſaid de<lb></lb>monſtration. </s> <s>For this time let the Reader content himſelf with <lb></lb>the knowledge of ſo ingenious and profitable a Concluſion; of the <lb></lb>truth of which he may, with ſmall expence and much pleaſure, be <lb></lb>aſſured by means of the experiment to be made in the ſame man<lb></lb>ner, with that which is laid down in the ſecond Corollary of<emph.end type="italics"></emph.end><pb xlink:href="040/01/618.jpg" pagenum="52"></pb><emph type="italics"></emph>the fourth<emph.end type="italics"></emph.end> Theorem <emph type="italics"></emph>of this, with its Table, and the uſe there<lb></lb>of annexed.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Hence it followeth, that when a River increaſeth in quick <lb></lb>height by the addition of new water, it alſo increaſeth in ve<lb></lb>locity; ſo that the velocity hath the ſame proportion to the velo<lb></lb>city that the quick height hath to the quick height; as may be <lb></lb>demonſtrated in the ſame manner.</s></p><p type="head"> <s>PROPOS. III. PROBLEME II.</s></p><p type="main"> <s><emph type="italics"></emph>Achanel of Water being given whoſe breadth exceeds not <lb></lb>twenty Palms, or thereabouts, and whoſe quick beight <lb></lb>is leſs than five Palms, to meaſure the quantity of the <lb></lb>Water that runneth thorow the Chanel in a time <lb></lb>given.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Place in the Chanel a Regulator, and obſerve the quick <lb></lb>height in the ſaid Regulator; then let the water be turned <lb></lb>away from the Chanel by a Chanellet of three or four Palms <lb></lb>in breadth, or thereabouts: And that being done, meaſure the <lb></lb>quantity of the water which paſſeth thorow the ſaid Chanellet, <lb></lb>as hath been taught in the ſecond Propoſition; and at the ſame <lb></lb>time obſerve exactly how much the quick height ſhall be abated <lb></lb>in the greater Chanel, by means of the diverſion of the Chancl<lb></lb>let; and all theſe particulars being performed, multiply the quick <lb></lb>height of the greater Chanel into it ſelf, and likewiſe multiply <lb></lb>into it ſelf the leſſer height of the ſaid bigger Chanel, and the <lb></lb>leſſer ſquare being taken, from the greater, the remainder ſhall <lb></lb>have the ſame proportion to the whole greater ſquare, as the wa<lb></lb>ter of the Chanellet diverted, hath to the water of the bigger <lb></lb>Chanel: And becauſe the water of the Chanellet is known by <lb></lb>the Method laid down in the firſt Theorem, and the terms of the <lb></lb>Theorem being alſo known, the quantity of the water which run<lb></lb>neth thorow the bigger Chanel, ſhall be alſo known by the Gol<lb></lb>den <emph type="italics"></emph>R<emph.end type="italics"></emph.end>ule, which was that that was deſired to be known. </s> <s>We <lb></lb>will explain the whole buſineſs by an example.</s></p><p type="main"> <s>Let a Chanel be, for example, 15 Palms broad, its quick height <lb></lb>before its diverſion by the Chanellet ſhall be ſuppoſed to be 24 <lb></lb>inches; but after the diverſion, let the quick height of the Chanel <lb></lb>be onely 22 inches. </s> <s>Therefore the greater height to the leſſer, <lb></lb>is as the number 11. to 12. But the ſquare of 11. is 121, and the <lb></lb>ſquare of 12. is 144, the difference between the ſaid leſſer <pb xlink:href="040/01/619.jpg" pagenum="53"></pb>ſquare and the greater is 23. Therefore the diverted water, is <lb></lb>to the whole water, as 23. to 144: which is well near as 1 to <lb></lb>6 6/23: and that is the proportion that the quantity of the water <lb></lb>which runneth through the Chanellet ſhall have, to all the water <lb></lb>that runneth thorow the great Chanel. </s> <s>Now if we ſhould finde <lb></lb>by the Rule mentioned above in the firſt Propoſition, that the <lb></lb>quantity of the water that runneth through the Chanellet, is <lb></lb><emph type="italics"></emph>v. </s> <s>g.<emph.end type="italics"></emph.end> an hundred Barrels, in the ſpace of 15 ſecond minutes of <lb></lb>an hour, it is manifeſt, that the water which runneth through the <lb></lb>great Chanel in the ſaid time of 35 min. </s> <s>ſec. </s> <s>ſhall be about 600 <lb></lb>Barrels.</s></p><p type="head"> <s><emph type="italics"></emph>The ſame operation performed another way.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And becauſe very often in applying the Theory to Practice <lb></lb>it happeneth, that all the neceſſary particulars in the The<lb></lb>ory cannot ſo eaſily be put in execution; therefore we will <lb></lb>here add another way of performing the ſame Problem, if it ſhould <lb></lb>chance to happen that the Chanellet could not commodiouſly be <lb></lb>diverted from the great Chanel, but that it were eaſier for the <lb></lb>water of another ſmaller Chanel to be brought into the greater <lb></lb>Chanel; which water of the ſmaller Chanel might be eaſily mea<lb></lb>ſured, as hath been ſhewen in the firſt Probleme; or in caſe that <lb></lb>there did fall into a greater Chanel, a leſſer Chanel that might <lb></lb>be diverted and meaſured. </s> <s>Therefore I ſay in the firſt caſe, If <lb></lb>we would meaſure the quantity of the water that runneth in a <lb></lb>certain time thorow the greater Chanel, into which another leſſer <lb></lb>Chanel that is meaſurable may be brought, we muſt firſt exactly <lb></lb>meaſure the Chanellet, and then obſerve the quick height of the <lb></lb>greater Chanel, before the introduction of the leſſer; and having <lb></lb>brought in the ſaid Chanellet, we muſt agnin find the propor<lb></lb>tion that the water of the Chanellet hath to all the water of the <lb></lb>great Ghanel; for theſe terms of the proportion being known, as <lb></lb>alſo the quantity of the water of the Chanellet, we ſhall alſo <lb></lb>come to know the quantity of the water that runneth thorow <lb></lb>the great Chanel. </s> <s>It is likewiſe manifeſt, that we ſhall obtain <lb></lb>our intent, if the caſe were that there entered into the great <lb></lb>Chanel, another leſſer Chanel that was meaſurable, and that <lb></lb>might be diverted.</s></p><p type="head"> <s>CONSIDERATION.</s></p><p type="main"> <s>It would be neceſſary to make uſe of this Doctrine in the di<lb></lb>ſtribution of the waters that are imploy'd to overflow the fields, <lb></lb>as is uſed in the <emph type="italics"></emph>Breſciau, Cremoneſe, Bergamaſe, Lodigian, Mila-<emph.end type="italics"></emph.end><pb xlink:href="040/01/620.jpg" pagenum="54"></pb><emph type="italics"></emph>neſe<emph.end type="italics"></emph.end> territories, and many other places, where very great ſuits <lb></lb>and differences ariſe, which not being to be determined with in<lb></lb>telligible reaſons, come oftentimes to be decided, by force of <lb></lb>armes; and inſtead of flowing their Grounds with Waters, they <lb></lb>cruelly flow them with the ſhedding of humane blood, impiouſly <lb></lb>inverting the courſe of Peace and Juſtice, ſowing ſuch diſorders <lb></lb>and feuds, as that they are ſometimes accompanied with the ru<lb></lb>ine of whole Cities, or elſe unprofitably charge them with vain, <lb></lb>and ſometimes prejudicial expences.</s></p><p type="head"> <s>PROPOS. IV. THEOR. II.</s></p><p type="main"> <s><emph type="italics"></emph>If a River increaſe in quick height, the quantitie of <lb></lb>Water which the River diſchargeth after the in<lb></lb>creaſe, hath the Proportion compounded of the <lb></lb>Proportions of the Quick height to the Quick <lb></lb>height, and of the velocity to the velocity.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let there be a River, which whilſt it is low, runneth thorow <lb></lb>the Regulator D F, with the Quick height A B, and after<lb></lb>wards let a Flood come; and then let it run with the height <lb></lb>D B, I ſay, that the quantity of the Water that is diſcharged <lb></lb>through D F, to that which diſchargeth through A F, hath the <lb></lb>proportion compounded of the proportions of the velocity <lb></lb>through D F to the velocity through A F, and of the height <lb></lb>D B to the height A B. </s> <s>As the velocity through D F is to the <lb></lb>velocity through A F, ſo let the line R be to the line S; and as <lb></lb>the height D B is to the height A B; ſo let the line S be to the <lb></lb><figure id="id.040.01.620.1.jpg" xlink:href="040/01/620/1.jpg"></figure><lb></lb>line T. </s> <s>And let a Section be ſuppoſed L M N equal to the <lb></lb>Section D F in height and length, but let it be in velocity equal <lb></lb>to the Section AF. </s> <s>Therefore the quantity of the Water that run<lb></lb>neth through D F to that which runneth through L N, ſhall be <pb xlink:href="040/01/621.jpg" pagenum="55"></pb>as the velocity through D F, to the velocity of L N, that is, to <lb></lb>the velocity through L N, that is, to the velocity through <emph type="italics"></emph>A F.<emph.end type="italics"></emph.end><lb></lb>therefore the quantity of Water which runneth through D <emph type="italics"></emph>F,<emph.end type="italics"></emph.end><lb></lb>to that which paſſeth through L N, ſhall have the proportion <lb></lb>that R hath to S; but the quantity of the Water that runneth <lb></lb>through L N, to that which runneth through <emph type="italics"></emph>A F<emph.end type="italics"></emph.end>; (the Sections <lb></lb>being equally ſwift) ſhall have the proportion that the Section <lb></lb>L N hath to the Section A F, that is, that the height <emph type="italics"></emph>B<emph.end type="italics"></emph.end> D hath to <lb></lb>the height <emph type="italics"></emph>B<emph.end type="italics"></emph.end> A, that is, that S hath to T. Therefore, by equal <lb></lb>proportion, the quantity of the Water which runneth by D F, <lb></lb>to that which runneth by A F, ſhall have the proportion of R to <lb></lb>T, that is, ſhall be compounded of the proportions of the height <lb></lb>D <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> to the height A <emph type="italics"></emph>B<emph.end type="italics"></emph.end>; and of the velocity through D F, to <lb></lb>the velocity through A F. </s> <s>And therefore if a River increaſe in <lb></lb>quick height, the quantity of the Water that runneth after the <lb></lb>increaſe, to that which runneth before the increaſe, hath the <lb></lb>proportion compounded, &c. </s> <s>Which was to be demonſtrated.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE I.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Hence it followeth, that we having ſhewn, that the quantity of <lb></lb>the Water which runneth, whilſt the River is high, to that <lb></lb>which ran, whilſt it was low, hath the proportion compounded <lb></lb>of the velocity to the velocity, and of the height to the height. <lb></lb></s> <s>And it having been demonſtrated, that the velocity to the velo<lb></lb>city is as the height to the height; it followeth, I ſay, that the <lb></lb>quantity of the Water that runneth, whilſt the River is high, to <lb></lb>that which runneth, whilſt it is low, hath duplicate proportion of <lb></lb>the height to the height, that is, the proportion that the ſquares <lb></lb>of the heights have.</s></p><p type="head"> <s><emph type="italics"></emph>COROLLARIE II.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Vpon which things dependeth the reaſon of that which I have <lb></lb>ſaid, in my ſecond Conſideration, that if by the diverſion of <lb></lb>5/9 of the Water that entereth by the Rivers into the Moor or <lb></lb>Fen, the Water be abated ſuch a meaſure, that ſame ſhall be <lb></lb>only one third of its whole height; but moreover diverting the 4/9, it <lb></lb>ſhall abate two other thirds, a moſt principal point; and ſuch, <lb></lb>that its not having been well underſtood, hath cauſed very great <lb></lb>diſorders, and there would now, more than ever, follow extream <lb></lb>dammage, if one ſhould put in execution the diverſion of the <emph type="italics"></emph>Sile<emph.end type="italics"></emph.end><lb></lb>and other Rivers; and it is manifeſt, that in the ſame manner, <lb></lb>wherewith it hath been demonſtrated, that the quantity of the <lb></lb>Water increaſing quadruple, the height would increaſe onely <pb xlink:href="040/01/622.jpg" pagenum="56"></pb>double, and the quantity increaſing nonuple, the height increa<lb></lb>ſeth triple; ſo that, by adding to units all the odde numbers, ac<lb></lb>cording to their Series, the heights increaſe according to the na<lb></lb>tural progreſſion of all the numbers, from units. </s> <s>As for exam<lb></lb>ple, there paſſing thorow a Regulator ſuch a certain quantity of <lb></lb>Water in one time; adding three of thoſe meaſures, the quick <lb></lb>height is two of thoſe parts, which at firſt was one; and con<lb></lb>tinuing to adde five of thoſe ſaid meaſures, the height is three of <lb></lb>thoſe parts which at firſt were one; and thus adding ſeven, and <lb></lb>then nine, and then 11. and then 13, &c. </s> <s>the heights ſhall be 4. <lb></lb>then 5, then 6. then 7, &c. </s> <s>And for the greater facility of the <lb></lb>Work, we have deſcribed the following Table, of which we will <lb></lb>declare the uſe: The Table is divided into three Series or Pro<lb></lb>greſſions of Numbers: the firſt Series containeth all the Num<lb></lb>bers in the Natural Progreſſion, beginning at a Unit, and is called <lb></lb>the Series of the Heights; the ſecond containeth all the odde <lb></lb>numbers, beginning at an unit, and is called the Series of the <lb></lb>Additions: the third containeth all the ſquare numbers, begin<lb></lb>ning at an unit, and is called the Series of Quantity.<lb></lb><arrow.to.target n="table73"></arrow.to.target></s></p><table><table.target id="table73"></table.target><row><cell>Heights.</cell><cell>1</cell><cell>2</cell><cell>3</cell><cell>4</cell><cell>5</cell><cell>6</cell><cell>7</cell><cell>8</cell><cell>9</cell><cell>10</cell><cell>11</cell></row><row><cell>Additions.</cell><cell>1</cell><cell>3</cell><cell>5</cell><cell>7</cell><cell>9</cell><cell>11</cell><cell>13</cell><cell>15</cell><cell>17</cell><cell>19</cell><cell>21</cell></row><row><cell>Quantities.</cell><cell>1</cell><cell>4</cell><cell>9</cell><cell>16</cell><cell>25</cell><cell>36</cell><cell>49</cell><cell>64</cell><cell>81</cell><cell>100</cell><cell>121</cell></row></table><p type="head"> <s><emph type="italics"></emph>The uſe of the afore-mentioned Table.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Firſt, if we ſuppoſe the whole quick height of a River of Run<lb></lb>ning Water to be divided into any number of equal parts, at <lb></lb>pleaſure, and would abate the ſame one fift, by means of a divi<lb></lb>ſron; let there be found in the Table in the Series of heights the <lb></lb>number 5. the denominator of the part which the River is to a<lb></lb>bate, and take the number that is immediately under it in the <lb></lb>row of Additions, which is 9. which let be ſubſtracted from the <lb></lb>number 25. placed underneath the ſame in the row of Quanti<lb></lb>ties, the remainder 16. ſignifieth that of the 25. parts of Water <lb></lb>that ran in the River, whilſt it was 5 meaſures high, there do <lb></lb>onely run 16. parts; ſo that to make it abate 1/5 it is neceſſary to <lb></lb>take 9/25 from the Water that the whole River did carry; ſo that <lb></lb>with ſubſtracting ſomewhat more than one third of the Water of <lb></lb>the River, it is abated but only one fift.</s></p><p type="main"> <s>2. And thus, in the ſecond place, if on the contrary, one would <lb></lb>know how much water is to be added to the ſaid River to make <lb></lb>it increaſe one fift more in height, ſo as that it may run in the <pb xlink:href="040/01/623.jpg" pagenum="57"></pb>Regulator 6. of thoſe parts high; of which it ran before but 5. let <lb></lb>6 be found in the row of heights, and let the number 11. ſtand<lb></lb>ing under the ſame be taken and added to the number 25. <lb></lb>that is placed under the number 9. in the Additions, and 5. in <lb></lb>the heights, and you ſhall have 36; which is the quantity of the <lb></lb>water that runneth with the height of the River, when it is high <lb></lb>6 of thoſe parts, whereof it was before but 5.</s></p><p type="main"> <s>3. But if it ſhould be deſired, to know how much water it is <lb></lb>requiſite to add to make the River riſe ſo, as that it may run in <lb></lb>height 8. of thoſe parts of which before it ran but 5; one <lb></lb>ought to take the ſum of the number of the Series of Additions <lb></lb>ſtanding under 8. 7. and 6, which are 15. 13. and 11. that is, 39. <lb></lb>and this ſhall be the ſumme that muſt be added to 25: So that <lb></lb>to make the River to run 8. of thoſe parts in height, of which it <lb></lb>before did run 5, it will be neceſſary to add 39. of thoſe parts, <lb></lb>of which the River before was 25.</s></p><p type="main"> <s>4. Likewiſe the ſame Table giveth the quantity of water <lb></lb>that runneth from time to time through a River, that increaſeth <lb></lb>by the addition of new water to the ſame in one of its heights, the <lb></lb>quantity of its water be known. </s> <s>As for example: If we knew that <lb></lb>the River in one minute of an hour diſchargeth 2500. of thoſe mea<lb></lb>ſures of water, and runneth in height 5. parts in the Regulator, and <lb></lb>afterwards ſhould ſee that it runneth 8 Palms high, finding in the <lb></lb>row of quantity the number placed under 8. which is 64. we would <lb></lb>ſay that the River heightned, carrieth of water 64. of thoſe parts <lb></lb>whereof it carried before but 25; and becauſe before it carried <lb></lb>2500. meaſures, by the Golden Rule we will ſay, that the River <lb></lb>carrieth 6400. of thoſe meaſures, of which before it carried 2500.</s></p><p type="main"> <s>In this progreſs of Nature, is one thing really curious, and that <lb></lb>at firſt ſight ſeemeth to be ſomewhat Paradoxal, that we pro<lb></lb>ceeding ordinately in the diverſions and additions, with additi<lb></lb>ons and diverſions ſo unequal, the abatings do notwithſtanding <lb></lb>alwaies prove equal, and ſo do the riſings: And who would ever <lb></lb>think that a River in height, <emph type="italics"></emph>v. </s> <s>g.<emph.end type="italics"></emph.end> 10. Palms, running and carry<lb></lb>ing an hundred meaſures in a minute of an hour, is to abate but <lb></lb>one Palm, onely by the diverſion of 19. of thoſe meaſures; and <lb></lb>then again, that the buiſineſs cometh to that paſs, that it abateth <lb></lb>likewiſe a Palm by the diverſion of three onely of thoſe meaſures, <lb></lb>nay, by the diverſion of but one meaſure? </s> <s>and yet it is moſt <lb></lb>certain: And this truth meets with ſo manifeſt proofs in experi<lb></lb>ence, that it is very admirable! And for the full ſatisfaction of <lb></lb>thoſe, who not being able to comprehend ſubtil demonſtrati<lb></lb>ons, desire to be clearly inform'd by the matters of fact, and to <lb></lb>ſee with their bobily eyes, and touch with their hands, what their <lb></lb>underſtanding and reaſon cannot reach unto: I will hear add <lb></lb>another very eaſie way to reduce all to an experiment, the <pb xlink:href="040/01/624.jpg" pagenum="58"></pb>which may be made in little, in great, or in very great; of <lb></lb>which I make uſe frequently, to the admiration of ſuch as ſee it.</s></p><p type="main"> <s>I prepared an hundred Siphons, or, if you will, bowed Pipes, <lb></lb>all equal; and placed them at the brim of a Veſſel, wherein the <lb></lb>water is kept at one and the ſame level (whether all the Syphons <lb></lb>work, or but a certain number of them) the mouths by which <lb></lb>the water iſſueth being all placed in the ſame level, parallel to <lb></lb>the Horizon; but lower in level than the water in the Veſſel; and <lb></lb>gathered all the water falling from the Syphons into another <lb></lb>Veſſel ſtanding lower than the former, I made it to run away <lb></lb>thorow a Chanel, in ſuch manner inclined, that wanting water <lb></lb>from the Syphons, the ſaid Chanel remained quite dry.</s></p><p type="main"> <s>And this done, I meaſured the quick height of the Chanel <lb></lb>with care, and afterwards divided it exactly into 10 equal parts, <lb></lb>and cauſing 19. of thoſe Syphons to be taken away, ſo that the <lb></lb>Chanel did not run water, ſave onely with 81 of thoſe Syphons, <lb></lb>I again obſerved the quick height of the water in the ſame ſite <lb></lb>obſerved before, and found that its height was diminiſhed pre<lb></lb>ciſely the tenth part of all its firſt height; and thus continuing to <lb></lb>take away 17. other Syphons, the height was likewiſe diminiſh<lb></lb>ed 1/1. of all its firſt quick height; and trying to take away 15. <lb></lb>Syphons, then 13, then 11, then 9, then 7, then 5, and then 3. <lb></lb>alwaies in theſe diverſions, made in order as hath been ſaid, there <lb></lb>enſued ſtill an abatement of 1/1. of the whole height.</s></p><p type="main"> <s>And here was one thing worthy of obſervation, that the water <lb></lb>encreaſing in [<emph type="italics"></emph>or through<emph.end type="italics"></emph.end>] the Chanel, its quick height was diffe<lb></lb>rent in different ſites of the Chanel, that is ſtill leſſer, the more <lb></lb>one approached to the Out-let; notwithſtanding which the abate<lb></lb>ment followed in all places proportionably, that is in all its ſites <lb></lb>the firſt part of the height of that ſite diminiſhed: And more<lb></lb>over the water iſſued from the Chanel, and dilated into a broader <lb></lb>courſe, from which likewiſe having divers Out-lets and Mouths; <lb></lb>yet nevertheleſs in that breadth alſo the quick heights ſucceſſive<lb></lb>ly varied and altered in the ſame proportions. </s> <s>Nor did I here <lb></lb>deſiſt my obſervation, but the water being diminiſhed, that iſſu<lb></lb>ed from the Syphons, and there being but one of them left that <lb></lb>diſcharged water; I obſerved the quick height that it made in the <lb></lb>above-ſaid ſites, (the which was likewiſe 1/1. of all the firſt height) <lb></lb>there being added to the water of that Syphon, the water of <lb></lb>three other Syphons; ſo that all the water was of 4 Syphons, <lb></lb>and conſequently quadruple to the firſt Syphon; but the quick <lb></lb>height was onely double, and adding five Siphons, the quick <lb></lb>height became triple, and with adding ſeven Syphons, the height <lb></lb>increaſed quadruple; and ſo by adding of 9. it increaſed quin<lb></lb>tuple, and by adding of 11. it increaſed ſextuple, and by ad<pb xlink:href="040/01/625.jpg" pagenum="59"></pb>ding of 13. it increaſed ſeptuple, and by adding of 15. octuple, <lb></lb>and by adding of 17. nonuple, and laſtly by adding 19. Syphons; <lb></lb>ſo that all the water was centuple to the water of one Syphon, <lb></lb>yet nevertheleſs the quick height of all this water was onely de<lb></lb>cuple to the firſt height conjoyned by the water that iſſued from <lb></lb>one onely Syphon.</s></p><p type="main"> <s>For the more clear underſtanding of all which, I have made <lb></lb>the following Figure; in which we have the mouth A, that <lb></lb>maintaineth the water of the Veſſel B C in the ſame level; though <lb></lb>it continually run; to the brim of the Veſſel are put 25. Sy<lb></lb>phons (and there may be many more) divided into 5 Claſſes, <lb></lb>D E F G H, and the firſt D, are of one onely Syphon; the ſecond <lb></lb>E, of three Syphons; the third F, of five; the fourth G, of 7; the <lb></lb>fifth H, of 9; and one may ſuppoſe the ſixth of 11, the ſeventh <lb></lb>of 13 Syphons, and ſo of the other Claſſes, all containing in con<lb></lb>ſequent odd numbers ſucceſſively (we are content to repreſent in <lb></lb>the Figure no more but the five forenamed Claſſes to avoid con<lb></lb>fuſion) the gathered water D E F G H, which runneth thorow <lb></lb>the Chanel I K L, and falleth into the out-let M N O P; and ſo <lb></lb>much ſufficeth for the explanation of this experiment.</s></p><figure id="id.040.01.625.1.jpg" xlink:href="040/01/625/1.jpg"></figure><pb xlink:href="040/01/626.jpg" pagenum="60"></pb><p type="head"> <s>PROPOS. V. PROB. III.</s></p><p type="main"> <s><emph type="italics"></emph>Any River of any bigneſs, if being given to examine the <lb></lb>quantity of the Water that runneth thorow the River <lb></lb>in a time aſſigned.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>By what we have ſaid already in the two preceding Pro<lb></lb>blems, we may alſo reſolve this that we have now before <lb></lb>us; and it is done, by diverting in the firſt place from the <lb></lb>great River a good big meaſurable Chanel, as is taught in the <lb></lb>ſecond Probleme, and obſerving the abatement of the River, <lb></lb>cauſed by the diverſion of the Chanel; and finding the proporti<lb></lb>on that the Water of the Chanel hath to that of the River, then <lb></lb>let the Water of the Chanel be meaſured by the ſecond Pro<lb></lb>bleme, and work as above, and you ſhall have your deſire.</s></p><p type="head"> <s>CONSIDERATION. I.</s></p><p type="main"> <s>And although it ſeemeth as if it might prove difficult, and <lb></lb>almoſt impoſſible to make uſe of the Regulator number, if <lb></lb>one be about to meaſure the water of ſome great River, <lb></lb>and conſequently would be impoſſible, or at leaſt very difficult <lb></lb>to reduce the Theory of the firſt Probleme into practice: Yet ne<lb></lb>vertheleſs, I could ſay that ſuch great conceits of meaſuring the <lb></lb>water of a great River, are not to come into the minds of any <lb></lb>but great Perſonages, and potent Princes; of whom it is expected <lb></lb>for their extraordinary concerns, that they will make theſe kinde <lb></lb>of enquiries; as if here in <emph type="italics"></emph>Italy<emph.end type="italics"></emph.end> it ſhould be of the Rivers <emph type="italics"></emph>Tyber, <lb></lb>Velino, Chiana, Arno, Serchio, Adice,<emph.end type="italics"></emph.end> in which it ſeemeth real<lb></lb>ly difficult to apply the <emph type="italics"></emph>R<emph.end type="italics"></emph.end>egulator, to finde exactly the quick <lb></lb>height of the <emph type="italics"></emph>R<emph.end type="italics"></emph.end>iver: But becauſe in ſuch like caſes ſometimes <lb></lb>it would turn to account to be at ſome charge, to come to the <lb></lb>exact and true knowledge of the quantity of water which that <lb></lb><emph type="italics"></emph>R<emph.end type="italics"></emph.end>iver carrieth, by knowledge whereof, other greater diſ<lb></lb>burſments might afterwards be avoided, that would oft times be <lb></lb>made in vain; and prevent the diſguſts, which ſometimes happen <lb></lb>amongſt Princes: Upon this ground I think it will be well to <lb></lb>ſhew alſo the way how to make uſe of the <emph type="italics"></emph>R<emph.end type="italics"></emph.end>egulator in theſe <lb></lb>great <emph type="italics"></emph>R<emph.end type="italics"></emph.end>ivers; in which if we will but open our eyes, we ſhall meet <lb></lb>with good ones, and thoſe made without great coſt or labour, <lb></lb>which will ſerve our turn.</s></p><p type="main"> <s>For upon ſuch like <emph type="italics"></emph>R<emph.end type="italics"></emph.end>ivers there are Wears, or Lockes made, <pb xlink:href="040/01/627.jpg" pagenum="61"></pb>to cauſe the Waters to riſe, and to turn them for the ſervice of <lb></lb>Mills, or the like. </s> <s>Now in theſe Caſes it is ſufficient, that one <lb></lb>erect upon the two extreames of the Weare two Pilaſters either <lb></lb>of Wood or Brick, which with the bottome of the Weare do <lb></lb>compoſe our Regulator, wherewith we may make our deſired <lb></lb>operation, yea the Chanel it ſelf diverted ſhall ſerve, without <lb></lb>making any other diverſion or union. </s> <s>And in brief, if the bu<lb></lb>fineſſes be but managed by a judicious perſon, there may wayes <lb></lb>and helps be made uſe of, according to occaſion, of which it <lb></lb>would be too tedious to ſpeak, and therefore this little that hath <lb></lb>been hinted ſhall ſuſſice.</s></p><p type="head"> <s>CONSIDERATION II.</s></p><p type="main"> <s>From what hath been declared, if it ſhall be well under<lb></lb>ſtood, may be deduced many benefits and conveniences, <lb></lb>not onely in dividing of Running Waters for infinite uſes <lb></lb>that they are put to in turning of Corne-Mills, Paper-Mills, <lb></lb>Gins, Powder-Mills, Rice-Mills, Iron Mills, Oil-Mills, Saw<lb></lb>ing-Mills, Mirtle-Mills, Felling-Mills, Fulling-Mills, Silk-Mills, <lb></lb>and ſuch other Machines; but alſo in ordering Navigable Cha<lb></lb>nels, diverting Rivers and Chanels of Waters, or terminating <lb></lb>and limiting the ſizes of Pipes for Fountains: In all which af<lb></lb>fairs there are great errours committed, to the loſſe of much <lb></lb>expence, the Chanels and Pipes that are made, ſometimes not <lb></lb>being ſufficient to carry the deſigned Waters, and ſometimes they <lb></lb>are made bigger than is neceſſary; which diſorders ſhall be <lb></lb>avoided, if the Engineer be adviſed of the things aboveſaid: and <lb></lb>in caſe that to theſe Notions there be added the knowledge of <lb></lb>Philoſophy and Mathematicks, agreeable to the ſublime Diſco<lb></lb>veries of <emph type="italics"></emph>Signore Galilæo,<emph.end type="italics"></emph.end> and the further improvement thereof <lb></lb>by <emph type="italics"></emph>Signore Evangeliſta Torricelli,<emph.end type="italics"></emph.end> Mathematician to the Grand <lb></lb><emph type="italics"></emph>Duke of Tuſcany,<emph.end type="italics"></emph.end> who hath ſubtilly and admirably handled this <lb></lb>whole buſineſſe of Motion, one ſhall then come to the know<lb></lb>ledge of particular notions of great curioſity in the Theoricks, <lb></lb>and of extraordinary benefit in the Practicks that daily occur in <lb></lb>theſe buſineſſes.</s></p><p type="main"> <s>And to ſhew, in effect, of what utility theſe Notions are, I <lb></lb>have thought fit to inſert, in this place, the Conſiderations by <lb></lb>me made upon the Lake of <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> and to repreſent, <lb></lb>at large, by the experience of the laſt year 1641. the moſt Se<lb></lb>rene <emph type="italics"></emph>Erizzo,<emph.end type="italics"></emph.end> then Duke of the ſaid Republique. </s> <s>Being <lb></lb>therefore at <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> in the year aforeſaid, I was requeſted by the <lb></lb>moſt Illuſtrious and moſt Excellent <emph type="italics"></emph>Signore Giovanni Baſa-<emph.end type="italics"></emph.end><pb xlink:href="040/01/628.jpg" pagenum="62"></pb><emph type="italics"></emph>donna,<emph.end type="italics"></emph.end> a Senatour of great worth and merit, that I would inge<lb></lb>nuouſly deliver my opinion touching the ſtate of the Lake <lb></lb>of <emph type="italics"></emph>Venice<emph.end type="italics"></emph.end>; and after I had diſcourſed with his Honour ſeve<lb></lb>ral times, in the end I had order to ſet down the whole <lb></lb>buſineſſe in writing, who having afterwards read it privately, <lb></lb>the ſaid <emph type="italics"></emph>Signore<emph.end type="italics"></emph.end> imparted the ſame, with like privacy, to the <lb></lb>moſt Serene PRINCE, and I received order to repreſent the <lb></lb>ſame to the full <emph type="italics"></emph>Colledge,<emph.end type="italics"></emph.end> as accordingly I did in the Moneth <lb></lb>of <emph type="italics"></emph>May,<emph.end type="italics"></emph.end> the ſame year, and it was as followeth.</s></p><figure id="id.040.01.628.1.jpg" xlink:href="040/01/628/1.jpg"></figure><pb xlink:href="040/01/629.jpg" pagenum="63"></pb><p type="head"> <s>CONSIDER ATIONS <lb></lb>Concerning the <lb></lb>LAKE <lb></lb>OF <lb></lb>VENICE. <lb></lb>BY</s></p><p type="head"> <s>D. BENEDETTO CASTELLI, <lb></lb>Abbot of S. <emph type="italics"></emph>Benedetto Aloyſio,<emph.end type="italics"></emph.end> Mathematician to <lb></lb>Pope <emph type="italics"></emph>VR BAN VIII.<emph.end type="italics"></emph.end> and Profeſſor in <lb></lb>ROME.</s></p><p type="head"> <s><emph type="italics"></emph>CONSIDERATION I.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Though the principal cauſe be but one <lb></lb>onely, that in my judgment threatneth <lb></lb>irreparable ruine to the Lake of <lb></lb><emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> in the preſent ſtate in which it <lb></lb>now ſtands; Yet nevertheleſſe, I think <lb></lb>that two Heads may be conſidered. <lb></lb></s> <s>And this Conſideration may peradven<lb></lb>ture ſerve us for to facilitate and explain <lb></lb>the opportune remedies, though not to <lb></lb>render the ſtate of things abſolutely unchangeable and eternal: <lb></lb>an enterprize impoſſible, and eſpecially in that which having had <lb></lb>ſome beginning, ought likewiſe neceſſarily to have its end; or <lb></lb>at leaſt to prevent the danger for many hundreds of years; and <lb></lb>poſſibly it may, in the mean time, by the mutation it ſelf be <lb></lb>brought into a better condition.</s></p><p type="main"> <s>I ſay therefore, that the preſent diſorder may be conſidered <lb></lb>under two Heads; One is the very notable diſcovery of Land <lb></lb>that is obſerved at the time of low Water, the which, beſides <lb></lb>the obſtructing of Navigation in the Lake and alſo in the <lb></lb>Chanels, doth likewiſe threaten another miſchief and diſorder <pb xlink:href="040/01/630.jpg" pagenum="64"></pb>worthy of very particular conſideration, which is, That the Sun <lb></lb>drying up that mudde, eſpecially in the times of hot Summers, <lb></lb>doth raiſe thence the putrified and pernicious vapours, fogs, and <lb></lb>exhalations that infect the Air, and may render the City unha<lb></lb>bitable.</s></p><p type="main"> <s>The ſecond Head is the great Stoppage that daily is grow<lb></lb>ing in the Ports, eſpecially of <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> at <emph type="italics"></emph>Malamoco<emph.end type="italics"></emph.end>; concerning <lb></lb>which matters I will hint certain general points, and then <lb></lb>will proceed to the more particular and important affairs.</s></p><p type="main"> <s>And firſt, I ſay, that I hold it altogether impoſſible to effect <lb></lb>any thing, though never ſo profitable, which doth not bring with <lb></lb>it ſome miſchief; and therefore the good and the hurt ought to <lb></lb>be very well weighed, and then the leſſe harmful part to be im<lb></lb>braced.</s></p><p type="main"> <s>Secondly, I propoſe to conſideration, that the ſo notable diſ<lb></lb>covery of Earth & Mud, hath not been long obſerved, as I under<lb></lb>ſtand, from old perſons that can remember paſſages for fifty <lb></lb>years paſt; which thing being true, as to me it ſeemeth moſt <lb></lb>true, it ſhould appear that it could not but be good to reduce <lb></lb>matters to that paſſe that they were at formerly, (laying aſide <lb></lb>all affection or paſſion that ſelf-flattering minds have entertained <lb></lb>for their own conceits) or at leaſt it ſhall be neceſſary ſpeedily to <lb></lb>conſult the whole.</s></p><p type="main"> <s>Thirdly, I hold that it is neceſſary to weigh, whether from the <lb></lb>foreſaid diſcovery of Land, it followeth, that onely the Earth ri<lb></lb>ſeth, as it is commonly thought by all, without diſpute; or whe<lb></lb>ther the Waters are abated and faln away; or elſe whether it <lb></lb>proceedeth from both the one and other cauſe. </s> <s>And here it would <lb></lb>be ſeaſonable to enquire, what ſhare the ſaid cauſes may have, <lb></lb>each conſidered apart in the foreſaid effect. </s> <s>For, in the firſt <lb></lb>caſe, if the Earth have been raiſed, it would be neceſſary to <lb></lb>conſider of taking it down, and removing it: But if the Wa<lb></lb>ters have failed or abated, I believe that it would be extreamly ne<lb></lb>ceſſary to reſtore and raiſe them: And if both theſe reaſons have <lb></lb>conſpired in this effect, it will be neceſſary to remedy them each <lb></lb>apart. </s> <s>And I do, for my part, think, that the ſo notable appea<lb></lb>rance of Shelves at the time of low Water, proceeds principally <lb></lb>from the decreaſe and abatement of the Waters, which may <lb></lb>confidently be affirmed to need no other proof, in regard that the <lb></lb><emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> hath been actually diverted which did formerly diſcharge <lb></lb>its Water into the Lake.</s></p><p type="main"> <s>As to the other point of the great Stoppage of Ports, I hold, <lb></lb>that all proceedeth from the violence of the Sea, which being <lb></lb>ſometimes diſturbed by windes, eſpecially at the time of the wa<lb></lb>ters flowing, doth continually raiſe from its bottome immenſe <pb xlink:href="040/01/631.jpg" pagenum="65"></pb>heaps of ſand, carrying them by the tide; and force of the waves <lb></lb>into the Lake; it not having on its part any ſttength of current <lb></lb>that may raiſe and carry them away, they ſink to the bottom, and <lb></lb>ſo they choke up the Ports. </s> <s>And that this effect happeneth in <lb></lb>this manner, we have moſt frequent experiences thereof along the <lb></lb>Sea-coaſts: And I have obſerved in <emph type="italics"></emph>Tuſcany<emph.end type="italics"></emph.end> on the <emph type="italics"></emph>Roman<lb></lb>ſhores,<emph.end type="italics"></emph.end> and in the Kingdom of of <emph type="italics"></emph>Naples,<emph.end type="italics"></emph.end> that when a river fal<lb></lb>leth into the Sea, there is alwaies ſeen in the Sea it ſelf, at the place <lb></lb>of the rivets out-let, the reſemblance, as it were, of an half-Moon, <lb></lb>or a great ſhelf of ſettled ſand under water, much higher then the <lb></lb>reſt of the ſhore, and it is called in <emph type="italics"></emph>Tuſcany, il Cavallo<emph.end type="italics"></emph.end>; and here <lb></lb>in <emph type="italics"></emph>Venice, lo Scanto<emph.end type="italics"></emph.end>: the which cometh to be cut by the current <lb></lb>of the river, one while on the right ſide, another while on the <lb></lb>left, and ſometimes in the midſt, according as the Wind fits. </s> <s>And <lb></lb>a like effect I have obſerved in certain little Rillets of water, <lb></lb>along the Lake of <emph type="italics"></emph>Bolſena<emph.end type="italics"></emph.end>; with no other difference, ſave that of <lb></lb>ſmall and great.</s></p><p type="main"> <s>Now whoſo well conſidereth this effect, plainly ſeeth that it <lb></lb>proceeds from no other, than from the contrariety of the ſtream <lb></lb>of the River, to the <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> of the Sea waves; ſeeing that <lb></lb>great abundance of ſand which the Sea continually throws upon <lb></lb>the ſhore, cometh to be driven into the Sea by the ſtream of the <lb></lb>river; and in that place where thoſe two impediments meet <lb></lb>with equal force, the ſand ſetleth under water, and thereupon is <lb></lb>made that ſame Shelf or <emph type="italics"></emph>Cavallo<emph.end type="italics"></emph.end>; the which if the river carry <lb></lb>water, and that any conſiderable ſtore, it ſhall be thereby cut <lb></lb>and broken; one while in one place, and another while in ano<lb></lb>ther; as hath been ſaid, according as the Wind blows: And <lb></lb>through that Chanel it is that Veſſels fall down into the Sea, and <lb></lb>again make to the river, as into a Port. </s> <s>But if the Water of <lb></lb>the river ſhall not be continual or ſhall be weak, in that caſe the <lb></lb>force of the Sea-Wind ſhall drive ſuch a quantity of ſand into <lb></lb>the mouth of the Port, and of the river, as ſhall wholly choak it <lb></lb>up. </s> <s>And hereupon there are ſeen along the Sea-ſide, very many <lb></lb>Lakes and Meers, which at certain times of the year abound with <lb></lb>waters, and the Lakes bear down that encloſure, and run into <lb></lb>the Sea.</s></p><p type="main"> <s>Now it is neceſſary to make the like reflections on our Ports <lb></lb>of <emph type="italics"></emph>Venice, Malamocco, Bondolo,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Chiozza<emph.end type="italics"></emph.end>; which in a certain <lb></lb>ſenſe are no other than Creeks, mouths, and openings of the ſhore <lb></lb>that parts the Lake from the main Sea; and therefore I hold that <lb></lb>if the Waters in the Lake were plentiful, they would have <lb></lb>ſtrength to ſcowr the mouths of the Ports thorowly, & with great <lb></lb>force; but the Water in the Lake failing, the Sea will with<lb></lb>out any oppoſal, bring ſuch a drift of ſand into the Ports; that if <pb xlink:href="040/01/632.jpg" pagenum="66"></pb>it doth not wholly choke them up, it ſhall render them at leaſt <lb></lb>unprofitable, and impoſſible for Barks and great Veſſels.</s></p><p type="main"> <s>Many other conſiderations might be propounded concerning <lb></lb>theſe two heads of the ſtoppage of the Ports, and of the appea<lb></lb>rance of the Ouze and Mud in the Lakes, but ſo much ſhall ſuf<lb></lb>fice us to have hinted, to make way for diſcourſing of the opera<lb></lb>tions about the oportune remedies.</s></p><p type="main"> <s>Yet before that I propound my opinion, I ſay, That I know <lb></lb>very well that my propoſal, at firſt ſight, will ſeem abſurd and in<lb></lb>convenient; and therefore, as ſuch, will perhaps be rejected by <lb></lb>the moſt: and ſo much the rather, for that it will prove directly <lb></lb>contrary to what hath hitherto been, and as I hear, is intended to <lb></lb>be done. </s> <s>And I am not ſo wedded to my opinions, but that I <lb></lb>do conſider what others may judge thereof: But be it as it will, <lb></lb>I am obliged to ſpeak my thoughts freely, and that being done, <lb></lb>I will leawe it to wiſer men than my ſelf; when they ſhall have <lb></lb>well conſidered my reaſons, to judge and deliberate of the <emph type="italics"></emph>quid <lb></lb>agendum:<emph.end type="italics"></emph.end> And if the ſentence ſhall go againſt me, I appeal to the <lb></lb>moſt equitable and inexorable Tribunal of Nature, who not <lb></lb>caring in the leaſt to pleaſe either one party or another, will be <lb></lb>alwaies a punctual and inviolable executrix of her eternal De<lb></lb>crees, againſt which neither humane deliberations, nor our vain <lb></lb>deſires; ſhall ever have power to rebell. </s> <s>I added by word of <lb></lb>mouth that which followeth.</s></p><p type="main"> <s>Though your Highneſs intereſt your ſelf in this Noble Col<lb></lb>ledge, and cauſe it to be confirmed in the ^{*} Senate by univerſal <lb></lb><arrow.to.target n="marg969"></arrow.to.target><lb></lb>Vote, that the Winds do not blow, that the Sea doth not fluctuate, <lb></lb>that the Rivers do not run; yet ſhall the Winds be alwaies deaf, <lb></lb>the Sea ſhall be conſtant in its inconſtancy, and the Rivers moſt <lb></lb>obſtinate: And theſe ſhall be my Judges, and to their determi<lb></lb>nation I refer my ſelf.</s></p><p type="margin"> <s><margin.target id="marg969"></margin.target>* In <emph type="italics"></emph>Pregadi,<emph.end type="italics"></emph.end> a <lb></lb>particular Coun<lb></lb>cil, the Senators of <lb></lb>which have great <lb></lb>Authority.</s></p><p type="main"> <s>By what hath been ſaid, in my opinion, that is made very clear <lb></lb>and manifeſt, which in the beginning of this diſcourſe I glanced <lb></lb>at; namely, That the whole diſorder, although it be divided into <lb></lb>two heads, into the diſcovery of the Mud, and of the ſtoppage <lb></lb>Ports, yet nevertheleſs, by the application of one onely remedy, <lb></lb>and that in my eſteem very eaſie, the whole ſhall be removed: <lb></lb>And this it is; That there be reſtored into the Lake as much <lb></lb>Water as can be poſſible, and in particular from the upper parts <lb></lb>of <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> taking care that the Water be as free from Mud as is <lb></lb>poſſible. </s> <s>And that this is the true and real remedy of the prece<lb></lb>dent diſorders, is manifeſt: For in the paſſage that this Water <lb></lb>ſhall make thorow the Lakes, it ſhall of it ſelf by degrees clear <lb></lb>the Chanels in ſundry parts of them, according to the currents <lb></lb>that it ſhall ſucceſſively acquire, and in this manner being diſ<pb xlink:href="040/01/633.jpg" pagenum="67"></pb>perſed thorow the Lake, it ſhall maintain the waters in the ſame, <lb></lb>and in the Chanels much higher, as I ſhall prove hereafter; a <lb></lb>thing that will make Navigation commodious; and that, which <lb></lb>moreover is of great moment in our buſineſſe; thoſe Shelves <lb></lb>of Mud which now diſcover themſelves at the time of Low<lb></lb>Waters ſhall be alwayes covered, ſo that the putrefaction of <lb></lb>the Air ſhall alſo be remedied.</s></p><p type="main"> <s>And laſtly, this abundance of Water being alwayes to diſ<lb></lb>charge it ſelf into the Sea by the Ports, I do not doubt, but that <lb></lb>their bottomes will be ſcoured. </s> <s>And that theſe effects muſt fol<lb></lb>low, Nature her ſelf ſeemeth to perſwade, there remaining onely <lb></lb>one great doubt, whether that abundance of Water that ſhall be <lb></lb>brought into the Lake may be really ſufficient to make the Wa<lb></lb>ters riſe ſo much as to keep the Shelves covered, and to facilitate <lb></lb>Navigation, which ought to be at leaſt half a ^{*} Brace, or there<lb></lb><arrow.to.target n="marg970"></arrow.to.target><lb></lb>abouts. </s> <s>And indeed it ſeemeth at firſt ſight to be impoſſible, <lb></lb>that the ſole Water of the ^{*} <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> let into the Lake, and diſ<lb></lb><arrow.to.target n="marg971"></arrow.to.target><lb></lb>perſed over the ſame, can occaſion ſo notable an height of water; <lb></lb>and the more to confirm the difficulties, one might ſay, reducing <lb></lb>the reaſon to calculation, that in caſe the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> were 40. Bra<lb></lb>ces broad, and two and an half high, and the breadth of the <lb></lb>Lake were 20000. Braces, it would ſeem neceſſary that the <lb></lb>height of the water of the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> dilated and diſtended thorow <lb></lb>the Lake would be but onely 1/200 of a Brace in height, which is <lb></lb>imperceptible, and would be of no avail to our purpoſe; nay <lb></lb>more, it being very certain that the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> runneth very muddy <lb></lb>and foul, this would occaſion very great miſchief, filling and <lb></lb>contracting the Lake, and for that reaſon this remedy ought, as <lb></lb>pernicious, to be totally excluded and condemned.</s></p><p type="margin"> <s><margin.target id="marg970"></margin.target>* A <emph type="italics"></emph>Venice<emph.end type="italics"></emph.end> Brace <lb></lb>is 11/16 of our yard.</s></p><p type="margin"> <s><margin.target id="marg971"></margin.target>* A River of <lb></lb>that name.</s></p><p type="main"> <s>I here confeſſe that I am ſurprized at the forme of the Argu<lb></lb>ment, as if I were in a certain manner convinced, that I dare not <lb></lb>adventure to ſay more, or open my mouth in this matter; but <lb></lb>the ſtrength it ſelf of the Argument, as being founded upon <lb></lb>the means of Geometrical and Arithmetical Calculation, hath <lb></lb>opened me the way to diſcover a very crafty fraud that is couch<lb></lb>ed in the ſame Argument, which fraud I will make out to any <lb></lb>one that hath but any inſight in <emph type="italics"></emph>Geometry<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Arithmetick.<emph.end type="italics"></emph.end><lb></lb>And as it is impoſſible, that ſuch an argument ſhould be produced <lb></lb>by any but ſuch as have taſted of theſe, in ſuch affairs, moſt pro<lb></lb>fitable, and moſt neceſſary Sciences; ſo do not I pretend to make <lb></lb>my ſelf underſtood, ſave onely by ſuch, to whom I will evince <lb></lb>ſo clearly, as that more it cannot be deſired, the errour and fraud <lb></lb>wherein thoſe Ancients and Moderns have been, and alwayes <lb></lb>are intangled, that have in any way yet handled this matter of <lb></lb>conſidering the Meaſure and Quantity of the Waters that move. <pb xlink:href="040/01/634.jpg" pagenum="68"></pb>And ſo great is the eſteem that I have for that which I am now <lb></lb>about to ſay touching this particular, that I am content that all <lb></lb>the reſt of my Diſcourſe be rejected; provided, that that be per<lb></lb>fectly underſtood, which I am hereafter to propoſe, I holding <lb></lb>and knowing it to be a main Principle, upon which all that is <lb></lb>founded that can be ſaid either well or handſomely on this parti<lb></lb>cular. </s> <s>The other Diſcourſes may have an appearance of being <lb></lb>probable, but this hits the mark as full as can be deſired, arriving <lb></lb>at the higheſt degree of certainty.</s></p><p type="main"> <s>I have, ſeventeen years ſince, as I repreſented to the moſt Se<lb></lb>rene Prince, and to the Right Honourable the Preſident of the <lb></lb>Lords the Commiſſioners of the ^{*}Sewers, written a Treatiſe of the <lb></lb><arrow.to.target n="marg972"></arrow.to.target><lb></lb>Meaſure of the waters that move, in which I Geometrically de<lb></lb>monſtrate and declare this buſineſſe, and they who ſhall have <lb></lb>well underſtood the ground of my Diſcourſe, will reſt fully ſa<lb></lb>tisfied with that which I am now about to propoſe: But that all <lb></lb>may become rhe more eaſie, I will more briefly explicate and <lb></lb>declare ſo much thereof as I have demonſtrated in the Diſcourſe, <lb></lb>which will ſuffice for our purpoſe: And if that ſhould not be <lb></lb>enough, we have alwayes the experiment of a very eaſie and <lb></lb>cheap way to clear up the whole buſineſſe. </s> <s>And moreover I <lb></lb>will take the boldneſſe to affirm, that in caſe there ſhould not for <lb></lb>the preſent any deliberation be made concerning this affair, ac<lb></lb>cording to my opinion; yet nevertheleſſe it will be, at ſome <lb></lb>time or other; or if it be not, things will grow worſe and <lb></lb>worſe.</s></p><p type="margin"> <s><margin.target id="marg972"></margin.target>* <emph type="italics"></emph>I. </s> <s>Savii dell' <lb></lb>Acque,<emph.end type="italics"></emph.end> a particu<lb></lb>lar Council that <lb></lb>take care of the <lb></lb>Lakes and other <lb></lb>Aquatick affairs.</s></p><p type="main"> <s>For more clear underſtanding, therefore, it ought to be known, <lb></lb>that it being required, as it is generally uſed, to meaſure the wa<lb></lb>ters of a River, its breadth and its depth is taken, and theſe two <lb></lb>dimenſions being multiplied together, the product is affirmed to <lb></lb>be the quantity of that River: As for example, if a River ſhall <lb></lb>be 100. feet broad, and 20. feet high, it will be ſaid, that that <lb></lb>River is 2000 feet of Water, and ſo if a Ditch ſhall be 15. feet <lb></lb>broad, and 5. feet high, this ſame Ditch will be affirmed to be <lb></lb>75. feet of Water: And this manner of meaſuring Running <lb></lb>Water hath been uſed by the Ancients, and by Moderns, with <lb></lb>no other difference, ſave onely that ſome have made uſe of the <lb></lb>Foot, others of the Palme, others of the Brace, and others of <lb></lb>other meaſures.</s></p><p type="main"> <s>Now becauſe that in obſerving theſe Waters that move, I fre<lb></lb>quently found, that the ſame Water of the ſame River was in <lb></lb>ſome ſites of its Chanel pretty big, and in others much leſſe, <lb></lb>not arriving in ſome places to the twentieth, nor to the hundreth <lb></lb>part of that which it is ſeen to be in other places; therefore this <lb></lb>vulgar way of meaſuring the Waters that move, for that they did <pb xlink:href="040/01/635.jpg" pagenum="69"></pb>not give me a certain and ſtable meaſure and quantity of Water, <lb></lb>began deſervedly to be ſuſpected by me, as difficult and defective, <lb></lb>being alwayes various, and the meaſure, on the contrary, being <lb></lb>to be alwayes determinate, and the ſame; it is therefore written, <lb></lb>that <emph type="italics"></emph>Pondus & Pondus, Menſura & Menſura, utrumque abomi<lb></lb>nabile eſt apud Deum,<emph.end type="italics"></emph.end> Exod. </s> <s>I conſidered that in the Terri<lb></lb>tory of <emph type="italics"></emph>Breſcia,<emph.end type="italics"></emph.end> my native Countrey, and in other places, where <lb></lb>Waters are divided to overflow the Grounds, by the like way of <lb></lb>meaſuring them, there were committed grievous and moſt impor<lb></lb>tant errours, to the great prejudice of the Publique and of Pri<lb></lb>vate perſons, neither they that ſell, nor they that buy under<lb></lb>ſtanding the true quantity of that which is ſold and bought: In <lb></lb>regard that the ſame ſquare meaſure, as is accuſtomed in thoſe <lb></lb>parts, aſſigned one particular perſon, carried to ſometimes above <lb></lb>twice or thrice as much water, as did the ſame ſquare meaſure aſ<lb></lb>ſigned to another. </s> <s>Which thing proveth to be the ſame incon<lb></lb>venience, as if the meaſure wherewith Wine and Oil is bought <lb></lb>and ſold, ſhould hold twice or thrice as much Wine or Oil at one <lb></lb>time as at another. </s> <s>Now this Conſideration invited my minde <lb></lb>and curioſity to the finding out of the true meaſure of Running <lb></lb>Waters. </s> <s>And in the end, by occaſion of a moſt important bu<lb></lb>ſineſſe that I was imployed in ſome years ſince, with great in<lb></lb>tenſeneſſe of minde, and with the ſure direction of <emph type="italics"></emph>Geometry,<emph.end type="italics"></emph.end> I <lb></lb>have diſcovered the miſtake, which was, that we being upon the <lb></lb>buſineſſe of taking the meaſure of the Waters that move, do make <lb></lb>uſe of two dimenſions onely, namely, breadth and depth, keep<lb></lb>ing no account of the length. </s> <s>And yet the Water being, though <lb></lb>running, a Body, it is neceſſary in forming a conceit of its quan<lb></lb>tity, in relation to another, to keep account of all the three Di<lb></lb>menſions, that is of length, breadth, and depth.</s></p><p type="main"> <s>Here an objection hath been put to me, in behalf of the ordi<lb></lb>nary way of meaſuring Running Waters, in oppoſition to what <lb></lb>I have above conſidered and propoſed: and I was told, Its true, <lb></lb>that in meaſuring a Body that ſtands ſtill, one ought to take all <lb></lb>the three Dimenſions; but in meaſuring a Body that continually <lb></lb>moveth, as the Water, the caſe is not the ſame: For the length <lb></lb>is not to be had, the length of the water that moveth being infi<lb></lb>nite, as never finiſhing its running; and conſequently is incom<lb></lb>prehenſible by humane underſtanding, and therefore with reaſon, <lb></lb>nay upon neceſſity it cometh to be omitted.</s></p><p type="main"> <s>In anſwer to this, I ſay, that in the aboveſaid Diſcourſe, two <lb></lb>things are to be conſidered diſtinctly; Firſt, whether it be poſſible <lb></lb>to frame any conceit of the quantity of the Body of the Water <lb></lb>with two Dimenſions onely. </s> <s>And ſecondly, whether this length <lb></lb>be to be found. </s> <s>As to the firſt, I am very certain that no man, let <pb xlink:href="040/01/636.jpg" pagenum="70"></pb>him be never ſo great a Wit, can never promiſe to frame a con<lb></lb>ceit of the quantity of the Body of Water, without the third <lb></lb>Dimenſion of length: and hereupon I return to affirm, that the <lb></lb>vulgar Rule of meaſuring Running water is vain and erroneous. <lb></lb></s> <s>This point being agreed on, I come to the ſecond, which is, Whe<lb></lb>ther the third Dimenſion of length may be meaſured. </s> <s>And I ſay, <lb></lb>that if one would know the whole length of the water of a <lb></lb>Fountain or River, thereby to come to know the quantity of all <lb></lb>the Water, it would prove an impoſſible enterprize, nay the <lb></lb>knowing of it would not be uſeful. </s> <s>But if one would know how <lb></lb>much water a Fountain, or a River carrieth in a determinate time <lb></lb>of an hour, of a day, or of a moneth, &c. </s> <s>I ſay, that it is a very <lb></lb>poſſible and profitable enquiry, by reaſon of the innumerable <lb></lb>benefits that may be derived thence, it much importing to know <lb></lb>how much Water a Chanel carrieth in a time given; and I have <lb></lb>demonſtrated the ſame above in the beginning of this Book; and <lb></lb>of this we ſtand in need in the buſineſſe of the Lake, that ſo we <lb></lb>may be able to determine how much ſhall be the height of the <lb></lb><emph type="italics"></emph>Brent,<emph.end type="italics"></emph.end> when it is ſpread all over the Lake: For the three dimen<lb></lb>ſions of a Body being given, the Body is known; and the quan<lb></lb>tity of a Body being given, if you have but two dimenſions, the <lb></lb>third ſhall be known. </s> <s>And thus diving farther and farther into <lb></lb>this Conſideration, I found that the Velocity of the courſe of the <lb></lb>water may be an hundred times greater or leſſer in one part of <lb></lb>its Chanel than in another. </s> <s>And therefore although there ſhould <lb></lb>be two mouths of Waters equal in bigneſſe; yet nevertheleſs it <lb></lb>might come to paſſe, that one might diſcharge an hundred or a <lb></lb>thouſand times more water than another: and this would be, if <lb></lb>the water in one of the mouths ſhould run with an hundred or a <lb></lb>thouſand times greater velocity, than the other; for that it <lb></lb>would be the ſame as to ſay, that the ſwifter was an hundred or <lb></lb>a thouſand times longer, than the ſlower: and in this manner I <lb></lb>diſcovered that to keep account of the velocity, was the keeping <lb></lb>account of the Length.</s></p><p type="main"> <s>And therefore it is manifeſt, that when two Mouths diſcharge <lb></lb>the ſame quantity of Wa r in an equal velocity, it is neceſſary <lb></lb>that the leſs ſwift Mouth be ſo much bigger than the more ſwift; <lb></lb>as the more ſwift exceedeth in velocity the leſs ſwift; as for <lb></lb>example.</s></p><p type="main"> <s>In caſe two Rivers ſhould carry equal quantity of water in <lb></lb>equal times, but that one of them ſhould be four times more <lb></lb>ſwift than the other, the more ſlow ſhould of neceſſity be four <lb></lb>times more large. </s> <s>And becauſe the ſame River in any part <lb></lb>thereof alwaies diſchargeth the ſame quantity of Water in equal <lb></lb>times (as is demonſtrated in the firſt Propoſition of the firſt <pb xlink:href="040/01/637.jpg" pagenum="71"></pb><arrow.to.target n="marg973"></arrow.to.target><lb></lb>Book^{*} of the meaſure of Running Watets;) but yet doth not <lb></lb>run thorowout with the ſame velocity: Hence it is, that the vul<lb></lb>gar meaſures of the ſaid River, in divers parts of its Chanel, are <lb></lb>alwaies divers; inſomuch, that if a River paſſing through its cha<lb></lb>nel had ſuch velocity, that it ran 100 Braces in the 1/60 of an hour<lb></lb>and afterwards the ſaid River ſhould be reduced to ſo much tardi, <lb></lb>ty of motion, as that in the ſame time it ſhould not run more than <lb></lb>one Brace, it would be neceſſary that that ſame River ſhould be<lb></lb>come 100. times bigger in that place where it was retarded; I <lb></lb>mean, 100. times bigger than it was in the place where it was <lb></lb>ſwifter. </s> <s>And let it be kept well in mind, that this point rightly <lb></lb>underſtood, will clear the underſtanding to diſcover very many <lb></lb>accidents worthy to be known. </s> <s>But for this time let it ſuffice, <lb></lb>that we have onely declared that which makes for our purpoſe, <lb></lb>referring apprehenſive and ſtudious Wits to the peruſal of my <lb></lb>aforenamed Treatiſe; for therein he ſhall finde profit and delight <lb></lb>both together.</s></p><p type="margin"> <s><margin.target id="marg973"></margin.target>* He here intends <lb></lb>the Demonſtrati<lb></lb>ons following, at <lb></lb>the end of the firſt <lb></lb>Book</s></p><p type="main"> <s>Now applying all to our principal intent, I ſay, That by what <lb></lb>hath been declared it is manifeſt, that if the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> were 40. Bra<lb></lb>ces broad, and 2 1/2 high, in ſome one part of its Chanel, that after<lb></lb>wards the ſame Water of the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> falling into the Lake, andpaſ<lb></lb>ſing thorow the ſame to the Sea, it ſhould loſe ſo much of its ve<lb></lb>locity, that it ſhould run but one Brace, in the time wherein <lb></lb>whilſt it was in its Chanel at the place aforeſaid, it ran 100. Bra<lb></lb>ces. </s> <s>It would be abſolutely neceſſary, that increaſing in mea<lb></lb>ſure, it ſhould become an hundred times ^{*} thicker; and therefore <lb></lb><arrow.to.target n="marg974"></arrow.to.target><lb></lb>if we ſhould ſuppoſe that the Lake were 20000. Braces, the <lb></lb><emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> that already hath been ſuppoſed in its Chanel 100. Braces, <lb></lb>being brought into the Lake, ſhould be 100. times 100. Brates; <lb></lb>that is, ſhall be 10000. Braces in thickneſs, and conſequently ſhall <lb></lb>be in height half a Brace; that is, 100/200 of a Brace, and not 1/2. of a <lb></lb>Brace, as was concluded in the Argument.</s></p><p type="margin"> <s><margin.target id="marg974"></margin.target>* Deeper.</s></p><p type="main"> <s>Now one may ſee into what a groſs errour of 99. in 100. one <lb></lb>may fall through the not well underſtanding the true quantity <lb></lb>of Running Water, which being well underſtood, doth open a <lb></lb>direct way to our judging aright in this moſt conſiderable affair.</s></p><p type="main"> <s>And therefore admitting that wich hath been demonſtrated, <lb></lb>I fay, that I would (if it did concern me) greatly encline to con<lb></lb>ſult upon the returning of the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> again into the Lake: For it <lb></lb>being moſt evident, that the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> in the Chanel of its mouth, is <lb></lb>much ſwifter than the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> being brought into the Lake, it will <lb></lb>certainly follow thereupon, that the thickneſs of the Water of <lb></lb><emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> in the Lake, ſhall be ſo much greater than that of <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> in <lb></lb><emph type="italics"></emph>Brent,<emph.end type="italics"></emph.end> by how much the <emph type="italics"></emph>Bront<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> is ſwifter than thh <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end><lb></lb>in the Lake.</s></p><pb xlink:href="040/01/638.jpg" pagenum="72"></pb><p type="main"> <s>1. From which operation doth follow in the firſt place, that <lb></lb>the Lake being filled and increaſed by tbeſe Waters, ſhall be <lb></lb>more Navigable, and paſſible, than at preſent we ſee it to be.</s></p><p type="main"> <s>2. By the current of theſe Waters, the Chanels will be ſcour<lb></lb>ed, and will be kept clean from time to time.</s></p><p type="main"> <s>3. There will not appear at the times of low-waters ſo many <lb></lb>Shelves, and ſuch heaps of Mud, as do now appear.</s></p><p type="main"> <s>4. The Ayr will become more wholeſom, for that it ſhall not <lb></lb>be ſo infected by putrid vapours exhaled by the Sun, ſo long as <lb></lb>the Miery Ouze ſhall be covered by the Waters.</s></p><p type="main"> <s>5. Laſtly, in the current of theſe advantagious Waters,, which <lb></lb>muſt iſſue out of the Lake into the Sea, beſides thoſe of the Tyde, <lb></lb>the Ports will be kept ſcoured, and clear: And this is as much as <lb></lb>I ſhall offer for the preſent, touching this weighty buiſineſs; al<lb></lb>waies ſubmitting my ſelf to ſounder judgements.</s></p><p type="main"> <s>Of the above-ſaid Writing I preſented a Copy at <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> at a <lb></lb>full Colledge, in which I read it all, and it was hearkned to with <lb></lb>very great attention; and at laſt I preſented it to the Duke, and <lb></lb>left ſome Copies thereof with ſundry Senators, and went my way, <lb></lb>promiſing with all intenſeneſs to apply my pains with reiterated <lb></lb>ſtudies in the publick ſervice; and if any other things ſhould come <lb></lb>into my minde, I promiſed to declare them ſincerely, and ſo took <lb></lb>leave of <emph type="italics"></emph>His ſerenity,<emph.end type="italics"></emph.end> and that Noble Council. </s> <s>When I was <lb></lb>returned to <emph type="italics"></emph>Rome,<emph.end type="italics"></emph.end> this buſineſs night and day continually run<lb></lb>ning in my mind, I hapned to think of another admirable and <lb></lb>moſt important conceit, which with effectual reaſons, confirmed <lb></lb>by exact operations, I with the Divine aſſiſtance, made clear and <lb></lb>manifeſt; and though the thing at firſt ſight ſeemed to me a moſt <lb></lb>extravagant Paradox, yet notwithſtanding, having ſatisfied my <lb></lb>ſelf of the whole buſineſs, I ſent it in writing to the moſt Illuſtri<lb></lb>ous and moſt Noble <emph type="italics"></emph>Signore Gio. </s> <s>Baſadonna<emph.end type="italics"></emph.end>; who after he had <lb></lb>well conſidered my Paper, carried it to the Council; and after <lb></lb>that thoſe Lords had for many months maturely conſidered <lb></lb>thereon, they in the end reſolved to ſuſpend the execution of the <lb></lb>diverſion which they had before conſulted to make of the River <lb></lb><emph type="italics"></emph>Sile,<emph.end type="italics"></emph.end> and of four other Rivers, which alſo fall into the Lake; a <lb></lb>thing by me blamed in this ſecond Paper, as moſt prejudicial, <lb></lb>and harmful. </s> <s>The writing ſpake as followeth.</s></p><pb xlink:href="040/01/639.jpg" pagenum="73"></pb><p type="head"> <s>CONSIDERATIONS <lb></lb>Concerning the <lb></lb>LAKE <lb></lb>OF <lb></lb>VENICE.</s></p><p type="head"> <s><emph type="italics"></emph>CONSIDERATION II.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>If the diſcourſing well about the truth of <lb></lb>things, Moſt Serene Prince, were as the <lb></lb>carrying of Burdens, in which we ſee <lb></lb>that an hundred Horſes carry a greater <lb></lb>weight than one Horſe onely; it would <lb></lb>ſeem that one might make more account <lb></lb>of the opinion of many men, than of <lb></lb>one alone; But becauſe that diſcourſing <lb></lb>more reſembleth running, than carrying <lb></lb>Burdens, in which we ſee that one Barb alone runneth faſter <lb></lb>than an hundred heavy-heel'd Jades; therefore I have ever more <lb></lb>eſteemed one Concluſion well managed, and well conſidered by <lb></lb>one underſtanding man, although alone, than the common and <lb></lb>Vulgar opinions; eſpecially, when they concern abſtruce and <lb></lb>arduous points: Nay in ſuch caſes the opinions moulded and <lb></lb>framed by the moſt ignorant and ſtupid Vulgar, have been ever <lb></lb>ſuſpected by me as falſe, for that it would be a great wonder if <lb></lb>in difficult matters a common capacity ſhould hit upon that <lb></lb>which is handſom, good, and true. </s> <s>Hence I have, and do hold <lb></lb>in very great veneration the ſumme of the Government of the <lb></lb>moſt Serene, and eternal Republick of <emph type="italics"></emph>Venice<emph.end type="italics"></emph.end>; which although, <lb></lb>as being in nature a Common-wealth, it ought to be governed by <lb></lb>the greater part; yet nevertheleſs, in arduous affairs, it is alwaies <lb></lb>directed by the Grave Judgement of few, and not judged blindly <pb xlink:href="040/01/640.jpg" pagenum="74"></pb>by the <emph type="italics"></emph>Plebeian<emph.end type="italics"></emph.end> Rout. </s> <s>Tis true, that he that propoundeth Pro<lb></lb>poſitions far above the reach of common capacity, runneth a <lb></lb>great hazard of being very often condemned without further Pro<lb></lb>ceſs, or knowledge of the Cauſe; but yet for all that, the truth <lb></lb>is not to be deſerted in moſt weighty affairs, but ought rather to <lb></lb>be explained in due place and time with all poſſible perſpicuity; <lb></lb>that ſo being well underſtood, and conſidered, it may come after<lb></lb>wards for the Common good to be embraced.</s></p><p type="main"> <s>This which I ſpeak in general, hath often been my fortune in <lb></lb>very many particulars, not onely when I have kept within the <lb></lb>bounds of meer ſpeculation, but alſo when I have chanced to de<lb></lb>ſcend to Practice, and to Operations: and your Highneſs know<lb></lb>eth very well what befel me the laſt Summer 1641. when in obe<lb></lb>dience to your Soveraign Command, I did in full Colledge repre<lb></lb>ſent my thoughts touching the ſtate of the Lake of <emph type="italics"></emph>Venice<emph.end type="italics"></emph.end>; for <lb></lb>there not being ſuch wanting, who without ſo much as vouch<lb></lb>ſafing to underſtand me, but having onely had an inkling, and <lb></lb>bad apprehenſion of my opinion, fell furiouſly upon me, and by <lb></lb>violent means both with the Pen and Preſs, full of Gall, did abuſe <lb></lb>me in reward of the readineſs that I had expreſt to obey and <lb></lb>ſerve them: But I was above meaſure encouraged and pleaſed, to <lb></lb>ſee that thoſe few who vouchſafed to hear me, were all either <lb></lb>thorowly perſwaded that my opinion was well grounded, or at <lb></lb>leaſt ſuſpended their prudent verdict to more mature deliberati<lb></lb>on. </s> <s>And though at the firſt bout I chanced to propoſe a thing <lb></lb>that was totally contrary to the moſt received and antiquated <lb></lb>opinion, and to the reſolutions and conſultations taken above an <lb></lb>hundred years ago: Moved by theſe things, and to ſatisfie alſo <lb></lb>to the promiſe that I had made of tendering unto them what <lb></lb>ſhould farther offer it ſelf unto me touching the ſame buſineſs; I <lb></lb>have reſolved to preſent to the Throne of your Highneſs, another <lb></lb>Conſideration of no leſs importance, which perhaps at firſt ſight <lb></lb>will appear a ſtranger Paradox; but yet brought to the Teſt and <lb></lb>Touch-ſtone of experience, it ſhall prove moſt clear and evident. <lb></lb></s> <s>If it ſhall be accounted of, ſo that it ſucceedeth to the benefit of <lb></lb>your Highneſs, I ſhall have obtained my defire and intent: And <lb></lb>if not, I ſhall have ſatisfied my ſelf, and ſhall not have been <lb></lb>wanting to the Obligation of your moſt faithful Servant, and na<lb></lb>tive ſubject.</s></p><p type="main"> <s>That which I propounded in the Mouths paſs, touching the <lb></lb>moſt important buſineſs of the Lake, though it did onely expreſ<lb></lb>ly concern the point of the diverſion of the Mouth of the Lake, <lb></lb>already made and put in execution; yet it may be underſtood <lb></lb>and applyed alſo to the diverſion under debate, to be made of <lb></lb>the other five Rivers, and of the <emph type="italics"></emph>Sile<emph.end type="italics"></emph.end> in particular.</s></p><pb xlink:href="040/01/641.jpg" pagenum="75"></pb><p type="main"> <s>Now touching this, I had the fortune to offer an admirable <lb></lb>accident that we meet with when we come to the effect, which <lb></lb>I verily believe will be an utter ruine to the Lake of <emph type="italics"></emph>Ve<lb></lb>nice.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>I ſay therefore, that by diverting theſe five Rivers that re<lb></lb>main, although their water that they diſcharge for the preſent in<lb></lb>to the Lake is not all taken together 4/5 parts of what the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end><lb></lb>alone did carry, yet nevertheleſſe the abatement of the water of <lb></lb>the Lake which ſhall enſue upon this laſt diverſion of four parts, <lb></lb>which was the whole water, ſhall prove double to that which hath <lb></lb>happened by the diverſion of <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> onely, although that the <lb></lb><emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> alone carried five parts of that water, of which the Rivers <lb></lb>that are to be diverted carry four: A wonder really great, and <lb></lb>altogether unlikely; for the reducing all this Propoſition to be <lb></lb>underſtood, is as if we ſhould ſay, that there being given us <lb></lb>three Rivers, of which the firſt diſchargeth five parts, the ſecond <lb></lb>three, and the third one, and that from the diverſion of the <lb></lb>firſt, there did follow ſuch a certain abatement or fall; from <lb></lb>the taking away of the ſecond there ought to follow alſo ſo <lb></lb>much more abatement; And laſtly, from the withdrawing of <lb></lb>the third the water ought to fall ſo much more, which is wholly <lb></lb>impoſſible: And yet it is moſt certain, and beſides the demon<lb></lb>ſtration that perſwades me to it, which I ſhall explain in due <lb></lb>time, I can ſet before your eyes ſuch an experiment as is not to <lb></lb>be denied by any one, although obſtinate: and I will make it <lb></lb>plainly ſeen and felt, that by taking away only four parts of the <lb></lb>five, which ſhall have been taken away, the abatement proveth <lb></lb>double to the abatement enſuing upon the diverting firſt of the <lb></lb>five onely; which thing being true, as moſt certainly it is, it <lb></lb>will give us to underſtand how pernicious this diverſion of five <lb></lb>Rivers is like to prove, if it ſhall be put in execution.</s></p><p type="main"> <s>By this little that I have hinted, and the much that I could <lb></lb>ſay, let your Highneſſe gather with what circumſpection this bu<lb></lb>ſineſſe ought to be managed, and with how great skill he ought <lb></lb>to be furniſhed who would behave himſelf well in theſe difficult <lb></lb>affairs.</s></p><p type="main"> <s>I have not at this time explained the demonſtration, nor have <lb></lb>I ſo much as propounded the way to make the Experiment, that <lb></lb>I am able to make in confirmation of what I have ſaid, that ſo <lb></lb>by ſome one or others miſ-apprehending the Demonſtration, <lb></lb>and maiming the Experiment, the truth may not happen to ſhine <lb></lb>with leſſe clarity than it doth, when all miſts of difficulty are re<lb></lb>moved: and if ſo be, no account ſhould be made of the Reaſons <lb></lb>by me alledged, and that men ſhould ſhut their eyes againſt the <lb></lb>Experiments that without coſt or charge may be made, I do de<pb xlink:href="040/01/642.jpg" pagenum="76"></pb>clare and proteſt that there ſhall follow very great dammages <lb></lb>to the Fields of the main Land, and extraordinary ſummes <lb></lb>ſhall be expended to no purpoſe. </s> <s>The Lake undoubtedly will <lb></lb>become almoſt dry, and will prove impaſſible for Navigation, <lb></lb>with a manifeſt danger of corrupting the Air: And in the laſt <lb></lb>place there will unavoidably enſue the choaking and ſtoppage of <lb></lb>the Ports of <emph type="italics"></emph>Venice.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Upon the 20th. </s> <s>of <emph type="italics"></emph>December,<emph.end type="italics"></emph.end> 1641. I imparted this my ſecond <lb></lb>Conſideration to the moſt Excellent <emph type="italics"></emph>Signore Baſadonna,<emph.end type="italics"></emph.end> preſen<lb></lb>ting him with a Copy thereof amongſt other Writings, which I <lb></lb>have thought good to inſert, although they ſeem not to belong <lb></lb>directly to our buſineſſe of the Lake.</s></p><p type="head"> <s>The way to examine the MUD and SAND <lb></lb>that entereth and remaineth in the <lb></lb>LAKE of <emph type="italics"></emph>VENICE.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>To the moſt Excellent<emph.end type="italics"></emph.end></s></p><p type="head"> <s>SIGNORE GIO. BASADONNA.</s></p><p type="main"> <s>Two very conſiderable Objections have been made a<lb></lb>gainſt my opinion concerning the Lake of <emph type="italics"></emph>Venice:<emph.end type="italics"></emph.end> One <lb></lb>was that, of which I have ſpoken at large in my firſt <lb></lb>Conſideration, namely, that the <emph type="italics"></emph>Brents<emph.end type="italics"></emph.end> having been taken out of <lb></lb>the Lake, cannot have been the occaſion of the notable fall of <lb></lb>the Waters in the Lake, as I pretend, and conſequently, that <lb></lb>the turning <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> into the Lake would be no conſiderable reme<lb></lb>dy, in regard that the water of <emph type="italics"></emph>Brent,<emph.end type="italics"></emph.end> and the great expanſion <lb></lb>of the Lake over which the water of <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> is to diffuſe and <lb></lb>ſpread being conſidered, it is found that the riſe proveth in<lb></lb>ſenſible.</s></p><p type="main"> <s>The ſecond Objection was, that the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> is very muddy, and <lb></lb>therefore if it ſhould fall muddy into the Lake, the Sand would <lb></lb>ſink and fill up the ſame.</s></p><p type="main"> <s>Touching the firſt Query, enough hath been ſaid in my firſt <lb></lb>Conſideration, where I have plainly diſcovered the deceipt of the <lb></lb>Argument, and ſhewn its fallacy; It remaineth now to examine <pb xlink:href="040/01/643.jpg" pagenum="77"></pb>the ſecond: to which in the firſt place I ſay, that one of the firſt <lb></lb>things that I propoſed in this affair was, that I held it impoſſible <lb></lb>to do any act, though never ſo beneficial, that was not alſo ac<lb></lb>companied by ſome inconvenience and miſchief; and therefore <lb></lb>we are to conſider well the profit, and the loſſe and prejudice; <lb></lb>and they both being weighed, we ſhall be able to chooſe the leſ<lb></lb>ſer evil: Secondly, I admit it to be moſt true, that <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> is at ſome <lb></lb>times muddy, but it is alſo true, that for the greater part of the <lb></lb>year it is not muddy. </s> <s>Thirdly, I do not ſee nor underſtand <lb></lb>what ſtrength this objection hath, being taken ſo at large, and in <lb></lb>general; and methinks that it is not enough to ſay, that the <lb></lb><emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> runneth muddy, and to aſſert that it depoſeth its Muddi<lb></lb>neſſe in the Lake, but we ought moreover to proceed to particu<lb></lb>lars, and ſhew how much this Mud is, and in what time this <lb></lb>choaking up of the Ports may be effected. </s> <s>For the Reaſons are <lb></lb>but too apparent and particular, that conclude the ruine of the <lb></lb>Lake, and that in a very ſhort time, (for mention is made of <lb></lb>dayes) the Waters diverſion being made, and moreover we <lb></lb>have the circumſtance of an Experiment, the ſtate of things be<lb></lb>ing obſerved to have grown worſe ſince the ſaid diverſion. </s> <s>And <lb></lb>I have demonſtrated, that in caſe the Diverſion of the <emph type="italics"></emph>Sile<emph.end type="italics"></emph.end> and <lb></lb>the other Rivers ſhould be put in execution, the Lake would in a <lb></lb>few dayes become almoſt dry; and the Ports would be loſt, with <lb></lb>other miſchievous conſequences. </s> <s>But on the other ſide, al<lb></lb>though that we did grant the choaking of them, we may very <lb></lb>probably ſay, that it will not happen, ſave onely in the ſucceſſion <lb></lb>of many and many Centuries of years. </s> <s>Nor can I think it pru<lb></lb>dent counſel to take a reſolution and imbrace a Deſigne now, to <lb></lb>obtain a benefit very uncertain, and more than that, which only <lb></lb>ſhall concern thoſe who are to come very many Ages after us, <lb></lb>and thereby bring a certain inconvenience upon our ſelves, and <lb></lb>upon our children that are now alive and preſent.</s></p><p type="main"> <s>Let it be alledged therefore, (although I hold it falſe) that by <lb></lb>the diverſions of the Rivers the Lake may be kept in good con<lb></lb>dition for ſeveral years to come.</s></p><p type="main"> <s>But I ſay confidently, and hope to demonſtrate it; That the <lb></lb>Diverſions will bring the Lake, even in our dayes, to be almoſt <lb></lb>dry, and at leaſt will leave ſo little water in it, that it ſhall ceaſe <lb></lb>to be Navigable, and the Ports ſhall moſt infallibly be choaked <lb></lb>up. </s> <s>I will therefore ſay upon experience, in anſwer to this Ob<lb></lb>jection, that it is very neceſſary firſt well to diſcourſe, and ratio<lb></lb>nally to particularize and aſcertain the beſt that may be this <lb></lb>point of the quantity of this ſinking Mud or Sand.</s></p><p type="main"> <s>Now I fear I ſhall make my ſelf ridiculous to thoſe, who mea<lb></lb>ſuring the things of Nature with the ſhallowneſſe of their brains <pb xlink:href="040/01/644.jpg" pagenum="78"></pb>do think that it is abſolutely impoſſible to make this enquiry, and <lb></lb>will ſay unto me, <emph type="italics"></emph>Quis menſus eſt pugillo aquas, & terram palmo <lb></lb>ponderavit<emph.end type="italics"></emph.end>? </s> <s>Yet nevertheleſs I will propound a way whereby, <lb></lb>at leaſt in groſs, one may find out the ſame.</s></p><p type="main"> <s>Take a Veſſel of Cylindrical Figure, holding two barrels of <lb></lb>water, or thereabouts; and then fill it with the water of <emph type="italics"></emph>Brent,<emph.end type="italics"></emph.end><lb></lb>at its Mouth or Fall into the Lake; but in the Lake at the time <lb></lb>that the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> runneth muddy, and after it hath begun to run <lb></lb>muddy for eight or ten hours, to give the mud time to go as far <lb></lb>as S. <emph type="italics"></emph>Nicolo,<emph.end type="italics"></emph.end> to iſſue into the Sea; and at the ſame time take <lb></lb>another Veſſel, like, and equal to the firſt, and fill it with the wa<lb></lb>ter of the Lake towards S. <emph type="italics"></emph>Nicolo,<emph.end type="italics"></emph.end> (but take notice that this ope<lb></lb>ration ought to be made at the time when the waters go out, <lb></lb>and when the Sea is calm) and then, when the waters ſhall have <lb></lb>ſetled in the aforeſaid Veſſels, take out the clear water, and con<lb></lb>ſider the quantity of Sand that remains behind, and let it be ſet <lb></lb>down, or kept in mind: And I am eaſily induced to think, that <lb></lb>that ſhall be a greater quantity of Sand which ſhall be left in the <lb></lb>firſt Veſſel, than that left in the ſecond Veſſel. </s> <s>Afterwards <lb></lb>when the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> ſhall come to be clear, let both the operations be <lb></lb>repeated, and obſerve the quantity of Sand in the aforeſaid Veſ<lb></lb>ſels; for if the Sand in the firſt Veſſel ſhould be moſt, it would <lb></lb>be a ſign, that in the revolution of a year the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> would depoſe <lb></lb>Sand in the Lake: And in this manner one may calculate to a <lb></lb>ſmall matter what proportion the Sand that entreth into the Lake, <lb></lb>hath to that which remains: And by that proportion one may <lb></lb>judge how expedient it ſhall be for publick benefit. </s> <s>And if at <lb></lb>ſeveral times of the year you carefully repeat the ſame operati<lb></lb>ons, or rather obſervations, you would come to a more exact <lb></lb>knowledge in this buſineſs: And it would be good to make the <lb></lb>ſaid operations at thoſe times, when the Lake is diſturbed by <lb></lb>ſtrong high Winds, and made muddy by its own Mud, raiſed by <lb></lb>the commotion of the Waters.</s></p><p type="main"> <s>This notion would give us great light, if the ſame obſervations <lb></lb>ſhould be made towards the Mouth of <emph type="italics"></emph>Lio,<emph.end type="italics"></emph.end> at ſuch time as the <lb></lb>waters flow and ebb, in calm ſeaſons; for ſo one ſhould come to <lb></lb>know whether the waters of the Lake are more thick at the going <lb></lb>out, than at the entrance. </s> <s>I have propounded the foregoing <lb></lb>way of meaſuring Sands and Mud, to ſhew that we are not ſo <lb></lb>generally, and inconſiderately to pronounce any ſentence, but <lb></lb>proceed to ſtricter inquiries, and then deliberate what ſhall be <lb></lb>moſt expedient to be done. </s> <s>Others may propoſe more exqui<lb></lb>ſite examinations, but this ſhall ſerve me for the preſent.</s></p><p type="main"> <s>I will add onely, that if any one had greater curioſity (it would <lb></lb>be profitable to have it) in inveſtigating more exactly the quan<pb xlink:href="040/01/645.jpg" pagenum="79"></pb>tity of the Water that entereth into the Lake, by the means that <lb></lb>I have ſhewen in the beginning of this Book: When he ſhall <lb></lb>have found the proportion of the quantity of water to the quan<lb></lb>tity of Sand or Mud, he ſhall come to know how much Sand the <lb></lb><emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> ſhall leave in the Lake in the ſpace of a year. </s> <s>But to <lb></lb>perform theſe things, there are required perſons of diſcretion, and <lb></lb>fidelity, and that are imployed by publick Order; for there <lb></lb>would thence reſult eminent benefit and profit.</s></p><p type="main"> <s><emph type="italics"></emph>Here are wanting<emph.end type="italics"></emph.end> LETTERS <emph type="italics"></emph>from ſeveral perſons.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>To the Reverend Father, <emph type="italics"></emph>Franceſco di<emph.end type="italics"></emph.end></s></p><p type="head"> <s>S. GIUSEPPE.</s></p><p type="main"> <s>In execution of the command that you laid upon me in your <lb></lb>former Letters, by order from the moſt Serene, my Lord, <lb></lb><emph type="italics"></emph>Prince Leopold<emph.end type="italics"></emph.end>; that I ſhould ſpeak my judgment concern<lb></lb>ing the diſimboguement of the River called <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> whe<lb></lb>ther it ought to be let into the Sea, or into <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end>; I ſay, that <lb></lb>I chanced 18. years ſince to be preſent, when the ſaid Mouth was <lb></lb>opened into the Sea, and that of <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> ſtopt; which work was <lb></lb>done to remedy the great Innundation that was made in all that <lb></lb>Country, and Plain of <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> that lyeth between the River <emph type="italics"></emph>Arno,<emph.end type="italics"></emph.end><lb></lb>and the Mountains of <emph type="italics"></emph>S. Giuliano,<emph.end type="italics"></emph.end> and the River <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end>; which <lb></lb>Plain continued long under water, inſomuch that not onely in the <lb></lb>Winter, but alſo for a great part of the Summer, thoſe fields <lb></lb>were overflowed; and when that the Mouth of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> was <lb></lb>effectually opened into the Sea, the place was preſently freed from <lb></lb>the waters. </s> <s>and drained, to the great ſatisfaction of the Owners <lb></lb>of thoſe Grounds. </s> <s>And here I judge it worth your notice, that <lb></lb>for the generality of thoſe that poſſeſs eſtates in thoſe parts, they <lb></lb>deſired that the Mouth of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> might ſtand open to the <lb></lb>Sea, and thoſe who would have it open into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> are perſons <lb></lb>that have no other concernment there, ſave the hopes of gaining <lb></lb>by having the diſpoſe of Commiſſions, and the like, &c,</s></p><p type="main"> <s>But for the more plain underſtanding of that which is to be <lb></lb>ſaid, it muſt be known, That the reſolution of opening the ſaid <lb></lb>Mouth into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> was taken in the time of the Great Duke <lb></lb><emph type="italics"></emph>Ferdinando<emph.end type="italics"></emph.end> the firſt, upon the ſame motives that are at this time <lb></lb>again propoſed, as your Letters tell me, Since that, it manifeſt<lb></lb>ly appearing, that <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> had, and hath its Mouth open to <lb></lb>the Sea, the Plain hathbeen kept dry; and it being alſo true, that <pb xlink:href="040/01/646.jpg" pagenum="80"></pb>the fury of the South, and South-Weſt-Winds carryed ſuch <lb></lb>abundance of ſand into the Mouth, or Out-let of <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end><lb></lb>that it wholly ſtopt it up: eſpecially when the waters on <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end><lb></lb>ſide were low and ſhallow, And they think, that turning the <lb></lb>Lake of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> and the <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> maintaining <lb></lb>continually its own Mouth with the force of its waters open to the <lb></lb>Sea, and conſequently alſo <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> they would have had the <lb></lb>Out-let clear and open; and in this manner they think, that the <lb></lb>Plain of <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end> would have been freed from the waters. </s> <s>The bu<lb></lb>ſineſs paſſeth for current, at firſt ſight; but experience proveth <lb></lb>the contrary, and Reaſon confirmeth the ſame: For the height <lb></lb>of the water of thoſe Plains, was regulated by the height of the <lb></lb>waters in the Mouth of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end>; that is, The waters at the <lb></lb>Mouth being high, the waters alſo do riſe in the fields; and when <lb></lb>the waters at the Mouth are low, the waters of the fields do like<lb></lb>wiſe abate: Nor is it enough to ſay, That the Out-let or Vent <lb></lb>of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> is continual, but it muſt be very low: Now if <lb></lb><emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> did determine in <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> it is manifeſt that it <lb></lb>would determine high; for <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> terminating in the Sea, when <lb></lb>ever it more and more aboundeth with water, and riſeth, it is ne<lb></lb>ceſlary that alſo <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> hath its level higher, and conſe<lb></lb>quently ſhall keep the waters in the Plains higher. </s> <s>Nay, it hath <lb></lb>happened ſometimes (and I ſpeak it upon my own ſight) that <lb></lb><emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> hath reverſed its courſe upwards towards <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end>; <lb></lb>which caſe will ever happen, whenſoever the <emph type="italics"></emph>Piſan<emph.end type="italics"></emph.end> waters chance <lb></lb>to be lower than the level of thoſe of <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end>; for in that caſe <lb></lb>the waters of <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> return back upon the Plains thorow <emph type="italics"></emph>Fiume <lb></lb>morto<emph.end type="italics"></emph.end> in ſuch ſort, that the Muddineſſes, and the <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> have <lb></lb>been obſerved to be carried by this return as farr as the Walls of <lb></lb><emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end>; and then before ſuch time as ſo great waters can be aſ<lb></lb>ſwaged, which come in with great fury, and go out by little and <lb></lb>little, there do paſs very many days, and moneths, nay ſome<lb></lb>times one being never able to find the waters of <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end><lb></lb>when at the ſhalloweſt, ſo low as the Sea in level; (which is the <lb></lb>loweſt place of the waters) it thence doth follow, that the wa<lb></lb>ters of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> ſhould never at any time of the year, ſo long <lb></lb>as they determine in <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> be ſo low, as they come to be when <lb></lb>the ſame <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> determineth in the Sea. </s> <s>Tis true indeed, <lb></lb>that the Mouth of <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> opened into the Sea, is ſubject to <lb></lb>the inconvenience of being ſtopt up by the force of Winds: But <lb></lb>in this caſe, it is neceſſary to take ſome pains in opening it; which <lb></lb>may eaſily be done, by cutting that Sand a little which ſtayeth <lb></lb>in the Mouth, after that the Wind is laid; and it is enough if you <lb></lb>make a Trench little more than two Palms in breadth; for the <lb></lb>water once beginning to run into it, it will in a few hours carry <pb xlink:href="040/01/647.jpg" pagenum="81"></pb>that Sand away with it, and there will enſue a deep and broad <lb></lb>Trench that will drain away all the water of the Plains in very lit<lb></lb>tle time. </s> <s>And I have found by practice, that there having been <lb></lb>a great quantity of Sand driven back, by the fury of the South<lb></lb>Weſt-Wind, into the Mouth of <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> I having cauſed the <lb></lb>little gutter to be made in the Morning, ſomewhat before Noon, <lb></lb>a Mouth hath been opened of 40. Braces wide, and notably deep, <lb></lb>inſomuch that the water, which before had incommoded all the <lb></lb>Champian ran away in leſs than three dayes, and left the Coun<lb></lb>try free and dry, to the admiration of all men. </s> <s>There was pre<lb></lb>ſent upon the place, at this buſineſs, on the ſame day that I <lb></lb>opened the Mouth, the moſt Serene great Duke, the moſt Serene <lb></lb>Arch-Dutcheſs Mother, all the Commiſſioners of Sewers, with <lb></lb>many other Perſons and Peaſants of thoſe parts; and they all ſaw <lb></lb>very well, that it was never poſſible that a little Bark of eight <lb></lb>Oars, which was come from <emph type="italics"></emph>Legorn<emph.end type="italics"></emph.end> to wait upon the great <lb></lb>Duke, ſhould ever be able to maſter the Current, and to make <lb></lb>up into <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end>; and his Highneſs, who came with an intent <lb></lb>to cauſe the ſaid Mouth towards the Sea to be ſtopt; and that <lb></lb>into <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> to be opened, changed his judgement, giving order <lb></lb>that it ſhould be left open towards the Sea, as it was done. </s> <s>And <lb></lb>if at this day it ſhall return into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> I am very certain that it <lb></lb>will be neceſſary to open it again into the Sea. </s> <s>And there was <lb></lb>alſo charge and order given to a perſon appointed for the pur<lb></lb>poſe, that he ſhould take care to open the ſaid Mouth, as hath <lb></lb>been ſaid upon occaſion. </s> <s>And thus things have ſucceeded very <lb></lb>well unto this very time. </s> <s>But from the middle of <emph type="italics"></emph>October,<emph.end type="italics"></emph.end> until <lb></lb>this firſt of <emph type="italics"></emph>February,<emph.end type="italics"></emph.end> there having continued high South, and <lb></lb>South-Weſt-Winds, with frequent and abundant Rains; it is no <lb></lb>wonder that ſome innundation hath happened; but yet I will <lb></lb>affirm, that greater miſchiefs would have followed, if the Mouth <lb></lb>had been opened into <emph type="italics"></emph>Serchio.<emph.end type="italics"></emph.end> This which I have hitherto ſaid, <lb></lb>is very clear and intelligible to all ſuch as have but competent in<lb></lb>ſight, and indifferent skill in theſe affairs. </s> <s>But that which I am <lb></lb>now about to propoſe farther, will, I am very certain, be under<lb></lb>ſtood by your ſelf, but it will ſeem ſtrange and unlikely to many <lb></lb>others. </s> <s>The point is, that I ſay, That by raiſing the level of <lb></lb><emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> one half Brace, onely at its Mouth, (it will peni<lb></lb>penitrate into <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> farther than it would into the Sea) it ſhall <lb></lb>cauſe the waters to riſe three, or perhaps more Braces upon the <lb></lb>fields towards <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> and ſtill more by degrees as they ſhall recede <lb></lb>farther from the Sea-ſide; and thus there will follow very great <lb></lb>Innundations, and conſiderable miſchiefs. </s> <s>And to know that <lb></lb>this is true, you are to take notice of an accident, which I give <lb></lb>warning of in my diſcourſe of the Meaſure of Running Waters: <pb xlink:href="040/01/648.jpg" pagenum="82"></pb>where alſo I give the reaſon thereof, ^{*} <emph type="italics"></emph>Coroll.<emph.end type="italics"></emph.end> 14. The ac<lb></lb>cident is this, That there coming a Land-Flood, for example, <lb></lb>into <emph type="italics"></emph>Arno,<emph.end type="italics"></emph.end> which maketh it to riſe above its ordinary Mouth <lb></lb>wthin <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> or a little above or below the City ſix or ſeven Bra<lb></lb>ces; this ſame height becometh alwaies leſſer and leſſer, the more <lb></lb>we approach towards the Sea-ſide; inſomuch, that near to the <lb></lb>Sea the ſaid River ſhall be raiſed hardly half a Brace: Whence <lb></lb>it followeth of neceſſary conſequence, that ſhould I again be at <lb></lb>the Sea-ſide, and knowing nothing of what hapneth, ſhould ſee <lb></lb>the River <emph type="italics"></emph>Arno<emph.end type="italics"></emph.end> raiſed by the acceſſion of a Land-flood, one third <lb></lb>of a Brace; I could certainly infer, that the ſame River was raiſed <lb></lb>in <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end> thoſe ſame ſix or ſeven Braces. </s> <s>And that which I ſay of <lb></lb><emph type="italics"></emph>Arno,<emph.end type="italics"></emph.end> is true of all Rivers that fall into the Sea. </s> <s>Which thing <lb></lb>being true, it is neceſſary to make great account of every ſmall <lb></lb>riſing, that <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> maketh towards the Sea-ſide by fal<lb></lb>ling into <emph type="italics"></emph>Serchio.<emph.end type="italics"></emph.end> For although the riſing of <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> by <lb></lb>being to diſgorge its Waters into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> towards the Sea, were <lb></lb>onely a quarter of a Brace; we might very well be ſure, that fart <lb></lb>from the Sea, about <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> and upon thoſe fields the riſe ſhall be <lb></lb>much greater, and ſhall become two or three Braces: And be<lb></lb>cauſe the Countrey lyeth low, that ſame riſe will cauſe a conti<lb></lb>nual Innundation of the Plains, like as it did before; I cauſed the <lb></lb>Mouth to be opened into the Sea. </s> <s>And therefore I conclude <lb></lb>that the Mouth of <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> ought by no means to be opened <lb></lb>into <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end>; but ought to be continued into the Sea, uſing all <lb></lb>diligence to keep it open after the manner aforeſaid, ſo ſoon as <lb></lb>ever the Wind ſhall be laid. </s> <s>And if they ſhall do otherwiſe, I <lb></lb>confidently affirm, that there will daily follow greater damages; <lb></lb>not onely in the Plains, but alſo in the wholeſomneſs of the <lb></lb>Air; as hath been ſeen in times paſt. </s> <s>And again, It ought with <lb></lb>all care to be procured, that no waters do by any means run or <lb></lb>fall from the Trench of <emph type="italics"></emph>Libra,<emph.end type="italics"></emph.end> into the Plain of <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> for theſe <lb></lb>Waters being to diſcharge into <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> they maintain it <lb></lb>much higher than is imagined, according to that which I have de<lb></lb>monſtrated in my conſideration upon the ſtate of the Lake of <lb></lb><emph type="italics"></emph>Venice.<emph.end type="italics"></emph.end> I have ſaid but little, but I ſpeak to you, who under<lb></lb>ſtandeth much, and I ſubmit all to the moſt refined judgment of <lb></lb>our moſt Serene Prince <emph type="italics"></emph>Leopold,<emph.end type="italics"></emph.end> whoſe hands I beſeech you in all <lb></lb>humility to kiſs in my name, and implore the continuance of his <lb></lb>Princely favour to me; and ſo deſiring your prayers to God for <lb></lb>me, I take my leave.</s></p><p type="main"> <s><emph type="italics"></emph>Rome<emph.end type="italics"></emph.end> 1. Feb. <lb></lb></s> <s>1642.</s></p><p type="main"> <s><emph type="italics"></emph>Your moſt affectionate Servant,<emph.end type="italics"></emph.end></s></p><p type="main"> <s>D. BENEDETTO CASTELLI.</s></p><pb xlink:href="040/01/649.jpg" pagenum="83"></pb><p type="head"> <s>The anſwer to a Letter written by BAR<lb></lb>TOLOTTI, touching the <lb></lb>difficultyes obſerved.</s></p><p type="head"> <s><emph type="italics"></emph>The former part of the Letter is omitted, and the diſcourſe <lb></lb>beginneth at the firſt Head.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And firſt I ſay, Whereas I ſuppoſe that the level of the <emph type="italics"></emph>Ser<lb></lb>chio<emph.end type="italics"></emph.end> is higher than that of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end>; this is moſt true, <lb></lb>at ſuch time as the waters of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> are diſcharged in<lb></lb>to the Sea; but I did never ſay that things could never be brought <lb></lb>to that paſs, as that the level of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> ſhould be higher than <lb></lb><emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end>: and ſo I grant that it will follow, that the waters of <lb></lb><emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> ſhall go into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> and its very poſſible, that the <lb></lb>Drain of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> into <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> may be continuate; and I far<lb></lb>ther grant, that its poſſible, that the <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> doth never diſgorge <lb></lb>thorow <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> towards <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end>; Nay, I will yet farther grant <lb></lb>that it might have happened, that <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> might have had <lb></lb>ſuch a fall into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> as would have ſufficed to have turned <lb></lb>Mills: But then I add withall, that the Plains of <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> and the <lb></lb>City it ſelf muſt be a meer Lake.</s></p><p type="main"> <s>2. <emph type="italics"></emph>Signore Bartololti<emph.end type="italics"></emph.end> ſaith confidently, that when the Sea ſwel<lb></lb>leth by the South-Weſt, or other Winds, the level of <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> in <lb></lb>the place marked A in the Platt, diſtant about 200. Braces, riſeth <lb></lb>very little: But that <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> in D, and in E, many miles <lb></lb>more up into Land riſeth very much, and that certain Fiſhermen <lb></lb>confirm this, and ſhew him the ſignes of the riſing of the Water. <lb></lb></s> <s>I grant it to be very true, and I have ſeen it with my own eyes: <lb></lb>But this cometh to paſs, when the Mouth of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> is ſtopt <lb></lb>up by the Sea; as I ſhall ſhew by and by. </s> <s>And this riſing near <lb></lb>the Sea-ſide, is of no conſiderable prejudice to the fields. </s> <s>And <lb></lb>this is as much as I find to be true in the aſſertion of <emph type="italics"></emph>Signore Bar<lb></lb>tolotti,<emph.end type="italics"></emph.end> (without his confirming it by any other proof; as indeed <lb></lb>it needs none) That the level of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> riſeth in E, and ma<lb></lb>ny miles farther upwards it riſeth much; nor did I ever affirm the <lb></lb>contrary.</s></p><p type="main"> <s>3. Concerning the difficulty of opening the Mouth of <emph type="italics"></emph>Fiume <lb></lb>morto<emph.end type="italics"></emph.end> into the Sea, that which <emph type="italics"></emph>Il Caſtellano<emph.end type="italics"></emph.end> ſaith is moſt certain; <lb></lb>namely, That at the entrance upon the opening of the Mouth, it <lb></lb>is neceſſary to make a deep Trench: But I ſay, that at that time <lb></lb>it is difficult to open it, unleſs upon great occaſions; for that the <pb xlink:href="040/01/650.jpg" pagenum="84"></pb>difficulty proceedeth from the waters of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> being low, <lb></lb>and the fields drained.</s></p><p type="main"> <s>4. As to the particular of the Cauſes that you tell me men <lb></lb>preſs ſo much unto the moſt <emph type="italics"></emph>Serene Grand Duke,<emph.end type="italics"></emph.end> and to the <lb></lb>Prince, I have not much to ſay, becauſe it is not my profeſſion; <lb></lb>nor have I conſidered of the ſame: Yet I believe, that when the <lb></lb>Prince and his Highneſſe ſee the benefit of his People and Sub<lb></lb>jects in one ſcale of the Ballance, and the accomodation of <lb></lb>Huntſmen in the other, his Highneſſe will incline to the profit <lb></lb>of his ſubjects; ſuch have I alwayes found his Clemency and <lb></lb>Nobleneſſe of minde. </s> <s>But if I were to put in my vote upon <lb></lb>this buſineſſe, I would ſay, that the points of Spears, and the <lb></lb>mouths of Guns, the yelping of Dogs, the wilyneſſe of Huntſ<lb></lb>men, who run thorow and narrowly ſearch all thoſe Woods, <lb></lb>Thickets and Heathes, are the true deſtroyers of Bucks and <lb></lb>Boares, and not a little Salt-water, which ſetleth at laſt in ſome <lb></lb>low places, and ſpreadeth not very far. </s> <s>Yet nevertheleſſe, I will <lb></lb>not enter upon any ſuch point, but confine my ſelf ſolely to the <lb></lb>buſineſſe before me.</s></p><p type="main"> <s>5. That Experiment of joyning together the water of <emph type="italics"></emph>Fiume <lb></lb>morto,<emph.end type="italics"></emph.end> and that of <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> by a little trench to ſee what advan<lb></lb>tage the Level E hath upon the Level I, doth not give me full <lb></lb>ſatisfaction, taken ſo particularly, for it may come to paſſe, that <lb></lb>ſometimes E may be higher, and ſometimes A lower, and I do <lb></lb>not queſtion but that when <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> is low, and <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> full <lb></lb>of Water, the level of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> will be higher than that of <lb></lb><emph type="italics"></emph>Serchio.<emph.end type="italics"></emph.end> But <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> being full, and <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> ſcant of Wa<lb></lb>ter, the contrary will follow, if the Mouth ſhall be opened to <lb></lb>the Sea. </s> <s>And here it ſhould ſeem to me, that it ought to be <lb></lb>conſidered, that there is as much advantage from E to the Sea <lb></lb>through the little Trench opened anew into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> as from E to <lb></lb>the Sea by the Mouth of <emph type="italics"></emph>Fiume morto.<emph.end type="italics"></emph.end> But the difficulty (which <lb></lb>is that we are to regard in our caſe) is, that the courſe of the <lb></lb>Waters thorow the Trench is three times longer than the courſe <lb></lb>of the Mouth of <emph type="italics"></emph>Fiums morto,<emph.end type="italics"></emph.end> as appeareth by the Draught or <lb></lb>Plat which you ſent me, which I know to be very exactly drawn, <lb></lb>for that the ſituation of thoſe places are freſh in my memory. <lb></lb></s> <s>Here I muſt give notice, that the waters of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> determi<lb></lb>ning thorow the Trench in <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> (the waters of which <emph type="italics"></emph>Fiume <lb></lb>morto<emph.end type="italics"></emph.end> are, for certain, never ſo low as the Sea) their pendency or <lb></lb>declivity ſhall, for two cauſes, be leſſe than the pendency of thoſe <lb></lb>waters through the Mouth towards the Sea, that is, becauſe of <lb></lb>the length of the line through the Trench, and becauſe of the <lb></lb>height of their entrance into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> a thing which is of very <lb></lb>great import in diſcharging the waters which come ſuddenly, as <pb xlink:href="040/01/651.jpg" pagenum="85"></pb>he ſhall plainly ſee, who ſhall have underſtood my Book of the <lb></lb>Meaſure of Running Waters And this was the Reaſon why all <lb></lb>the Countrey did grow dry upon the opening of the Mouth into <lb></lb>the Sea. </s> <s>And here I propoſe to conſideration that which the Pea<lb></lb>ſants about <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end> relate, namely, That the Water in the Fields <lb></lb>doth no conſiderable harm by continuing there five or ſix, yea, or <lb></lb>eight dayes. </s> <s>And therefore the work of the Countrey is to o<lb></lb>pen the Mouth of <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> in ſuch manner, that the Water <lb></lb>being come, they may have the Trench free and ready, when that <lb></lb>the Water cometh it may have a free drain, and may not ſtay <lb></lb>there above eight or nine dayes, for then the overflowings be<lb></lb>come hurtful. </s> <s>It is to be deſired alſo, that if any Propoſition is <lb></lb>produced touching theſe affairs, it might be propounded the moſt <lb></lb>diſtinctly that may be poſſible, and not conſiſt in generals, eſpe<lb></lb>cially when the Diſpute is of the riſings, of velocity, of tardity, <lb></lb>of much and little water; things that are all to be ſpecified by <lb></lb>meaſures.</s></p><p type="main"> <s>6. Your Letter ſaith, in the next place, that <emph type="italics"></emph>Signore Barto<lb></lb>lotti<emph.end type="italics"></emph.end> confeſſeth, that if the Mouth of the <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> might al<lb></lb>wayes be kept open, it would be better to let it continue as it is: <lb></lb>the which, that I may not yield to him in courteſie, I confeſſe, <lb></lb>for the keeping it ſtopt on all ſides would be a thing moſt per<lb></lb>nicious. </s> <s>But admitting of his confeſſion I again reply, that <emph type="italics"></emph>Fi<lb></lb>ume morto<emph.end type="italics"></emph.end> ought not to be let into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> but immediately in<lb></lb>to the Sea; becauſe although ſometimes the Mouth to Sea<lb></lb>wards be ſtopt up, yet for all that, the raiſing of the Bank above <lb></lb>the Plains (which is all the buſineſſe of importance) ſhall be ever <lb></lb>leſſer, if we make uſe of the Mouth leading to the Sea, than u<lb></lb>ſing that of <emph type="italics"></emph>Serchio.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>7. I will not omit to mention a kinde of ſcruple that I have <lb></lb>concerning the poſition of <emph type="italics"></emph>Sign. </s> <s>Bartolotti,<emph.end type="italics"></emph.end> that is, where he ſaith <lb></lb>that the two Mouths A and D are equal to the like Mouths into <lb></lb>the Sea; Now it ſeems to me, that the Mouth A of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end><lb></lb>into <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> is abſolutely within <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> nor can it be made low<lb></lb>er, and is regulated by the height of <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end>: But the Mouth <lb></lb>of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> terminates, and ought to be underſtood to ter<lb></lb>minate in the Sea it ſelf, the loweſt place. </s> <s>And this I believe <lb></lb>was very well peroeived by <emph type="italics"></emph>Sig. </s> <s>Bartolotti,<emph.end type="italics"></emph.end> but I cannot tell why <lb></lb>he paſt it over without declaring it: and we ſee not that the <lb></lb>Mouth D falleth far from the Sea, which Mouth ought to be let <lb></lb>into the Sea it ſelf, and ſo the advantage of the <emph type="italics"></emph>M<emph.end type="italics"></emph.end>outh into the <lb></lb>Sea more clearly appeareth.</s></p><p type="main"> <s>8. That which <emph type="italics"></emph>Sig. </s> <s>Bartolotti<emph.end type="italics"></emph.end> addeth, that when it is high <lb></lb>Waters, at ſuch time as the Waters are out, and when Winds <lb></lb>choak up <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> they not only retard it, but return the <pb xlink:href="040/01/652.jpg" pagenum="86"></pb>courſe of the Waters upwards very leaſurely, perſwadeth me <lb></lb>more readily to believe that <emph type="italics"></emph>Sig. </s> <s>Bartolotti<emph.end type="italics"></emph.end> knoweth very well, <lb></lb>that the Mouth of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> let into <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end> is hurtful: for <lb></lb>by this he acknowledgeth that the Mouth towards the Sea doth <lb></lb>in ſuch ſort drain the Countrey of the Waters, as that they be<lb></lb>come very low; and therefore upon every little <emph type="italics"></emph>impetus<emph.end type="italics"></emph.end> the wa<lb></lb>ters turn their courſe: And from the motions, being exceeding <lb></lb>ſlow, is inferred, that the abundance of Sea-water that com<lb></lb>eth into <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> is ſo much as is believed, and as <emph type="italics"></emph>Sig. </s> <s>Bat<lb></lb>tolotti<emph.end type="italics"></emph.end> affirmeth.</s></p><p type="main"> <s>9. After that <emph type="italics"></emph>Sig. </s> <s>Bartolotti<emph.end type="italics"></emph.end> hath ſaid what he promiſeth a<lb></lb>bove, namely, that when the Windes blowing ſtrongly do ſtop <lb></lb>up <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> and not onely retard but turn the courſe up<lb></lb>wards, the time being Rainy, and the Mouth of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> ſhut <lb></lb>up, the Waves of the Sea paſſe over the Bank of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end>; at <lb></lb>that time, ſaith <emph type="italics"></emph>Signore Bartolotti,<emph.end type="italics"></emph.end> the Champain ſhall know the <lb></lb>benefit of <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> diſcharged into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> and the mouth A <lb></lb>ſhall ſtand alwayes open; and <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> may alwayes con<lb></lb>ſtantly run out, as alſo the Rains and Rain-waters, although the <lb></lb>hurtful Tempeſt ſhould laſt many dayes, &c. </s> <s>And I reply, that <lb></lb>all the Art conſiſts in this; for the benefit of thoſe Fields doth <lb></lb>not depend on, or conſiſt in ſaying, that <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> is alwayes <lb></lb>open, and <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> draineth continually; But all the buſi<lb></lb>neſſe of profit lyeth and conſiſteth in maintaining the Waters <lb></lb>low in thoſe Plaines, and thoſe Ditches, which ſhall never be ef<lb></lb>fected whilſt the World ſtands, if you let <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> into <emph type="italics"></emph>Ser<lb></lb>chio<emph.end type="italics"></emph.end>; but yet it may, by opening the mouth into the Sea: and <lb></lb>ſo much reaſon and nature proveth, and (which importeth) Ex<lb></lb>perience confirmeth.</s></p><p type="main"> <s>10. In the tenth place I come to conſider the anſwer that <lb></lb>was made to another Propoſition in the Letter which I writ to <lb></lb>Father <emph type="italics"></emph>Franceſco,<emph.end type="italics"></emph.end> which prudently of it ſelf alone might ſerve <lb></lb>to clear this whole buſineſſe. </s> <s>I ſaid in my Letter, That great <lb></lb>account is to be made of every ſmall riſing and ebbing of the <lb></lb>Waters neer to the Sea in <emph type="italics"></emph>Fiume morto,<emph.end type="italics"></emph.end> for that theſe riſings and <lb></lb>fallings, although that they be ſmall neer to the Sea-ſide, yet ne<lb></lb>vertheleſſe, they operate and are accompanied by notable riſings <lb></lb>and fallings within Land, and far from the Sea-ſide, and I have <lb></lb>declared by an example of <emph type="italics"></emph>Arno,<emph.end type="italics"></emph.end> in which a Land-flood falling, <lb></lb>that made it increaſe above its ordinary height within <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end> ſix or <lb></lb>ſeven Braces, that this height of the ſame Flood becometh ſtill <lb></lb>leſſer, the neerer we approach to the Sea-coaſts. </s> <s>Nor ſhall the <lb></lb>ſaid River be raiſed hardly half a Brace; whereupon it neceſſ<lb></lb>rily followeth, that if I ſhould return to the Sea-ſide, and not <lb></lb>knowing any think of that which happeneth at <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> and ſeeing <pb xlink:href="040/01/653.jpg" pagenum="87"></pb>the River <emph type="italics"></emph>Arno<emph.end type="italics"></emph.end> raiſed by a Land-flood half a Brace, I might con<lb></lb>fidently affirm the ſaid River to be raiſed in <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end> thoſe ſix or ſe<lb></lb>ven Braces, &c. </s> <s>From ſuch like accidents I conclude in the ſame <lb></lb>Letter, that it is neceſſary to make great account of every little <lb></lb>riſe that <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> ſhall make towards the Sea. </s> <s>Now cometh <lb></lb><emph type="italics"></emph>Bartolotti<emph.end type="italics"></emph.end> (and perhaps becauſe I knew not how to expreſs my <lb></lb>ſelf better, underſtandeth not my Propoſition) and ſpeaketh that <lb></lb>which indeed is true, but yet beſides our caſe: Nor have I ever <lb></lb>ſaid the contrary; and withall doth not apply it to his purpoſe. <lb></lb></s> <s>Nay I ſay, that if he had well applyed it, this alone had been a<lb></lb>ble to have made him change his opinion. </s> <s>And becauſe he ſaith, <lb></lb>that I ſaid, that it is true, when the abatement proceedeth from <lb></lb>ſome cauſe above, as namely by Rain, or opening of Lakes; <lb></lb>But when the cauſe is from below, that is, by ſome ſtop, as for <lb></lb>inſtance ſome Fiſhers Wears or Locks, or ſome impediment re<lb></lb>mote from the Sea, although at the Level it ſhall riſe ſome Braces <lb></lb>where the impediment is, yet that riſing ſhall go upwards; and <lb></lb>here he finiſheth his Diſcourſe, and concludeth not any thing <lb></lb>more. </s> <s>To which I ſay firſt, that I have alſo ſaid the ſame in the <lb></lb>Propoſition, namely, that a Flood coming (which maketh <emph type="italics"></emph>Arno<emph.end type="italics"></emph.end><lb></lb>to riſe in <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end> ſix or ſeven Braces (which I take to be a ſuperiour <lb></lb>cauſe whether it be Rain or the opening of Lakes, as beſt plea<lb></lb>ſeth <emph type="italics"></emph>Bartolotti<emph.end type="italics"></emph.end>) in ſuch a caſe I ſay, and in no other (for towards <lb></lb>the Sea-coaſts it ſhall not cauſe a riſing of full half a Brace; and <lb></lb>therefore ſeeing <emph type="italics"></emph>Arno<emph.end type="italics"></emph.end> at the Sea-ſide to be raiſed by a Flood, whe<lb></lb>ther of Rain, or of opening of Lakes half a Brace) it may be <lb></lb>inferred, that at <emph type="italics"></emph>Piſa<emph.end type="italics"></emph.end> it ſhall be raiſed thoſe ſix or ſeven Braces; <lb></lb>which variety, well conſidered, explaineth all this affair in favour <lb></lb>of my opinion: For the riſing that is made by the impediment <lb></lb>placed below, of Fiſhing Weares and Locks, operateth at the be<lb></lb>ginning, raiſing the Waters that are neer to the impediment; <lb></lb>and afterwards leſs and leſs, as we retire upwards from the im<lb></lb>pediment: provided yet that we ſpeak not of a Flood that com<lb></lb>meth by acceſſion, but onely of the ordinary Water impeded. <lb></lb></s> <s>But there being a new acceſſion, as in our caſe, then the Water <lb></lb>of the Flood, I ſay, ſhall make a greater riſing in the parts ſuperi<lb></lb>our, far from the impediment; and theſe impediments ſhall <lb></lb>come to be thoſe that ſhall overflow the Plains, as happened <lb></lb>eighteen or nineteen years ago, before the opening of <emph type="italics"></emph>Fiume <lb></lb>morto<emph.end type="italics"></emph.end> into the Sea, The ſame will certainly follow, if <emph type="italics"></emph>Fiume <lb></lb>morto<emph.end type="italics"></emph.end> be let into <emph type="italics"></emph>Serchio.<emph.end type="italics"></emph.end> Here I could alledge a very pretty <lb></lb>caſe that befell me in <emph type="italics"></emph>la ^{*} Campagna di Roma,<emph.end type="italics"></emph.end> neer to the Sea<lb></lb><arrow.to.target n="marg975"></arrow.to.target><lb></lb>ſide. </s> <s>where I drained a Bog or Fen, of the nature of the Wa<lb></lb>ters of <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> and I ſucceeded in the enterprize, the Waters in their <lb></lb>ſite towards the Sea abating only three Palmes, and yet in the <pb xlink:href="040/01/654.jpg" pagenum="88"></pb>Fen they fell more than fifteen Palmes. </s> <s>But the buſineſſe <lb></lb>would be long, and not ſo eaſily to be declared, and I am cer<lb></lb>tain that <emph type="italics"></emph>Sig. </s> <s>Bartolotti<emph.end type="italics"></emph.end> having conſidered this, would alter his <lb></lb>judgment, and withall would know that remitting that impedi<lb></lb>ment anew, which I had left for leſſe than three Palmes towards <lb></lb>the Sea, the Waters in the Fen would return with the firſt Floods <lb></lb>and Raines to the ſame height as before, as likewiſe <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end><lb></lb>will do if it ſhall be let again into <emph type="italics"></emph>Serchio.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg975"></margin.target>* The Countrey <lb></lb>or Province lying <lb></lb>round the City, <lb></lb>heretofore called <lb></lb><emph type="italics"></emph>Latium<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Here I intreat your Honour to do me the favour to importune <lb></lb><emph type="italics"></emph>P. Franceſco<emph.end type="italics"></emph.end> in my behalf, that he would be pleaſed to deelare <lb></lb>my meaning in the aforeſaid Letter to <emph type="italics"></emph>Sig. </s> <s>Bartolotti,<emph.end type="italics"></emph.end> for I hope <lb></lb>that if he will underſtand this point, he will be no longer ſo te<lb></lb>nacious in his opinion.</s></p><p type="main"> <s>Next that theſe Lords in the Commiſſion of Sewers, with the <lb></lb>Right Honourable the Marqueſſe of S. <emph type="italics"></emph>Angelo,<emph.end type="italics"></emph.end> and your Honour <lb></lb>do approve of my judgment, doth very much rejoyce me; but <lb></lb>becauſe that I know that they do it not in deſign to complement <lb></lb>me, but onely to ſerve his Highneſs our Grand Duke, I freely <lb></lb>profeſs that I will pretend no farther obligations from them there<lb></lb>in, than I account my ſelf to owe to thoſe whoſe opinions are <lb></lb>contrary to mine, for that I know that they have the ſame end. <lb></lb></s> <s>The definitive ſentence of this whole buſineſs is, that they give <lb></lb>theſe Plains, theſe Draines, and theſe Waters farre fetcht ap<lb></lb>pellations.</s></p><p type="main"> <s>11. As to the quantity of the Water that <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> diſ<lb></lb>chargeth into the Sea, there are very great diſputes about it, and <lb></lb>I have been preſent at ſome of them. </s> <s>But let your Honour be<lb></lb>lieve me, that as this is not continual, but only during a few <lb></lb>dayes, ſo it will never be of any great prejudice to theſe Fields; <lb></lb>and if your Lordſhip would be aſcertained thereof, you may <lb></lb>pleaſe to go to <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> at about a mile's diſtance from the <lb></lb>Sea, in the time of theſe ſtrong Windes, and obſerve the cur<lb></lb>rent from thence upwards, for you ſhall finde it extream ſlow, <lb></lb>and conſequently will know that the quantity of the Water that <lb></lb>is repuls'd is very ſmall. </s> <s>And this ſeems to be contradicted by the <lb></lb>rule of Riſings proceeding from cauſes below, which occaſion no <lb></lb>conſiderable alteration far from the Sea.</s></p><p type="main"> <s>I am neceſſitated to go to morrow out of <emph type="italics"></emph>Rome<emph.end type="italics"></emph.end> with his Emi<lb></lb>nence Cardinal <emph type="italics"></emph>Gaetano<emph.end type="italics"></emph.end> about certain affairs touching Waters, <lb></lb>therefore I ſhall not farther inlarge, but for a cloſe to this tedious <lb></lb>Diſcourſe, I conclude in few words, that <emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> is by no <lb></lb>means to be let into <emph type="italics"></emph>Serchio,<emph.end type="italics"></emph.end> nor are there any means intermedi<lb></lb>ate courſes to be taken, for they will alwayes be prejudicial; but <lb></lb><emph type="italics"></emph>Fiume morto<emph.end type="italics"></emph.end> is to be diſcharged immediately into the Sea. </s> <s>When <lb></lb>it is ſtopt up by the fury of the Sea waves, I affirm that it is a <pb xlink:href="040/01/655.jpg" pagenum="89"></pb>ſign that there is no need of opening it; and if there be any oc<lb></lb>caſion to open it, it is eaſily done. </s> <s>As for the reſt your Lordſhip <lb></lb>may pleaſe to keep account of all the particulars that occur, for <lb></lb>the memory of things paſt is our Tutreſſe in thoſe that are to <lb></lb>come. </s> <s>If occaſion ſhall offer, I intreat you to bow humbly in <lb></lb>my name to His Highneſs the Grand Duke, and the moſt Serene <lb></lb>Prince <emph type="italics"></emph>Leopold<emph.end type="italics"></emph.end>; and to attend the ſervice of Their Highneſſes, for <lb></lb>you ſerve I rinces of extraordinary merit; And to whom I my <lb></lb>ſelf am alſo exceedingly obliged. </s> <s>In the controverſies that ariſe <lb></lb>reſpect the pious end of ſpeaking the Truth, for then every <lb></lb>thing will ſucceed happily. </s> <s>I kiſs the hands of <emph type="italics"></emph>Padre Franceſco,<emph.end type="italics"></emph.end><lb></lb>of <emph type="italics"></emph>Sig. </s> <s>Bartolotti,<emph.end type="italics"></emph.end> and of your Lordſhip.</s></p><p type="main"> <s><emph type="italics"></emph>Rome, 14. March<emph.end type="italics"></emph.end> 1642.</s></p><p type="main"> <s><emph type="italics"></emph>Your Honours<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>most Obliged Servant<emph.end type="italics"></emph.end></s></p><p type="main"> <s>D. <emph type="italics"></emph>BENEDETTO CASTELLI.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Vpon this occaſion I will here inſert a Diſcourſe that I made <lb></lb>upon the Draining and improvement of the <emph type="italics"></emph>Pontine Fens,<emph.end type="italics"></emph.end><lb></lb>for that I think that whatſoever may be done well and to pur<lb></lb>poſe in this matter hath abſolute dependance on the perfect know<lb></lb>ledge of that ſo important Propoſition, by me demonſtrated and <lb></lb>explained in my Treatiſe of the <emph type="italics"></emph>Menſuration<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Running Wa<lb></lb>ters,<emph.end type="italics"></emph.end> namely, That the ſame water of a River doth continually <lb></lb>change Meaſures, according as it altereth and changeth the ve<lb></lb>locity of its courſe; ſo that the meaſure of the thickneſſe of a <lb></lb>River in one Site, to the meaſure of the ſame River in another <lb></lb>Site, hath the ſame proportion reciprocally that the velocity in <lb></lb>this ſite hath to the velocity in the firſt ſite. </s> <s>And this is a Truth <lb></lb>ſo conſtant and unchangeable, that it altereth not in the leaſt <lb></lb>point on any occurrences of the Waters that change: and <lb></lb>being well underſtood, it openeth the way to the knowledge of <lb></lb>ſundry advertiſements in theſe matters, which are all reſolved by <lb></lb>this ſole Principle; and from it are derived very conſiderable be<lb></lb>nefits; and without theſe it is impoſſible to do any thing with <lb></lb>abſolute perfection</s></p><pb xlink:href="040/01/656.jpg"></pb><pb xlink:href="040/01/657.jpg" pagenum="91"></pb><p type="head"> <s>A <lb></lb>CONSIDERATION <lb></lb>Upon the <lb></lb>DRAINING <lb></lb>OF THE <lb></lb>Pontine Fenns. <lb></lb></s> <s>BY</s></p><p type="head"> <s>D. BENEDETTO CASTELLI, Abbot <lb></lb>of S. BENEDETTO ALOISIO, and Profeſſor <lb></lb>of the <emph type="italics"></emph>Mathematicks<emph.end type="italics"></emph.end> to P. <emph type="italics"></emph>Urban<emph.end type="italics"></emph.end> VIII. in the <lb></lb>Univerſity of <emph type="italics"></emph>ROME.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>CONSIDERATION<emph.end type="italics"></emph.end> III.</s></p><p type="main"> <s>Amongſt the enterprizes by me eſteemed, if not ab<lb></lb>ſolutely impoſſible, , at leaſt exceeding difficult, <lb></lb>one was that famous one of Draining the <emph type="italics"></emph>Pontine <lb></lb>Fenns<emph.end type="italics"></emph.end>; and therefore I was thorowly reſolved <lb></lb>never to apply my minde thereunto, although <lb></lb>by my Patrons I ſhould be commanded to the <lb></lb>ſame: accounting that it was an occaſion rather of loſing repu<lb></lb>tation by the miſcarriage of the attempt, than of gaining fame by <lb></lb>reducing things to a better paſs then they now are at. </s> <s>Yet never<lb></lb>theleſs, having of late years obſerved the place, and ſailed through <lb></lb>thoſe Chanels, and thoſe Waters; after I had made ſome reflection <lb></lb>thereupon, I thought that the enterprize was not ſo difficult as <lb></lb>I had at firſt conceited it to be; and I am the more confirmed in <lb></lb>this opinion, upon the inducement of that which I have written <pb xlink:href="040/01/658.jpg" pagenum="92"></pb>Geometrically in my Treatiſe of the Menſuration of Running <lb></lb>Waters; ſo that talking with ſeveral perſons, I adventured to <lb></lb>affirm, in diſcoures, that this improvement might poſſibly be <lb></lb>brought into a good eſtate.</s></p><p type="main"> <s>Now I have reſolved to ſet down my thoughts in writing, and <lb></lb>to honour this my Paper with the Noble Name of your Lordſhip, <lb></lb>to render it the more credible and conſpicuous at the firſt view, <lb></lb>if it ſhould chance that the Subject I treat of, were not of ſuch <lb></lb>moment, as that it did deſerve to be valued for any other reaſon. <lb></lb></s> <s>Pardon me, Sir, if I have been too bold, and continue me in the <lb></lb>number of your Servants.</s></p><p type="main"> <s>The enterprize of Draining a great part of the Territories of <lb></lb>the <emph type="italics"></emph>Pontine Fenns,<emph.end type="italics"></emph.end> hath been undertaken both in the time of <lb></lb>the antient <emph type="italics"></emph>Romans,<emph.end type="italics"></emph.end> and laſt of all, in our days; yea in the late <lb></lb>times by <emph type="italics"></emph>Sixtus<emph.end type="italics"></emph.end> V. </s> <s>I do not doubt in the leaſt, but that it will <lb></lb>be poſſible yet to reduce things to a very good paſs; and if I be not <lb></lb>miſtaken, with a very ſmall charge in compariſon of the profit that <lb></lb>would be received from thoſe rich Grounds. </s> <s>This improvement <lb></lb>was of great expence in the time of <emph type="italics"></emph>Sixtus Quintus,<emph.end type="italics"></emph.end> but by rea<lb></lb>ſon the thing was not rightly underſtood, there were made many <lb></lb>Drains; a great part of which were unprofitable and vain: and <lb></lb>amongſt ſo many operations, there hapned ſome to be made that <lb></lb>ſucceeded, as was deſired; but not being underſtood, they were <lb></lb>held in no account; and thus the buſineſs being neglected, the <lb></lb>waters are returned into the ſame ſtate as they were at firſt, be<lb></lb>fore the improvement. </s> <s>Here I have by familiar diſcourſes <lb></lb>with my friends, explained this enterprize undertaken by <emph type="italics"></emph>Six<lb></lb>tus<emph.end type="italics"></emph.end> V. and haply alſo by ſome more antient, with the example of <lb></lb>the Fable of <emph type="italics"></emph>Orilo,<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Arioſto.<emph.end type="italics"></emph.end> This Monſter was made up with <lb></lb>ſuch enchantment, that men fought with him alwayes in vain; <lb></lb>for though in the Combate he were cut in pieces, thoſe divided <lb></lb>Members preſently re-united, and returned to the fight more <lb></lb>fierce then ever. </s> <s>But the <emph type="italics"></emph>Paladine Aſtolfo<emph.end type="italics"></emph.end> coming to undertake <lb></lb>him, after a long diſpute, at the end he cut his head ſheer off <lb></lb>from the ſhoulders at one blow; and nimbly alighting from his <lb></lb>Horſe, took the Monſtrous head, and mounting again, as he rid <lb></lb>away he fell to ſhave the Pole of that Monſter, and ſo he loſt <lb></lb>the Lock of Hair, in which alone the enchantment lay; and then <lb></lb>the horrible Head in an inſtant manifeſted ſigns of death, and the <lb></lb>trunk which ran, ſeeking to reunite to it anew, gave the laſt gaſp, <lb></lb>and in this manner the enchantment ended. </s> <s>The Book of Fate <lb></lb>ſerved admirably to the <emph type="italics"></emph>Paladine,<emph.end type="italics"></emph.end> whereby he came to under<lb></lb>ſtand that Charm; for by ſhaving his whole head, the enchanted <lb></lb>hairs came to be cut off amongſt the reſt: In the ſame manner, I <lb></lb>ſay, that it hath ſometimes happened in Draining thoſe Fields; <pb xlink:href="040/01/659.jpg" pagenum="93"></pb>for that amongſt ſo many tryals as have been made, that alſo <lb></lb>was light upon, on which the improvement and remedy to the <lb></lb>diſorder did depend. </s> <s>And to us my fore-named Treatiſe ſhall <lb></lb>ſerve for a Rule, which being well underſtood, ſhall make us to <lb></lb>know wherein conſiſteth, and whereon dependeth this miſcarri<lb></lb>age, and conſequently it will be eaſie to apply thereunto a ſeaſo<lb></lb>nable remedy.</s></p><p type="main"> <s>And firſt I ſay, That there is no doubt but that the waters <lb></lb>continue ſo high on thoſe Plains becauſe they are ſo high in the <lb></lb>principal River, which ought to receive them, and carry them <lb></lb>into the Sea. </s> <s>Now the Cauſes of the height of the River, may <lb></lb>in my judgement be reduced to one alone; which is that by me <lb></lb>ſo often mentioned for the moſt Potent one, and declared in my <lb></lb>afore-named Tractate; to wit, The tardity of the motion of the <lb></lb>waters, which doth alwayes infallibly, and preciſely cauſe the <lb></lb>ſelf ſame Running Water to change the meaſure of its thickneſs <lb></lb>at ſuch a rate, that the more it encreaſeth in velocity, the more <lb></lb>it decreaſeth in meaſure; and the more it decreaſeth in velocity, <lb></lb>the more it encreaſeth in meaſure: As for example; If a River <lb></lb>run in ſuch a place with the velocity of moving a mile in the <lb></lb>ſpace of an hour, and afterwards the ſame River in another place <lb></lb>doth encreaſe in velocity, ſo as to make three miles an hour; <lb></lb>that ſame River ſhall diminiſh in thickneſs two thirds: And on <lb></lb>the contrary, If it ſhall diminiſh in velocity ſo, as that it runneth <lb></lb>but half a mile in the ſame time, it ſhall encreaſe the double in <lb></lb>thickneſs and meaſure. </s> <s>And in a word, look what proportion <lb></lb>the velocity in the firſt place, hath to the velocity in the ſecond, <lb></lb>and ſuch hath reciprocally the meaſure of the thickneſs in the <lb></lb>ſecond place, to the meaſure in the firſt; as I have clearly demon<lb></lb>ſtrated in my Treatiſe: Which I repeat ſo frequently, that I <lb></lb>fear the Profeſſors of Polite Learning will charge me with Tua<lb></lb>tologie, and vain Repetition. </s> <s>But I am ſo deſirous in this moſt <lb></lb>important point to be well underſtood, becauſe it will then be <lb></lb>eaſie to comprehend all the reſt; and without this it is impoſſible <lb></lb>(I will not ſay difficult, but abſolutely impoſſible) to underſtand, <lb></lb>or ever to effect any thing to purpoſe. </s> <s>And the better to ex<lb></lb>plain the example, let it be ſuppoſed, <lb></lb><figure id="id.040.01.659.1.jpg" xlink:href="040/01/659/1.jpg"></figure><lb></lb>That the water of a River A D, <lb></lb>runneth high at the level of A F, <lb></lb>with ſuch a certain velocity; and let <lb></lb>it, by the ſame water, be velocitated <lb></lb>three times more; I ſay, that it will <lb></lb>abate 1/3, and ſhall ſtand at the level <lb></lb>in B E; and if it ſhall more veloci<lb></lb>tate, it will abate the more at the Sea; But if it ſhould retard <pb xlink:href="040/01/660.jpg" pagenum="94"></pb>more than it did at the level AF, it would riſe yet more above <lb></lb>the ſaid level A F; although that the ſelf ſame quantity of water <lb></lb>runneth all the while. </s> <s>By the above-named ſolid Principle I <lb></lb>reſolve extravagant Problems in my Treatiſe, and aſſign the Rea<lb></lb>ſons of admirable effects of Running Waters: But as for what <lb></lb>concerneth our purpoſe of the <emph type="italics"></emph>Pontine Fenns,<emph.end type="italics"></emph.end> we have the Cau<lb></lb>ſes very plain and clear; for which, by the trampling of Cattle <lb></lb>which paſs thorow the <emph type="italics"></emph>Draining River,<emph.end type="italics"></emph.end> the waters abate ſo nota<lb></lb>bly, that it is as it were a miracle for thoſe Reeds, Flags, and <lb></lb>Weeds that ſpring up, encreaſe, and ſpread all over the River, <lb></lb>ſtop and impede that velocity of the waters which they would <lb></lb>have by means of their declivity. </s> <s>But that paſſage of thoſe Beaſts, <lb></lb>treading down thoſe Weeds unto the bottom of the River, in ſuch <lb></lb>ſort, as that they no longer hinder the Current of the Water; <lb></lb>and the ſame Waters increaſing in their courſe, they do dimi<lb></lb>niſh in meaſure and height; and by this meanes the Ditches of the <lb></lb>Plains empty into the ſame ſucceſsfully, and leave them free <lb></lb>from Waters, and Drained. </s> <s>But theſe Weeds in a ſhort <lb></lb>time ſprouting up anew, and raiſing their ſtalkes thorow the <lb></lb>body of the Waters, they reduce things to the ſame evil <lb></lb>ſtate, as before, retarding the velocity of the Water, ma<lb></lb>king it to increaſe in height, and perhaps do occaſion grea<lb></lb>ter miſchiefs; ſeeing that thoſe many knots which each plant <lb></lb>ſhoots forth, begets a greater multitude of Stalks, which much <lb></lb>more incumbering the Water of the River, are a greater impe<lb></lb>diment unto its velocity, and conſequently make the height <lb></lb>of the waters to encreaſe ſo much the more, and do more miſchief <lb></lb>than before.</s></p><p type="main"> <s>Another head to which theſe harms may be reduced, but pro<lb></lb>ceeding from the ſame Root, which hath a great part in this <lb></lb>diſorder, is the impediment of thoſe Wears in the River which <lb></lb>are made by heightning the bed of the ſame, for placing of fiſh<lb></lb>ing-nets; of which <emph type="italics"></emph>Piſcaries<emph.end type="italics"></emph.end> I reckoned above ten, when I made <lb></lb>a voyage thorow thoſe waters to <emph type="italics"></emph>Sandolo.<emph.end type="italics"></emph.end> And theſe Fiſhing<lb></lb>Wears are ſuch impediments, that ſome one of them makes the <lb></lb>water of the River in the upper part to riſe half a Palm, and <lb></lb>ſometimes a whole Palm, and more; ſo that when they are all <lb></lb>gathered together, theſe impediments amount to more than ſeven, <lb></lb>or poſſibly than eight Palms.</s></p><p type="main"> <s>There concurreth for a third moſt Potent Cauſe of the waters <lb></lb>continuing high in the evacuating, or Draining Chanel, and con<lb></lb>ſequently on the Plains; The great abundance of water that iſſu<lb></lb>eth from <emph type="italics"></emph>Fiume Siſto,<emph.end type="italics"></emph.end> the waters of which do not keep within its <lb></lb>Banks when they are abundant; but encreaſing above its Chanel, <lb></lb>they unite with thoſe of the Evacuator, and diſperſing thorow <pb xlink:href="040/01/661.jpg" pagenum="95"></pb>the Fens are raiſed with great prejudice, and much grea<lb></lb>ter than is conceived, according to what hath been demon<lb></lb>ſtrated in the Second Conſideration upon the <emph type="italics"></emph>Lake of Venice.<emph.end type="italics"></emph.end><lb></lb>Nor is it to any purpoſe to ſay, that if we ſhould meaſure <lb></lb>all the Waters that disimbogue from <emph type="italics"></emph>Fiume Siſto,<emph.end type="italics"></emph.end> and gather <lb></lb>them into one ſumme, we ſhould not finde them to be ſuch, <lb></lb>as that they ſhall be able to make the Waters of the Fens <lb></lb>to increaſe, by reaſon of the great expanſion of them, over <lb></lb>which that body of water is to diſtend: for to this inſtance we <lb></lb>anſwer wich that which we have given notice of in the Firſt Con<lb></lb>ſideration touching the <emph type="italics"></emph>Lake of Venice,<emph.end type="italics"></emph.end> treating of the abate<lb></lb>ment that is cauſed by the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> let into the Lake. </s> <s>And more<lb></lb>over, if I ſhall adde thereto that which I write in the Second <lb></lb>Conſideration, it will be very apparent how greatly harmfull <lb></lb>and prejudicial theſe excurfions of Waters from <emph type="italics"></emph>Fiume Siſto<emph.end type="italics"></emph.end><lb></lb>may be, which are not kept under, and confined within the <lb></lb>River: Therefore, proceeding to the proviſions, and ope<lb></lb>rations that are to be accounted Principall, I reduce them to <lb></lb>three Heads.</s></p><p type="main"> <s>In the firſt place it is neceſſary to throw down thoſe Weares, <lb></lb>and to take the Piſciaries quite away, obſerving a Maxime, in <lb></lb>my judgment, infallible, that Fiſhing and Sowing are two things <lb></lb>that can never conſiſt together; Fiſhing being on the Water, and <lb></lb>Sowing on land.</s></p><p type="main"> <s>Secondly, it will be neceſſary to cut under Water in the bot<lb></lb>tome of the River thoſe Weeds and Plants that grow and in<lb></lb>creaſe in the River, and leave them to be carried into the Sea by <lb></lb>the Stream; for by this means theſe Reeds ſhall not ſpring up <lb></lb>and diſtend along the bottome of the River, by means of the <lb></lb>Beaſts treading upon them; And the ſame ought to be done <lb></lb>often, and with care, and muſt not be delaied till the miſ<lb></lb>chief increaſe, and the Champain Grounds be drowned, but <lb></lb>one ought to order matters ſo, as that they may not drown. <lb></lb></s> <s>And I will affirm, that otherwiſe this principal point would be<lb></lb>come a moſt conſiderable inconvenience.</s></p><p type="main"> <s>Thirdly, it is neceſſary to make good the Banks of <emph type="italics"></emph>Fiume Siſto<emph.end type="italics"></emph.end><lb></lb>on the left hand, and to procure that thoſe Waters may run in <lb></lb>the Chanel, and not break forth. </s> <s>And it is to be noted, that <lb></lb>it is not enough to do one or two of thoſe things, but we are to <lb></lb>put them all in execution; for omitting any thing, the whole <lb></lb>machine will be out of tune, and ſpoiled. </s> <s>But proceeding with <lb></lb>due care, you ſhall not only Drain the <emph type="italics"></emph>Pontine Fens,<emph.end type="italics"></emph.end> but by <lb></lb>means of this laſt particular the Current of <emph type="italics"></emph>Fiums Sisto<emph.end type="italics"></emph.end> ſhall <lb></lb>ſcowr its own Chanel of its ſelf, even to the carrying part of it <lb></lb>away: and haply with this abundance of water that it ſhall <pb xlink:href="040/01/662.jpg" pagenum="96"></pb>bear, the Mouth <emph type="italics"></emph>della Torre<emph.end type="italics"></emph.end> may be opened, and kept open <lb></lb>into the Sea. </s> <s>And it would, laſt of all, be of admirable bene<lb></lb>fit to cleanſe <emph type="italics"></emph>Fiume Sisto<emph.end type="italics"></emph.end> from many Trees and Buſhes where<lb></lb>with it is overgrown.</s></p><p type="main"> <s>And with this I conclude, that the Improvement or Drain <lb></lb>poſſible to be made conſiſteth in theſe three particulars. </s> <s>Firſt, <lb></lb>in taking away the Fiſhing Weares, leaving the Courſe <lb></lb>of the Waters free. </s> <s>Secondly, in keeping the Principal <lb></lb>Rivers clear from Weeds and Plants. </s> <s>Thirdly, in keeping <lb></lb>the water of <emph type="italics"></emph>Fiume Sisto<emph.end type="italics"></emph.end> in its own Chanel. </s> <s>All which are <lb></lb>things that may be done with very little charge, and to the <lb></lb>manifeſt benefit of the whole Country, and to the rendering <lb></lb>the Air wholſomer in all thoſe Places adjoyning to the <emph type="italics"></emph>Pon<lb></lb>tine Fens.<emph.end type="italics"></emph.end></s></p><figure id="id.040.01.662.1.jpg" xlink:href="040/01/662/1.jpg"></figure><pb xlink:href="040/01/663.jpg" pagenum="97"></pb><p type="head"> <s>A <lb></lb>CONSIDERATION <lb></lb>Upon the <lb></lb>DRAINING <lb></lb>Of the Territories of <lb></lb>Bologna, Ferrara, <lb></lb>AND <lb></lb>Romagna.</s></p><p type="head"> <s>BY <lb></lb>D. BENEDETTO CASTELLI, Abbot <lb></lb>of S. BENEDETTO ALOISIO, <emph type="italics"></emph>Mathematician<emph.end type="italics"></emph.end><lb></lb>to P. <emph type="italics"></emph>Vrban<emph.end type="italics"></emph.end> VIII. and Profeſſor in the <lb></lb>Univerſity of <emph type="italics"></emph>ROME.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The weghty buſineſſe of the Draining of <lb></lb>the Territories of <emph type="italics"></emph>Bologna, Ferrara,<emph.end type="italics"></emph.end><lb></lb>and <emph type="italics"></emph>Romagna<emph.end type="italics"></emph.end> having been punctually <lb></lb>handled and declared in writing from <lb></lb>the excellent memory of the Right Ho<lb></lb>nourable and Noble <emph type="italics"></emph>Monſignore Corſini,<emph.end type="italics"></emph.end><lb></lb>who was heretofore Deputed Commiſ<lb></lb>ſary General, and Viſitor of thoſe Wa<lb></lb>ters; I am not able to make ſuch ano<lb></lb>ther Diſcourſe upon the ſame Subject, but will only ſay ſome<lb></lb>what for farther confirmation of that which I have ſaid in this <lb></lb>Book upon the <emph type="italics"></emph>Lake of Venice,<emph.end type="italics"></emph.end> upon the <emph type="italics"></emph>Pontine Fens,<emph.end type="italics"></emph.end> and up<lb></lb>on the Draining of thoſe Plains of <emph type="italics"></emph>Piſa,<emph.end type="italics"></emph.end> lying between the Ri<lb></lb>vers <emph type="italics"></emph>Arno<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Serchio<emph.end type="italics"></emph.end>; whereby it is manifeſt, that in all the <pb xlink:href="040/01/664.jpg" pagenum="98"></pb>aforementioned Caſes, and in the preſent one that we are in hand <lb></lb>with, there have, in times paſt, very groſſe Errours been com<lb></lb>mitted, through the not having ever well underſtood the true <lb></lb>meaſure of Running waters; and here it is to be noted, that the <lb></lb>buſineſſe is, that in <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> the diverſion of the waters of the <lb></lb>Lake, by diverting the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> was debated, and in part executed, <lb></lb>without conſideration had how great abatement of water might <lb></lb>follow in the Lake, if the <emph type="italics"></emph>Brent<emph.end type="italics"></emph.end> were diverted, as I have ſhewn <lb></lb>in the firſt Conſideration upon this particular, from which act <lb></lb>there hath inſued very bad conſequences, not only the difficulty <lb></lb>of Navigation, but it hath infected the wholſomneſſe of the Air, <lb></lb>and cauſed the ſtoppage of the Ports of <emph type="italics"></emph>Venice.<emph.end type="italics"></emph.end> And on the <lb></lb>contrary, the ſame inadvertency of not conſidering what riſing of <lb></lb>the Water the <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> and other Rivers being opened into the Val<lb></lb>leys of <emph type="italics"></emph>Bologna<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> might cauſe in the ſaid Valleys, is <lb></lb>the certain cauſe that ſo many rich and fertile Fields are drown<lb></lb>ed under water, converting the happy habitations and dwellings <lb></lb>of men into miſerable receptacles for Fiſhes: Things which <lb></lb>doubtleſſe would never have happened, if thoſe Rivers had been <lb></lb>kept at their height, and <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> had been turn'd into <emph type="italics"></emph>Main-Po,<emph.end type="italics"></emph.end><lb></lb>and the other Rivers into that of <emph type="italics"></emph>Argenta,<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Volano.<emph.end type="italics"></emph.end> Now <lb></lb>there having ſufficient been ſpoken by the above-named <emph type="italics"></emph>Monſig. <lb></lb></s> <s>Corſini<emph.end type="italics"></emph.end> in his Relation, I will only adde one conceit of my own, <lb></lb>which after the Rivers ſhould be regulated, as hath been ſaid, I <lb></lb>verily believe would be of extraordinary profit, I much doubt in<lb></lb>deed that I ſhall finde it a hard matter to perſwade men to be of <lb></lb>my mind, but yet nevertheleſs I will not queſtion, but that thoſe, <lb></lb>at leaſt, who ſhall have underſtood what I have ſaid and demon<lb></lb>ſtrated concerning the manners and proportions, according to <lb></lb>which the abatements and riſings of Running waters proceed, <lb></lb>that are made by the Diverſions and Introductions of Waters, <lb></lb>will apprehend that my conjecture is grounded upon Reaſon. <lb></lb></s> <s>And although I deſcend not to the exactneſſe of particulars, I <lb></lb>will open the way to others, who having obſerved the requiſite <lb></lb>Rules of conſidering the quantity of the waters that are intro<lb></lb>duced, or that happen to be diverted, ſhall be able with punctu<lb></lb>ality to examine the whole buſineſſe, and then reſolve on that <lb></lb>which ſhall be expedient to be done.</s></p><p type="main"> <s>Reflecting therefore upon the firſt Propoſition, that the <lb></lb>Riſings of a Running Water made by the acceſſion of new water <lb></lb>into the River, are to one another, as the Square-Roots of the <lb></lb>quantity of the water that runneth; and conſequently, that the <lb></lb>ſame cometh to paſs in the Diverſions: Inſomuch, that a River <lb></lb>running in height one ſuch a certain meaſure, to make it encreaſe <lb></lb>double in height, the water is to be encreaſed to three times as <pb xlink:href="040/01/665.jpg" pagenum="99"></pb>much as it ran before; ſo that when the water ſhall be quadru<lb></lb>ple, the height ſhall be double; and if the water were centuple, <lb></lb>the height would be decuple onely, and ſo from one quantity <lb></lb>to another: And on the contrary, in the Diverſions; If of the <lb></lb>100. parts of water that run thorow a River, there ſhall be di<lb></lb>verted 19/160, the height of the River diminiſheth onely 1/10, and con<lb></lb>tinuing to divert 17/100, the height of the River abateth likewiſe 1/10, <lb></lb>and ſo proceeding to divert 15/100 and then 13/100, and then 11/100, and <lb></lb>then 9/100, and then 7/100, and then 5/100, and then 3/106, alwaies by <lb></lb>each of theſe diverſions, the height of the Running Water di<lb></lb>miniſheth the tenth part: although that the diverſions be ſo une. <lb></lb></s> <s>qual. </s> <s>Reflecting I ſay upon this infallible Truth, I have had a <lb></lb>conceit, that though the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> and other Rivers were diverted <lb></lb>from the Valleyes, and there was onely left the <emph type="italics"></emph>Chanel of Navi<lb></lb>gation,<emph.end type="italics"></emph.end> which was onely the 1/20 part of the whole water that fal<lb></lb>leth into the Valleys; yet nevertheleſs, the water in thoſe ſame <lb></lb>Valleyes would retain a tenth part of that height that became <lb></lb>conjoyned by the concourſe of all the Rivers: And therefore I <lb></lb>ſhould think that it were the beſt reſolution to maintain the <emph type="italics"></emph>Gha<lb></lb>nel of Navigation<emph.end type="italics"></emph.end> (if it were poſſible) continuate unto the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <lb></lb><emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> and from thence to carry it into the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Volano<emph.end type="italics"></emph.end>; for <lb></lb>beſides that it would be of very great eaſe in the Navigation of <lb></lb><emph type="italics"></emph>Bologna,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> the ſaid water would render the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> oſ <lb></lb><emph type="italics"></emph>Volano<emph.end type="italics"></emph.end> navigable as far as to the very Walls of <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> and con<lb></lb>ſequently the Navigation would be continuate from <emph type="italics"></emph>Bologna<emph.end type="italics"></emph.end> to <lb></lb>the Sea-ſide.</s></p><p type="main"> <s>But to manage this enterprize well, it is neceſſary to meaſure <lb></lb>the quantity of the Water that the Rivers diſcharge into the Val<lb></lb>leys, and that which the <emph type="italics"></emph>Chanel of Navigation<emph.end type="italics"></emph.end> carryeth, in man<lb></lb>ner as I have demonſtrated at the beginning of this Book; for this <lb></lb>once known, we ſhall alſo come to know, how profitable this di<lb></lb>verſion of the <emph type="italics"></emph>Chanel of Navigation<emph.end type="italics"></emph.end> from the Valleys is like to <lb></lb>prove; which yet would ſtill be unprofitable, if ſo be that all <lb></lb>the Rivers that diſcharge their waters into the Valleys, ſhould <lb></lb>not ſirſt be Drained, according to what hath been above ad<lb></lb>vertiſed.</s></p><p type="main"> <s>Abbot CASTELLI, <emph type="italics"></emph>in the preſent conſideration referring <lb></lb>himfelf to the Relation of<emph.end type="italics"></emph.end> Monſig. </s> <s>Corſini, <emph type="italics"></emph>grounded upon the Ob<lb></lb>ſervations and Precepts of the ſaid Abbot; as is ſeen in the pre<lb></lb>ſent Diſcourſe. </s> <s>I thought it convenient for the compleating of the <lb></lb>Work of our Aulhour, upon theſe ſubjects, to inſert it in this <lb></lb>place.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/666.jpg" pagenum="100"></pb><p type="head"> <s>A <lb></lb>Relation of the Waters in the Territories <lb></lb>of <emph type="italics"></emph>Bologna<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ferrara.<emph.end type="italics"></emph.end><lb></lb>BY</s></p><p type="head"> <s>The Right Honourable and Illuſtrious, <emph type="italics"></emph>Monſig<lb></lb>nore<emph.end type="italics"></emph.end> CORSINI, a Native of <emph type="italics"></emph>Juſcany,<emph.end type="italics"></emph.end> Su<lb></lb>perintendent of the general DRAINS, <lb></lb>and Preſident of <emph type="italics"></emph>Romagna-<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The <emph type="italics"></emph>Rheno,<emph.end type="italics"></emph.end> and other Brooks of <emph type="italics"></emph>Romagna,<emph.end type="italics"></emph.end> were by the <lb></lb>advice of <emph type="italics"></emph>P. </s> <s>Agoſtino Spernazzati<emph.end type="italics"></emph.end> the Jeſuite, towards <lb></lb>the latter end of the time of <emph type="italics"></emph>Pope Clement<emph.end type="italics"></emph.end> VIII. notwith<lb></lb>ſtanding the oppoſition of the <emph type="italics"></emph>Bologneſi,<emph.end type="italics"></emph.end> and others concerned <lb></lb>therein, diverted from their Chanels, for the more commodious <lb></lb>cleanſing of the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> and of its two Branches of <emph type="italics"></emph>Prima<lb></lb>ro,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Volano<emph.end type="italics"></emph.end>; in order to the introducing the water of the <lb></lb><emph type="italics"></emph>Main-Po<emph.end type="italics"></emph.end> into them, to the end that their wonted Torrents being <lb></lb>reſtored, they might carry the Muddy-water thence into the Sea, <lb></lb>and reſtore to the City the Navigation which was laſt, as is ma<lb></lb>nifeſt by the Brief of the ſaid <emph type="italics"></emph>Pope Clement,<emph.end type="italics"></emph.end> directed to the <emph type="italics"></emph>Car<lb></lb>dinal San Clemence,<emph.end type="italics"></emph.end> bearing date the 22. of <emph type="italics"></emph>Auguſt,<emph.end type="italics"></emph.end> 1604.</s></p><p type="main"> <s>The work of the ſaid cleanſing, and introducing of the ſaid <lb></lb>P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> either as being ſuch in it ſelf, or by the contention of the <lb></lb><emph type="italics"></emph>Cardinal Legates<emph.end type="italics"></emph.end> then in theſe parts; and the jarrings that hap<lb></lb>ned betwixt them, proved ſo difficult, that after the expence of <lb></lb>vaſt ſumms in the ſpace of 21. years, there hath been nothing <lb></lb>done, ſave the rendring of it the more difficult to be effected.</s></p><p type="main"> <s>Interim, the Torrents with their waters, both muddy and <lb></lb>clear, have damaged the Grounds lying on the right hand of the <lb></lb>P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Argenta,<emph.end type="italics"></emph.end> and the <emph type="italics"></emph>Rheno<emph.end type="italics"></emph.end> thoſe on its Banks; of which I <lb></lb>will ſpeak in the firſt place, as of that which is of greater impor<lb></lb>tance, and from which the principal cauſe of the miſchiefs that <lb></lb>reſult from the reſt doth proceed.<lb></lb><arrow.to.target n="marg976"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg976"></margin.target>* Or Lordſhip.</s></p><p type="main"> <s>This <emph type="italics"></emph>Rbeno<emph.end type="italics"></emph.end> having overflowed the ^{*} Tennency of <emph type="italics"></emph>Sanmartina,<emph.end type="italics"></emph.end><lb></lb>in circumference about fourteen miles given it before, and part <lb></lb>of that of <emph type="italics"></emph>Cominale<emph.end type="italics"></emph.end> given it afterwards, as it were, for a recepta<lb></lb>cle; from whence, having depoſed the matter of its muddineſs, <lb></lb>it iſſued clear by the Mouths of <emph type="italics"></emph>Maſi,<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Lievaloro,<emph.end type="italics"></emph.end> into <lb></lb>the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Primaro,<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Volano<emph.end type="italics"></emph.end>; did break down the encom<pb xlink:href="040/01/667.jpg" pagenum="101"></pb>paſſing Bank or Dam towards S. <emph type="italics"></emph>Martino,<emph.end type="italics"></emph.end> and that of its new <lb></lb>Chanel on the right hand neer to <emph type="italics"></emph>Torre del Fondo.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>By the breaches on this ſide it ſtreamed out in great abun<lb></lb>dance from the upper part of <emph type="italics"></emph>Cominale,<emph.end type="italics"></emph.end> and in the parts about <lb></lb><emph type="italics"></emph>Raveda, Pioggio, Caprara, Chiare di Reno, Sant' Agoſtino, San <lb></lb>Proſpero, San Vincenzo,<emph.end type="italics"></emph.end> and others, and made them to become <lb></lb>incultivable: it made alſo thoſe places above but little fruitful, <lb></lb>by reaſon of the impediments that their Draines received, finding <lb></lb>the Conveyances called <emph type="italics"></emph>Riolo<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Scorſuro,<emph.end type="italics"></emph.end> not only filled by <emph type="italics"></emph>la <lb></lb>Motta<emph.end type="italics"></emph.end> and <emph type="italics"></emph>la Belletta,<emph.end type="italics"></emph.end> but that they turned backwards of them<lb></lb>ſelves.</s></p><p type="main"> <s>But by the Mouths in the incloſing Bank or Dam at <emph type="italics"></emph>Borgo di<emph.end type="italics"></emph.end><lb></lb>S. <emph type="italics"></emph>Martino<emph.end type="italics"></emph.end> iſſuing with violence, it firſt gave obſtruction to the <lb></lb>ancient Navigation of <emph type="italics"></emph>la Torre del la Foſſa,<emph.end type="italics"></emph.end> and afterwards to <lb></lb>the moderne of the mouth of <emph type="italics"></emph>Maſi,<emph.end type="italics"></emph.end> ſo that at preſent the Com<lb></lb>merce between <emph type="italics"></emph>Bologna<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Ferrara<emph.end type="italics"></emph.end> is loſt, nor can it ever be <lb></lb>in any durable way renewed, whilſt that this exceeds its due <lb></lb>bounds, and what ever moneys ſhall be imployed about the ſame <lb></lb>ſhall be without any equivalent benefit, and to the manifeſt </s></p><p type="main"> <s><arrow.to.target n="marg977"></arrow.to.target><lb></lb>and notable prejudice of the ^{*} Apoſtolick Chamber.</s></p><p type="margin"> <s><margin.target id="marg977"></margin.target>* The Popes <lb></lb>Exchequer.</s></p><p type="main"> <s>Thence paſſing into the Valley of <emph type="italics"></emph>Marzara,<emph.end type="italics"></emph.end> it ſwelleth high<lb></lb>er, not only by the riſing of the water, but by the raiſing of the <lb></lb>bottome, by reaſon of the matter ſunk thither after Land<lb></lb>floods, and dilateth ſo, that it covereth all the Meadows there<lb></lb>abouts, nor doth it receive with the wonted facility the Drains of <lb></lb>the upper Grounds, of which the next unto it lying under the wa<lb></lb>ters that return upwards by the Conveyances, and the more re<lb></lb>mote, not finding a paſſage for Rain-waters that ſettle, become <lb></lb>either altogether unproſitable or little better.</s></p><p type="main"> <s>From this Valley, by the Trench or Ditch of <emph type="italics"></emph>Marzara,<emph.end type="italics"></emph.end> or of <lb></lb><emph type="italics"></emph>la Duca<emph.end type="italics"></emph.end> by <emph type="italics"></emph>la Buova,<emph.end type="italics"></emph.end> or mouth of <emph type="italics"></emph>Caſtaldo de Roſſi,<emph.end type="italics"></emph.end> and by the <lb></lb>new paſſage it falleth into the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Argenta,<emph.end type="italics"></emph.end> which being to re<lb></lb>ceive it clear, that ſo it may ſink farther therein, and receiving <lb></lb>it muddy, becauſe it hath acquired a quicker courſe, there will <lb></lb>ariſe a very contrary effect.</s></p><p type="main"> <s>Here therefore the ſuperficies of the water keeping high, until <lb></lb>it come to the Sea, hindereth the Valleys of <emph type="italics"></emph>Ravenna,<emph.end type="italics"></emph.end> where <lb></lb>the River <emph type="italics"></emph>Senio,<emph.end type="italics"></emph.end> thoſe of <emph type="italics"></emph>San Bernardino<emph.end type="italics"></emph.end> where <emph type="italics"></emph>Santerno<emph.end type="italics"></emph.end> was <lb></lb>turned, thoſe of <emph type="italics"></emph>Buon' acquiſto,<emph.end type="italics"></emph.end> and thoſe of <emph type="italics"></emph>Marmorto,<emph.end type="italics"></emph.end> where <lb></lb>the <emph type="italics"></emph>Idice, Quaderna, Sellero<emph.end type="italics"></emph.end> ſall in, from ſwallowing and taking <lb></lb>in their Waters by their uſual In-lets, yet many times, as I my <lb></lb>ſelf have ſeen in the <emph type="italics"></emph>Viſitation,<emph.end type="italics"></emph.end> they drink them up plentifully, <lb></lb>whereupon, being conjoyned with the muddineſſe of thoſe Ri<lb></lb>vers that fall into the ſame, they ſwell, and dilate, and overflow <lb></lb>ſome grounds, and deprive others of their Drains in like manner <pb xlink:href="040/01/668.jpg" pagenum="102"></pb>as hath been ſaid of that of <emph type="italics"></emph>Marrara,<emph.end type="italics"></emph.end> inſomuch that from the <lb></lb>Point of S. <emph type="italics"></emph>Giorgio,<emph.end type="italics"></emph.end> as far as S. <emph type="italics"></emph>Alberto<emph.end type="italics"></emph.end> all thoſe that are between <lb></lb>the Valleys and P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> are ſpoiled, of thoſe that are between Valley <lb></lb>and Valley many are in a very bad condition, and thoſe that are <lb></lb>ſome conſiderable ſpace above not a little damnified.</s></p><p type="main"> <s>In fine, by raiſing the bottom or ſand of the Valleys, and the <lb></lb>bed of <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> and the too great repletion of the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Primaro<emph.end type="italics"></emph.end><lb></lb>with waters, the Valleys of <emph type="italics"></emph>Comacchio<emph.end type="italics"></emph.end> (on which ſide the Banks <lb></lb>are very bad) and ^{*} <emph type="italics"></emph>Poleſine di<emph.end type="italics"></emph.end> S. <emph type="italics"></emph>Giorgio<emph.end type="italics"></emph.end> are threatned with a <lb></lb><arrow.to.target n="marg978"></arrow.to.target><lb></lb>danger, that may in time, if it be not remedied, become irrepa<lb></lb>rable, and at preſent feeleth the incommodity of the Waters, <lb></lb>which penetrating thorow the pores of the Earth do ſpring up in <lb></lb>the ſame, which they call <emph type="italics"></emph>Purlings,<emph.end type="italics"></emph.end> which is all likely to redound <lb></lb>to the prejudice of <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> ſo noble a City of <emph type="italics"></emph>Italy,<emph.end type="italics"></emph.end> and ſo im<lb></lb>portant to the <emph type="italics"></emph>Eccleſtaſtick State.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg978"></margin.target>+ <emph type="italics"></emph>Poleſine<emph.end type="italics"></emph.end> is a <lb></lb>plat of Ground al<lb></lb>moſt ſurrounded <lb></lb>with Bogs or wa<lb></lb>ters, like an Iſland</s></p><p type="main"> <s>Which particulars all appear to be atteſted under the hand of <lb></lb>a Notary in the <emph type="italics"></emph>Viſitation<emph.end type="italics"></emph.end> which I made upon the command of <lb></lb>His Holineſſe, and are withall known to be true by the ^{*}<emph type="italics"></emph>Ferrareſt<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg979"></arrow.to.target><lb></lb>themſelves, of whom (beſides the requeſt of the <emph type="italics"></emph>Bologneſi<emph.end type="italics"></emph.end>) the <lb></lb>greater part beg compaſſion with ſundry <emph type="italics"></emph>Memorials,<emph.end type="italics"></emph.end> and reme<lb></lb>dies, aſwell for the miſchiefs paſt, as alſo for thoſe in time to <lb></lb>come, from which I hold it a duty of Conſcience, and of Cha<lb></lb>rity to deliver them.</s></p><p type="margin"> <s><margin.target id="marg979"></margin.target>* People of <emph type="italics"></emph>Fer<lb></lb>rara.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Pope <emph type="italics"></emph>Clement<emph.end type="italics"></emph.end> judged, that the ſufficient means to effect this <lb></lb>was the ſaid Introduction of the <emph type="italics"></emph>Main Po<emph.end type="italics"></emph.end> into the Chancl of <lb></lb><emph type="italics"></emph>Ferrara<emph.end type="italics"></emph.end>; a reſolution truly Heroical, and of no leſſe beauty <lb></lb>than benefit to that City, of which I ſpeak not at preſent, be<lb></lb>cauſe I think that there is need of a readier and more acco<lb></lb>modate remedy.</s></p><p type="main"> <s>So that I ſee not how any other thing can be ſo much conſide<lb></lb>rable as the removal of <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> omitting for this time to ſpeak of <lb></lb><arrow.to.target n="marg980"></arrow.to.target><lb></lb>^{*} incloſing it from Valley to Valley untill it come to the Sea, as <lb></lb>the Dukes of <emph type="italics"></emph>Ferrara<emph.end type="italics"></emph.end> did deſign, foraſmuch as all thoſe <emph type="italics"></emph>Ferra<lb></lb>reſi<emph.end type="italics"></emph.end> that have intereſt in the <emph type="italics"></emph>Poleſine di<emph.end type="italics"></emph.end> S. <emph type="italics"></emph>Giorgio,<emph.end type="italics"></emph.end> and on the <lb></lb>right hand of the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Argenta<emph.end type="italics"></emph.end> do not deſire it, and do, but too <lb></lb>openly, proteſt againſt it; and becauſe that before the Chanel <lb></lb>were made as far as the Sea, many hundreds of years would be <lb></lb>ſpent, and yet would not remedy the dammages of thoſe who <lb></lb>now are agrieved, but would much increaſe them, in regard the <lb></lb>Valleys would continue ſubmerged, the Drains ſtopped, and the <lb></lb>other Brooks obſtructed, which would of neceſſity drown not a <lb></lb>few Lands that lie between Valley and Valley; and in fine, in <lb></lb>regard it hath not from <emph type="italics"></emph>San Martina<emph.end type="italics"></emph.end> to the Sea for a ſpace of ſif<lb></lb>ty miles a greater fall then 19, 8, 6, feet, it would want that force <lb></lb>which they themſelves who propound this project do require it to <pb xlink:href="040/01/669.jpg" pagenum="103"></pb>have, that ſo it may not depoſe the matter of the muddineſs when <lb></lb>it is intended to be let into <emph type="italics"></emph>Volana.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg980"></margin.target>* In Chanels <lb></lb>made by hand.</s></p><p type="main"> <s>So that making the Line of the bottome neer to <emph type="italics"></emph>Vigarano,<emph.end type="italics"></emph.end> it <lb></lb>would riſe to thoſe prodigious termes that they do make bigger, <lb></lb>and they may thence expect thoſe miſchiefs, for which they <lb></lb>will not admit of introducing it into the ſaid P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Volana.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Amongſt the wayes therefore that I have thought of for effect<lb></lb>ing that ſame remotion, and which I have cauſed to be viewed by <lb></lb>skilful men that have taken a level thereof, (with the aſſiſtance of <lb></lb>the venerable Father, <emph type="italics"></emph>D. </s> <s>Benedetto Caſtelli<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Caſina,<emph.end type="italics"></emph.end> a man of <lb></lb>much fidelity and honeſty, and no leſs expert in ſuch like affairs <lb></lb>touching waters, than perfect in the <emph type="italics"></emph>Mathematick<emph.end type="italics"></emph.end> Diſciplines) two <lb></lb>onely, the reſt being either too tedious, or too dangerous to the <lb></lb>City, have ſeemed to me worthy, and one of them alſo more than <lb></lb>the other, to offer to your Lordſhip.</s></p><p type="main"> <s>The one is to remit it into the Chanel of <emph type="italics"></emph>Volana,<emph.end type="italics"></emph.end> thorow which <lb></lb>it goeth of its own accord to the Sea.</s></p><p type="main"> <s>The other is to turn it into <emph type="italics"></emph>Main-Po<emph.end type="italics"></emph.end> at <emph type="italics"></emph>Stellata,<emph.end type="italics"></emph.end> for, as at other <lb></lb>times it hath done, it will carry it to the Sea happily.</s></p><p type="main"> <s>As to what concerns the making choice of the firſt way, that <lb></lb>which ſeemeth to perſwade us to it is, that we therein do nothing <lb></lb>that is new, in that it is but reſtored to the place whence it was <lb></lb>removed in the year 1522. in the time of Pope <emph type="italics"></emph>Adrian,<emph.end type="italics"></emph.end> by an <lb></lb>agreement made in way of contract, between <emph type="italics"></emph>Alfonſo,<emph.end type="italics"></emph.end> Duke of <lb></lb><emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> and the <emph type="italics"></emph>Bologneſi<emph.end type="italics"></emph.end>; and that it was diverted for reaſons, <lb></lb>that are either out of date, or elſe have been too long time <lb></lb>deferred.</s></p><p type="main"> <s>In like manner the facility wherewith it may be effected, let<lb></lb>ting it run into the divided P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> whereby it will be turned to <emph type="italics"></emph>Fer<lb></lb>rara,<emph.end type="italics"></emph.end> or elſe carrying it by <emph type="italics"></emph>Torre del Fondo,<emph.end type="italics"></emph.end> to the mouth of <emph type="italics"></emph>Maſi,<emph.end type="italics"></emph.end><lb></lb>and from thence thorow the Trench made by the <emph type="italics"></emph>Ferrareſi,<emph.end type="italics"></emph.end><lb></lb>along by <emph type="italics"></emph>Panaro,<emph.end type="italics"></emph.end> where alſo finding an ample Bed, and high and <lb></lb>thick Banks, that will ſerve at other times for it, and for the wa<lb></lb>ters of P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> there may a great expence be ſpared.</s></p><p type="main"> <s>That what ever its Fall be, it would maintain the ſame, not <lb></lb>having other Rivers, which with their Floods can hinder it; and <lb></lb>that running confined between good Banks, without doubt it <lb></lb>would not leave <emph type="italics"></emph>la Motto<emph.end type="italics"></emph.end> by the way; but eſpecially, that it <lb></lb>would be ſufficient if it came to <emph type="italics"></emph>Codigoro,<emph.end type="italics"></emph.end> where being aſſiſted by <lb></lb>the Ebbing and Flowing of the Sea, it would run no hazard of <lb></lb>having its Chanel filled up from thence downwards.</s></p><p type="main"> <s>That there might thence many benefits be derived to the City, <lb></lb>by means of the Running Waters, and alſo no mean Navigation <lb></lb>might be expected.</s></p><p type="main"> <s>On the contrary it is objected, That it is not convenient to <pb xlink:href="040/01/670.jpg" pagenum="104"></pb>think of returning this Torrent into the divided P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> by reaſon of <lb></lb>the peril that would thence redound to this City.</s></p><p type="main"> <s>And that going by <emph type="italics"></emph>Torre del Fondo,<emph.end type="italics"></emph.end> through <emph type="italics"></emph>Sanmartina<emph.end type="italics"></emph.end> to <lb></lb>the Mouth <emph type="italics"></emph>de Maſi<emph.end type="italics"></emph.end> by the Chappel of <emph type="italics"></emph>Vigarano<emph.end type="italics"></emph.end> unto the Sea, it is <lb></lb>by this way 70. miles; nor is the Fall greater than 26. 5. 6. Feet, ſo <lb></lb>that it would come to fall but 4. inches & an half, or thereabouts <lb></lb>in a mile; whereas the common opinion of the skilfull (to the <lb></lb>end that the Torrents may not depoſe their ſand that they bring <lb></lb>with them in Land-Floods) requireth the twenty fourth part of <lb></lb>the hundredth part of their whole length, which in our caſe, <lb></lb>accounting according to the meaſure of theſe places, is 16. inches <lb></lb><arrow.to.target n="marg981"></arrow.to.target><lb></lb>a ^{*} mile; whereupon the ſinking of the Mud and Sand would <lb></lb>moſt certainly follow, and ſo an immenſe heightning of the Line <lb></lb>of the Bottom, and conſequently a neceſſity of raiſing the Banks, <lb></lb>the impoſſibility of maintaining them, the danger of breaches <lb></lb>and decayes, things very prejudicial to the <emph type="italics"></emph>Iſlets<emph.end type="italics"></emph.end> of this City, and <lb></lb>of <emph type="italics"></emph>San Giorgio,<emph.end type="italics"></emph.end> the obſtruction of the Drains, which from the <lb></lb>Tower of <emph type="italics"></emph>Tienne<emph.end type="italics"></emph.end> downwards, fall into the ſaid Chanel; to wit, <lb></lb>thoſe of the Sluices of <emph type="italics"></emph>Goro,<emph.end type="italics"></emph.end> and the Drains, of the Meadows of <lb></lb><emph type="italics"></emph>Ferrara<emph.end type="italics"></emph.end>: And moreover, the damages that would ariſe unto the <lb></lb>ſaid <emph type="italics"></emph>Iſlet<emph.end type="italics"></emph.end> of S. <emph type="italics"></emph>Giorgio,<emph.end type="italics"></emph.end> and the Valleys of <emph type="italics"></emph>Comachio,<emph.end type="italics"></emph.end> by the wa<lb></lb>ters that ſhould enter into the <emph type="italics"></emph>Goro<emph.end type="italics"></emph.end> or Dam of the Mills of <emph type="italics"></emph>Belri<lb></lb>guardo,<emph.end type="italics"></emph.end> thorow the Trenches of <emph type="italics"></emph>Quadrea,<emph.end type="italics"></emph.end> which cannot be ſtopt, <lb></lb>becauſe they belong to the Duke of <emph type="italics"></emph>Modena,<emph.end type="italics"></emph.end> who hath right of <lb></lb>diverting the waters of that place at his pleaſure to the work of <lb></lb>turning Mills.</s></p><p type="margin"> <s><margin.target id="marg981"></margin.target>* The inch of <lb></lb>theſe places is <lb></lb>ſomewhat bigger <lb></lb>than ours.</s></p><p type="main"> <s>The greater part of which Objections, others pretend to prove <lb></lb>frivolous, by ſaying, that its running there till at the laſt it was <lb></lb>turned another way, is a ſign that it had made ſuch an elevation <lb></lb>of the Line, of its Bed as it required; denying that it needeth <lb></lb>ſo great a declivity as is mentioned above; and that for the fu<lb></lb>ture it would riſe no more.</s></p><p type="main"> <s>That the ſaid Dra ns and Ditches did empty into the ſame, <lb></lb>whilſt P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> was there; ſo that they muſt needs be more able to do <lb></lb>ſo when onely <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> runs that way.</s></p><p type="main"> <s>That there would no Breaches follow, or if they did, they <lb></lb>would be onely of the water of <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> which in few hours might <lb></lb>be taken away (in thoſe parts they call damming up of Breaches, <lb></lb>and mending the Bank, <emph type="italics"></emph>taking away the Breaches<emph.end type="italics"></emph.end>) and its a que<lb></lb>ſtion whether they would procure more inconvenience than bene<lb></lb>fit, for that its Mud and Sand might in many places, by filling <lb></lb>them up, occaſion a ſeaſonable improvement.</s></p><p type="main"> <s>Now omitting to diſcourſe of the ſolidity of the reaſons on the <lb></lb>oneſide, or on the other, I will produce thoſe that move me to <lb></lb>ſuſpend my allowance of this deſign.</s></p><pb xlink:href="040/01/671.jpg" pagenum="105"></pb><p type="main"> <s>The firſt is, that although I dare not ſubſcribe to the opinion <lb></lb>of thoſe that require 16. inches Declivity in a mile to <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> to <lb></lb>prevent its depoſing of Mud; yet would I not be the Author that <lb></lb>ſhould make a trial of it with ſo much hazard, for having to ſa<lb></lb>tisfie my ſelf in ſome particulars cauſed a Level to be taken of <lb></lb>the Rivers <emph type="italics"></emph>L'amone, Senio,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Santerno,<emph.end type="italics"></emph.end> by <emph type="italics"></emph>Bernardino Aleotti,<emph.end type="italics"></emph.end><lb></lb>we found that they have more Declivity by much than Artiſts re<lb></lb>quire, as alſo the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> hath from <emph type="italics"></emph>la Botta de Ghiſlieri<emph.end type="italics"></emph.end> to the <lb></lb>Chappel of <emph type="italics"></emph>Vigarano,<emph.end type="italics"></emph.end> for in the ſpace of four miles its Bottom<lb></lb>Line falleth five feet and five inches. </s> <s>So that I hold it greater <lb></lb>prudence to depend upon that example, than to go contrary to a <lb></lb>common opinion, eſpecially ſince, that the effects cauſed by <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end><lb></lb>it ſelf do confirm me in the ſame, for when it was forſaken by <lb></lb>the P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> after a few years, either becauſe it had choaked up its <lb></lb>Chanel with Sand, or becauſe its too long journey did increaſe <lb></lb>it, it alſo naturally turned aſide, and took the way of the ſaid <lb></lb>P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> towards <emph type="italics"></emph>Stellata.<emph.end type="italics"></emph.end> Nay, in thoſe very years that it did run that <lb></lb>way, it only began (as relations ſay) to make Breaches, an evi<lb></lb>dent ſign that it doth depoſe Sand, and raiſe its Bed; which a<lb></lb>greeth with the teſtimony of ſome that were examined in the <lb></lb><emph type="italics"></emph>Viſitation<emph.end type="italics"></emph.end> of the Publique Notary, who found great benefit by <lb></lb>having Running Water, and ſome kind of paſſage for Boats, <lb></lb>and yet nevertheleſs affirm that it for want of Running Water <lb></lb>had made too high Stoppages and Shelfes of Sand; ſo that if <lb></lb>it ſhould be reſtored to the Courſe that it forſook, I much fear <lb></lb>that after a ſhort time, if not ſuddenly, it would leave it a<lb></lb>again.</s></p><p type="main"> <s>The ſecond I take from the obſervation of what happened to <lb></lb><emph type="italics"></emph>Panaro,<emph.end type="italics"></emph.end> when with ſo great applauſe of the <emph type="italics"></emph>Ferareſi,<emph.end type="italics"></emph.end> it was <lb></lb>brought by Cardinal <emph type="italics"></emph>Serra<emph.end type="italics"></emph.end> into the ſaid Chanel of <emph type="italics"></emph>Volana<emph.end type="italics"></emph.end>; for <lb></lb>that notwithſtanding that it had Running Waters in much grea<lb></lb>ter abundance than <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end>; yet in the time that it continued in <lb></lb>that Chanel it raiſed its Bed well neer five feet, as is to be ſeen <lb></lb>below the Sluice made by Cardinal <emph type="italics"></emph>Capponi<emph.end type="italics"></emph.end> to his new Chanel; <lb></lb>yea, the ſaid Cardinal <emph type="italics"></emph>Serra<emph.end type="italics"></emph.end> who deſired that this his under taking <lb></lb>ſhould appear to have been of no danger nor damage, was con<lb></lb>ſtrained at its Overflowings, to give it Vent into <emph type="italics"></emph>Sanmartina,<emph.end type="italics"></emph.end> that <lb></lb>it might not break in upon, and prejudice the City; which dan<lb></lb>ger I ſhould more fear from <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> in regard it carrieth a greater <lb></lb>abundance of Water and Sand</s></p><p type="main"> <s>Thirdly, I am much troubled (in the uncertainty of the ſuc<lb></lb>ceſs of the affair) at the great expence thereto required; For in <lb></lb>regard I do not approve of letting it in, neer to the Fortreſſe, <lb></lb>for many reſpects, and carrying it by <emph type="italics"></emph>la Torre del Fondo<emph.end type="italics"></emph.end> to the <lb></lb>Month <emph type="italics"></emph>de Maſt,<emph.end type="italics"></emph.end> it will take up eight miles of double Banks, a <pb xlink:href="040/01/672.jpg" pagenum="106"></pb>thing not eaſie to be procured, by reaſon that the Grounds lie <lb></lb>under Water; but from the Mouth <emph type="italics"></emph>de Maſi<emph.end type="italics"></emph.end> unto <emph type="italics"></emph>Codigoro,<emph.end type="italics"></emph.end> it <lb></lb>would alſo be neceſſary to make new Scowrings of the Chanel; <lb></lb>to the end, that the Water approaching (by wearing and carry<lb></lb>ing away the Earth on both ſhores, might make a Bed ſufficient <lb></lb>for its Body, the depth made for <emph type="italics"></emph>Panaro<emph.end type="italics"></emph.end> not ſerving the turn, as <lb></lb>I conceive; and if it ſhould ſuffice, when could the people of <lb></lb><emph type="italics"></emph>Ferrara<emph.end type="italics"></emph.end> hope to be re-imburſed and ſatisfied for the charge <lb></lb>thereof?</s></p><p type="main"> <s>Fourthly, it ſerves as an Argument with me, to ſee that the <lb></lb>very individual perſons concerned in the Remotion or Diverſion <lb></lb>of the ſaid Torrent, namely, the <emph type="italics"></emph>Bologneſi<emph.end type="italics"></emph.end> do not incline unto it, <lb></lb>and that the whole City of <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> even thoſe very perſons who <lb></lb>at preſent receive damage by it, cannot indure to hear thereof. <lb></lb></s> <s>The reaſon that induceth theſe laſt named to be ſo averſe thereto, <lb></lb>is, either becauſe that this undertaking will render the introducti<lb></lb>on of the Water of <emph type="italics"></emph>Main-Po<emph.end type="italics"></emph.end> more difficult; or becauſe they fear <lb></lb>the danger thereof; The others decline the Project, either for <lb></lb>that they know that <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> cannot long continue in that Courſe, <lb></lb>or becauſe they fear that it is too much expoſed to thoſe mens re<lb></lb>vengeful Cutting of it who do not deſire it ſhould; and if a <lb></lb>man have any other wayes, he ought, in my opinion, to forbear <lb></lb>that, which to ſuch as ſtand in need of its Removal, is leſſe ſatiſ<lb></lb>factory, and to ſuch as oppoſe it, more prejudicial.</s></p><p type="main"> <s>To conclude, I exceedingly honour the judgment of Cardinal <lb></lb><emph type="italics"></emph>Capponi,<emph.end type="italics"></emph.end> who having to his Natural Ability and Prudence added <lb></lb>a particular Study, Obſervation, and Experience of theſe Wa<lb></lb>ters for the ſpace of three years together, doth not think that <lb></lb><emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> can go by <emph type="italics"></emph>Volana<emph.end type="italics"></emph.end>; to which agreeth the opinion of Car<lb></lb>dinal S. <emph type="italics"></emph>Marcello,<emph.end type="italics"></emph.end> Legate of this City, of whom, for his exqui<lb></lb>ſite underſtanding, we ought to make great account. </s> <s>But if e<lb></lb>ver this ſhould be reſolved on, it would be materially neceſſary <lb></lb>to unite the Quick and Running Waters of the little Chanel of <lb></lb><emph type="italics"></emph>Cento,<emph.end type="italics"></emph.end> of the Chanel <emph type="italics"></emph>Navilio,<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Guazzaloca,<emph.end type="italics"></emph.end> and at its very <lb></lb>beginning thoſe of <emph type="italics"></emph>Dardagna,<emph.end type="italics"></emph.end> which at preſent, is one of the <lb></lb>Springs or Heads of <emph type="italics"></emph>Panaro,<emph.end type="italics"></emph.end> that ſo they might aſſiſt it in carry<lb></lb>ing its Sand, and the matter of its Muddineſs into the Sea; and <lb></lb>then there would not fail to be a greater evacuation and ſcowr<lb></lb>ing; but withall the Proprietors in the Iſlet of <emph type="italics"></emph>San Giorgio<emph.end type="italics"></emph.end> and <lb></lb>of <emph type="italics"></emph>Ferrara<emph.end type="italics"></emph.end> muſt prepare themſelves to indure the inconveniences <lb></lb>of Purlings or Sewings of the Water from the River thorow <lb></lb>the Boggy Ground thereabouts.</s></p><p type="main"> <s>I ſhould more eaſily incline therefore to carry it into <emph type="italics"></emph>Main-Po<emph.end type="italics"></emph.end><lb></lb>at <emph type="italics"></emph>Stellata,<emph.end type="italics"></emph.end> for the Reaſons that Cardinal <emph type="italics"></emph>Capponi<emph.end type="italics"></emph.end> moſt ingeni<lb></lb>ouſly enumerates in a ſhort, but well-grounded Tract of his: not <pb xlink:href="040/01/673.jpg" pagenum="107"></pb>becauſe that indeed it would not both by Purlings and by Brea<lb></lb>ches occaſion ſome inconvenience; eſpecially, in the beginning: <lb></lb>but becauſe I hold this for the incomodities of it, to be a far leſs <lb></lb>evil than any of the reſt; and becauſe that by this means there is <lb></lb>no occaſion given to them of <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> to explain that they are <lb></lb>deprived of the hope of ever ſeeing the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> again under the Walls <lb></lb>of their City: To whom, where it may be done, it is but reaſon <lb></lb>that ſatisfaction ſhould be given.</s></p><p type="main"> <s>It is certain that P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> was placed by Nature in the midſt of this <lb></lb>great Valley made by the <emph type="italics"></emph>Appennine<emph.end type="italics"></emph.end> Hills, and by the Alps, to <lb></lb>carry, as the Maſter-Drain to the Sea, that is the grand receptacle <lb></lb>of all Waters; thoſe particular ſtreams which deſcend from <lb></lb>them.</s></p><p type="main"> <s>That the <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> by all Geographers, <emph type="italics"></emph>Strabo, Pliuy, Solimas, <lb></lb>Mella,<emph.end type="italics"></emph.end> and others is enumerated among the Rivers that fall into <lb></lb>the ſaid P<emph type="italics"></emph>o.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>That although P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> ſhould of it ſelf change its courſe, yet would <lb></lb><emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> go to look it out, if the works erected by humane ind uſtry <lb></lb>did not obſtruct its paſſage; ſo that it neither is, nor ought to <lb></lb>ſeem ſtrange, if one for the greater common good ſhould turn it <lb></lb>into the ſame.</s></p><p type="main"> <s>Now at <emph type="italics"></emph>Stellata<emph.end type="italics"></emph.end> it may go ſeveral waies into P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> as appeareth <lb></lb>by the levels that were taken by my Order; of all which I ſhould <lb></lb>beſt like the turning of it to <emph type="italics"></emph>la Botta de' Ghiſlieri,<emph.end type="italics"></emph.end> carrying it <lb></lb>above <emph type="italics"></emph>Bondeno<emph.end type="italics"></emph.end> to the Church of <emph type="italics"></emph>Gambarone,<emph.end type="italics"></emph.end> or a little higher or <lb></lb>lower, as ſhall be judged leaſt prejudicial, when it cometh to the <lb></lb>execution, and this for two principal reaſons: The one becauſe <lb></lb>that then it will run along by the confines of the Church P tri<lb></lb>mony, without ſeparating <emph type="italics"></emph>Ferrara<emph.end type="italics"></emph.end> from the reſt of it; The other <lb></lb>is, Becauſe the Line is ſhorter, and conſequently the fall greater; <lb></lb>for that in a ſpace of ten miles and one third, it falleth twenty ſix <lb></lb>feet, more by much than is required by Artiſts; and would go <lb></lb>by places where it could do but little hurt, notwithſtanding that <lb></lb>the perſons interreſſed ſtudy to amplifie it incredibly.</s></p><p type="main"> <s>On the contrary, there are but onely two objections that are <lb></lb>worthy to be examined; One, That the Drains and Ditches of <lb></lb>S. <emph type="italics"></emph>Bianca,<emph.end type="italics"></emph.end> of the Chanel of <emph type="italics"></emph>Cento,<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Burana,<emph.end type="italics"></emph.end> and all thoſe <lb></lb>others that enter into P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> do hinder this diverſion of <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> by the <lb></lb>encreaſing of the waters in the P<emph type="italics"></emph>o.<emph.end type="italics"></emph.end> The other is that P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> riſing <lb></lb>about the Tranſom of the <emph type="italics"></emph>Pilaſter<emph.end type="italics"></emph.end>-Sluice, very near 20 feet, the <lb></lb><emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> would have no fall into the ſame; whereupon it would riſe <lb></lb>to a terrible height, at which it would not be poſſible to make, or <lb></lb>keep the Banks made, ſo that it would break out and drown <lb></lb>the Meadowes, and cauſe miſchiefs, and damages unſpeakable <lb></lb>and irreparable; as is evident by the experiment made upon <pb xlink:href="040/01/674.jpg" pagenum="108"></pb><emph type="italics"></emph>Panaro,<emph.end type="italics"></emph.end> which being confined between Banks, that it might go <lb></lb>into P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> this not being neither in its greateſt excreſcenſe, it broke <lb></lb>out into the territories of <emph type="italics"></emph>Final,<emph.end type="italics"></emph.end> and of <emph type="italics"></emph>Ferrara.<emph.end type="italics"></emph.end> And though <lb></lb>that might be done, it would thereupon enſue, that there being <lb></lb>let into the Chanel of P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> 2800, ſquare feet of water (for ſo much <lb></lb>we account thoſe of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Panaro,<emph.end type="italics"></emph.end> taken together in their <lb></lb>greateſt heights) the ſuperficies of it would riſe at leaſt four feet, <lb></lb>inſomuch that either it would be requiſite to raiſe its Banks all the <lb></lb>way unto the Sea, to the ſame height, which the treaſures of the <lb></lb><emph type="italics"></emph>Indies<emph.end type="italics"></emph.end> would not ſuffice to effect; or elſe there would be a neceſ<lb></lb>ſity of enduring exceſſive Breaches. </s> <s>To theſe two Heads are the <lb></lb>Arguments reduced, which are largely amplified againſt our opi<lb></lb>nion; and I ſhall anſwer firſt to the laſt, as moſt material.</s></p><p type="main"> <s>I ſay therefore, that there are three caſes to be conſidered: <lb></lb>Firſt, P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> high, and <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> low. </s> <s>Secondly, <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> high, and P<emph type="italics"></emph>o<emph.end type="italics"></emph.end><lb></lb>low. </s> <s>Thirdly, <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> and P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> both high together.</s></p><p type="main"> <s>As to the firſt and ſecond, there is no difficulty in them; for if <lb></lb>P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> ſhall not be at its greateſt height, <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> ſhall ever have a fall <lb></lb>into it, and there ſhall need no humane Artifice about the Banks: <lb></lb>And if <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> ſhall be low, P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> ſhall regurgitate and flow up into <lb></lb>the Chanel of it; and alſo from thence no inconvenience ſhall <lb></lb>follow. </s> <s>The third remains, from which there are expected ma<lb></lb>ny miſchiefs; but it is a moſt undoubted truth, that the excreſcen<lb></lb>cies of <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> as coming from the adjacent <emph type="italics"></emph>Appennines<emph.end type="italics"></emph.end> and Rains, <lb></lb>are to continue but ſeven, or eight hours at moſt, and ſo would <lb></lb>never, or very rarely happen to be at the ſame time with thoſe of <lb></lb>P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> cauſed by the melting of the ſnowes of the Alps, at leaſt 400. <lb></lb>miles diſtance from thence. </s> <s>But becauſe it ſometimes may hap<lb></lb>pen, I reply, that when it cometh to paſs, <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> ſhall not go into <lb></lb>P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> but it ſhall have allowed it one or two Vents; namely, into <lb></lb>the Chanel of <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> as it hath ever had; and into <emph type="italics"></emph>Sanmartina,<emph.end type="italics"></emph.end><lb></lb>where it runneth at preſent, and wherewith there is no doubt, but <lb></lb>that the perſons concerned will be well pleaſed, it being a great <lb></lb>benefit to them, to have the water over-flow their grounds once <lb></lb>every four or five years, inſtead of ſeeing it anoy them continu<lb></lb>ally. </s> <s>Yea, the Vent may be regulated, reſerving for it the Cha<lb></lb>nel in which <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> at preſent runneth; and inſtead of turning it <lb></lb>by a Dam at <emph type="italics"></emph>la Betta de Chiſlieri,<emph.end type="italics"></emph.end> perhaps, to turn it by help of <lb></lb>ſtrong Sluices, that may upon all occaſions be opened and ſhut. <lb></lb></s> <s>And for my part, I do not queſtion but that the Proprietors <lb></lb>themſelves in <emph type="italics"></emph>Sanmartina<emph.end type="italics"></emph.end> would make a Chanel for it; which <lb></lb>receiving, and confining it in the time of the Vents, might carry <lb></lb>the Sand into the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Primaro:<emph.end type="italics"></emph.end> Nor need there thence be fear<lb></lb>ed any ſtoppage by Mud and Sand, ſince that it is ſuppoſed that <lb></lb>there will but very ſeldom be any neceſſity of uſing it; ſo that <pb xlink:href="040/01/675.jpg" pagenum="109"></pb>time would be allowed, upon occaſion, to ſcowr and cleanſe <lb></lb>it.</s></p><p type="main"> <s>And in this manner all thoſe Prodigies vaniſh that are raiſed <lb></lb>with ſo much fear from the enterance of the Water of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end><lb></lb>ſwelled into P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> when it is high, to which there needeth no other <lb></lb>anſwer; yet nevertheleſſe we do not take that quantity of Wa<lb></lb>ter, that is carried by <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> and by <emph type="italics"></emph>Panaro,<emph.end type="italics"></emph.end> to be ſo great as is affir<lb></lb>med: For that P. D. <emph type="italics"></emph>Benedetto Caſtelli<emph.end type="italics"></emph.end> hath no leſſe accutely <lb></lb>than accurately obſerved the meaſures of this kind, noting that <lb></lb>the breadth and depth of a River is not enough to reſolve the <lb></lb>queſtion truly, but that there is reſpect to be had to the velocity <lb></lb>of the Waters, and the term of time, things hitherto not conſi<lb></lb>dered by the Skilful in theſe affairs; and therefore they are not <lb></lb>able to ſay what quantity of Waters the ſaid Rivers carry, nor <lb></lb>to conclude of the riſings that will follow thereupon. </s> <s>Nay, it <lb></lb>is moſt certain, that if all the Rivers that fall into <emph type="italics"></emph>Po,<emph.end type="italics"></emph.end> which are <lb></lb>above thirty, ſhould riſe at the rate that theſe compute <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> to <lb></lb>do, an hundred feet of Banks would not ſuffice, and yet they <lb></lb>have far fewer: So that this confirmes the Rule of R. P. D. <emph type="italics"></emph>Bene<lb></lb>detto,<emph.end type="italics"></emph.end> namely, that the proportion of the height of the Water <lb></lb>of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> to the height of the Water of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> in P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> is <lb></lb>compounded of the proportion of the breadth of the Chanel of <lb></lb><emph type="italics"></emph>Po<emph.end type="italics"></emph.end> to that of <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> and of the velocity of the Water of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end><lb></lb>in <emph type="italics"></emph>Po<emph.end type="italics"></emph.end> to the velccity of the Water of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end>; a manifeſt <lb></lb>argument that there cannot in it, by this new augmentation of <lb></lb>Waters follow any alteration that neceſſitates the raiſing of its <lb></lb>Banks, as appeareth by the example of <emph type="italics"></emph>Panaro,<emph.end type="italics"></emph.end> which hath been <lb></lb>ſo far from ſwelling P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> that it hath rather aſſwaged it, for it hath <lb></lb>carried away many Shelfs and many Iſlets that had grown in its <lb></lb>Bed, for want of Waters ſufficient to bear away the matter of <lb></lb>Land-floods in ſo broad a Chanel; and as is learnt by the trial <lb></lb>made by us in <emph type="italics"></emph>Panaro<emph.end type="italics"></emph.end> with the Water of <emph type="italics"></emph>Burana<emph.end type="italics"></emph.end>; for erecting <lb></lb>in the River ſtanding marks, and ſhutting the ſaid Sluice, we could <lb></lb>ſee no ſenſible abatement, nor much leſs after we had opened it <lb></lb>ſenſible increaſment; by which we judge that the ſame is to ſuc<lb></lb>ceed to P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> by letting in of <emph type="italics"></emph>Reno, Burana<emph.end type="italics"></emph.end> having greater pro<lb></lb>portion to <emph type="italics"></emph>Panaro<emph.end type="italics"></emph.end> than <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> to P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> conſidering the ſtate of thoſe <lb></lb>Rivers in which the Obſervation was made. </s> <s>So that there is no <lb></lb>longer any occaſion for thoſe great raiſings of Banks, and the <lb></lb>danger of the ruptures as well of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> as of P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> do vaniſh, as al<lb></lb>ſo the fear leſt that the Sluices which empty into P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> ſhould re<lb></lb>ceive obſtruction: which if they ſhould, yet it would be over in <lb></lb>a few hours. </s> <s>And as to the Breaches of <emph type="italics"></emph>Panaro<emph.end type="italics"></emph.end> which happened <lb></lb>in 1623. I know not why, ſeeing that it is confeſſed that the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end><lb></lb>was not, at that time, at its height, one ſhould rather charge it <pb xlink:href="040/01/676.jpg" pagenum="110"></pb>with the crime, than quit it thereof. </s> <s>The truth is, that the <lb></lb>Bank was not made of proof, ſince that the ſame now continu<lb></lb>eth whole and good, and <emph type="italics"></emph>Panaro<emph.end type="italics"></emph.end> doth not break out; nay, there <lb></lb>was, when it brake more than a foot and half of its Banks above <lb></lb>the Water, and to ſpare; but it broke thorow by a Moles wor<lb></lb>king, or by the hole of a Water-Rat, or ſome ſuch vermine; <lb></lb>and by occaſion of the badneſs of the ſaid Banks, as I finde by <lb></lb>the teſtimony of ſome witneſſes examined by my command, that <lb></lb>I might know the truth thereof. </s> <s>Nor can I here forbear to ſay, <lb></lb>that it would be better, if in ſuch matters men were more candid <lb></lb>and ſincere. </s> <s>But to ſecure our ſelves nevertheleſſe, to the ut<lb></lb>moſt of our power, from ſuch like Breaches which may happen <lb></lb>at the firſt, by reaſon of the newneſſe of the Banks, I preſuppoſe <lb></lb>that from P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> unto the place whence <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> is cut, there ought to <lb></lb>be a high and thick Fence made with its Banks, ſo that there <lb></lb>would be no cauſe to fear any whatſoever acceſſions of Water, <lb></lb>although that concurrence of three Rivers, which was by ſome <lb></lb>more ingeniouſly aggravated than faithfully ſtated by that which <lb></lb>was ſaid above were true; to whom I think not my ſelf bound <lb></lb>to make any farther reply, neither to thoſe who ſay that <emph type="italics"></emph>Po<emph.end type="italics"></emph.end> will <lb></lb>aſcend upwards into <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> ſince that theſe are the ſame perſons <lb></lb>who would introduce a ſmall branch of the ſaid P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> into the <lb></lb>Chanel of <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> that ſo it may conveigh to the Sea, not <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end><lb></lb>onely, but alſo all the other Brooks of which we complained; <lb></lb>and becauſe that withal it is impoſſible, that a River ſo capacious <lb></lb>as <emph type="italics"></emph>Po<emph.end type="italics"></emph.end> ſhould be incommoded by a Torrent, that, as I may ſay, <lb></lb>hath no proportion to it.</s></p><p type="main"> <s>I come now to the buſineſſe of the Ditches and Draines; and <lb></lb>as to the Conveyance of <emph type="italics"></emph>Burana,<emph.end type="italics"></emph.end> it hath heretofore been deba<lb></lb>ted to turn it into <emph type="italics"></emph>Main-Po,<emph.end type="italics"></emph.end> ſo that in this caſe it will receive no <lb></lb>harm, and though it were not removed, yet would it by a Trench <lb></lb>under ground purſue the courſe that it now holdeth, and alſo <lb></lb>would be able to diſ-imbogue again into the ſaid new Chanel of <lb></lb><emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> which conforming to the ſuperficies of the Water of <emph type="italics"></emph>Po,<emph.end type="italics"></emph.end><lb></lb>would continue at a lower level than that which <emph type="italics"></emph>Panara<emph.end type="italics"></emph.end> had <lb></lb>when it came to <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> into which <emph type="italics"></emph>Burana<emph.end type="italics"></emph.end> did nevertheleſſe <lb></lb>empty it ſelf for ſome time.</s></p><p type="main"> <s>The Conveyance or Drain of <emph type="italics"></emph>Santa Bianca,<emph.end type="italics"></emph.end> and the little <lb></lb>Chanel of <emph type="italics"></emph>Cento<emph.end type="italics"></emph.end> may alſo empty themſelves by two ſubterranean <lb></lb>Trenches, without any prejudice where they run at preſent, or <lb></lb>without any more works of that nature, they may be turned into <lb></lb>the ſaid new Chanel, although with ſomewhat more of incon<lb></lb>venience; and withall, the Chanel of <emph type="italics"></emph>Ferrara,<emph.end type="italics"></emph.end> left dry, would <lb></lb>be a ſufficient receptacle for any other Sewer or Drain whatſoe<lb></lb>ver, that ſhould remain there.</s></p><pb xlink:href="040/01/677.jpg" pagenum="111"></pb><p type="main"> <s>All which Operations might be brought to perfection with <lb></lb>150. thouſand Crowns, well and faithfully laid out; which ſumm <lb></lb>the <emph type="italics"></emph>Bologneſi<emph.end type="italics"></emph.end> will not be unwilling to provide; beſides that thoſe <lb></lb><emph type="italics"></emph>Ferrareſi<emph.end type="italics"></emph.end> ought to contribute to it, who ſhall partake of the <lb></lb>benefit.</s></p><p type="main"> <s>Let me be permitted in this place to propoſe a thing which I <lb></lb>have thought of, and which peradventure might occaſion two <lb></lb>benefits at once, although it be not wholly new. </s> <s>It was in the <lb></lb>time of <emph type="italics"></emph>Pope Paul<emph.end type="italics"></emph.end> V. propounded by one <emph type="italics"></emph>Creſcenzio<emph.end type="italics"></emph.end> an Ingi<lb></lb>neer, to cut the <emph type="italics"></emph>Main-Po,<emph.end type="italics"></emph.end> above <emph type="italics"></emph>le Papozze<emph.end type="italics"></emph.end>; and having made a <lb></lb>ſufficient evacuation to derive the water thereof into the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <lb></lb><emph type="italics"></emph>Adriano,<emph.end type="italics"></emph.end> and ſo to procure it to be Navigable, which was not at <lb></lb>that time effected, either by reaſon of the oppoſitions of thoſe, <lb></lb>whoſe poſſeſſions were to be cut thorow, or by reaſon of the <lb></lb>great ſum of money that was neceſſary for the effecting of it: But <lb></lb>in viewing thoſe Rivers, we have obſerved, that the ſedge cutting <lb></lb>might eaſily be made below <emph type="italics"></emph>le Papozze,<emph.end type="italics"></emph.end> in digging thorow the <lb></lb>Bank called <emph type="italics"></emph>Santa Maria,<emph.end type="italics"></emph.end> & drawing a Trench of the bigneſs that <lb></lb>skilful Artiſts ſhall judge meet unto the P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> ^{*} of <emph type="italics"></emph>Ariano,<emph.end type="italics"></emph.end> below the <lb></lb><arrow.to.target n="marg982"></arrow.to.target><lb></lb><emph type="italics"></emph>Secche<emph.end type="italics"></emph.end> of the ſaid S. <emph type="italics"></emph>Maria<emph.end type="italics"></emph.end>; which as being a work of not <lb></lb>above 160. Perches in length, would be finiſhed with onely <lb></lb>12000. Crowns.</s></p><p type="margin"> <s><margin.target id="marg982"></margin.target>* Of <emph type="italics"></emph>Adriano.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Firſt; it is to be believed, that the waters running that way, <lb></lb>would not fail to open that Mouth into the Sea, which at pre<lb></lb>ſent is almoſt choakt up by the Shelf of Sand, which the new <lb></lb>Mouth of <emph type="italics"></emph>Ponto Virro<emph.end type="italics"></emph.end> hath brought thither; and that it would <lb></lb>again bring into uſe the Port <emph type="italics"></emph>Goro,<emph.end type="italics"></emph.end> and its Navigation.</s></p><p type="main"> <s>And haply experience might teach us, that the ſuperficies of <lb></lb>P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> might come to fall by this aſſwagement of Water, ſo that the <lb></lb>acceſſion of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> would queſtionleſs make no riſing in it: <lb></lb>Whereupon, if it ſhould ſo fall out, thoſe Princes would have <lb></lb>no reaſon to complain; who ſeem to queſtion, leſt by this new <lb></lb>acceſſion of water into P<emph type="italics"></emph>o,<emph.end type="italics"></emph.end> the Sluices might be endangered. <lb></lb></s> <s>Which I thought not fit to omit to repreſent to your Lordſhip; <lb></lb>not, that I propoſe it to you as a thing abſolutely certain, but that <lb></lb>you might, if you ſo pleaſed, lay it before perſons whoſe judge<lb></lb>ments are approved in theſe affairs.</s></p><p type="main"> <s>I return now from where I degreſt, and affirm it as indubita<lb></lb>ble, that <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end> neither can, nor ought to continue longer where <lb></lb>it at this day is; and that it cannot go into any other place but <lb></lb>that, whither <emph type="italics"></emph>Cardinal Capponi<emph.end type="italics"></emph.end> deſigned to carry it, and which <lb></lb>at preſent pleaſeth me better than any other; or into <emph type="italics"></emph>Volana,<emph.end type="italics"></emph.end><lb></lb>whence it was taken away; the vigilance of Men being able to <lb></lb>obviate part of thoſe miſchiefs, which it may do there.</s></p><p type="main"> <s>But from its Removal, beſides the alleviation of the harm <pb xlink:href="040/01/678.jpg" pagenum="112"></pb>which by it ſelf is cauſed, there would alſo reſult the diminution <lb></lb>of that which is occaſioned by the other Brooks, to the right hand <lb></lb>of the <emph type="italics"></emph>Po<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Argenta<emph.end type="italics"></emph.end>; foraſmuch as the ſaid <emph type="italics"></emph>Po<emph.end type="italics"></emph.end> wanting all the <lb></lb>water of <emph type="italics"></emph>Reno,<emph.end type="italics"></emph.end> it would of neceſſity come to ebb in ſuch man<lb></lb>ner, that the Valleys would have a greater Fall into the ſame, <lb></lb>and conſequently it would take in, and ſwallow greater abun<lb></lb>dance of water; and by this means the Ditches and Draines <lb></lb>of the Up-Lands would likewiſe more eaſily Fall into them; eſ<lb></lb>pecially if the ſcouring of <emph type="italics"></emph>Zenzalino<emph.end type="italics"></emph.end> were brought to perfection, <lb></lb>by which the waters of <emph type="italics"></emph>Marrara<emph.end type="italics"></emph.end> would fall into <emph type="italics"></emph>Marmorta<emph.end type="italics"></emph.end>: And <lb></lb>if alſo that of <emph type="italics"></emph>Baſtia<emph.end type="italics"></emph.end> were enlarged, and finiſhed, by which there <lb></lb>might enter as much water into the ſaid P<emph type="italics"></emph>o<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Argenta,<emph.end type="italics"></emph.end> as is taken <lb></lb>from it by the removal of <emph type="italics"></emph>Reno<emph.end type="italics"></emph.end>; although that by that meanes <lb></lb>the water of the Valleys would aſſwage double: Nor would the <lb></lb>people of <emph type="italics"></emph>Argenta,<emph.end type="italics"></emph.end> the Iſles of S. <emph type="italics"></emph>Giorgio,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Comacchio<emph.end type="italics"></emph.end> have any <lb></lb>cauſe to complain; for that there would not be given to them <lb></lb>more water than was taken away: Nay ſometimes whereas they <lb></lb>had Muddy waters, they would have clear; nor need they to fear <lb></lb>any riſing: And furthermore, by this means a very great quan<lb></lb>tity of ground would be reſtored to culture; For the effecting of <lb></lb>all which, the ſumm of 50. thouſand Crowns would go very far, <lb></lb>and would ſerve the turn at preſent touching thoſe Brooks, car<lb></lb>rying them a little farther in the mean time, to fill up the greater <lb></lb>cavities of the Valleys, that we might not enter upon a vaſter <lb></lb>and harder work, that would bring with it the difficulties of other <lb></lb>operations, and ſo would hinder the benefit which theſe people <lb></lb>expect from the paternal charity of His Holineſs.</s></p><pb xlink:href="040/01/679.jpg" pagenum="113"></pb><p type="head"> <s>TO <lb></lb>The Right Honourable, <lb></lb>MONSIGNORE <lb></lb>D. </s> <s>Ferrante Ceſarini.</s></p><p type="main"> <s>My Treatiſe of the MENSURATION of RUN<lb></lb>NING WATERS, Right Honourable, and <lb></lb>moſt Noble Sir, hath not a greater Preroga<lb></lb>tive than its having been the production of the <lb></lb>command of Pope <emph type="italics"></emph>Vrban<emph.end type="italics"></emph.end> VIII. when His Ho<lb></lb>lineſs was pleaſed to enjoyn me to go with <lb></lb><emph type="italics"></emph>Monſignore Corſini,<emph.end type="italics"></emph.end> in the Viſitation that was <lb></lb>impoſed upon him in the year 1625. of the Waters of <emph type="italics"></emph>Ferrara, <lb></lb>Bologna, Romagna,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Romagnola<emph.end type="italics"></emph.end>; for that, on that occaſion <lb></lb>applying my whole Study to my ſervice and duty, I publiſhed in <lb></lb>that Treatiſe ſome particulars till then not rightly underſtood and <lb></lb>conſidered (that I knew) by any one; although they be in them<lb></lb>ſelves moſt important, and of extraordinary conſequence. </s> <s>Yet <lb></lb>I muſt render thanks to Your Lordſhip for the honour you have <lb></lb>done to that my Tract; but wiſh withal, that your Eſteem of it <lb></lb>may not prejudice the univerſal Eſteem that the World hath of <lb></lb>Your Honours moſt refined judgement.</s></p><p type="main"> <s>As to that Point which I touch upon in the Concluſion, name<lb></lb>ly, That the conſideration of the Velocity of Running Water ſup<lb></lb>plyeth the conſideration of the ^{*} Length omitted in the common <lb></lb><arrow.to.target n="marg983"></arrow.to.target><lb></lb>way of meaſuring Running Waters; Your Lordſhip having com<lb></lb>manded me that in favour of <emph type="italics"></emph>Practiſe,<emph.end type="italics"></emph.end> and for the perfect diſco<lb></lb>very of the diſorder that commonly happeneth now adayes in <lb></lb>the diſtribution of the Waters of Fountains, I ſhould demon<lb></lb>ſtrate that the knowledge of the Velocity ſerveth for the finding <lb></lb>of the Length: I have thought fit to ſatisfie your Command by <lb></lb>relating a Fable; which, if I do not deceive my ſelf, will make <lb></lb>out to us the truth thereof; inſomuch that the reſt of my Treatiſe <lb></lb>ſhall thereby alſo become more manifeſt and intelligible, even to <pb xlink:href="040/01/680.jpg" pagenum="432"></pb>thoſe who finde therein ſome kinde of obſcurity.</s></p><p type="margin"> <s><margin.target id="marg983"></margin.target>* Larghezza, but <lb></lb>miſprinted.</s></p><p type="main"> <s>In the dayes of yore, before that the admirable Art of Wea<lb></lb>ving was in uſe, there was found in <emph type="italics"></emph>Perſia<emph.end type="italics"></emph.end> a vaſtand unvaluable <lb></lb>Treaſure, which conſiſted in an huge multitude of pieces of Er<lb></lb>meſin, or Damask, I know not whether; which, as I take it, <lb></lb>amounted to near two thouſand pieces; which were of ſuch a <lb></lb>nature, that though their Breadth and Thickneſs were finite and <lb></lb>determinate, as they uſe to be at this day; yet nevertheleſs, their <lb></lb>Length was in a certain ſenſe infinite, for that thoſe two thouſand <lb></lb>pieces, day and night without ceaſing, iſſued out with their ends <lb></lb>at ſuch a rate, that of each piece there iſſued 100. Ells a day, from <lb></lb>a deep and dark Cave, conſecrated by the Superſtition of thoſe <lb></lb>people, to the fabulous <emph type="italics"></emph>Arachne.<emph.end type="italics"></emph.end> In thoſe innocent and early <lb></lb>times (I take it to have been, in that ſo much applauded and <lb></lb>deſired Golden age) it was left to the liberty of any one, to cut <lb></lb>off of thoſe pieces what quantity they pleaſed without any diffi<lb></lb>culty: But that felicity decaying and degenerating, which was <lb></lb>altogether ignorant of <emph type="italics"></emph>Meum<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Tuum<emph.end type="italics"></emph.end>; terms certainly moſt <lb></lb>pernicious, the Original of all evils, and cauſe of all diſcords; <lb></lb>there were by thoſe people ſtrong and vigilant Guards placed <lb></lb>upon the Cave, who reſolved to make merchandize of the Stuffes; <lb></lb>and in this manner they began to ſet a price upon that ineſtima<lb></lb>ble Treaſure, ſelling the propriety in thoſe pieces to divers Mer<lb></lb>chants; to ſome they ſold a right in one, to ſome in two, and to <lb></lb>ſome in more. </s> <s>But that which was the worſt of all, There was <lb></lb>found out by the inſatiable avarice of theſe men crafty inventions <lb></lb>to deceive the Merchants alſo; who came to buy the aforeſaid <lb></lb>commodity, and to make themſelves Maſters, ſome of one <lb></lb>ſome of two, and ſome of more ends of thoſe pieces of ſtuff; <lb></lb>and in particular, there were certain ingenuous Machines placed <lb></lb>in the more ſecret places of the Cave, with which at the pleaſure <lb></lb>of the Guards, they did retard the velocity of thoſe Stuffs, in <lb></lb>their iſſuing out of the Cave; inſomuch, that he who ought to have <lb></lb>had 100. Ells of Stuff in a day, had not above 50, and he who <lb></lb>ſhould have had 400, enjoyed the benefit of 50. onely; and ſo all <lb></lb>the reſt were defrauded of their Rights, the ſurpluſage being ſold, <lb></lb>appropriated, and ſhared at the will of the corrupt Officers: So <lb></lb>that the buſineſs was without all order or juſtice, inſomuch that <lb></lb>the Goddeſs <emph type="italics"></emph>Arachne<emph.end type="italics"></emph.end> being diſpleaſed at thoſe people, deprived <lb></lb>every one of their benefit, and with a dreadful Earthquake for <lb></lb>ever cloſing the mouth of the Cave, in puniſhment of ſo much <lb></lb>impiety and malice: Nor did it avail them to excuſe themſelves, <lb></lb>by ſaying that they allowed the Buyer the Breadth and Thick<lb></lb>neſs bargained for; and that of the Length, which was infinite, <pb xlink:href="040/01/681.jpg" pagenum="115"></pb>there could no account be kept: For the wiſe and prudent <lb></lb>Prieſt of the Sacred <emph type="italics"></emph>Grotto<emph.end type="italics"></emph.end> anſwered, That the deceit lay in the <lb></lb>length, which they were defrauded of, in that the velocity of the <lb></lb>ftuffe was retarded, as it iſſued out of the Cave: and although <lb></lb>the total length of the Piece was infinite, for that it never cea<lb></lb>ſed coming forth, and ſo was not to be computed; yet never<lb></lb>theleſs its length conſidered, part by part, as it came out of the <lb></lb>Cave, and was bargained for, continued ſtill finite, and might <lb></lb>be one while greater, and another while leſſer, according as the <lb></lb>Piece was conſtituted in greater or leſſer velocity; and he added <lb></lb>withall, that exact Juſtice required, that when they ſold a piece <lb></lb>of ſtuff, and the propriety or dominion therein, they ought not <lb></lb>only to have aſcertained the breadth and thickneſſe of the Piece, <lb></lb>but alſo to have determined the length, determining its ve<lb></lb>locity.</s></p><p type="main"> <s>The ſame diſorder and confuſion, that was repreſented in the <lb></lb>Fable, doth come to paſſe in the Hiſtory of the Diſtribution of <lb></lb>the Waters of Conduits and Fountains, ſeeing that they are ſold <lb></lb>and bought, having regard only to the two Dimenſions, I mean <lb></lb>of Breadth and Height of the Mouth that diſchargeth the Wa<lb></lb>ter; and to remedy ſuch an inconvenience, it is neceſſary to de<lb></lb>termine the length in the velocity; for never ſhall we be able to <lb></lb>make a gueſſe at the quantity of the Body of Running Water, <lb></lb>with the two Dimenſions only of Breadth and Height, without <lb></lb>Length.</s></p><p type="main"> <s>And to the end, that the whole buſineſs may be reduced <lb></lb>to a moſt eaſie practice, by which the waters of Aqueducts <lb></lb>may be bought and ſold juſtly, and with meaſures alwayes ex<lb></lb>act and conſtant.</s></p><p type="main"> <s>Firſt, the quantity of the Water ought diligently to be exa<lb></lb>mined, which the whole principal ^{*} Pipe diſchargeth in a time <lb></lb>certain, as for inſtance, in an hour, in half an hour, or in a leſſe <lb></lb>interval of time, (for knowing which I have a moſt exact and <lb></lb>eaſie Rule) and finding that the whole principal pipe diſchar<lb></lb>geth <emph type="italics"></emph>v. </s> <s>g.<emph.end type="italics"></emph.end> a thouſand Tuns of Water in the ſpace of one or <lb></lb>more hours, in ſelling of this water, it ought not to be uttered by <lb></lb>the ordinary and falſe meaſure, but the diſtribution is to be <lb></lb>made with agreement to give and maintain to the buyer ten or <lb></lb>twenty, or a greater number of Tuns, as the bargain ſhall be <lb></lb>made, in the ſpace of an hour, or of ſome other ſet and deter<lb></lb>minate time. </s> <s>And here I adde, that if I were to undertake to <lb></lb>make ſuch an adjuſtment, I would make uſe of a way to divide <lb></lb>and meaſure the time with ſuch accurateneſſe, that the ſpace of <lb></lb>an hour ſhould be divided into four, ſix, or eight thouſand parts <pb xlink:href="040/01/682.jpg" pagenum="116"></pb>without the leaſt errour; which Rule was taught me by my <lb></lb>Maſter <emph type="italics"></emph>Sign. </s> <s>Galilæo Galilæi,<emph.end type="italics"></emph.end> Chief Philoſopher to the moſt Se<lb></lb>rene <emph type="italics"></emph>Grand Duke<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Tuſcany.<emph.end type="italics"></emph.end> And this way will ſerve eaſily and <lb></lb>admirably to our purpoſe and occaſion; ſo that we ſhall <lb></lb>thereby be able to know how many Quarts of Water an A<lb></lb>queduct will diſcharge in a given time of hours, moneths, or <lb></lb>years. </s> <s>And in this manner we may conſtitute a Cock that ſhall <lb></lb>diſcharge a certain and determinate quantity of water in a time <lb></lb>given.</s></p><p type="main"> <s>And becauſe daily experience ſhews us, that the Springs of A<lb></lb>queducts do not maintain them alwayes equally high, and full <lb></lb>of Water, but that ſometimes they increaſe, and ſometimes de<lb></lb>creaſe, which accident might poſſibly procure ſome difficulty in <lb></lb>our diſtribution: Therefore, to the end that all manner of ſcru<lb></lb>ple may be removed, I conceive that it would be convenient to <lb></lb>provide a Ciſtern, according to the occaſion, into which there <lb></lb>might alwayes fall one certain quantity of water, which ſhould <lb></lb>not be greater than that which the principal pipe diſchargeth in <lb></lb>times of drought, when the Springs are bare of water, that ſo in <lb></lb>this Ciſtern the water might alwayes keep at one conſtant height. <lb></lb></s> <s>Then to the Ciſtern ſo prepared we are to faſten the Cocks of <lb></lb>particular perſons, to whom the Water is ſold by the Reverend <lb></lb>Apoſtolique Chamber, according to what hath been obſerved <lb></lb>before; and that quantity of Water which remaineth over and <lb></lb>above, is to be diſcharged into another Ciſtern, in which the <lb></lb>Cocks of the Waters for publick ſervices, and of thoſe which <lb></lb>people buy upon particular occaſions are to be placed. </s> <s>And <lb></lb>when the buſineſſe ſhall have been brought to this paſſe, there <lb></lb>will likewiſe a remedy be found to the ſo many diſorders that <lb></lb>continually happen; of which, for brevity ſake, I will inſtance <lb></lb>in but four only, which concern both publique and private bene<lb></lb>fit, as being, in my judgment, the moſt enormous and intole<lb></lb>rable.</s></p><p type="main"> <s>The firſt inconvenience is, that in the common way of meaſu<lb></lb>ring, diſpenſing, and ſelling the Waters of Aqueducts, it is not <lb></lb>underſtood, neither by the Buyer nor Seller, what the quantity <lb></lb>truly is that is bought and ſold; nor could I ever meet with any <lb></lb>either Engineer or Architect, or Artiſt, or other that was able to <lb></lb>decypher to me, what one, or two, or ten inches of water was. <lb></lb></s> <s>But by our above declared Rule, for diſpenſing the Waters of <lb></lb>Aqueducts we may very eaſily know the true quantity of Water <lb></lb>that is bought or ſold, as that it is ſo many Tuns an hour, ſo ma<lb></lb>ny a day, ſo many in a year, &c.</s></p><p type="main"> <s>The ſecond diſorder that happeneth, at preſent, in the diſtri<pb xlink:href="040/01/683.jpg" pagenum="117"></pb>bution of Aqueducts is, that as the buſineſſe is now governed, it <lb></lb>lieth in the power of a ſordid Maſon to take unjuſtly from one, <lb></lb>and give undeſervedly to another more or leſſe Water than be<lb></lb>longeth to them of right: And I have ſeen it done, of my <lb></lb>own experience. </s> <s>But in our way of meaſuring and diſtri<lb></lb>buting Waters, there can no fraud be committed; and put<lb></lb>ting the caſe that they ſhould be committed, its an eaſie mat<lb></lb>ter to know it, and amend it, by repairing to the Tribunal <lb></lb>appointed.</s></p><p type="main"> <s>Thirdly, it happens very often, (and we have examples there<lb></lb>of both antient and modern) that in diſpenſing the Water after <lb></lb>the common and vulgar way; there is ſometimes more Water diſ<lb></lb>pended than there is in the Regiſter, in which there will be regi<lb></lb>ſtred, as they ſay, two hundred inches (for example) and there <lb></lb>will be diſpenſed two hundred and fifty inches, or more. </s> <s>Which <lb></lb>paſſage happened in the time of <emph type="italics"></emph>Nerva<emph.end type="italics"></emph.end> the Emperour, as <emph type="italics"></emph>Giulio <lb></lb>Frontino<emph.end type="italics"></emph.end> writes, in his 2. Book, <emph type="italics"></emph>De Aquaductibus Vrbis Romæ,<emph.end type="italics"></emph.end><lb></lb>where he obſerveth that they had <emph type="italics"></emph>in Commentariis 12755. Qui<lb></lb>naries<emph.end type="italics"></emph.end> of Water; and found that they diſpenſed 14018. <emph type="italics"></emph>Qui<lb></lb>naries.<emph.end type="italics"></emph.end> And the like Errour hath continued, and is in uſe alſo <lb></lb>modernly until our times. </s> <s>But if our Rule ſhall be obſerved, <lb></lb>we ſhall incur no ſuch diſorder, nay there will alwayes be given <lb></lb>to every one his ſhare, according to the holy end of exact juſtice, <lb></lb>which <emph type="italics"></emph>dat unicuique quod ſuum eſt.<emph.end type="italics"></emph.end> As on the contrary, it is <lb></lb>manifeſt, that His Divine Majeſty hateth and abominateth <emph type="italics"></emph>Pon<lb></lb>dus & pondus, Menſura & menſura,<emph.end type="italics"></emph.end> as the Holy Ghoſt ſpeak<lb></lb>eth by the mouth of <emph type="italics"></emph>Solomon<emph.end type="italics"></emph.end> in the <emph type="italics"></emph>Proverbs, Chap. </s> <s>20. Pondus <lb></lb>& Pondus, Menſura & Menſura, utrumque abominabile eſt apud <lb></lb>Deum.<emph.end type="italics"></emph.end> And therefore who is it that ſeeth not that the way of <lb></lb>dividing and meaſuring of Waters, commonly uſed, is expreſly <lb></lb>againſt the Law of God. </s> <s>Since that thereby the ſame meaſure <lb></lb>is made ſometimes greater, and ſometimes leſſer; A diſorder ſo <lb></lb>enormous and execrable, that I ſhall take the boldneſs to ſay, that <lb></lb>for this ſole reſpect it ought to be condemned and prohibited like<lb></lb>wiſe by human Law, which ſhould Enact that in this buſineſs there <lb></lb>ſhould be imployed either this our Rule, or ſome other that <lb></lb>is more exquiſite and practicable, whereby the meaſure <lb></lb>might keep one conſtant and determinate tenor, as we make it, <lb></lb>and not, as it is now, to make <emph type="italics"></emph>Pondus & Pondus, Menſur a & <lb></lb>Menſura.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And this is all that I had to offer to Your moſt Illuſtrious <lb></lb>Lordſhip, in obedience to your commands, reſerving to my ſelf <lb></lb>the giving of a more exact account of this my invention, when <lb></lb>the occaſion ſhall offer, of reducing to practice ſo holy, juſt, and <pb xlink:href="040/01/684.jpg" pagenum="118"></pb>neceſſary a reformation of the Meaſure of Running Waters and <lb></lb>of Aqueducts in particular: which Rule may alſo be of great <lb></lb>benefit in the diviſion of the greater Waters to over-flow <lb></lb>Grounds, and for other uſes: I humbly bow,</s></p><p type="main"> <s><emph type="italics"></emph>Your Most Devoted,<emph.end type="italics"></emph.end><lb></lb>and <lb></lb><emph type="italics"></emph>Moſt Obliged Servant,<emph.end type="italics"></emph.end></s></p><p type="main"> <s>D. </s> <s>Benedetto Caſtelli, <emph type="italics"></emph>Abb. </s> <s>Caſin.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>FINIS.</s></p><pb xlink:href="040/01/685.jpg"></pb><p type="head"> <s>A TABLE</s></p><p type="head"> <s>Of the moſt obſervable matters in this Treatiſe of the <lb></lb>MENSURATION of RUNNING <lb></lb>WATERS.<lb></lb><arrow.to.target n="table74"></arrow.to.target></s></p><table><table.target id="table74"></table.target><row><cell>A</cell><cell></cell></row><row><cell>Abatements <emph type="italics"></emph>of a River in different and unequal Diverſions, is alwaies equal, which is proved with<emph.end type="italics"></emph.end> 100. Syphons.</cell><cell><emph type="italics"></emph>Page<emph.end type="italics"></emph.end> 75</cell></row><row><cell>Arno <emph type="italics"></emph>River when it riſeth upon a Land-Flood near the Sea one third of a Brace, it riſeth about<emph.end type="italics"></emph.end> Piſa 6. <emph type="italics"></emph>or 7. Braces.<emph.end type="italics"></emph.end></cell><cell>82</cell></row><row><cell>B</cell><cell></cell></row><row><cell><emph type="italics"></emph>Banks near to the Sea lower, than far from thence. Corollary<emph.end type="italics"></emph.end> XIV.</cell><cell>16</cell></row><row><cell>Brent <emph type="italics"></emph>River diverted from the Lake o<emph.end type="italics"></emph.end>f Venice, <emph type="italics"></emph>and its effects.<emph.end type="italics"></emph.end></cell><cell>64</cell></row><row><cell>Brent <emph type="italics"></emph>ſuppoſed inſufficient to remedy the inconveniences of the Lake, and the falſity of that ſuppoſition.<emph.end type="italics"></emph.end></cell><cell>67</cell></row><row><cell>Brent, <emph type="italics"></emph>and its benefits in the Lake.<emph.end type="italics"></emph.end></cell><cell>70</cell></row><row><cell><emph type="italics"></emph>Its Depoſition of Sand in the Lake, bow great it is.<emph.end type="italics"></emph.end></cell><cell>78, 79</cell></row><row><cell><emph type="italics"></emph>Bridges over Rivers, and how they are to be made. Appendix<emph.end type="italics"></emph.end> VIII.</cell><cell>20</cell></row><row><cell>Burana <emph type="italics"></emph>River, its riſing, and falling in<emph.end type="italics"></emph.end> Panaro.</cell><cell>110</cell></row><row><cell>C</cell><cell></cell></row><row><cell>Caſtelli <emph type="italics"></emph>applyed himſelf to this Study by Order of<emph.end type="italics"></emph.end> Urban VIII.</cell><cell>2</cell></row><row><cell>Chanel of Navigation <emph type="italics"></emph>in the Valleys of<emph.end type="italics"></emph.end> Bologna, <emph type="italics"></emph>and its inconveniences.<emph.end type="italics"></emph.end></cell><cell>99</cell></row><row><cell><emph type="italics"></emph>Carried into the<emph.end type="italics"></emph.end> Po <emph type="italics"></emph>of<emph.end type="italics"></emph.end> Ferrara, <emph type="italics"></emph>and its benefits<emph.end type="italics"></emph.end></cell><cell>ibid.</cell></row><row><cell>Ciampoli <emph type="italics"></emph>alover of theſe Obſervations of Waters.<emph.end type="italics"></emph.end></cell><cell>3</cell></row><row><cell>D</cell><cell></cell></row><row><cell><emph type="italics"></emph>Difficulty of this buſineſs of Meaſuring Waters.<emph.end type="italics"></emph.end></cell><cell>2</cell></row><row><cell><emph type="italics"></emph>Diſorders that happen in the diſtribution of the Waters of Aqueducts, and their re-medies.<emph.end type="italics"></emph.end></cell><cell>113</cell></row><row><cell><emph type="italics"></emph>Diſtribution of the Waters of Fountains, and Aqueducts. Appendix<emph.end type="italics"></emph.end> X.</cell><cell>22</cell></row><row><cell><emph type="italics"></emph>Diſtribution of Water to over-flow Grounds. Appendix<emph.end type="italics"></emph.end> XI.</cell><cell>23, 69, 70</cell></row><row><cell><emph type="italics"></emph>Diverſion of<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>and other Brooks of<emph.end type="italics"></emph.end> Romagna, <emph type="italics"></emph>adviſed by<emph.end type="italics"></emph.end> P. Spernazzati <emph type="italics"></emph>to what end it was.<emph.end type="italics"></emph.end></cell><cell>100</cell></row><row><cell><emph type="italics"></emph>Drains and Ditches, the benefit they receive by cutting away the Weeds and Reeds. Appendix<emph.end type="italics"></emph.end> IX.</cell><cell>21</cell></row><row><cell><emph type="italics"></emph>Drains and Sewers obſtructed, in the Diverſion of<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>into<emph.end type="italics"></emph.end> Main Po, <emph type="italics"></emph>and a remedy for the ſame.<emph.end type="italics"></emph.end></cell><cell>110</cell></row><row><cell>E</cell><cell></cell></row><row><cell><emph type="italics"></emph>Engineers unverſ'd in the matters of Waters.<emph.end type="italics"></emph.end></cell><cell>2</cell></row><row><cell><emph type="italics"></emph>Erour found in the common way of Meaſuring Running Waters.<emph.end type="italics"></emph.end></cell><cell>68, 69</cell></row><row><cell><emph type="italics"></emph>Errour in deriving the Water of<emph.end type="italics"></emph.end> Acqua Paola. <emph type="italics"></emph>Appendix<emph.end type="italics"></emph.end> II.</cell><cell>17, 18</cell></row><pb xlink:href="040/01/686.jpg"></pb><row><cell><emph type="italics"></emph>Errour of<emph.end type="italics"></emph.end> Bartolotti.</cell><cell>86, 87</cell></row><row><cell><emph type="italics"></emph>Errours of Engineers in the Derivation of Chenels. Corollary<emph.end type="italics"></emph.end> XII.</cell><cell>12</cell></row><row><cell><emph type="italics"></emph>Errour of Engineers in Meaſuring of<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>in<emph.end type="italics"></emph.end> Po. <emph type="italics"></emph>Appendix<emph.end type="italics"></emph.end> III.</cell><cell>ibid.</cell></row><row><cell><emph type="italics"></emph>Errour of other Engineers, contrary to the precedent. Appendix<emph.end type="italics"></emph.end> IV.</cell><cell>Ibid.</cell></row><row><cell><emph type="italics"></emph>Errour of<emph.end type="italics"></emph.end> Giovanni Fontana <emph type="italics"></emph>in Meaſuring Waters, Corollary<emph.end type="italics"></emph.end> XI.</cell><cell>9</cell></row><row><cell><emph type="italics"></emph>Errour of<emph.end type="italics"></emph.end> Giulio Frontino <emph type="italics"></emph>in Meaſuring the Waters of Aqueducts. Appen-dix<emph.end type="italics"></emph.end> I.</cell><cell>17</cell></row><row><cell><emph type="italics"></emph>Errours committed in cutting the Bank at<emph.end type="italics"></emph.end> Bondeno, <emph type="italics"></emph>in the ſwellings of<emph.end type="italics"></emph.end> Po: <emph type="italics"></emph>Corollary<emph.end type="italics"></emph.end>XIII.</cell><cell>81</cell></row><row><cell>F</cell><cell></cell></row><row><cell><emph type="italics"></emph>Fenns<emph.end type="italics"></emph.end> Pontine, <emph type="italics"></emph>Drained by Pope<emph.end type="italics"></emph.end> Sixtus Quintus, <emph type="italics"></emph>with vaſt expence.<emph.end type="italics"></emph.end></cell><cell>92</cell></row><row><cell><emph type="italics"></emph>The ruine and miſcarriage thereof.<emph.end type="italics"></emph.end></cell><cell>93</cell></row><row><cell><emph type="italics"></emph>Tardity of the principal Chanel that Drains them, cauſe of the Drowning.<emph.end type="italics"></emph.end></cell><cell>ibid.</cell></row><row><cell><emph type="italics"></emph>They are obſtructed by the Fiſhing-Wears, which ſuell the River.<emph.end type="italics"></emph.end></cell><cell>94</cell></row><row><cell><emph type="italics"></emph>Waters of<emph.end type="italics"></emph.end> Fiume Siſto, <emph type="italics"></emph>which flow in great abundance into the<emph.end type="italics"></emph.end> Evacuator <emph type="italics"></emph>of the ſaid Fenns.<emph.end type="italics"></emph.end></cell><cell>94, 95</cell></row><row><cell><emph type="italics"></emph>Remedies to the diſorders of thoſe Fenns.<emph.end type="italics"></emph.end></cell><cell>95, 96</cell></row><row><cell>Fontana Giovanni, <emph type="italics"></emph>his errours in Meaſuring Waters. Corollary<emph.end type="italics"></emph.end> XI.</cell><cell>9</cell></row><row><cell>Fiume Morto, <emph type="italics"></emph>whether it ought to fall into the Sea, or into<emph.end type="italics"></emph.end> Serchio,</cell><cell>79</cell></row><row><cell><emph type="italics"></emph>Let into<emph.end type="italics"></emph.end> Serchio <emph type="italics"></emph>and its inconveniences.<emph.end type="italics"></emph.end></cell><cell>79, 80</cell></row><row><cell><emph type="italics"></emph>The dangerous riſing of its Waters, when to be expected.<emph.end type="italics"></emph.end></cell><cell>81</cell></row><row><cell><emph type="italics"></emph>Its inconveniences when it is higher in level than<emph.end type="italics"></emph.end> Serchio, <emph type="italics"></emph>and why it riſeth moſt On the Sea-coaſts, at ſuch time as the Winds make the Sea to ſuell.<emph.end type="italics"></emph.end></cell><cell>83</cell></row><row><cell>G</cell><cell></cell></row><row><cell>Galilæo Galilæi. <emph type="italics"></emph>hoxourably mentioned.<emph.end type="italics"></emph.end></cell><cell><emph type="italics"></emph>Page<emph.end type="italics"></emph.end> 2, 28</cell></row><row><cell><emph type="italics"></emph>His Rule for meaſuring the time.<emph.end type="italics"></emph.end></cell><cell>49</cell></row><row><cell>H</cell><cell></cell></row><row><cell><emph type="italics"></emph>Height,<emph.end type="italics"></emph.end> vide <emph type="italics"></emph>Quick<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Heights different, made by the ſame ſtream of a Brock or Torrent, according to the divers Velocities in the entrance of the River. Corollary<emph.end type="italics"></emph.end> I.</cell><cell>6</cell></row><row><cell><emph type="italics"></emph>Heights different, made by the Torrent in the River, according to the different heights of the River. Corollary<emph.end type="italics"></emph.end> II.</cell><cell>ibid.</cell></row><row><cell>K</cell><cell></cell></row><row><cell><emph type="italics"></emph>Knowledge of Motion how much it importeth.<emph.end type="italics"></emph.end></cell><cell>1</cell></row><row><cell>L</cell><cell></cell></row><row><cell><emph type="italics"></emph>t<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Lake of<emph.end type="italics"></emph.end> Perugia, <emph type="italics"></emph>and, he Obſervation made on it. Appendix<emph.end type="italics"></emph.end> XII.</cell><cell>42</cell></row><row><cell><emph type="italics"></emph>Lake of<emph.end type="italics"></emph.end> Thraſimenus <emph type="italics"></emph>and Conſiderations upon it, a Letter written to<emph.end type="italics"></emph.end> Sig. Galilæo Galilæi.</cell><cell>28</cell></row><row><cell><emph type="italics"></emph>Lake of<emph.end type="italics"></emph.end> Venice, <emph type="italics"></emph>and Conſiderations upon it.<emph.end type="italics"></emph.end></cell><cell>63, 73</cell></row><row><cell><emph type="italics"></emph>Low Waters which let the bottom of it be diſcovered.<emph.end type="italics"></emph.end></cell><cell>64</cell></row><row><cell><emph type="italics"></emph>The ſtoppage and choaking of the Ports, a main cauſe of the diſorders of the Lake, and the grand remedy to thoſe diſorders what it is.<emph.end type="italics"></emph.end></cell><cell>66</cell></row><row><cell><emph type="italics"></emph>Lakes and Metrs along the Sea-coaſts, and the cauſes thereof.<emph.end type="italics"></emph.end></cell><cell>65</cell></row><row><cell><emph type="italics"></emph>Length of Waters, how it is to be Meaſured.<emph.end type="italics"></emph.end></cell><cell>70</cell></row><row><cell>M</cell><cell></cell></row><row><cell><emph type="italics"></emph>Meaſure and Diſtributions of Waters. Appendix<emph.end type="italics"></emph.end> V.</cell><cell>18</cell></row><pb xlink:href="040/01/687.jpg"></pb><row><cell><emph type="italics"></emph>Meaſure of Rivers that fall into others difficult. Coroll.<emph.end type="italics"></emph.end> X:</cell><cell>9</cell></row><row><cell><emph type="italics"></emph>Meaſure of the Running Water of a Chanel of an height known by a<emph.end type="italics"></emph.end> Regulator <emph type="italics"></emph>of a Mea-ſure given, in a time aſſigned. Propoſition<emph.end type="italics"></emph.end> I. <emph type="italics"></emph>Problem<emph.end type="italics"></emph.end> I.</cell><cell>50</cell></row><row><cell><emph type="italics"></emph>Meaſure of the Water of any River, of any greatneſs, in a time given. Propoſition<emph.end type="italics"></emph.end> V. <emph type="italics"></emph>Problem<emph.end type="italics"></emph.end> III.</cell><cell>60</cell></row><row><cell><emph type="italics"></emph>Meaſure that ſhewes how much Water a River diſchargeth in a time given.<emph.end type="italics"></emph.end></cell><cell>48</cell></row><row><cell><emph type="italics"></emph>Mole-holes,<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Motion the principal ſubject of Philoſophy.<emph.end type="italics"></emph.end></cell><cell>1</cell></row><row><cell><emph type="italics"></emph>Mud.<emph.end type="italics"></emph.end> Vide <emph type="italics"></emph>Sand.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell>N</cell><cell></cell></row><row><cell><emph type="italics"></emph>Navigation from<emph.end type="italics"></emph.end> Bologna <emph type="italics"></emph>to<emph.end type="italics"></emph.end> Ferrara, <emph type="italics"></emph>is become impoſſible, till ſuch time as<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>be diverted.<emph.end type="italics"></emph.end></cell><cell>101</cell></row><row><cell><emph type="italics"></emph>Navigation in the Lake of<emph.end type="italics"></emph.end> Venice <emph type="italics"></emph>endangered, and how restored.<emph.end type="italics"></emph.end></cell><cell>65, 70</cell></row><row><cell>P</cell><cell></cell></row><row><cell><emph type="italics"></emph>Perpendicularity of the Banks of the River, to the upper ſuperficies of it.<emph.end type="italics"></emph.end></cell><cell>37</cell></row><row><cell><emph type="italics"></emph>Perpendicularity of the Banks to the bottom.<emph.end type="italics"></emph.end></cell><cell>37</cell></row><row><cell><emph type="italics"></emph>Perugia.<emph.end type="italics"></emph.end> Vide <emph type="italics"></emph>Lake.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Pontine.<emph.end type="italics"></emph.end> Vide <emph type="italics"></emph>Fenns.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Ports of<emph.end type="italics"></emph.end> Venice, Malamocco, Bondolo, <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Chiozza, <emph type="italics"></emph>choaked up for want of Water in the Lake.<emph.end type="italics"></emph.end></cell><cell>65</cell></row><row><cell><emph type="italics"></emph>Proportions of unequal Sections of equal Velocity, and of equal Sections of unequal Velo-city. Axiome<emph.end type="italics"></emph.end> IV. <emph type="italics"></emph>and<emph.end type="italics"></emph.end> V.</cell><cell>38</cell></row><row><cell><emph type="italics"></emph>Proportions of equal and unequal quantities of Water, which paſs by the Sections of dif-ferent Rivers. Propoſition<emph.end type="italics"></emph.end> II.</cell><cell>39</cell></row><row><cell><emph type="italics"></emph>Proportions of unequal Sections that in equal times diſcharge equal quantities of Water. Propoſition<emph.end type="italics"></emph.end> III.</cell><cell>41</cell></row><row><cell><emph type="italics"></emph>Proportion wherewith one River falling into another, varieth in height. Propo-ſition<emph.end type="italics"></emph.end> IV.</cell><cell>44</cell></row><row><cell><emph type="italics"></emph>Proportion of the Water diſcharged by a River in the time of Flood, to the Water diſcharged in an equal time by the ſaid River, before or after the Flood. Propoſition<emph.end type="italics"></emph.end> V.</cell><cell>44</cell></row><row><cell><emph type="italics"></emph>Proportion of the Heights made by two equal Brooks or Streams falling into the ſame River. Propoſition<emph.end type="italics"></emph.end> VI.</cell><cell>45</cell></row><row><cell><emph type="italics"></emph>Proportion of the Water which a River diſchargeth encreaſing in Quick-height by the ad-dition of new Water, to that which it diſchargeth after the encreaſe is made. Propo-ſition<emph.end type="italics"></emph.end> IV. <emph type="italics"></emph>Theor.<emph.end type="italics"></emph.end> II.</cell><cell>54</cell></row><row><cell><emph type="italics"></emph>Proportion of a River when high, to it ſelf when low. Coroll.<emph.end type="italics"></emph.end> I.</cell><cell>55</cell></row><row><cell>Q</cell><cell></cell></row><row><cell><emph type="italics"></emph>Quantity of Running Waters is never certain, if with the Vulgar way of Meaſuring them, their Velocities be not conſidered.<emph.end type="italics"></emph.end></cell><cell>32</cell></row><row><cell><emph type="italics"></emph>Quantities of Waters which are diſcharged by a River, anſwer in equality to the Velocities and times in which they are diſcharged. Axiome<emph.end type="italics"></emph.end> I, II, III.</cell><cell>38</cell></row><row><cell>Quick-Height <emph type="italics"></emph>of a River, what it is. Definition<emph.end type="italics"></emph.end> V.</cell><cell>48</cell></row><row><cell>R</cell><cell></cell></row><row><cell><emph type="italics"></emph>Reaſon of the Proverb,<emph.end type="italics"></emph.end> Take heed of the ſtill Waters. <emph type="italics"></emph>Coroll.<emph.end type="italics"></emph.end> VI.</cell><cell>7</cell></row><row><cell><emph type="italics"></emph>Reaſons of<emph.end type="italics"></emph.end> Monſignore Corſini <emph type="italics"></emph>againſt the diverſion of<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>into the<emph.end type="italics"></emph.end> Po <emph type="italics"></emph>of<emph.end type="italics"></emph.end>Volano.</cell><cell>105</cell></row><row><cell><emph type="italics"></emph>Reaſons of<emph.end type="italics"></emph.end> Cardinal Capponi <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Monſig. Corſini, <emph type="italics"></emph>for the turning of<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>into Main<emph.end type="italics"></emph.end> Po.</cell><cell>106</cell></row><pb xlink:href="040/01/688.jpg"></pb><row><cell><emph type="italics"></emph>Two objections on the contrary, and anſwers to them.<emph.end type="italics"></emph.end></cell><cell>104 <emph type="italics"></emph>&<emph.end type="italics"></emph.end> 105</cell></row><row><cell><emph type="italics"></emph>What ought to be the proportion of the Heights of<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>in<emph.end type="italics"></emph.end> Reno, <emph type="italics"></emph>and of<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>in<emph.end type="italics"></emph.end>Po.</cell><cell>110</cell></row><row><cell><emph type="italics"></emph>Regulator what it is. Definition<emph.end type="italics"></emph.end> IV.</cell><cell>48</cell></row><row><cell><emph type="italics"></emph>Relation of the Waters of<emph.end type="italics"></emph.end> Bologna <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Ferrara, <emph type="italics"></emph>by<emph.end type="italics"></emph.end> Monſignore Corſini</cell><cell>100</cell></row><row><cell>Reno <emph type="italics"></emph>in the Valleys, and its bad effects.<emph.end type="italics"></emph.end></cell><cell>100, 101</cell></row><row><cell><emph type="italics"></emph>Two wayes to divert it.<emph.end type="italics"></emph.end></cell><cell>103</cell></row><row><cell><emph type="italics"></emph>The facility and utility of thoſe wayes.<emph.end type="italics"></emph.end></cell><cell>Ibid.</cell></row><row><cell><emph type="italics"></emph>The difficulties objected.<emph.end type="italics"></emph.end></cell><cell>104</cell></row><row><cell><emph type="italics"></emph>Reply to<emph.end type="italics"></emph.end> Bartolotti <emph type="italics"></emph>touching the dangers of turning<emph.end type="italics"></emph.end> Fiume Morto <emph type="italics"></emph>into<emph.end type="italics"></emph.end> Serchio.</cell><cell>83</cell></row><row><cell><emph type="italics"></emph>Retardment of the courſe of a River cauſed by its Banks. Appendix<emph.end type="italics"></emph.end> VII.</cell><cell>19</cell></row><row><cell><emph type="italics"></emph>Riſings made by Flood-Gates but ſmall. Appendix<emph.end type="italics"></emph.end> XIII.</cell><cell>26</cell></row><row><cell><emph type="italics"></emph>Rivers that are ſhallow ſwell much upon ſmall ſhowers, ſuch as are deep riſe but little upon great Floods. Corollary<emph.end type="italics"></emph.end> III.</cell><cell>6</cell></row><row><cell><emph type="italics"></emph>Rivers the higher they are, the ſwifter.<emph.end type="italics"></emph.end></cell><cell>Ibid.</cell></row><row><cell><emph type="italics"></emph>Rivers the higher they are, theleſſe they encreaſe upon Floods.<emph.end type="italics"></emph.end></cell><cell>49</cell></row><row><cell><emph type="italics"></emph>Rivers when they are to have equal and when like Velocity.<emph.end type="italics"></emph.end></cell><cell>Ibid.</cell></row><row><cell><emph type="italics"></emph>Rivers in falling into the Sea, form a Shelf of Sand called<emph.end type="italics"></emph.end> Cavallo.</cell><cell>65</cell></row><row><cell><emph type="italics"></emph>Five Rivers to be diverted from the Lake of<emph.end type="italics"></emph.end> Venice, <emph type="italics"></emph>and the inconveniences that would enſue thereupon.<emph.end type="italics"></emph.end></cell><cell>74, 75</cell></row><row><cell><emph type="italics"></emph>A River of Quick-height, and Velocity in its Regulator being given, if the Height be redoubled by new Water, it redoubleth alſo in Velocity. Propoſition<emph.end type="italics"></emph.end> II. <emph type="italics"></emph>The-orem<emph.end type="italics"></emph.end> I.</cell><cell>51</cell></row><row><cell><emph type="italics"></emph>Keepeth the proportion of the heights, to the Velocities. Corollary<emph.end type="italics"></emph.end></cell><cell>52</cell></row><row><cell>S</cell><cell></cell></row><row><cell><emph type="italics"></emph>Sand and Mud that entereth into the Lake of<emph.end type="italics"></emph.end> Venice, <emph type="italics"></emph>and the way to examine it.<emph.end type="italics"></emph.end></cell><cell>76</cell></row><row><cell><emph type="italics"></emph>Seas agitated and driven by the Winds ſtop up the Ports.<emph.end type="italics"></emph.end></cell><cell>64, 65</cell></row><row><cell><emph type="italics"></emph>Sections of a River what they are. Definition<emph.end type="italics"></emph.end> I.</cell><cell>37</cell></row><row><cell><emph type="italics"></emph>Sections equally ſwift what they are. Definition<emph.end type="italics"></emph.end> II.</cell><cell>Ibid.</cell></row><row><cell><emph type="italics"></emph>Sections of a River being given, to conceive others equal to them, of different breadth, height and Velocity. Petition.<emph.end type="italics"></emph.end></cell><cell>38</cell></row><row><cell><emph type="italics"></emph>Sections of the ſame River, and their Proportions to their Velocities. Coroll.<emph.end type="italics"></emph.end> I.</cell><cell>42</cell></row><row><cell><emph type="italics"></emph>Sections of a River diſcharge in any whatſoever place of the ſaid River, equal quantities of Water in equal times. Propoſition<emph.end type="italics"></emph.end> I.</cell><cell>39</cell></row><row><cell>Sile <emph type="italics"></emph>River what miſchiefes it threatneth, diverted from the Lake.<emph.end type="italics"></emph.end></cell><cell>74</cell></row><row><cell><emph type="italics"></emph>Spirtings of Waters grow bigger the higher they go. Coroll.<emph.end type="italics"></emph.end> XVI.</cell><cell>16</cell></row><row><cell><emph type="italics"></emph>Sreams of Rivers how they encreaſe and vary. Coroll.<emph.end type="italics"></emph.end> I.</cell><cell>6</cell></row><row><cell><emph type="italics"></emph>Streams retarded, and the effects thereof. Coroll.<emph.end type="italics"></emph.end> IX.</cell><cell>8</cell></row><row><cell>T</cell><cell></cell></row><row><cell><emph type="italics"></emph>Table of the Heights, Additions, and Quantities of Waters, and its uſe.<emph.end type="italics"></emph.end></cell><cell>56</cell></row><row><cell><emph type="italics"></emph>Thraſimenus.<emph.end type="italics"></emph.end> Vide <emph type="italics"></emph>Lake.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Time how its meaſured in theſe Operations of the Waters.<emph.end type="italics"></emph.end></cell><cell>49</cell></row><row><cell><emph type="italics"></emph>Torrents encreaſe at the encreaſing of a River, though they carry no more Water than before: Coroll.<emph.end type="italics"></emph.end> IV.</cell><cell>6</cell></row><row><cell><emph type="italics"></emph>Torrents when they depoſe and carry away the Sand. Coroll.<emph.end type="italics"></emph.end> V.</cell><cell>7</cell></row><row><cell><emph type="italics"></emph>Torrents and their effects in a River.<emph.end type="italics"></emph.end></cell><cell>6, 7</cell></row><row><cell><emph type="italics"></emph>Torrents that fall into the Valleys, or into<emph.end type="italics"></emph.end> Po <emph type="italics"></emph>of<emph.end type="italics"></emph.end> Volano, <emph type="italics"></emph>and their miſchiefs prevent-ed, by the diverting of<emph.end type="italics"></emph.end> Reno <emph type="italics"></emph>into<emph.end type="italics"></emph.end> Main Po.</cell><cell>100</cell></row><row><cell><emph type="italics"></emph>Tyber and the cauſes of its inundations. Coroll.<emph.end type="italics"></emph.end> VIII.</cell><cell>8</cell></row><pb xlink:href="040/01/689.jpg"></pb><row><cell>V</cell><cell></cell></row><row><cell><emph type="italics"></emph>Valleys of<emph.end type="italics"></emph.end> Bologna <emph type="italics"></emph>and<emph.end type="italics"></emph.end> Ferrara, <emph type="italics"></emph>their inundations and diſorders, whence they pro-ceed.<emph.end type="italics"></emph.end></cell><cell>97</cell></row><row><cell><emph type="italics"></emph>Velocity of the Water ſhewn by ſeveral Examples.<emph.end type="italics"></emph.end></cell><cell>3</cell></row><row><cell><emph type="italics"></emph>Its proportion to the Meaſure.<emph.end type="italics"></emph.end></cell><cell>5</cell></row><row><cell><emph type="italics"></emph>Velocities equal, what they are.<emph.end type="italics"></emph.end></cell><cell>47</cell></row><row><cell><emph type="italics"></emph>Velocities like, what they are.<emph.end type="italics"></emph.end></cell><cell>47, 48</cell></row><row><cell><emph type="italics"></emph>Velocities of Water known, how they help us in finding the Lengths.<emph.end type="italics"></emph.end></cell><cell>113</cell></row><row><cell><emph type="italics"></emph>A Fable to explain the truth thereof.<emph.end type="italics"></emph.end></cell><cell>Ibid.</cell></row><row><cell><emph type="italics"></emph>Venice.<emph.end type="italics"></emph.end> Vide <emph type="italics"></emph>Lake.<emph.end type="italics"></emph.end></cell><cell></cell></row><row><cell><emph type="italics"></emph>Vſe of the<emph.end type="italics"></emph.end> Regulator <emph type="italics"></emph>in meaſuring great Rivers. Conſideration I.<emph.end type="italics"></emph.end></cell><cell>60</cell></row><row><cell>W</cell><cell></cell></row><row><cell><emph type="italics"></emph>Waters falling, why they diſgroß. Coroll.<emph.end type="italics"></emph.end> XVI.</cell><cell>16</cell></row><row><cell><emph type="italics"></emph>Waters, how the Length of them is Meaſured.<emph.end type="italics"></emph.end></cell><cell>70</cell></row><row><cell><emph type="italics"></emph>Waters that are imployed to flow Grounds, how they are to be diſtributed.<emph.end type="italics"></emph.end></cell><cell>19, 53, 54</cell></row><row><cell><emph type="italics"></emph>Waters to be carryed in Pipes, to ſerve Aquaducts and Conduits, how they are to be Mea-ſured.<emph.end type="italics"></emph.end></cell><cell>115, 116</cell></row><row><cell><emph type="italics"></emph>Way to know the riſing of Lakes by Raines.<emph.end type="italics"></emph.end></cell><cell>28</cell></row><row><cell><emph type="italics"></emph>Way of the Vulgar to Meaſure the Waters of Rivers.<emph.end type="italics"></emph.end></cell><cell>68</cell></row><row><cell><emph type="italics"></emph>Wind Gun, and Tortable Fountain of<emph.end type="italics"></emph.end> Vincenzo Vincenti <emph type="italics"></emph>of<emph.end type="italics"></emph.end> Urbin.</cell><cell>11</cell></row><row><cell><emph type="italics"></emph>Windes contrary, retard, and make Rivers encreaſe. Coroll.<emph.end type="italics"></emph.end> VII.</cell><cell>8</cell></row></table><p type="head"> <s>The END of the TABLE of the Second Part <lb></lb>of the Firſt TOME.</s></p> </chap> <chap> <p type="head"><s>MATHEMATICAL <lb></lb>Collections and Tranſlations: <lb></lb>THE SECOND <lb></lb>TOME: <lb></lb>IN TWO PARTS.</s></p><p type="head"> <s><emph type="italics"></emph>THE FIRST PART,<emph.end type="italics"></emph.end></s></p><p type="head"> <s>Containing,</s></p><p type="main"> <s><emph type="italics"></emph>I.<emph.end type="italics"></emph.end> GALILEUS GALILEUS His <emph type="italics"></emph>MATHEMATI<lb></lb>CAL Diſcourſes<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Demonſtrations,<emph.end type="italics"></emph.end> touching two <lb></lb><emph type="italics"></emph>NEW SCIENCES,<emph.end type="italics"></emph.end> pertaining to the <emph type="italics"></emph>MECHA<lb></lb>NICKS<emph.end type="italics"></emph.end> and <emph type="italics"></emph>LOCAL MOTIONS:<emph.end type="italics"></emph.end> With an <lb></lb><emph type="italics"></emph>Appendix<emph.end type="italics"></emph.end> of the <emph type="italics"></emph>CENTRE of GRAVITY<emph.end type="italics"></emph.end> of ſome <lb></lb><emph type="italics"></emph>SOLIDS.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>II.<emph.end type="italics"></emph.end> GALILEUS His <emph type="italics"></emph>MECHANICKS:<emph.end type="italics"></emph.end> with ſome <lb></lb>Additionall <emph type="italics"></emph>Pieces.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>III.<emph.end type="italics"></emph.end> RHENATUS DES CARTES His <emph type="italics"></emph>MECHA<lb></lb>NICKS,<emph.end type="italics"></emph.end> Tranſlated from the FRENCH <emph type="italics"></emph>Manuſcript.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>IV.<emph.end type="italics"></emph.end> ARCHIMEDES His Tract <emph type="italics"></emph>De Insidentibus Humido,<emph.end type="italics"></emph.end> or of <lb></lb>the <emph type="italics"></emph>NATATION<emph.end type="italics"></emph.end> of <emph type="italics"></emph>BODIES:<emph.end type="italics"></emph.end> With the Notes <lb></lb>and Demonſtrations of NICHOLAUS TARTALEA, and <lb></lb>FEDERICUS COMMANDINUS.</s></p><p type="main"> <s><emph type="italics"></emph>V.<emph.end type="italics"></emph.end> GALILEUS His <emph type="italics"></emph>Diſcourſe<emph.end type="italics"></emph.end> of <emph type="italics"></emph>NATATION.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>VI.<emph.end type="italics"></emph.end> NICOLAUS TARTALEA, His <emph type="italics"></emph>Inventions<emph.end type="italics"></emph.end> for <emph type="italics"></emph>Diving<emph.end type="italics"></emph.end> un<lb></lb>der <emph type="italics"></emph>Water, Raiſing<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ships<emph.end type="italics"></emph.end> ſunk, &c.</s></p><p type="head"> <s><emph type="italics"></emph>By THOMAS SALUSBURY, Eſq<emph.end type="italics"></emph.end>;</s></p><p type="head"> <s><emph type="italics"></emph>LONDON,<emph.end type="italics"></emph.end><lb></lb>Printed by WILLIAM LEYBOURN, <emph type="italics"></emph>Anno Dom. <lb></lb>MD CLXV.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/690.jpg"></pb> </chap><pb xlink:href="040/01/691.jpg"></pb> <chap> <p type="head"> <s>MATHEMATICAL <lb></lb>DISCOURSES <lb></lb>AND <lb></lb>DEMONSTRATIONS, <lb></lb>TOVCHING <lb></lb>Two <emph type="italics"></emph>NEW SCIENCES<emph.end type="italics"></emph.end>; pertaining to <lb></lb>THE <lb></lb>MECHANICKS <lb></lb>AND <lb></lb>LOCAL MOTION:</s></p><p type="head"> <s>BY <lb></lb><emph type="italics"></emph>GALILÆVS GALILÆVS LYNCEVS,<emph.end type="italics"></emph.end><lb></lb>Chiefe <emph type="italics"></emph>Phyloſopher<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Mathematitian<emph.end type="italics"></emph.end> to the moſt <lb></lb>Serene <emph type="italics"></emph>GRAND DVKE<emph.end type="italics"></emph.end> of <emph type="italics"></emph>TVSCANY.<emph.end type="italics"></emph.end><lb></lb>WITH <lb></lb><emph type="italics"></emph>AN APPENDIX OF THE<emph.end type="italics"></emph.end><lb></lb>Centre of Gravity <lb></lb>Of ſome <emph type="italics"></emph>SOLIDS.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>Engliſhed from the Originall <emph type="italics"></emph>Latine<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Italian, <lb></lb>By THOMAS SALUSBURY, Eſq<emph.end type="italics"></emph.end>;</s></p><p type="head"> <s><emph type="italics"></emph>LONDON,<emph.end type="italics"></emph.end><lb></lb>Printed by WILLIAM LEYBOURN, <emph type="italics"></emph>Anno Dom. <lb></lb> MDCLXV.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/692.jpg" pagenum="1"></pb><p type="head"> <s>GALILEUS, <lb></lb>HIS <lb></lb>DIALOGUES <lb></lb>OF <lb></lb>MOTION.</s></p> </chap> <chap> <pb xlink:href="040/01/693.jpg"></pb><p type="head"> <s>The Firſt Dialogue.</s></p><p type="head"> <s><emph type="italics"></emph>INTERLOCUTORS,<emph.end type="italics"></emph.end></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 reſort (Gentlemen) to <lb></lb><arrow.to.target n="marg984"></arrow.to.target><lb></lb>your Famous Arſenal of <emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> preſen<lb></lb>teth, in my thinking, to your Speculative <lb></lb><arrow.to.target n="marg985"></arrow.to.target><lb></lb>Wits, a large field to Philoſophate in: <lb></lb>and more particularly, as to that part <lb></lb>which is called the <emph type="italics"></emph>Mechanicks:<emph.end type="italics"></emph.end> in re<lb></lb>gard that there all kinds of Engines, and <lb></lb>Machines are continually put in uſe, by a <lb></lb>huge number of Artificers of all ſorts; <lb></lb>amongſt whom, as well through the obſervations of their Prede<lb></lb>ceſſors, as thoſe, which through their own care they continually <lb></lb>are making, it's probable, that there are ſome very learned, and <lb></lb>bravely diſcours'd Men.</s></p><p type="margin"> <s><margin.target id="marg984"></margin.target><emph type="italics"></emph>A Deſcription of <lb></lb>the Arſenal of<emph.end type="italics"></emph.end><lb></lb>Venice.</s></p><p type="margin"> <s><margin.target id="marg985"></margin.target><emph type="italics"></emph>It is a large field <lb></lb>for Wits to Philo<lb></lb>ſophate in.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. Sir, you are not therein miſtaken: and I my ſelf, out of <pb xlink:href="040/01/694.jpg" pagenum="2"></pb>a natural Curioſitie, do frequentlie for my Recreation viſit that <lb></lb>place, and confer with theſe perſons; which for a certain prehe<lb></lb><arrow.to.target n="marg986"></arrow.to.target><lb></lb>minence that they have above the reſt we call ^{*} <emph type="italics"></emph>Overſeers<emph.end type="italics"></emph.end>: whoſe <lb></lb>diſcourſe hath oft helped me in the inveſtigation of not only won<lb></lb>derful, but abſtruce, and incredible Effects: and indeed I have been <lb></lb>at a loſſe ſometimes, and deſpaired to penetrate how that could <lb></lb>poſſibly come to paſſe, which far from all expectation my ſenſes <lb></lb>demonſtrated to be true; and yet that which not long ſince that <lb></lb>good Old man told us, is a ſaying and propoſition, though com<lb></lb><arrow.to.target n="marg987"></arrow.to.target><lb></lb>mon enough, yet in my opinion wholly vain, as are many others, <lb></lb>often in the mouths of unskilful perſons; introduced by them, as <lb></lb>I ſuppoſe, to ſhew that they underſtand how to ſpeak ſomething <lb></lb>about that, of which nevertheleſſe 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"></emph>The Opinion of <lb></lb>Common Artificers <lb></lb>are often falſe.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>It may be Sir, you ſpeak of that laſt propoſition which <lb></lb>he affirmed, when we deſired to underſtand, why they made <lb></lb><arrow.to.target n="marg988"></arrow.to.target><lb></lb>ſo much greater proviſion of ſupporters, and other proviſions, <lb></lb>and reinforcements about that Galeaſſe, which was to be launcht <lb></lb>than is made about leſſer Veſſels, and he anſwered us, that they did <lb></lb>ſo to avoid the peril of breaking its Keel, through the mighty <lb></lb>weight of its vaſt bulk, an inconvenience to which leſſer ſhips are <lb></lb>not subject.</s></p><p type="margin"> <s><margin.target id="marg988"></margin.target><emph type="italics"></emph>Great Ships apter <lb></lb>than others to break <lb></lb>their Keels in <lb></lb>Launching, accor<lb></lb>ding to ſome.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>I do intend the ſame, and chiefly that laſt concluſion, <lb></lb>which he added to his others, and which I alwaies eſteemed a vain <lb></lb>conceit of the Vulgar, namely, That in theſe and other Machines <lb></lb>we muſt not argue from the leſſe to the greater, becauſe many <lb></lb>Mechanical Inventions take in little, which hold not in great. </s> <s>But <lb></lb>being that all the Reaſons of the Mechanicks, have their founda<lb></lb>tions from Geometry; in which I ſee not that greatneſſe and <lb></lb>ſmalneſſe make Circles, Triangles, Cilinders, Cones, or any other <lb></lb>ſolid Figures ſubject to different paſſions: when the great Ma<lb></lb>chine is conformed in all its members to the proportions of the <lb></lb>leſſe that is uſeful, and fit for exerciſe to which it is deſigned; I <lb></lb>cannot ſee why it alſo ſhould not be exempt from the unlucky, <lb></lb>ſiniſter, and deſtructive accidents that may befall it.</s></p><p type="main"> <s>SALV The ſaying of the Vulgar is abſolutely vain, and ſo <lb></lb>falſe, that its contrary may be affirmed with equal truth, ſaying, <lb></lb><arrow.to.target n="marg989"></arrow.to.target><lb></lb>That many Machines may be made more perfect in great than lit<lb></lb>tle: As for inſtance, a Clock that ſhews and ſtrikes the Houres, <lb></lb>may be made more exact in one certain ſize, than in another leſſe. <lb></lb></s> <s>With better ground is that ſame concluſion uſurped by other more <lb></lb>intelligent perſons, who refer the cauſe of ſuch effects in theſe <lb></lb>great Machines different from what is collected from the pure, and <lb></lb>abſtracted Demonſtrations of Geometry, to the imperfection of <lb></lb>the matter, which is ſubject to many alterations, and defects. <lb></lb></s> <s>But here, I know not whether I may without contracting ſome <pb xlink:href="040/01/695.jpg" pagenum="3"></pb>ſuſpition of Arrogance ſay, that thither alſo doth the recourſe to <lb></lb>the defects of the matter (able to blemiſh the perfecteſt Mathe<lb></lb>matical Demonſtrations) ſuffice to excuſe the diſobedience of <lb></lb><arrow.to.target n="marg990"></arrow.to.target><lb></lb>Machines in concrete, to the ſame abſtracted and Ideal: yet not<lb></lb>withſtanding I will ſpeak it, affirming, That abſtracting all imper<lb></lb>fections from the Matter, and ſuppoſing it moſt perfect, and unal<lb></lb>terable, and from all accidental mutation exempt, yet neverthe<lb></lb>leſſe its only being Material, cauſeth, that the greater Machine, <lb></lb>made of the ſame matter, and with the ſame proportions, as the <lb></lb>leſſer; ſhall anſwer in all other conditions to the leſſer in exact <lb></lb>Symetry, except in ſtrength, and reſiſtance againſt violent invaſi<lb></lb>ons: but the greater it is, ſo much in proportion ſhall it be wea<lb></lb>ker. </s> <s>And becauſe I ſuppoſe the Matter to be unalterable, that is <lb></lb>alwaies the ſame, it is manifeſt, that one may produce Demonſtra<lb></lb>tions of it, no leſſe ſimply and purely Mathematical, then of eter<lb></lb>nal, and neceſſary Affections: Therefore, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> Revoke the <lb></lb>opinion which you, and, it may be, all the reſt hold, that have ſtu<lb></lb>died the Mechanicks; that Machines, and Frames compoſed of the <lb></lb>ſame Matter, with punctual obſervation of the ſelf ſame proporti<lb></lb>on between their parts, ought to be equally, or to ſay better, pro<lb></lb>portionally diſpoſed to Reſiſt; and to yield to External injuries <lb></lb>and aſſaults: For if it may be Geometrically demonſtrated, that <lb></lb>the greater are alwaies in proportion leſs able to reſiſt, than the <lb></lb>leſſe; ſo that in fine there is not only in all Machines & Fabricks <lb></lb>Artiſicial, but Natural alſo, a term neceſſarily aſcribed, beyond <lb></lb>which neither Art, nor Nature may paſſe; may paſſe, I ſay, al<lb></lb>waies obſerving the ſame proportions with the Identity of the <lb></lb>Matter.</s></p><p type="margin"> <s><margin.target id="marg989"></margin.target><emph type="italics"></emph>Many Machines <lb></lb>may be made more <lb></lb>exact in great than <lb></lb>in little.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg990"></margin.target><emph type="italics"></emph>Great Material <lb></lb>Machines, al<lb></lb>though framed In <lb></lb>the ſame proportion <lb></lb>as others of the <lb></lb>ſame Matter that <lb></lb>are leſſer, are leſſe <lb></lb>ſtrong and able to <lb></lb>reſiſt external Im<lb></lb>petuſs's than the <lb></lb>leſſer.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>I already feel my Brains to turn round, and my Mind, <lb></lb>(like a Cloud unwillingly opened by the Lightning,) I perceive <lb></lb>to be ſurprized with a tranſcient, and unuſual Light, which from <lb></lb>affar off twinkleth, and ſuddenly aſtoniſheth me; and with ab<lb></lb>ſtruce, ſtrange, and indigeſted imaginations. </s> <s>And from what hath <lb></lb>been ſpoken, it ſeems to follow, that, it is a thing impoſſible to <lb></lb>frame two Fabricks of the ſame Matter, alike, and unequal, and <lb></lb>between themſelves in proportion equally able to Reſiſt; and <lb></lb>were it to be done, yet it would be impoſſible to find two only <lb></lb>Launces of the ſame wood, alike between themſelves in ſtrength, <lb></lb><arrow.to.target n="marg991"></arrow.to.target><lb></lb>and toughneſſe, but unequal in bigneſſe.</s></p><p type="margin"> <s><margin.target id="marg991"></margin.target><emph type="italics"></emph>A Wooden Launce <lb></lb>fixed in a Wall at <lb></lb>Right-Angles, and <lb></lb>reduced to ſuch a <lb></lb>length and thick<lb></lb>neſſe as that it may <lb></lb>endure, but made a <lb></lb>hairs breadth big<lb></lb>ger, breaketh with <lb></lb>its own weight, is <lb></lb>ſingly one and no <lb></lb>more.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>So it is Sir; and the better to aſſure you that we con<lb></lb>cur in opinion, I ſay, that if we take a Launce of wood of ſuch a <lb></lb>length and thickneſſe, that being fixed faſt <emph type="italics"></emph>(v. </s> <s>g.)<emph.end type="italics"></emph.end> in a Wall at <lb></lb>Right Angles, that is parallel to the Horizon, it is reduced to the <lb></lb>utmoſt length, that it will hold at, ſo that lengthened never<lb></lb>ſo-little more, it would break, being over-burthened with its own <pb xlink:href="040/01/696.jpg" pagenum="4"></pb>weight, there could not be another ſuch-a-one in the World: So <lb></lb>that if its length (for example) were Centuple to its thickneſſe, <lb></lb>there cannot be found another Launce of the ſame Matter, that <lb></lb>being in length Centuple to its thickneſſe, ſhall be able to ſuſtain <lb></lb>it ſelf preciſely, as that did, and no more: for all that are bigger <lb></lb>ſhall break, and the leſſer ſhall be able, beſides their own, to ſuſtain <lb></lb>ſome additional weight. </s> <s>And this that I ſay of the <emph type="italics"></emph>State of bear<lb></lb>ing it ſelf,<emph.end type="italics"></emph.end> I would have underſtood to be ſpoken of every other <lb></lb>Conſtitution, and thus if one Tranſome bear or ſuſtain the force <lb></lb>often Tranſomes equal to it, ſuch another Beam cannot bear the <lb></lb>weight of ten that are equal to it. </s> <s>Now be pleaſed, Sir, and you <lb></lb><arrow.to.target n="marg992"></arrow.to.target><lb></lb><emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> to obſerve, how true Concluſions, though at the firſt <lb></lb>ſight they ſeem improbable, yet never ſo little glanced at, do depoſe <lb></lb>the Vailes which obſcure them, and make a voluntary ſhew of their <lb></lb>ſecrets nakedly, and ſimply. </s> <s>Who ſees not, that a Horſe falling <lb></lb><arrow.to.target n="marg993"></arrow.to.target><lb></lb>from a height of three or four yards, will break his bones, but a <lb></lb>Dog falling ſo many yards, or a Cat eight or ten, will receive no <lb></lb>hurt; nor likewiſe a Graſhopper from a Tower, nor an Ant thrown <lb></lb>from the Orbe of the Moon? </s> <s>Little Children eſcape all harm in <lb></lb>their falls, whereas perſons grown up break either their ſhins or <lb></lb>faces. </s> <s>And as leſſer Animals are in proportion more robuſtious, <lb></lb>and ſtrong than greater, ſo the leſſer Plants better ſupport them<lb></lb>ſelves: and I already believe, that both of you think, that an Oake <lb></lb>two hundred foot high could not ſupport its branches ſpread like <lb></lb><arrow.to.target n="marg994"></arrow.to.target><lb></lb>one of an indifferent ſize; and that Nature could not have made <lb></lb>an Horſe as big as twenty Horſes, nor a Giant ten times as tall as a <lb></lb>Man, unleſſe ſhe did it either miraculouſly, or elſe by much alte<lb></lb>ring the proportion of the Members, and particularly of the Bones, <lb></lb>enlarging them very much above the Symetry of common Bones. <lb></lb></s> <s>To ſuppoſe likewiſe, that in Artificial Machines, the greater and <lb></lb>leſſer are with equal facility made, and preſerved, is a manifeſt Er<lb></lb>rour: and thus for inſtance, ſmall Spires, Pillars, and other ſolid <lb></lb>figures may be ſafely moved, laid along, and reared upright, with<lb></lb>out danger of breaking them; but the very great upon every ſini<lb></lb>ſter accident fall in pieces, and for no other reaſon but their own <lb></lb>weight. </s> <s>And here it is neceſſary that I relate an accident, worthy <lb></lb>of notice, as are all thoſe events that occur unexpectedly, eſpecial<lb></lb>ly when the means uſed to prevent an inconvenience, proveth in <lb></lb><arrow.to.target n="marg995"></arrow.to.target><lb></lb>fine the moſt potent cauſe of the diſorder. </s> <s>There was a very great <lb></lb>Pillar of Marble laid along, and two Rowlers were put under the <lb></lb>ſame neer to the ends of it; it came into the mind of a certain In<lb></lb>gineer ſome time after, that it would be expedient, the better to <lb></lb>ſecure it from breaking in the midſt through its own weight, to <lb></lb>put under it in that part yet another Rowler: the counſel ſeemed <lb></lb>generally very ſeaſonable, but the ſucceſſe demonſtrated it to be <pb xlink:href="040/01/697.jpg" pagenum="5"></pb>wholly contrary: for many moneths had not paſt, before the Pil<lb></lb>lar crackt, and broke in the middle juſt upon the new Rowler.</s></p><p type="margin"> <s><margin.target id="marg992"></margin.target><emph type="italics"></emph>Truth upon a little <lb></lb>Courting, throweth <lb></lb>off her Vail, and <lb></lb>ſhews her Secrets <lb></lb>maked.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg993"></margin.target><emph type="italics"></emph>Great Animals <lb></lb>receive more harm <lb></lb>by a fall than leſ<lb></lb>ſer.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg994"></margin.target><emph type="italics"></emph>Nature could not <lb></lb>have made of mea<lb></lb>ner Horſes bigger, <lb></lb>and have retained <lb></lb>the ſame ſtrength, <lb></lb>but by altering <lb></lb>their Symetry.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg995"></margin.target><emph type="italics"></emph>A great Marble <lb></lb>Pillar broken by <lb></lb>its own weight, <lb></lb>and why.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SIMP. </s> <s>This was an accident truly ſtrange, and indeed <emph type="italics"></emph>preter <lb></lb>ſpem,<emph.end type="italics"></emph.end> eſpecially if it were derived from the addition of new ſup<lb></lb>port in the middle.</s></p><p type="main"> <s>SALV. </s> <s>From that doubtleſs it did proceed; and the known cauſe <lb></lb>of the Effect removeth the wonder: for the two pieces of the Pillar <lb></lb>being taken from off the Rowlers, one of thoſe bearers on which <lb></lb>one end of the Column had reſted, was by length of time rotten, and <lb></lb>ſunk away; and that in the midſt continuing ſound, and ſtrong, <lb></lb>occaſioned that half the Column lay hollow in the air without any <lb></lb>ſupport at the end; ſo that its own unweildy weight, made it do <lb></lb>that, which it would not have done, if it had reſted only upon the <lb></lb>two firſt Bearers, for as they had ſhrunk away it would have fol<lb></lb>lowed. </s> <s>And here none can think that this would have faln out in <lb></lb>a little Column, though of the ſame ſtone, and of a length anſwe<lb></lb>rable to its thickneſſe, in the very ſame proportion as the thick<lb></lb>neſs, and length of the great Pillar.</s></p><p type="main"> <s>SAGR. </s> <s>I am now aſſured of the effect, but do not yet compre<lb></lb>hend the cauſe, how in the augmentation of Matter, the Reſiſtance <lb></lb>and Strength ought not alſo to multiply at the ſame rate. </s> <s>And I <lb></lb>admire at it ſo much the more, in regard I ſee, on the contrary, in <lb></lb>other caſes the ſtrength of Reſiſtance againſt Fraction to encreaſe <lb></lb>much more than the enlargement of the matter encreaſeth. </s> <s>For if <lb></lb>(for example) there be two Nailes faſtned in a Wall, the one twice <lb></lb>asthick as the other, that ſhall bear a weight not only double to this, <lb></lb>but triple, and quadruple.</s></p><p type="main"> <s>SALV. </s> <s>You may ſay octuple, and not be wide of the truth: <lb></lb><arrow.to.target n="marg996"></arrow.to.target><lb></lb>nor is this effect contrary to the former, though in appearance it <lb></lb>ſeemeth ſo different.</s></p><p type="margin"> <s><margin.target id="marg996"></margin.target><emph type="italics"></emph>A Naile double <lb></lb>in thickneſſe to <lb></lb>another being faſt<lb></lb>ned in a Wall, ſu<lb></lb>ſtains a Weight <lb></lb>octuple to that of <lb></lb>the leſſer.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>Therefore <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> explain unto us theſe Riddles, and <lb></lb>level us theſe Rocks, if you can do it: for indeed I gueſſe this mat<lb></lb>ter of Reſiſtance to be a field repleniſhed with rare, and uſeful Con<lb></lb>templations, and if you be content that this be the ſubject of our <lb></lb>this-daies diſcourſe, it will be to me, and I believe to <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end><lb></lb>very acceptable.</s></p><p type="main"> <s>SALV. </s> <s>I cannot refuſe to ſerve you, ſince my Memory ſerveth <lb></lb><arrow.to.target n="marg997"></arrow.to.target><lb></lb>me, in minding me of that which I formerly learnt of our <emph type="italics"></emph>Accade<lb></lb>mick,<emph.end type="italics"></emph.end> who hath made many Speculations on this ſubject, and all <lb></lb>conformable (as his manner is) to Geometrical Demonſtration: <lb></lb>inſomuch that, not without reaſon, this of his may be called a <emph type="italics"></emph>New <lb></lb>Science<emph.end type="italics"></emph.end>; for though ſome of the Concluſions have been obſerved <lb></lb><arrow.to.target n="marg998"></arrow.to.target><lb></lb>by others, and in the firſt place by <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> yet nevertheleſſe are <lb></lb>they not any of the moſt curious, or (which more importeth) <lb></lb>proved by neceſſary Demonſtrations deduced from their primary, <pb xlink:href="040/01/698.jpg" pagenum="6"></pb>and indubitable fundamentals. </s> <s>And becauſe, as I ſay, I deſire de<lb></lb>monſtratively to aſſure you, and not with only probable diſcour<lb></lb>ſes to perſwade you; preſuppoſing, that you have ſo much know<lb></lb>ledge of the Mechanical Concluſions, by others heretofore funda<lb></lb>mentally handled, as ſufficeth for our purpoſe; it is requiſite, that <lb></lb>before we proceed any further, we conſider what effect that is which <lb></lb>opperates in the Fraction of a Beam of Wood, or other Solid, whoſe <lb></lb>parts are firmly connected; becauſe this is the firſt <emph type="italics"></emph>Notion,<emph.end type="italics"></emph.end> where<lb></lb>on the firſt and ſimple principle dependeth, which as familiarly <lb></lb>known, we may take for granted. </s> <s>For the clearer explanation <lb></lb>whereof; let us take the Cilinder, or Priſme, <emph type="italics"></emph>A. B.<emph.end type="italics"></emph.end> of Wood, or <lb></lb>other ſolid and coherent matter, faſtned above in <emph type="italics"></emph>A,<emph.end type="italics"></emph.end> and hanging <lb></lb>perpendicular; to which, at the other end <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> let there hang the <lb></lb>Weight <emph type="italics"></emph>C<emph.end type="italics"></emph.end>: It is manifeſt, that how great ſoever the Tenacity and <lb></lb>coherence of the parts of the ſaid Solid to one another be, ſo it be <lb></lb>not infinite, it may be overcome by the <lb></lb>Force of the drawing Weight C: whoſe <lb></lb>Gravity I ſuppoſe may be encreaſed as much <lb></lb><figure id="id.040.01.698.1.jpg" xlink:href="040/01/698/1.jpg"></figure><lb></lb>as we pleaſe; by the encreaſe whereof the <lb></lb>ſaid Solid in fine ſhall break, like as if it had <lb></lb>been a Cord. </s> <s>And, as in a Cord, we under<lb></lb>ſtand its reſiſtance to proceed from the mul<lb></lb>titude of the ſtrings or threads in the Hemp <lb></lb>that compoſe it, ſo in Wood we ſee its veins, <lb></lb>and grain diſtended lengthwaies, that render <lb></lb>it far more reſiſting againſt Fraction, then any <lb></lb>Rope would be, of the ſame thickneſſe: but <lb></lb>in a Cylinder of ſtone or Metal the Tenacity <lb></lb>of its parts, (which yet ſeemeth greater) de<lb></lb>pendeth on another kind of Cement, <lb></lb>than of ſtrings, or grains, and yet they alſo <lb></lb>being drawn with equivalent force, break.</s></p><p type="margin"> <s><margin.target id="marg997"></margin.target><emph type="italics"></emph>By Accademick <lb></lb>here, as in his <lb></lb>Dialogues of the <lb></lb>Syſteme,<emph.end type="italics"></emph.end> Galile<lb></lb>us <emph type="italics"></emph>meaneth him<lb></lb>ſelf.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg998"></margin.target>Ariſtotle <emph type="italics"></emph>the firſt <lb></lb>Obſerver of Me<lb></lb>chanical Concluſi<lb></lb>ons, but they nei<lb></lb>ther not the moſt <lb></lb>curious nor ſolidly <lb></lb>demonſtrated.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SIMP. </s> <s>If the thing ſucceed as you ſay, I underſtand well <lb></lb>enough, that the thread or grain of the Wood which is as long as <lb></lb>the ſaid Wood may make it ſtrong and able to Reſiſt a great vio<lb></lb>lence done to it to break it: But a Cord compoſed of ſtrings of <lb></lb>Hemp, no longer than two, or three foot a piece, how can it be ſo <lb></lb>ſtrong when it is ſpun out, it may be, to a hundred times that <lb></lb>length? </s> <s>Now I would farther underſtand your opinion concern<lb></lb>ing the Connection of the parts of Metals, Stones, and other mat<lb></lb>ters deprived of ſuch Ligatures, which nevertheleſſe, if I be not <lb></lb>deceived, are yet more tenacious.</s></p><p type="main"> <s>SALV. </s> <s>We muſt be neceſſitated to digreſſe into new Specu<lb></lb>lations, and not much to our purpoſe, if we ſhould reſolve thoſe <lb></lb>difficulties you ſtart.</s></p><pb xlink:href="040/01/699.jpg" pagenum="7"></pb><p type="main"> <s>SAGR. </s> <s>But if Digreſſions may lead us to the knowledge of <lb></lb>new Truths, what prejudice is it to us, that are not obliged to a <lb></lb>ſtrict and conciſe method, but that make our Congreſſions only <lb></lb>for our divertiſement to digreſſe ſometimes, leſt we let ſlip thoſe <lb></lb>Notions, which perhaps the offered occaſion being paſt, may never <lb></lb>meet with another opportunity of remembrance? </s> <s>Nay, who knows <lb></lb>not, that many times curioſity may thereby diſcover hints of more <lb></lb>worth, than the primarily intended Concluſions? </s> <s>Therefore I <lb></lb>entreat you to give ſatisfaction to <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> and my ſelf alſo, <lb></lb>no leſſe curious than he, and deſirous to underſtand what that <lb></lb>Cement is, that holdeth the parts of thoſe Solids ſo tenaciouſly <lb></lb>conjoyned, which yet nevertheleſſe in concluſion are diſſoluble: <lb></lb>a knowledge which furthermore is neceſſary for the underſtanding <lb></lb>of the coherence of the parts of thoſe very ligaments, whereof <lb></lb>ſome Solids are compoſed.</s></p><p type="main"> <s>SALV. Well, ſince it is your pleaſure, I will herein ſerve you. <lb></lb><arrow.to.target n="marg999"></arrow.to.target><lb></lb>And the firſt difficulty is, how the threads of a Cord or Rope <lb></lb>an hundred foot long ſhould ſo cloſely connect together (none <lb></lb>of them exceeding two or three foot) that it requireth a great <lb></lb>violence to break them. </s> <s>But tell me, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> cannot you hold <lb></lb>one ſingle ſtring of Hemp ſo faſt between your fingers by one <lb></lb><arrow.to.target n="marg1000"></arrow.to.target><lb></lb>end, that I pulling by the other end ſhould break it ſooner than <lb></lb>get it from you? </s> <s>Queſtionleſſe you might: when then, thoſe <lb></lb>threads are not only at the end, but alſo in every part of their <lb></lb>length, held faſt with much ſtrength by him that graſpeth them, is <lb></lb>it not apparent, that it is a much harder matter to pluck them <lb></lb>from him that holds them, then to break them? </s> <s>Now in the Cord, <lb></lb><arrow.to.target n="marg1001"></arrow.to.target><lb></lb>the ſame act of twiſting, binds the threads mutually within one <lb></lb>another, in ſuch ſort, that pulling the Cord with great force, the <lb></lb>threads of it break inſunder, but ſeparate and part not from one <lb></lb>another; as is plainly ſeen by viewing the ſhort ends of the ſaid <lb></lb>threads in the broken place, that are not a ſpan long; as they <lb></lb>would be, if the diviſion of the Cord had been made by the ſole <lb></lb>ſeperating of them in drawing the Cord, and not by breaking <lb></lb>them.</s></p><p type="margin"> <s><margin.target id="marg999"></margin.target><emph type="italics"></emph>What that Cement <lb></lb>is that Connecteth <lb></lb>the parts of Solids.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1000"></margin.target><emph type="italics"></emph>How a Rope or <lb></lb>Cord reſiſteth Fra<lb></lb>ction.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1001"></margin.target><emph type="italics"></emph>In breaking a Rope <lb></lb>the parts are not <lb></lb>ſeparated, but bro<lb></lb>kon.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>For confirmation of this, let me add, that the Cord is <lb></lb>ſometimes ſeen to break, not by pulling it length-waies, but by <lb></lb>over-twiſting it: an argument, in my judgment, concluding that <lb></lb>the threads are ſo enterchangeably compreſt by one another, that <lb></lb>thoſe compreſſings permit not the compreſſed to ſlip ſo very little, <lb></lb>as is requiſite to lengthen it out that it wind about the Cord, <lb></lb>which in the twining breaketh, and conſequently in ſome ſinall <lb></lb>meaſure ſwels in thickneſſe.</s></p><p type="main"> <s>SALV. </s> <s>You ſay very well; but conſider by the way, how one <lb></lb>truth draweth on another. </s> <s>That thread, which griped between the <pb xlink:href="040/01/700.jpg" pagenum="8"></pb>fingers, did not yield to follow him that would have forceably <lb></lb>drawn it from between them, reſiſted, becauſe it was ſtayed by a <lb></lb>double compreſſion, ſince the upper finger preſt no leſſe againſt <lb></lb>the nether, than it preſſed againſt that. </s> <s>And there is no queſtion, <lb></lb>that if of theſe two preſſures, one alone might be retained, there <lb></lb>would remain half of that Reſiſtance, which depended conjunctive<lb></lb>ly on them both: but becauſe you cannot with removing, <emph type="italics"></emph>v.g.<emph.end type="italics"></emph.end> the <lb></lb>upper finger take away its preſſion, without taking away the other <lb></lb>part alſo; it will be neceſſary by ſome new Artifice to retain one <lb></lb>of them, and to find a way that the ſame thread may compreſſe it <lb></lb>ſelf againſt the finger or other ſolid body upon which it is put; and <lb></lb>this is done by winding the ſame thread about the Solid. </s> <s>For the <lb></lb>better underſtanding whereof, I will briefly give it you in Figure; <lb></lb>and let <emph type="italics"></emph>A B<emph.end type="italics"></emph.end> and C<emph type="italics"></emph>D<emph.end type="italics"></emph.end> be two Cilinders, and between them let there <lb></lb>be diſtended the thread <emph type="italics"></emph>E F,<emph.end type="italics"></emph.end> which for greater plainneſſe I will <lb></lb>repreſent to be a ſmall Cord: there is no doubt but that the two <lb></lb>Cylinders being preſſed hard one againſt the other, the Cord <lb></lb><emph type="italics"></emph>E F<emph.end type="italics"></emph.end> pulled by the end <emph type="italics"></emph>F<emph.end type="italics"></emph.end> will Reſiſt no ſmal force before <lb></lb>it will ſlip from between the two Solids compreſſing it: but if <lb></lb>we remove one of them, though the Cord <lb></lb><figure id="id.040.01.700.1.jpg" xlink:href="040/01/700/1.jpg"></figure><lb></lb>continue touching the other, yet ſhall it not <lb></lb>by ſuch contact be hindered from ſlipping <lb></lb>away. </s> <s>But if holding it faſt, though but <lb></lb>gently in the point A, towards the top of the <lb></lb>Cylinder, we wind, or belay it about the <lb></lb>ſame ſpirally in A F L O T R, and pull it by <lb></lb>the end R: it is manifeſt, that it will begin <lb></lb>to preſſe the Cylinder, and if the windings <lb></lb>and wreathes be many, it ſhall in its effectual <lb></lb>drawing alwaies preſſe it ſo much the ſtrai<lb></lb>ter about the Cylinder: and by multiplying <lb></lb>the wreathes if you make the contact longer, <lb></lb>and conſequently more invincible, the more <lb></lb>difficult ſtill ſhall it be to withdraw the <lb></lb>Cord, and make it yield to the force that <lb></lb>pulls it. </s> <s>Now who ſeeth not, that the ſame <lb></lb>Reſiſtance is in the threads, which with many thouſand ſuch <lb></lb>twinings ſpin the thick Cord? </s> <s>Yea, the ſtreſſe of ſuch twiſting <lb></lb>bindeth with ſuch Tenacity, that a few Ruſhes, and of no great <lb></lb>length, (ſo that the wreaths and windings are but few where<lb></lb>with they entertwine) make very ſtrong bands, called, as I take it, <lb></lb><arrow.to.target n="marg1002"></arrow.to.target><lb></lb>^{*} Thum-ropes.</s></p><p type="margin"> <s><margin.target id="marg1002"></margin.target>* Fuſta.</s></p><p type="main"> <s>SAGR. </s> <s>Your Diſcourſe hath removed the wonder out of my <lb></lb>mind at two effects, whereof I did not well underſtand the rea<lb></lb>ſon; One was to ſee, how two, or at the moſt three twines of the <pb xlink:href="040/01/701.jpg" pagenum="9"></pb>Rope about the Axis of a Crane did not only hold it, that be<lb></lb>ing drawn by the immenſe force of the weight, which it held, it <lb></lb>ſlipt nor ſhrunk not; but that moreover turning the Crane about, <lb></lb>the ſaid Axis with the ſole touch of the Rope which begirteth it, <lb></lb>did in the after-turnings, draw and raiſe up vaſt ſtones, whilſt the <lb></lb>ſtrength of a little Boy ſufficed to hold and ſtay the other end of <lb></lb>the ſame Cord. </s> <s>The other is at a plain, but cunning, Inſtrument found <lb></lb>out by a young Kinſman of mine, by which with a Cord he could <lb></lb>let himſelf down from a window without much gauling the palmes <lb></lb>of his hands, as to his great ſmart not long before he had done. </s> <s>For <lb></lb><arrow.to.target n="marg1003"></arrow.to.target><lb></lb>the better underſtanding whereof, rake this Scheame: About ſuch <lb></lb>a Cylinder of Wood as A B, two Inches <lb></lb>thick, and ſix or eight Inches long, he cut a <lb></lb>hollow notch ſpirally, for one turn and a <lb></lb><figure id="id.040.01.701.1.jpg" xlink:href="040/01/701/1.jpg"></figure><lb></lb>half and no more, and of wideneſſe fit for <lb></lb>the Cord he would uſe; which he made to <lb></lb>enter through the notch at the end A, and <lb></lb>to come out at the other B, incircling after<lb></lb>wards the Cylinder in a barrel or ſocket of <lb></lb>Wood, or rather Tin, but divided length<lb></lb>waies, and made with Claſpes or Hinges to <lb></lb>open and ſhut at pleaſure: and then graſp<lb></lb>ing and holding the ſaid Barrel or Caſe with <lb></lb>both his hands, the rope being made faſt <lb></lb>above, he hung by his arms; and ſuch was <lb></lb>the compreſſion of the Cord between the <lb></lb>moving Socket and the Cylinder, that at <lb></lb>pleaſure griping his hands cloſer he could <lb></lb>ſtay himſelf without deſcending, and ſlacking his hold a little, he <lb></lb>could let himſelf down as he pleaſed.</s></p><p type="margin"> <s><margin.target id="marg1003"></margin.target><emph type="italics"></emph>An Hand-Pully <lb></lb>or Inſtrument in<lb></lb>vented by an ama<lb></lb>rous perſon to let <lb></lb>himſelf down from <lb></lb>any great height <lb></lb>with a Cord with<lb></lb>out gauling his <lb></lb>hands.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>Aningenious invention verily, and for a full explanati<lb></lb>on of its nature, me-thinks I diſcover, as it were by a ſhadow, the <lb></lb>light of ſome other additional diſcoveries: but I will not at this <lb></lb>time deviate any more from my purpoſe upon this particular: and <lb></lb>the rather in regard you are deſirous to hear my opinion of the <lb></lb>Reſiſtance of other Bodies againſt Fraction, whoſe texture is not <lb></lb><arrow.to.target n="marg1004"></arrow.to.target><lb></lb>with threads, and fibrous ſtrings, as is that of Ropes, and moſt <lb></lb>kinds of Wood: but the connection of their parts ſeem to de<lb></lb>pend on other Cauſes; which in my judgment may be reduced to <lb></lb>two heads; one is the much talked-of Repugnance that Nature <lb></lb>hath againſt the admiſſion of Vacuity: for another (this of Va<lb></lb>cuity not ſufficing) there muſt be introduced ſome glue, viſcous <lb></lb>matter, or Cement, that tenaciouſly connecteth the Corpuſcles of <lb></lb>which the ſaid Body is compacted.</s></p><p type="margin"> <s><margin.target id="marg1004"></margin.target><emph type="italics"></emph>Why ſuch Bodies <lb></lb>reſiſt Fraction that <lb></lb>are not connected <lb></lb>with Fibrous fila<lb></lb>ments.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>I will firſt ſpeak of <emph type="italics"></emph>Vacuity,<emph.end type="italics"></emph.end> ſhewing by plain experiments, <pb xlink:href="040/01/702.jpg" pagenum="10"></pb><arrow.to.target n="marg1005"></arrow.to.target><lb></lb>what and how great its virtue is. </s> <s>And firſt of all the ſeeing at <lb></lb>pleaſure two flat pieces of either Marble, Metal, or Glaſſe, exqui<lb></lb>ſitely planed, ſlickt, and poliſhed, that being laid upon one the <lb></lb>other, without any difficulty ſlide along upon each other, if drawn <lb></lb><arrow.to.target n="marg1006"></arrow.to.target><lb></lb>ſidewaies, (a certain argument that no glue connects them,) but <lb></lb>that going about to ſeperate them, keeping them equidiſtant, <lb></lb>there is found ſuch repugnance, that the uppermoſt will be lif<lb></lb>ted up, and will draw the other after it, and keep it perperually <lb></lb>raiſed, though it be pretty thick, and heavy, evidently proveth to <lb></lb>us, how much Nature abhorreth to admit, though for a ſhort mo<lb></lb>ment of time, the void ſpace, that would be between them, till <lb></lb>the concourſe of the parts of the Circum-Ambient Air ſhould have <lb></lb>poſſeſt, and repleated it. </s> <s>We ſee likewiſe, that if thoſe two Plates <lb></lb>be not exactly poliſhed, and conſequently their contact not every <lb></lb>where exquiſite; in going about to ſeparate them gently, there will <lb></lb>be found no Renitence more than that of their meer weight, but in <lb></lb>the ſudden raiſing, the nether Stone will riſe, and inſtantly fall <lb></lb>down again, following the upper only for that very ſmall time <lb></lb>which ſerveth for the expanſion of that little Air which interpo<lb></lb>ſeth betwixt the Plates, that did not every where touch, and for <lb></lb>the ingreſſion of the other circumfuſed. </s> <s>The like Reſiſtance, which <lb></lb>ſo ſenſibly diſcovers it ſelf betwixt the two Plates, cannot be <lb></lb>doubted to reſide alſo between the parts of a Solid, and that it en<lb></lb>tereth into their connection, at leaſt in part, and as their Concomi<lb></lb>tant Cauſe.</s></p><p type="margin"> <s><margin.target id="marg1005"></margin.target><emph type="italics"></emph>The firſt Cauſe of <lb></lb>the Cohorence of <lb></lb>Bodies is their Re<lb></lb>pugnance to Vacu<lb></lb>ity.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1006"></margin.target><emph type="italics"></emph>This is proved by <lb></lb>the Coherence of <lb></lb>two poliſhed Mar<lb></lb>bles.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. Hold, I pray you, and permit me to impart unto you a <lb></lb>particular Conſideration, juſt now come into my Mind, and this it <lb></lb>is; That ſeeing how the lower Plate followeth the upper, and is <lb></lb>by a ſpeedy motion raiſed, we are thereby aſcertained that (con<lb></lb>trary to the ſaying of many Philoſophers, and perchance of <emph type="italics"></emph>Ari<lb></lb>ſtotle<emph.end type="italics"></emph.end> himſelf) the Motion in <emph type="italics"></emph>Vacuity<emph.end type="italics"></emph.end> would not be Inſtantaneous; <lb></lb>for ſhould in be ſuch, the propoſed Plates without the leaſt repug<lb></lb>nance would Seperate; ſince the ſelf ſame inſtant of time would <lb></lb>ſuffice for their ſeparation, and for the concourſe of the Ambient <lb></lb>Air to repleat that <emph type="italics"></emph>Vacuity,<emph.end type="italics"></emph.end> which might remain between them. <lb></lb></s> <s>By the Inferiour Plates following the Superiour therefore may be <lb></lb>gathered, that in the <emph type="italics"></emph>Vacuity<emph.end type="italics"></emph.end> the Motion would not be Inſtanta<lb></lb><arrow.to.target n="marg1007"></arrow.to.target><lb></lb>neous. </s> <s>And alſo it may be inferred, that even betwixt thoſe Plates <lb></lb>there reſteth ſome <emph type="italics"></emph>Vacuity,<emph.end type="italics"></emph.end> at leaſt for ſome very ſhort time; that <lb></lb>is, for ſo long as the Ambient Air is moving whilſt it concurreth to <lb></lb>replete the <emph type="italics"></emph>Vacuum:<emph.end type="italics"></emph.end> for if there did no <emph type="italics"></emph>Vacuity<emph.end type="italics"></emph.end> remain, there <lb></lb>would be no need either of the Concourſe, or Motion of the Am<lb></lb>bient We muſt therefore ſay that <emph type="italics"></emph>Vacuity<emph.end type="italics"></emph.end> ſometimes is admit<lb></lb>ted, though by Violence or againſt Nature, (albeit it is my opi<lb></lb>nion, that nothing is contrary to Nature, but that which is im<pb xlink:href="040/01/703.jpg" pagenum="11"></pb>poſſible, which again never is.) But here ſtarts up another diffi<lb></lb>culty, and it is, That though Experience aſſures me of the truth of <lb></lb>the Concluſion, yet my Judgment is not thorowly ſatisfied of the <lb></lb>Cauſe, to which ſuch an effect may be aſcribed. </s> <s>For as much as <lb></lb>the effect of the Seperation of the two Plates, is in time before the <lb></lb>Vacuity which ſhould ſucceed by conſequence upon the Separa<lb></lb>tion. </s> <s>And becauſe, in my opinion, the Cauſe ought, if not in <lb></lb><arrow.to.target n="marg1008"></arrow.to.target><lb></lb>Time, at leaſt in Nature, to precede the Effect: and that of a Po<lb></lb>ſitive Effect, the Cauſe ought alſo to be Poſitive; I cannot con<lb></lb>ceive, how the Cauſe of the Adheſion of the two Plates, and of <lb></lb>their Repugnance to Separation, (Effects that are already in <lb></lb>Act) ſhould be aſſigned to Vacuity, which yet is not, but ſhould <lb></lb>follow. </s> <s>And of things that are not in being, there can be no Ope<lb></lb><arrow.to.target n="marg1009"></arrow.to.target><lb></lb>ration; according to the infallible Maxime of Philoſophy.</s></p><p type="margin"> <s><margin.target id="marg1007"></margin.target><emph type="italics"></emph>Vacuity partly the <lb></lb>cauſe of the Cohe<lb></lb>rence between the <lb></lb>parts of Solids.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1008"></margin.target><emph type="italics"></emph>Of a Poſitive Ef<lb></lb>fect the Cauſe is <lb></lb>Poſitive.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1009"></margin.target><emph type="italics"></emph>Non-entity is at<lb></lb>tended with Non<lb></lb>operation.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SIMP. </s> <s>But ſince you grant <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> this Axiome, I do not <lb></lb>think you will deny another that is moſt excellent, and true; to <lb></lb><arrow.to.target n="marg1010"></arrow.to.target><lb></lb>wit, That Nature doth not attempt Impoſſibilities: Upon which <lb></lb>Axiom I think the Solution of our doubt depends: becauſe there<lb></lb>fore a void ſpace is of it ſelf impoſſible, Nature forbids the doing <lb></lb>that, in conſequence of which Vacuity would neceſſarily ſucceed; <lb></lb>and ſuch an act is the ſeparation of the two Plates.</s></p><p type="margin"> <s><margin.target id="marg1010"></margin.target><emph type="italics"></emph>Nature doth not <lb></lb>attempt Impoſſibi<lb></lb>lities.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. Now, (admitting this which <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> alledgeth is a <lb></lb>ſufficient Solution of my Doubt) in perſuance of the diſcourſe <lb></lb>with which I began, it ſeemeth to me, that this ſame Repugnance <lb></lb>to Vacuity ſhould be a ſufficient Cement in the parts of a Solid of <lb></lb>Stone, Metal, or what other ſubſtance is more firmly conjoyned, <lb></lb>and averſe to Diviſion. </s> <s>For if a ſingle Effect, hath but one ſole <lb></lb>Cauſe, as I underſtand, and think; or if many be aſſigned, they <lb></lb>are reducible to one alone: why ſhould not this of Vacuity, which <lb></lb>certainly is one, be ſufficient to anſwer all Reſiſtances?</s></p><p type="main"> <s>SALV. </s> <s>I will not at this time enter upon this conteſt, whether <lb></lb>Vacuity, without other Cement, be in it ſelf alone ſufficient to <lb></lb>keep together the ſeparable parts of firm Bodies; but yet this I <lb></lb>ſay, that the Reaſon of the Vacuity, which is of force, and con<lb></lb>oluding in the two Plates, ſufficeth not of it ſelf alone for the <lb></lb>firm connection of the parts of a ſolid Cylinder of Marble, or <lb></lb>Metal, the which forced with great violence, pulling them ſtreight <lb></lb>out, in fine, divide and ſeparate. </s> <s>And in caſe I have found a way <lb></lb>to diſtinguiſh this already-known Reſiſtance dependent on Va<lb></lb>ouity, from all others whatſoever that may concur with it in <lb></lb>ſtrengthening the Connection, and make you ſee how that it alone <lb></lb>is not neer ſufficient for ſuch an Effect, would not you grant that <lb></lb>it would be neceſſary to introduce ſome other? </s> <s>Help him out, <emph type="italics"></emph>Sim<lb></lb>plicius,<emph.end type="italics"></emph.end> for he ſtands ſtudying what to anſwer.</s></p><p type="main"> <s>SIMP. </s> <s>The Suſpenſion of <emph type="italics"></emph>Sagredus<emph.end type="italics"></emph.end> muſt needs be upon ano<pb xlink:href="040/01/704.jpg" pagenum="12"></pb>ther account, there being no place left for doubting of ſo clear, and <lb></lb>neceſſary a Conſequence.</s></p><p type="main"> <s>SAGR. </s> <s>You Divine <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> I was thinking if a Million of <lb></lb>Gold <emph type="italics"></emph>per annum,<emph.end type="italics"></emph.end> coming from <emph type="italics"></emph>Spaine,<emph.end type="italics"></emph.end> not being ſufficient to pay <lb></lb>the Army, whether it was neceſſary to make any other proviſion <lb></lb>than of Money to pay the Souldiers. </s> <s>But proceed, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> and <lb></lb>ſuppoſing that I admit of your Conſequence, ſhew us how to ſe<lb></lb>parate the opperation of Vacuity from the other, that meaſuring <lb></lb>it we may ſee how it's inſufficient for the Effect of which we ſpeak.</s></p><p type="main"> <s>SALV. </s> <s>Your Genius hath prompted you. </s> <s>Well, I will tell you <lb></lb>the way to part the Virtue of Vacuity from the reſt, and then how <lb></lb>to meaſure it. </s> <s>And to ſever it, we will take a continuate matter, <lb></lb><arrow.to.target n="marg1011"></arrow.to.target><lb></lb>whoſe parts are deſtitute of all other Reſiſtance to Separation, ſave <lb></lb>only that of Vacuity, ſuch as Water at large hath been demon<lb></lb>ſtrated to be in a certain Tractate of our <emph type="italics"></emph>Accademick.<emph.end type="italics"></emph.end> So that <lb></lb>when ever a Cylinder of Water is ſo diſpoſed, that being drawn <lb></lb>we find a Reſiſtance againſt the ſeparation of its parts, this muſt <lb></lb>be acknowledged to proceed from no other cauſe, but from re<lb></lb>pugnance to Vacuity. </s> <s>But to make ſuch an experiment, I have <lb></lb>imagined a device, which with the help of a ſmall Diagram, may <lb></lb>be better expreſt than by my bare words. </s> <s>Let this Figure C A B D <lb></lb>be the Profile of a Cylinder of Metal, or of Glaſs, which muſt <lb></lb>be made hollow within, but turned exactly round; into whoſe <lb></lb>Concave muſt enter a Cylinder of Wood, exquiſitely fitted to <lb></lb>touch every where, whoſe Profile is noted by <lb></lb>E G H F, which Cylinder may be thruſt up<lb></lb><figure id="id.040.01.704.1.jpg" xlink:href="040/01/704/1.jpg"></figure><lb></lb>wards, and downwards: and this I would <lb></lb>have bored in the middle, ſo that there may <lb></lb>a rod of Iron paſs thorow, hooked in the end <lb></lb>K, and the other end I, ſhall grow thicker in <lb></lb>faſhion of a Cone, or Top; and let the <lb></lb>hole made for the ſame thorow the Cylinder <lb></lb>of Wood be alſo cut hollow in the upper <lb></lb>part, like a Conical Superficies, and exactly <lb></lb>fitted to receive the Conick end I, of the <lb></lb>Iron I K, as oft as it is drawn down by the <lb></lb>part K. </s> <s>Then I put the Cylinder of Wood <lb></lb>E H into the Concave Cylinder A D, and <lb></lb>would not have it come to touch the upper<lb></lb>moſt Superficies of the ſaid hollow Cylinder, <lb></lb>but that it ſtay two or three fingers breadth <lb></lb>from it: and I would have that ſpace filled with Water; which <lb></lb>ſhould be put therein, holding the Veſſel with the mouth C D up<lb></lb>wards; and thereupon preſs down the Stopper E H, holding the <lb></lb>Conical part I ſomewhat diſtant from the hollow that was made <pb xlink:href="040/01/705.jpg" pagenum="13"></pb>for it in the Wood, to leave way for the Air to go out, which in <lb></lb>thruſting down the Stopper will iſſue out by the hole of the <lb></lb>Wood, which therefore ſhould be made a little wider than the <lb></lb>thickneſs of the Hook of Iron I K. </s> <s>The Air being let out, and the <lb></lb>Iron pull'd back, which cloſe ſtoppeth the wood with its Conick <lb></lb>part I, then turn the veſſel with its mouth downwards, and faſten to <lb></lb>the hook K a Bucket that may receive into it ſand, or other weigh<lb></lb>ty matter, and you may hang ſo much weight thereat, that at length <lb></lb>the Superiour ſurface of the Stopper E F will ſeparate and forſake <lb></lb>the inferiour part of the Water; to which nothing elſe held it con<lb></lb>nected but the Repugnance againſt Vacuity: afterwards weighing <lb></lb>the Stopper with the Iron, the Bucket, and all that was in it, you <lb></lb>will have the quantity of the Force of the Vacuity. </s> <s>And if affixing <lb></lb>to a Cylinder of Marble, or Chriſtal, as thick as the Cylinder of <lb></lb>Water, ſuch a weight, that together with the proper weight of the <lb></lb>Marble or Chriſtal it ſelf, equalleth the gravity of all thoſe fore<lb></lb>named things, a Rupture follow thereupon; we may without <lb></lb>doubt affirm, that the only reaſon of Vacuity holdeth the parts of <lb></lb>Marble and Chriſtal conjoyned: but not ſufficing; and ſeeing <lb></lb>that to break it there muſt be added four times as much weight, <lb></lb>it muſt be confeſſed, that the Reſiſtance of Vacuity is one part of <lb></lb>ſive, and that the other Reſiſtance is quadruple to that of Vacuity.</s></p><p type="margin"> <s><margin.target id="marg1011"></margin.target><emph type="italics"></emph>How to meaſure <lb></lb>the Virtue of Va<lb></lb>cuity in Solids di<lb></lb>ſtinct from other <lb></lb>convenient Cauſes <lb></lb>of their Coherence. <lb></lb></s> <s>Water a Continu<lb></lb>ate Matter, and <lb></lb>void of all other a<lb></lb>verſion to ſeparati<lb></lb>on, ſave that of Va<lb></lb>cuity.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SIMP. </s> <s>It cannot be denied, but that the Invention is Ingen<lb></lb>ous: but I hold it to be ſubject to many difficulties, which makes <lb></lb>me queſtion it; for who ſhall aſſure us, that the Air cannot pene<lb></lb>trate between the Glaſs, and the Stopper, though it be cloſe ſtopt <lb></lb>with Flax, or other pliant matter? </s> <s>And alſo it's a Queſtion, whe<lb></lb>ther Wax or Turpentine will ſerve to make the Cone I, ſtop the <lb></lb>hole cloſe: Again, Why may not the parts of the Water with<lb></lb>draw and rarefie themſelves? </s> <s>Why may not the Air, or Exhalati<lb></lb>ons, or other more ſubtil Subſtances penetrate through the Poroſi<lb></lb>ties of the Wood, or Glaſs it ſelf?</s></p><p type="main"> <s>SALV. <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> is very nimble at raiſing doubts, and, in part, <lb></lb>helping us to reſolve them, as to the Penetration of the Air through <lb></lb>the Wood, or between the Wood and Glaſs. </s> <s>But I moreover <lb></lb>obſerve, that we may at the ſame time ſecure our ſelves, and with<lb></lb>all acquire new Notions, if the fore-named doubts take place; for <lb></lb>if the Water be by Nature, howbeit with violence, capable of ex<lb></lb>tention, as it falleth out in Air, you ſhall ſee the Stopper to de<lb></lb>ſcend: and if in the upper part of the Glaſs we make a ſmall pro<lb></lb>minent Boſs, as this V; in caſe any Air, or other more Tenuous or <lb></lb>Spirituous Matter ſhould penetrate thorow the Subſtance, or Poroſi<lb></lb>ty of the Glaſs, or Wood, it would be ſeen to reunite (the water <lb></lb>giving place) in the eminence V: which things not being percei<lb></lb>ved, we reſt aſſured that the Experiment was made with due <pb xlink:href="040/01/706.jpg" pagenum="14"></pb>caution: and ſee that the Water is not capable oſ extenſion, nor <lb></lb>the Glaſs permeable by any matter, though never ſo ſubtil.</s></p><p type="main"> <s>SAGR. </s> <s>And I, by means of theſe Diſcourſes have found the <lb></lb>Cauſe of an Effect, that hath for a long time puzled my mind <lb></lb><arrow.to.target n="marg1012"></arrow.to.target><lb></lb>with wonder, and kept it in Ignorance. </s> <s>I have heretofore ob<lb></lb>ſerved a Ciſtern, wherein, for the drawing thence of Water, there <lb></lb>was made a Pump, by ſome one that thought, perhaps, (but in <lb></lb>vain) to be thereby able to draw, with leſs labour, the ſame, or <lb></lb>greater quantity of Water, than with the ordinary Buckets; and <lb></lb>this Pump had its Sucker and Value on high, ſo that the Water <lb></lb>was made to aſcend by Attraction, and not by Impulſe, as do the <lb></lb>Pumps that work below. </s> <s>This, whilſt there is any Water in the <lb></lb>Ciſtern to ſuch a determinate height, will draw it plentifully; but <lb></lb>when the Water ebbeth below a certain Mark, the Pump will <lb></lb>work no more. </s> <s>I conceited, the firſt time that I obſerved this ac<lb></lb>cident, that the Engine ____ had been ſpoyled, and looking for <lb></lb>the Workman, that he might amend it; he told me, that there was <lb></lb>no defect at all, other than what was in the Water, which being <lb></lb>fallen too low, permitted not it ſelf to be raiſed to ſuch a height; <lb></lb><arrow.to.target n="marg1013"></arrow.to.target><lb></lb>and farther ſaid, that neither Pump, or other Machine, that raiſeth <lb></lb>the water by Attraction, was poſſibly able to make it riſe a hair <lb></lb>more than eighteen Braces, and be the Pumps wide or narrow, this <lb></lb>is the utmoſt limited meaſure of their height. </s> <s>And I have hitherto <lb></lb>been ſo dull of apprehenſion, that though I knew that a Rope, a <lb></lb>Stick, and a Rod of Iron might be ſo and ſo lengthened, that at <lb></lb>laſt, holding it up on high in the Air, its own weight would break <lb></lb>it, yet I never remembred, that the ſame would much more eaſily <lb></lb>happen in a Rope, or Thread of Water. </s> <s>And what other is that <lb></lb>which is attracted in the Pump than a Cylinder of Water, which <lb></lb>having its contraction above, prolonged more and more, in the end <lb></lb>arriveth to that term, beyond which being drawn, it breaketh by <lb></lb>its foregoing over-weight, juſt as if it was a Rope.</s></p><p type="margin"> <s><margin.target id="marg1012"></margin.target><emph type="italics"></emph>The Nature of the <lb></lb>attraction of Wa<lb></lb>ter by Pumps.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1013"></margin.target><emph type="italics"></emph>Water raiſed or at<lb></lb>tracted by a Pump <lb></lb>riſeth not above <lb></lb>eleven yards.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>It is even ſo as you ſay; and becauſe the ſaid height of <lb></lb>eighteen Braces is the prefixed term of the Elevation, to which any <lb></lb>quantity of Water, be it (that is to ſay, be the Pump) broad, <lb></lb>narrow, or even, ſo narrow as to the thickneſs of a ſtraw, can ſu<lb></lb>ſtain it ſelf; when ever we weigh the water contained in eighteen <lb></lb>Braces of Pipe, be it broad or narrow, we have the value of Reſi<lb></lb>ſtance of Vacuity in Cylinders of whatſoever ſolid matter, of the <lb></lb>thickneſs of the propoſed Pipes. </s> <s>And ſince I have ſaid ſo much, <lb></lb><arrow.to.target n="marg1014"></arrow.to.target><lb></lb>we will ſhew, that a man may eaſily find in all Metals, Stones, Tim<lb></lb>bers, Glaſſes, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> How far one may lengthen out Cylinders, <lb></lb>ſtrings, or rods of any thickneſs, beyond which, being oppreſt with <lb></lb>their own weight, they can no longer hold, but break in pieces. <lb></lb></s> <s>Take for example a Braſs wyer of any certain thickneſs, and length, <pb xlink:href="040/01/707.jpg" pagenum="15"></pb>and fixing one of its ends on high, add gradually more and more <lb></lb>weight to the other, till at laſt it break, and let the greateſt weight <lb></lb>that it can bear be <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> fifty pounds. </s> <s>It is manifeſt that fifty <lb></lb>pound of Braſs more than its own weight, which let us ſuppoſe, <lb></lb>for example, to be one eighth of an Ounce, drawn out into a <lb></lb>Wyer of the like thickneſs, would be the greateſt length of the <lb></lb>Wyer that could bear it ſelf. </s> <s>Then meaſure how long the Wyer <lb></lb>was which brake, and let it be for inſtance a y ard; and becauſe it <lb></lb>weighed one eighth of an Ounce; and poiſed, or bore it ſelf, and <lb></lb>fifty pounds more; which are Four Thouſand Eight Hundred <lb></lb>eighths of Ounces; we ſay, that all Wyers of Braſs, whatever <lb></lb>thickneſs they be of, can hold, at the length of Four Thouſand <lb></lb>Eight Hundred and one yards, and no more: and ſo, a Braſs Wyer <lb></lb>being able to hold to the length of 4801 yards; the Reſiſtance it <lb></lb>findeth dependent on Vacuity, in reſpect of the remainder, is as <lb></lb>much as is equivalent to the weight of a Rope of Water eighteen <lb></lb>Braces long, and of the ſame thickneſs with the ſaid Braſs Wyer: <lb></lb>and finding Braſs to be <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> nine times heavier than Water, in <lb></lb>any Wyer of Braſs, the Reſiſtance againſt Fraction dependent on <lb></lb>the reaſon of Vacuity, importeth as much as two Braces of the <lb></lb>ſame Wyer weigheth. </s> <s>And thus arguing, and operating, we may <lb></lb>find the length of the Wyers, or Threads of all Solid Matters re<lb></lb>duced to the utmoſt length that they can ſubſiſt of, and alſo what <lb></lb>part Vacuity hath in their Reſiſtance.</s></p><p type="margin"> <s><margin.target id="marg1014"></margin.target><emph type="italics"></emph>To what length Cy<lb></lb>linders or Ropes of <lb></lb>any Matter may <lb></lb>be prolonged, be<lb></lb>yond which being <lb></lb>charged they break <lb></lb>by their own weight<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>It reſteth now, that you declare to us wherein conſiſts <lb></lb>the remainder of that Tenacity, that is, what that Glue or Reni<lb></lb>tence is, which connecteth together the parts of a Solid, beſides <lb></lb>that which is derived from Vacuity; becauſe I cannot imagine <lb></lb>what that Cement is, that cannot be burnt, or conſumed in a ve<lb></lb>ry hot Furnace in two, three, or four Moneths, nor ten, nor an hun<lb></lb>dred; and yet Gold, Silver, and Glaſs, ſtanding ſo long Liquiſi<lb></lb>ed, when it is taken out, its parts return, upon cooling, to reunite, <lb></lb>and conjoyn, as before. </s> <s>And again, becauſe the ſame difficulty <lb></lb>which I meet within the Connection of the parts of the Glaſs, I <lb></lb>find alſo in the parts of the Cement, that is, what thing that <lb></lb>ſhould be which maketh them cleave ſo cloſs together.</s></p><p type="main"> <s>SALV. </s> <s>I told you but even now, that your Genius prompted <lb></lb>you: I am alſo in the ſame ſtrait: and alſo whereas I have in gene<lb></lb>ral told you, how that Repugnance againſt Vacuity is unqueſti<lb></lb>onably that which permits not, nnleſs with great violence, the ſe<lb></lb>paration of the two Plates, and moreover of the two great pieces of <lb></lb>the Pillar of Marble, or Braſs, I cannot ſee why it ſhould not alſo <lb></lb>take place, and be likewiſe the Cauſe of the Coherence of the leſ<lb></lb>ſer parts, and even of the very leaſt and laſt, of the ſame Matters: <lb></lb><arrow.to.target n="marg1015"></arrow.to.target><lb></lb>and being that of one ſole Effect, there is but one only true, and <pb xlink:href="040/01/708.jpg" pagenum="16"></pb>moſt potent Cauſe; if I can find no other Cement, why may I not <lb></lb>try whether this of Vacuity, which I have already found, may be <lb></lb>ſufficient?</s></p><p type="margin"> <s><margin.target id="marg1015"></margin.target><emph type="italics"></emph>There is but one <lb></lb>ſole Cauſe of one <lb></lb>ſole Effect.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SIMP. </s> <s>But when you have already demonſtrated the Reſi<lb></lb>ſtance of the great Vacuity in the ſeparation of the two great <lb></lb>parts of a Solid to be very ſmall in compariſon of that which con<lb></lb>necteth, and conſolidates the little Particles, or Atomes, why will <lb></lb>you not ſtill hold, for certain, that this is extreamly differing from <lb></lb>that?</s></p><p type="main"> <s>SALV. </s> <s>To this <emph type="italics"></emph>Sagredus<emph.end type="italics"></emph.end> anſwereth, That every particular <lb></lb>Souldier is ſtill paid with money collected by the general Impoſi<lb></lb>tions of Shillings and Pence, although a Million of Gold ſufficeth <lb></lb>not to pay the whole Army. </s> <s>And who knows, but that other ex<lb></lb>ceeding ſmall Vacuities may operate amongſt thoſe ſmall Atomes, <lb></lb>(even like as that was of the ſelf-ſame money) wherewith all <lb></lb>the parts are connected? </s> <s>I will tell you what I have ſometimes <lb></lb>fancied: and I give it you, not as an unqueſtionable Truth, but as a <lb></lb>kind of Conjecture very undigeſted, ſubmitting it to exacter con<lb></lb>ſiderations: Pick out of it what pleaſeth you, and judge of the reſt <lb></lb><arrow.to.target n="marg1016"></arrow.to.target><lb></lb>as you think fit. </s> <s>Conſidering ſometimes how the Fire, penetra<lb></lb>ting and inſinuating between the ſmall Atomes of this or that Me<lb></lb>tal, which were before ſo cloſely conſolidated, in the end ſepa<lb></lb>rates, and diſunites them; and how, the Fire being gone, they re<lb></lb>turn with the ſame Tenacity as before to Conſolidation, without <lb></lb>diminiſhing in quantity, (at all in Gold, and very little in other <lb></lb>Metals,) though they continue a long time melted; I have thought <lb></lb>that that might happen, by reaſon the extream ſmall parts of the <lb></lb>Fire, penetrating through the narrow pores of the Metal (through <lb></lb>which the leaſt parts of Air, or of many other Fluids, could not <lb></lb>for their cloſeneſs perforate) by repleating the ſmall interpoſing <lb></lb>Vacuities might free the minute parts of the ſame from the vio<lb></lb>lence, wherewith the ſaid Vacuities attract them one to another, <lb></lb>prohibiting their ſeparation: and thus becoming able to move <lb></lb>freely, their Maſs might become fluid, and continue ſuch, as long <lb></lb>as the ſmall parts of the Fire ſhould abide betwixt them: and that <lb></lb>thoſe departing, and leaving the former Vacuities, their wonted <lb></lb>attractions might return, and conſequently the Coheſion of the <lb></lb>parts. </s> <s>And, as to the Allegation made by <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> it may, in <lb></lb>my opinion, be thus reſolved; That although ſuch Vacuities ſhould <lb></lb>be very ſmall, and conſequently each of them eaſie to be over<lb></lb>come, yet nevertheleſs their innumerable multitude innumerably <lb></lb><arrow.to.target n="marg1017"></arrow.to.target><lb></lb>(if it be proper ſo to ſpeak) multiplieth the Reſiſtances: and we <lb></lb>have an evident proof what, and how great is the Force that reſul<lb></lb>teth from the conjunction of an immenſe number of very weak <lb></lb>Moments, in ſeeing a Weight of many thouſands of pounds, held <pb xlink:href="040/01/709.jpg" pagenum="17"></pb>by mighty Cables, to yield, and ſuffer it ſelf at laſt to be over<lb></lb>come by the aſſault of the innumerable Atomes of Water; which, <lb></lb>either carryed by the South-wind, or elſe by being diſtended into <lb></lb>very thin Miſts that move to and fro in the Air, inſinuate them<lb></lb>ſelves between ſtring and ſtring of the Hemp of the hardeſt twi<lb></lb>ſted Cables; nor can the immenſe force of the pendent Weight <lb></lb>prohibit their enterance; ſo that perforating the ſtrict paſſages be<lb></lb>tween the Pores, they ſwell the Ropes, and by conſequence ſhor<lb></lb>ten them, whereupon that huge Maſs is forcibly raiſed.</s></p><p type="margin"> <s><margin.target id="marg1016"></margin.target><emph type="italics"></emph>Moſt ſmall Va<lb></lb>cuities diſſemina<lb></lb>ted and interpoſed <lb></lb>between the ſmall <lb></lb>Corpuſcles of So<lb></lb>lids the probable <lb></lb>cauſe of the conſi<lb></lb>ſtence or connecti<lb></lb>on of thoſe Corpuſ<lb></lb>cles to one another,<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1017"></margin.target><emph type="italics"></emph>Innumerable A<lb></lb>tomes of Water in<lb></lb>ſinuating into Ca<lb></lb>bles draw and raiſe <lb></lb>an immenſe weight<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. There's no doubt but that ſo long as a Reſiſtance is not <lb></lb><arrow.to.target n="marg1018"></arrow.to.target><lb></lb>infinite, it may by a multitude of moſt minute Forces be over<lb></lb>come; inſomuch that a competent number even of Ants would <lb></lb>be able to carry to ſhore a whole ſhips lading of Corn: for Senſe <lb></lb>giveth us quotidian examples, that an Ant carrieth a ſingle grain <lb></lb>with eaſe; and its cleer, that in the Ship there are not infinite <lb></lb>grains, but that they are compriſed in a certain number; and if you <lb></lb>take another number four or ſix times bigger than that, and take <lb></lb>alſo another of Ants equal to it, and ſet them to work, they ſhall <lb></lb>carry the Corn, and the Ship alſo. </s> <s>It is true indeed, that it will be <lb></lb>needful that the number be great, as alſo in my judgment that of <lb></lb>the <emph type="italics"></emph>Vacuities,<emph.end type="italics"></emph.end> which hold together the ſinall parts of the <lb></lb>Mettal.</s></p><p type="margin"> <s><margin.target id="marg1018"></margin.target><emph type="italics"></emph>Any finite Reſi<lb></lb>ſtance is ſuperable <lb></lb>by any the leaſt <lb></lb>Force, multiplied.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>But though they were required to be infinite, do you <lb></lb>think it impoſſible?</s></p><p type="main"> <s>SAGR. </s> <s>Not if the Mettal were of an infinite maſſe; other<lb></lb>wiſe ----</s></p><p type="main"> <s>SALV. </s> <s>Otherwiſe what? </s> <s>Go to, feeing we are faln upon <lb></lb>Paradoxes, let us ſee if we can any way demonſtrate, how that <lb></lb>in a continuate finite extenſion, it is not impoſſible to finde infi<lb></lb>nite <emph type="italics"></emph>Vacuities:<emph.end type="italics"></emph.end> and then, if we gain nothing elſe, yet at leaſt we <lb></lb><arrow.to.target n="marg1019"></arrow.to.target><lb></lb>ſhall finde a ſolution of that moſt admirable Problem propound<lb></lb>ed by <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> amongſt thoſe which he himſelf calleth admirable, <lb></lb>I mean amongſt his <emph type="italics"></emph>Mechanical Queſtions<emph.end type="italics"></emph.end>; and the Solution may <lb></lb>haply be no leſſe plain and concluding, than that which he himſelf <lb></lb>brings thereupon, and different alſo from that which Learned <lb></lb><arrow.to.target n="marg1020"></arrow.to.target><lb></lb><emph type="italics"></emph>Monſig. </s> <s>di Guevara<emph.end type="italics"></emph.end> very acutely diſcuſſeth. </s> <s>But it is firſt requiſite <lb></lb>to declare a Propoſition not toucht by others, on which the ſolution <lb></lb>of the queſtion dependeth, which afterwards, if I deceive not my <lb></lb>ſelf, will draw along with it other new and admirable Notions; for <lb></lb>underſtanding whereof the more exactly, we will give it you in <lb></lb>a Scheme: We ſuppoſe, therefore an equilateral, and equian<lb></lb>gled Poligon of any number of Sides at pleaſure, deſcribed <lb></lb>about this Center G; and in this example let it be a Hexagon <lb></lb>A B C D E F; like to which, and concentrick with the ſame <lb></lb>muſt be diſtributed another leſſer, which we mark H I K L M N; <pb xlink:href="040/01/710.jpg" pagenum="18"></pb>and let one Side of the greater A B be prolonged indeterminately <lb></lb>towards S, and of the leſſe the correſpondent Side H I is to be <lb></lb>produced in like manner towards the ſame part, repreſenting the <lb></lb>Line H T, parallel to A S; and let another paſſe by the Center <lb></lb>equidiſtant from the former, namely G V. </s> <s>This done, we ſuppoſe <lb></lb>the greater Poligon to turn about upon the Line A S, carrying <lb></lb>with it the other leſſer Poligon. </s> <s>It is manifeſt, that the point B, <lb></lb>the term of the Side A B, ſtanding ſtill, whilſt the Revolution <lb></lb>begins, the angle A riſeth, and the point C deſcendeth, deſcribing <lb></lb>the arch C <expan abbr="q;">que</expan> ſo that the Side B C is applyed to the line B Q, <lb></lb>equal to it ſelf: but in ſuch converſion the angle I of the leſſer <lb></lb>Poligon riſeth above the Line I T. for that I B is oblique upon <lb></lb>A S: nor will the point I fall upon the parallel I T, before the <lb></lb>point C come to Q: and by that time I ſhall be deſcended unto <lb></lb>O after it had deſcribed the Arch I O, without the Line H T: and <lb></lb>at the ſame time the Side I K ſhall have paſs'd to O P. </s> <s>But the Cen<lb></lb>ter G ſhall have gone all this time out of the Line G V, on which it <lb></lb>ſhal not fall, until it ſhall firſt have deſcribed the Arch G C. </s> <s>Having <lb></lb>made this firſt ſtep, the greater Poligon ſhall be tranſpoſed to reſt <lb></lb>with the Side B C upon the Line B <expan abbr="q;">que</expan> the Side I K of the leſſer <lb></lb>upon the Line O P, having skipt all the Line I O without touching <lb></lb><figure id="id.040.01.710.1.jpg" xlink:href="040/01/710/1.jpg"></figure><lb></lb>it; and the Center G ſhall be removed to C, making its whole <lb></lb>courſe without the Parallel G V: And in fine all the Figure ſhall <lb></lb>be remitted into a Poſition like the firſt; ſo that the Revolution <lb></lb>being continued, and coming to the ſecond ſtep, the Side of the <lb></lb>greater Poligon D C ſhall remove to Q X; K L of the leſſer (ha<lb></lb>ving firſt skipt the Arch P Y) ſhall fall upon Y Z, and the Center <lb></lb>proceeding evermore without G V ſhall fall on it in R, after the <lb></lb>great skip C R. </s> <s>And in the laſt place, having finiſhed an entire <lb></lb>Converſion, the greater Poligon will have impreſſed upon A S, ſix <pb xlink:href="040/01/711.jpg" pagenum="19"></pb>Lines equal to its Perimeter without any interpoſitions or skips: <lb></lb>the leſſer Poligon likewiſe ſhall have traced ſix Lines equal to its <lb></lb>Perimeter, but diſcontinued by the interpoſition of five Arches, <lb></lb>under which are the Chords, parts of the parallel H T not toucht <lb></lb>by the Poligon: And laſtly, the Center G never hath toucht the <lb></lb>Parallel G V except in ſix points. </s> <s>From hence you may compre<lb></lb>hend, how that the Space paſſed by the leſſer Poligon, is almoſt <lb></lb>equal to that paſſed by the greater, that is the Line H T is almoſt <lb></lb>equal to A S, then which it is leſſer only the quantity of one of <lb></lb>theſe Arches, taking the Line H T, together with all its Arches. <lb></lb></s> <s>Now, this which I have declared and explained to you in the exam<lb></lb>ple of theſe Hexagons, I would have you underſtand to hold true <lb></lb>in all other Poligons, of what number of Sides ſoever they be, ſo <lb></lb>that they be like Concentrick, and Conjoyned; and that at the <lb></lb>Converſion of the greater, the other, how much ſoever leſſer, be <lb></lb>ſuppoſed to revolve therewith: that is, you muſt underſtand, I ſay, <lb></lb>that the Lines by them paſſed are very near equal, computing in<lb></lb>to the Space paſt by the leſſer, the Intervals under the little Ar<lb></lb>ches not toucht by any part of the Perimeter of the ſaid leſſer Po<lb></lb>ligon. </s> <s>Let therefore the greater Poligon, of a thouſand Sides, paſs <lb></lb>round, and meaſure out a continued Line equal to its Perimeter; <lb></lb>and in the ſame time the leſs paſſeth a Line almoſt as long, but <lb></lb>compounded of a thouſand Particles equal to its thouſand Sides, <lb></lb>but diſcontinued with the interpoſition of a thouſand void Spaces: <lb></lb>for ſuch may we call them, in relation to the thouſand little Lines <lb></lb>toucht by the Sides of the Poligon. </s> <s>And what hath been ſpoken <lb></lb>hitherto admits of no doubt or ſcruple. </s> <s>But tell me, in caſe that <lb></lb>about a Center, as ſuppoſe the point A, (in the former Scheme) <lb></lb>we ſhould deſcribe two Circles concentrick, and united together; <lb></lb>and that from the points C and B of their Semi-Diameters, there <lb></lb>be drawn the Tangents C E, and B F, and by the Center A the Pa<lb></lb>rallel A D; ſuppoſing the greater Circle to be turned upon the <lb></lb>Line B F, (drawn equal to its Circumference, as likewiſe the other <lb></lb>two C E, and A D;) when it hath compleated one Revolution, <lb></lb>what ſhall the leſſer Circle, and Center have done? </s> <s>The Center <lb></lb>ſhall doubtleſs have run over, and touched the whole Line A D, <lb></lb>and the leſs Circumference ſhall with its touches have meaſured <lb></lb>all C E, doing the ſame as did the Poligons above; and different <lb></lb>only in this, that the Line H T was not touched in all its Parts by <lb></lb>the Perimeter of the leſſer Poligon, but there were as many parts <lb></lb>left untoucht with the interpoſition of ſalts, or skipped ſpaces; as <lb></lb>were theſe parts touched by the Sides: but here in the Circles, <lb></lb>the Circumference of the leſſer Circle, never ſeparates from the <lb></lb>Line C E, ſo as to leave any of its parts untou cht; nor is the parts <lb></lb>touching of the Circumference, leſs than the part toucht of the <pb xlink:href="040/01/712.jpg" pagenum="20"></pb>Right-line. </s> <s>Now how is it poſſible that the leſſer Circle ſhould <lb></lb>without skips run a Line ſo much bigger than its Circumfe<lb></lb>rence?</s></p><p type="margin"> <s><margin.target id="marg1019"></margin.target>Ariſtotles <emph type="italics"></emph>admi<lb></lb>rable Problem of <lb></lb>two Concentrick <lb></lb>Circles that turn <lb></lb>round, and its true <lb></lb>reſolution.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1020"></margin.target>Monſig. </s> <s>Gueva <lb></lb>ra <emph type="italics"></emph>honourably men<lb></lb>tioned.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>I was conſidering whether one might not ſay, that like <lb></lb>as the Center of the Circle trailed alone upon A D toucht, it all <lb></lb>being yet but one ſole Point; ſo likewiſe might the Points of the <lb></lb>leſſer Circumference, drawn by the revolution of the greater, go <lb></lb>gliding along ſome ſmall part of the Line C E.</s></p><p type="main"> <s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>ALV. </s> <s>This cannot be, for two reaſons; firſt, becauſe there is <lb></lb>no reaſon why ſome of the touches like to C ſhould go gliding <lb></lb>along ſome part of the Line C E, more than others: and though <lb></lb>there ſhould; ſuch touches being (becauſe they are points) inſi<lb></lb>nite, the glidings along upon C E would be infinite; and ſo being, <lb></lb>they would make an infinite Line, but the Line C E is finite. </s> <s>The <lb></lb>other reaſon is, that the greater Circle, in its Revolution continu<lb></lb>ally changing contact, the leſſer Circle muſt of neceſſity do the <lb></lb>like; there being no other Point but B, by which a Right Line can <lb></lb>be drawn to the Center A, and paſſing through C; ſo that the <lb></lb>greater Circumference changing Contact, the leſs doth change it <lb></lb>alſo; nor doth any Point of the leſs touch more than one Point of <lb></lb>its Right-Line C E: beſides, that alſo in the converſion of the Po<lb></lb>ligons, no Point of the Perimeter of the leſs falls on more than one <lb></lb>Point of the Line, which was by the ſaid Perimeter traced, as may <lb></lb>be eaſily underſtood, conſidering the Line I K is parallel to B C, <lb></lb>whereupon, till juſt that B C fall on B R, I K continueth elevated <lb></lb>above I P, and toucheth it not before B C is on the very Point of <lb></lb>uniting with B Q, and then all in the ſame inſtant I K uniteth <lb></lb>with O P, and afterwards immediately riſeth above it again.</s></p><p type="main"> <s>SAGR. </s> <s>The buſineſs is really very intricate, nor can I think on <lb></lb>any Solution of it, therefore do you explain it to us as far as you <lb></lb>judge needful.</s></p><p type="main"> <s>SALV. </s> <s>I ſhould, for the evincing hereof, have recourſe to the <lb></lb>conſideration of the fore-deſcribed Poligons, the effect of which is <lb></lb>intelligible and already comprehended, and would ſay, that like as <lb></lb>in the Poligons of an hundred thouſand Sides, the Line paſſed and <lb></lb>meaſured by the Perimeter of the greater, that is by its hundred <lb></lb>thouſand Sides continually diſtended, is not conſiderably bigger <lb></lb>than that meaſured by the hundred thouſand Sides of the leſs, but <lb></lb>with the interpoſition of an hundred thouſand void ſpaces interve<lb></lb>ning; fo I would ſay in the Circles (which are Poligons of innu<lb></lb>merable Sides) that the Line meaſured by the infinite Sides of the <lb></lb>great Circle, lying continued one with another, to be equalled in <lb></lb>length by the Line traced by the infinite Sides of the leſs, but by <lb></lb>theſe including the interpoſition of the like number of intervening <lb></lb>Spaces: and like as the Sides are not quantitative, but yet infinite <pb xlink:href="040/01/713.jpg" pagenum="21"></pb>in number, ſo the interpoſing Vacuitics are not quantitative, but <lb></lb>infinite in number; that is, thoſe are infinite Points all filled, and <lb></lb>theſe are infinite points, part filled, and part empty. </s> <s>And here I <lb></lb>would have you note, that reſolving, and dividing a Line into quan<lb></lb>titative parts, and conſequently of a finite number, it is not poſſible <lb></lb>to diſpoſe them into a greater extention than that which they poſ<lb></lb>ſeſt whilſt they were continued, and connected, without the inter<lb></lb>poſition of a like number of void Spaces; but imagining it to be <lb></lb>reſolved into parts not quantitative, namely, into its infinite indivi<lb></lb>ſibles, we may conceive it produced to immenſity without the in<lb></lb>terpoſition of quantitative void ſpaces, but yet of infinite indiviſi<lb></lb>ble Vacuities. </s> <s>And this which is ſpoken of ſimple lines, ſhould alſo <lb></lb>be underſtood of Superficies, and Solid Bodies, conſidering that they <lb></lb>are compoſed of infinite Atomes not non-quantitative; if we would <lb></lb>divide them into certain quantitative parts, there's no queſtion, but <lb></lb>that we cannot diſpoſe them into Spaces more ample than the Solid <lb></lb>before occupied, unleſs with the interpoſition of a certain number <lb></lb>of quantitative void Spaces; void, I ſay, at leaſt of the matter of the <lb></lb>Solid: but if we ſhould propoſe the higheſt, and ultimate reſolution <lb></lb>made into the firſt, non-quantitative, but infinite firſt compoun<lb></lb>ding parts, we may be able to conceive ſuch compounding parts <lb></lb>extended unto an immenſe Space without the interpoſition of <lb></lb>quantitative void Spaces; but only of infinite non-quantitative Va<lb></lb>cuities: and in this manner a man may draw out, <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> a little Ball <lb></lb>of Gold into a very vaſt expanſion without admitting any quan<lb></lb>titative void Spaces; yet nevertheleſs we may admit the Gold to <lb></lb>be compounded of infinite induciſſible ones.</s></p><p type="main"> <s>SIMP. </s> <s>Me thinks that in this point you go the way of thoſe diſ<lb></lb>ſeminated Vacuities of a certain <emph type="italics"></emph>Ancient Philoſopher<emph.end type="italics"></emph.end> ------</s></p><p type="main"> <s>SALV. </s> <s>But you add not: [<emph type="italics"></emph>who denied Divine Providence:)<emph.end type="italics"></emph.end><lb></lb>as on ſuch another occaſion, ſufficiently beſides his purpoſe, a cer<lb></lb>tain Antagoniſt of our <emph type="italics"></emph>Accademick<emph.end type="italics"></emph.end> did ſubjoyn.</s></p><p type="main"> <s>SIMP. </s> <s>I ſee very well, and not without indignation, the malice <lb></lb>of ſuch contradictors; but I ſhall forbear theſe Cenſures, not only <lb></lb>upon the ſcore of Good-Manners, but becauſe I know how diſa<lb></lb>greeing ſuch Tenets are to the well-tempered, and well-diſpoſed <lb></lb>mind of a perſon, ſo Religious and Pious, yea, Orthodox and Ho<lb></lb>ly, as you, Sir. </s> <s>But returning to my purpoſe; I find many ſcruples <lb></lb>to ariſe in my mind about your laſt Diſcourſe, which I know not <lb></lb>how to reſolve. </s> <s>And this preſents its ſelf for one, that if the Cir<lb></lb>cumferences of two Circles are equall to the two Right Lines <lb></lb>C E, and B F, this taken continually, and that, with the interpoſi<lb></lb>tion of infinite void Points; how can A D, deſcribed by the Center, <lb></lb>which is but one ſole Point, be ſaid to be equal to the ſame, it con<lb></lb>taining infinite of them? </s> <s>Again, that ſame compoſing the Line of <pb xlink:href="040/01/714.jpg" pagenum="22"></pb>Points, the diviſible of indiviſibles, the quantitative of non-quan<lb></lb>titative, is a rock very hard, in my judgment, to paſs over: And <lb></lb>the very admitting of Vacuity, ſo thorowly confuted by <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end><lb></lb>no leſs puzleth me than thoſe difficulties themſelves.</s></p><p type="main"> <s>SALV. </s> <s>There be, indeed, theſe and other difficulties; but re<lb></lb>member, that we are amongſt Infinites, and Indiviſibles: thoſe in<lb></lb>comprehenſible by our finite underſtanding for their Grandure; <lb></lb>and theſe for their minuteneſs: nevertheleſs we ſee that Humane <lb></lb>Diſcourſe will not be beat off from ruminating upon them, in <lb></lb>which regard, I alſo aſſuming ſome liberty, will produce ſome of <lb></lb>my conceits, if not neceſſarily concluding, yet for novelty ſake, <lb></lb>which is ever the meſſenger of ſome wonder: but perhaps the car<lb></lb>rying you ſo far out of your way begun, may ſeem to you imper<lb></lb>tinent, and conſequently little pleaſing.</s></p><p type="main"> <s>SAGR. </s> <s>Pray you let us enjoy the benefit, and priviledge, of free <lb></lb>ſpeaking which is allowed to the living, and amongſt friends; eſpe<lb></lb>cially, in things arbitrary, and not neceſſary; different from Diſcourſe <lb></lb>with dead Books, which ſtart us a thouſand doubts, and reſolve not <lb></lb>one of them. </s> <s>Make us therefore partakers of thoſe Conſiderations, <lb></lb>which the courſe of our Conferences ſuggeſt unto you; for we <lb></lb>want no time, ſeeing we are diſengaged from urgent buſineſſes, to <lb></lb>continue and diſcuſſe the other things mentioned; and particular<lb></lb>ly, the doubts, hinted by <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> muſt by no means eſcape us.</s></p><p type="main"> <s>SAIV. </s> <s>It ſhall be ſo, ſince it pleaſeth you: and beginning at <lb></lb>the firſt, which was, how it's poſſible to imagine that a ſingle Point <lb></lb>is equal to a Line; in regard I can do no more for the preſent, I <lb></lb>will attempt to ſatisfie, or, at leaſt, qualifie one improbability with <lb></lb>another like it, or greater; as ſome times a Wonder is ſwallowed <lb></lb>up in a Miracle. </s> <s>And this ſhall be by ſhewing you two equal Su<lb></lb>perficies, and at the ſame time two Bodies, likewiſe equal, and <lb></lb>placed upon thoſe Superficies as their Baſes; and that go (both <lb></lb>theſe and thoſe) continually and equally diminiſhing in the ſelf<lb></lb><arrow.to.target n="marg1021"></arrow.to.target><lb></lb>ſame time, and that in their remainders reſt alwaies equal between <lb></lb>themſelves, and (laſtly) that, as well Superſicies, as Solids, deter<lb></lb>mine their perpetual precedent equalities, one of the Solids with <lb></lb>one of the Superficies in a very long Line; and the other Solid <lb></lb>with the other Superficies in a ſingle Point: that is, the latter in <lb></lb>one Point alone, the other in infinite.</s></p><p type="margin"> <s><margin.target id="marg1021"></margin.target><emph type="italics"></emph>The equal Super<lb></lb>ficies of two Solids <lb></lb>continually ſub<lb></lb>ſtracting from <lb></lb>them both equal <lb></lb>parts, are reduced, <lb></lb>the one into the <lb></lb>Circumference of a <lb></lb>Circle, and the o<lb></lb>ther into a Point.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>AGR. </s> <s>An admirable propoſal, really, yet let us hear you ex<lb></lb>plain and demonſtrate it.</s></p><p type="main"> <s>SALV. </s> <s>It is neceſſary to give you it in Figure, becauſe the proof <lb></lb>is purely Geometrical. </s> <s>Therefore ſuppoſe the Semicircle A F B, <lb></lb>and its Center to be C, and about it deſcribe the Rectangle <lb></lb>A D E B, and from the Center unto the Points D and E let there <lb></lb>be drawn the Lines C D, and C E; Then drawing the Semi-Dia<pb xlink:href="040/01/715.jpg" pagenum="23"></pb>meter C F, perpendicular to one of the two Lines A B, or D E <lb></lb>and immoveable; we ſuppoſe all this Figure to turn round about <lb></lb>that Perpendicular: It is manifeſt, that there will be deſcribed by <lb></lb>the Parallelogram A D E B, a Cylinder; by the Semi-circle A F B, <lb></lb>an Hemi-Sphære; and by the Triangle C D E a Cone. </s> <s>This pre<lb></lb>ſuppoſed, I would have you imagine the Hemiſphære to be taken <lb></lb>away, leaving behind the Cone, and that which ſhall remain of <lb></lb>the Cylinder; which for the Figure, which it ſhall retain like to a <lb></lb>Diſh, we will hereafter call a Diſh: touching which, and the <lb></lb>Cone, we will ſirſt demonſtrate that they are equal; and next <lb></lb>a Plain being drawn parallel to the Circle, which is the foot or <lb></lb>Baſe of the Diſh, whoſe Diameter is the Line D E, and its Center <lb></lb>F; we will demonſtrate, that ſhould the ſaid Plain paſs, <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> by <lb></lb>the Line G H, cutting the Diſh in the points G I, and O N; and <lb></lb>the Cone in the points H and L; it would cut the part of the <lb></lb>Cone C H L, equal alwaies to the part of the Diſh, whoſe Profile <lb></lb>is repreſented to us by the Triangles G A I, and B O N: and more<lb></lb>over we will prove the Baſe alſo of the ſame Cone, (that is the <lb></lb>Circle, whoſe Diameter is H L) to be equal to that circular Su<lb></lb>perficies, which is Baſe of the part of the Diſh; which is, as we <lb></lb>may ſay, a Rimme as broad as G I; (note here by the way what <lb></lb>Mathematical Definitions are: they be an impoſition of names, or, <lb></lb>we may ſay, abreviations of ſpeech, ordain'd and introduced to <lb></lb>prevent the trouble and pains, which you and I meet with, at pre<lb></lb>ſent, in that we have not agreed together to call <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> this Super<lb></lb>ficies a circular Rimme, and that very ſharp Solid of the Diſh a <lb></lb>round Razor:) now howſoever you pleaſe to call them, it ſufficeth <lb></lb>you to know, that the Plain produced to any diſtance at pleaſure, <lb></lb>ſo that it be parallel to the Baſe, <emph type="italics"></emph>viz.<emph.end type="italics"></emph.end> to the Circle whoſe Diame<lb></lb>ter D E cuts alwaies the two Solids, namely, the part of the Cone <lb></lb>C H L, and the upper part of the Diſh equal to one another: and <lb></lb>likewiſe the two Superficies, Baſis of the ſaid Solids, <emph type="italics"></emph>viz.<emph.end type="italics"></emph.end> the ſaid <lb></lb>Rimme, and the Circle H L, equal alſo to one another. </s> <s>Whence <lb></lb>followeth the forementioned Wonder; namely, that if we ſhould <lb></lb>ſuppoſe the cutting-plain to be <lb></lb>ſucceſſively raiſed towards the <lb></lb><figure id="id.040.01.715.1.jpg" xlink:href="040/01/715/1.jpg"></figure><lb></lb>Line A B, the parts of the Solid <lb></lb>cut are alwaies equall, as alſo the <lb></lb>Superficies, that are their Baſes, <lb></lb>are evermore equal; and, in <lb></lb>fine, raiſing the ſaid Plain higher <lb></lb>and higher, the two Solids (ever <lb></lb>equal) as alſo their Baſes, (Su<lb></lb>perficies ever equal) ſhall one couple of them terminate in a Cir<lb></lb>cumference of a Circle, and the other couple in one ſole point; <pb xlink:href="040/01/716.jpg" pagenum="24"></pb>for ſuch are the upper Verge or Rim of the Diſh, and the Vertex <lb></lb>of the Cone. </s> <s>Now whilſt that in the diminution of the two So<lb></lb>lids, they till the very laſt maintain their equality to one another, it <lb></lb>is, in my thoughts, proper to ſay, that the higheſt and ultimate terms <lb></lb>of ſuch Diminutions are equal, and not one infinitely bigger than <lb></lb>the other. </s> <s>It ſeemeth therefore, that the Circumference of an im<lb></lb>menſe Circle may be ſaid to be equal to one ſingle point; and <lb></lb>this that befalls in Solids, holdeth likewiſe in the Superficies their <lb></lb>Baſes; that they alſo in the common Diminution conſerving al<lb></lb>waies equality, in fine, determine at the inſtant of their ultimate <lb></lb>Diminution the one, (that is, that of the Diſh) in their Circum<lb></lb>ference of a Circle, the other (to wit, that of the Cone) in one <lb></lb>ſole point. </s> <s>And why may not theſe be called equal, if they be the <lb></lb>laſt remainders, and footſteps left by equal Magnitudes? </s> <s>And note <lb></lb>again, that were ſuch Veſſels capable of the immenſe Cœleſtial <lb></lb>Hemiſpheres: both their upper Rims, and the points of the contai<lb></lb>ned Cones (keeping evermore equally to one another) would fi<lb></lb>nally determine, thoſe, in Circumferences equal to thoſe of the <lb></lb>greateſt Circles of the Cœleſtial Orbes, and theſe in ſimplo points. <lb></lb></s> <s>Whence, according to that which ſuch Speculations perſwade us <lb></lb>to, all Circumferences of Circles, how unequal ſoever, may be <lb></lb>ſaid to be equal to one another, and each of them equal to one ſole <lb></lb>point.</s></p><p type="main"> <s>SAGR. </s> <s>The Speculation is, in my eſteem, ſo quaint and curi<lb></lb>ous, that, for my part, though I could, yet would I not oppoſe it, <lb></lb>for I take it for a piece of Sacriledge to deface ſo fine a Structure, <lb></lb>by ſpurning at it with any pedantick contradiction; yet for our en<lb></lb>tire ſatisfaction, give us the proof (which you ſay is Geometrical) <lb></lb>of the equality alwaies retained between thoſe Solids, and thoſe <lb></lb>their Baſes, which I think muſt needs be very ſubtil, the philoſo<lb></lb>phical Contemplation being ſo nice, which depends on the ſaid <lb></lb>Concluſion.</s></p><p type="main"> <s>SALV. </s> <s>The Demonſtration is but ſhort, and eaſie. </s> <s>Let us keep <lb></lb>to the former Figure, in which the Angle I P C being a Right An<lb></lb>gle, the Square of the Semi-Diameter I C is equal to the two <lb></lb>Squares of the Sides I P, and P C. </s> <s>But the Semi-Diameter I C, is <lb></lb>equal to A C, and this to G P; and C P is equal to P H; therefore <lb></lb>the Square of the Line G P is equal to the two Squares of I P, and <lb></lb>P H, and the Quadruple to the Quadruples; that is, the Quadrate <lb></lb>of the Diameter G N is equal to the two Quadrates I O, and H L: <lb></lb>and becauſe Circles are to each other, as the Squares of their Dia<lb></lb>meters; the Circle whoſe Diameter is G N, ſhall be equall to the <lb></lb>two Circles whoſe Diameters are I O, and H L; and taking away <lb></lb>the Common Circle, whoſe Diameter is I O; the reſidue of the <lb></lb>Circle G N ſhall be equal to the Circle, whoſe Diameter is H L. <pb xlink:href="040/01/717.jpg" pagenum="25"></pb>And this is as to the firſt part: Now as for the other part, we will, <lb></lb>for the preſent, omit its Demonſtration, as well becauſe that if you <lb></lb>would ſee it, you ſhall find it in the twelfth Propoſition of the Se<lb></lb><arrow.to.target n="marg1022"></arrow.to.target><lb></lb>cond Book <emph type="italics"></emph>De centro Gravitatis Solidorum,<emph.end type="italics"></emph.end> publiſhed by <emph type="italics"></emph>Signeur <lb></lb>Lucas Valerius,<emph.end type="italics"></emph.end> the new <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> of our Age; who upon ano<lb></lb>ther occaſion hath made uſe of it; as becauſe in our caſe it ſuffi<lb></lb>ceth to have ſeen, how the Superficies, already explained, are ever<lb></lb>more equal; and that alwaies diminiſhing equally, they in the end <lb></lb>determine, one in a ſingle point, and the other in the Circumfe<lb></lb>rence of a Circle, be it never-ſomuch bigger, for in this lyeth our <lb></lb>Wonder.</s></p><p type="margin"> <s><margin.target id="marg1022"></margin.target>Lucas Valerius, <lb></lb><emph type="italics"></emph>the other<emph.end type="italics"></emph.end> Archi<lb></lb>chimedes <emph type="italics"></emph>of our <lb></lb>Age, hath written <lb></lb>admirably,<emph.end type="italics"></emph.end> De <lb></lb>Centro Gravita<lb></lb>tis Solidorum.</s></p><p type="main"> <s>SAGR. </s> <s>The Demonſtration is as ingenious, as the reflection <lb></lb>grounded upon it is admirable. </s> <s>Now let us hear ſomewhat about <lb></lb>the other Doubt ſuggeſted by <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> if you have any particu<lb></lb>lars worth note to hint thereupon, but I ſhould incline to think it <lb></lb>impoſſible to be, in regard it is a Controverſie that hath been ſo <lb></lb>canvaſſed.</s></p><p type="main"> <s>SALV. </s> <s>You ſhall have ſome of my particular thoughts thereon; <lb></lb>firſt repeating what but even now I told you, namely, that Infini<lb></lb>ty alone, as alſo Indiviſibility, are things incompre henſible to us: <lb></lb>now think how they will be conjoyned together: and yet if you <lb></lb>would compound the Line of indiviſible points, you muſt make <lb></lb>them infinite; and thus it will be requiſite to apprehend in the <lb></lb>ſame inſtant both Infinite, and Indiviſible. </s> <s>The things that ar ſe<lb></lb>veral times have come into my mind, on this occaſion, are many; <lb></lb>part whereof, and the more conſiderable, it may be, I cannot upon <lb></lb>ſuch a ſudden remember; but it may happen, that in the ſequal <lb></lb>of the Diſcourſe, coming to put queſtions and doubts to you, and <lb></lb>particularly to <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> they may, on the other ſide, re-mind <lb></lb>me of that, which without ſuch excitement would have lain dor<lb></lb>mant in my Fancy: and therefore, with my wonted freedom, per<lb></lb>mit me that I produce any wild conjectures, for ſuch may we fitly <lb></lb>call them in compariſon of ſupernatural Doctrines, the only true <lb></lb>and certain determiners of our Controverſies, and unerring guides <lb></lb>in our obſcure, and dubious paths, or rather Laberinths.</s></p><p type="main"> <s>Amongſt the firſt Inſtances that are wont to be produced <lb></lb><arrow.to.target n="marg1023"></arrow.to.target><lb></lb>againſt thoſe that compound <emph type="italics"></emph>Continuum<emph.end type="italics"></emph.end> of Indiviſibles, this is uſu<lb></lb>ally one; That an Indiviſible, added to another Indiviſible, produ<lb></lb>ceth not a thing diviſible; for if that were ſo, it would follow, that <lb></lb>even the Indiviſibles were diviſible: for if two Indiviſibles, as for <lb></lb>example, two Points conjoyned, ſhould make a Quantity that <lb></lb>ſhould be a diviſible Line, much more ſuch ſhould one be that is <lb></lb>compounded of three, five, ſeven, or others, that are odd num<lb></lb>bers; the which Lines, being to be cut in two equal parts, render <lb></lb>diviſible that Indiviſible which was placed in the middle. </s> <s>In this <pb xlink:href="040/01/718.jpg" pagenum="26"></pb>and other Objections of this kind you may ſatisfie the propoſer of <lb></lb>them, telling him, that neither two Indiviſibles, nor ten, nor an <lb></lb>hundred, no, nor a thouſand can compound a Magnitude diviſible, <lb></lb>and quantitative, but being infinite they may.</s></p><p type="margin"> <s><margin.target id="marg1023"></margin.target>Continuum <emph type="italics"></emph>com<lb></lb>pounded of Indivi<lb></lb>ſibles.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SIMP. </s> <s>Here already riſeth a doubt, which I think unreſolvable; <lb></lb>and it is, that we being certain to find Lines one bigger than ano<lb></lb>ther, although both contain infinite Points, we muſt of neceſſity <lb></lb>confeſs, that we have found in the ſame Species a thing bigger than <lb></lb>infinite; becauſe the Infinity of the Points of the greater Line, ſhall <lb></lb>exceed the Infinity of the Points of the leſſer. </s> <s>Now this aſſigning <lb></lb>of an Infinite bigger than an Infinite is, in my opinion, a conceit <lb></lb>that can never by any means be apprehended.</s></p><p type="main"> <s>SALV. </s> <s>Theſe are ſome of thoſe difficulties, which reſult from <lb></lb>the Diſcourſes that our finite Judgments make about Infinites, gi<lb></lb>ving them thoſe attributes which we give to things finite and ter<lb></lb>minate; which I think is inconvenient; for I judge that theſe <lb></lb>terms of Majority, Minority, and Equality ſute not with Infinites, <lb></lb>of which we cannot ſay that one is greater, or leſs, or equal to ano<lb></lb>ther: for proof of which there cometh to my mind a Diſcourſe, <lb></lb>which, the better to explain, I will propound by way of Interroga<lb></lb>tories to <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> that ſtarted the queſtion.</s></p><p type="main"> <s>I ſuppoſe that you very well underſtand which are Square Num<lb></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></lb>proceeds from the multiplication of another Number into it ſelf; <lb></lb>and ſo four, and nine, are Square Numbers, that ariſing from two, <lb></lb>and this from three multiplied into themſelves.</s></p><p type="main"> <s>SALV. </s> <s>Very well; And you know alſo, that as the Products are <lb></lb>called Squares: the Produſors, that is, thoſe that are multiplied, are <lb></lb>called Sides, or Roots; and the others, which proceed not from <lb></lb>Numbers multiplied into themſelves, are not Squares. </s> <s>So that if I <lb></lb>ſhould ſay, all Numbers comprehending the Square, and the not <lb></lb>Square Numbers, are more than the Square alone, I ſhould ſpeak a <lb></lb>moſt unqueſtionable truth: Is it not ſo?</s></p><p type="main"> <s>SIMP. </s> <s>It cannot be denied.</s></p><p type="main"> <s>SALV. </s> <s>Farther queſtioning, if I ask you how many are the <lb></lb>Numbers Square, you can anſwer me truly, that they be as many, <lb></lb>as are their propper Roots; ſince every Square hath its Root, and <lb></lb>every Root its Square, nor hath any Square more than one ſole <lb></lb>Root, or any Root more than one ſole Square.</s></p><p type="main"> <s>SIMP. True.<lb></lb><arrow.to.target n="marg1024"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1024"></margin.target><emph type="italics"></emph>An Infinite Num<lb></lb>ber, as it contains <lb></lb>infinite Square <lb></lb>and Cupe Roots, ſo <lb></lb>it conta neth infi<lb></lb>nite Square and <lb></lb>Cube Numbers.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>But if I ſhall demand how many Roots there be, you <lb></lb>cannot deny but that they be as many as all Numbers, ſince there <lb></lb>is no Number that is not the Root of ſome Square: And this be<lb></lb>ing granted, it is requiſite to affirm, that Square Numbers are as <pb xlink:href="040/01/719.jpg" pagenum="27"></pb>many as their Roots, and Roots are all Numbers: and yet in the <lb></lb>beginning we ſaid, that all Numbers are far more than all Squares, <lb></lb>the greater part not being Squares: and yet nevertheleſs the num<lb></lb>ber of the Squares goeth diminiſhing alwaies with greater propor<lb></lb>tion, by how much the greater number it riſeth to; for in an hun<lb></lb>dred there are ten Squares, which is as much as to ſay, the tenth <lb></lb>part are Squares: in ten thouſand only the hundredth part are <lb></lb>Squares: in a Million only the thouſandth, and yet in an Infinite <lb></lb>Number, if we are able to comprehend it, we may ſay the Squares <lb></lb>are as many, as all Numbers put together.</s></p><p type="main"> <s>SAGR. </s> <s>What is to be reſolved then on this occaſion?</s></p><p type="main"> <s>SALV. </s> <s>I ſee no other deciſion that it may admit, but to ſay, <lb></lb>that all Numbers are infinite, Squares are infinite, their Roots are <lb></lb>infinite; and that neither is the multitude of Squares leſs than all <lb></lb>Numbers, nor this greater than that: and in concluſion, that the <lb></lb>Attributes of Equality, Majority, and Minority, have no place <lb></lb>in Infinites, but only in terminate quantities. </s> <s>And therefore when <lb></lb><emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> propoundeth to me many unequal <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ines, and demand<lb></lb>eth of me, how it can be, that in the greater there are no more <lb></lb>Points than in the leſs: I anſwer him, That there are neither more, <lb></lb>nor leſs, nor juſt ſo many; but in each of them infinite. </s> <s>Or if I <lb></lb>had anſwered him, that the Points in one, are as many as there are <lb></lb>Square Numbers; in another bigger, as many as all Numbers; in <lb></lb>a leſs, as many as the Cubick Numbers, might not I have given ſa<lb></lb>tisfaction, by aſſigning more to one, than to another, and yet to <lb></lb>every one infinite? </s> <s>And thus much as to the firſt difficulty.</s></p><p type="main"> <s>SAGR. Hold, I pray you, and give me leave to add unto what hath <lb></lb>been ſpoken hitherto, a thought which I juſt now light on, and it <lb></lb>is this, that granting what hath been ſaid, me-thinks, that not on<lb></lb>ly it's improper to ſay, one Infinite is greater than another Infinite, <lb></lb>but alſo, that it's greater than a Finite; for if an Infinite Number <lb></lb>were greater, <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> than a Million; it would thereupon follow, <lb></lb>that paſſing from the Million to others, and ſo to others continual<lb></lb>ly greater, one ſhould paſs on towards Infinity; which is not ſo: but <lb></lb>on the contrary, to how much the greater Numbers we go, ſo <lb></lb>much the more we depart from Infinite Number; becauſe in Num<lb></lb>bers, the greater you take, ſo much the rarer and rarer alwaies are <lb></lb>Square Numbers contained in them; but in Infinite Number the <lb></lb>Squares can be no leſs than all Numbers, as but juſt now was con<lb></lb>cluded: therefore the going towards Numbers alwaies greater, and <lb></lb>greater, is a departing farther from Infinite Number.</s></p><p type="main"> <s>SALV. </s> <s>And ſo by your ingenious Diſcourſe we may conclude, <lb></lb>that the Attributes of Greater, Leſſer, or Equal, have no place, <lb></lb>not only amongſt Infinites; but alſo betwixt Infinites, and Fi<lb></lb>nites.</s></p><pb xlink:href="040/01/720.jpg" pagenum="28"></pb><p type="main"> <s>I paſs now to another Conſideration; and it is, that in regard <lb></lb>that the Line, and every continued quantity are divideable conti<lb></lb>nually into diviſibles, I ſee not how we can avoid granting that the <lb></lb>compoſition is of infinite Indiviſibles: becauſe a diviſion and ſub<lb></lb>diviſion that may be proſecuted perpetually ſuppoſeth that the <lb></lb>parts are infinite; for otherwiſe the ſubdiviſion would be termina<lb></lb>ble: and the parts being Infinite, it followeth of conſequence <lb></lb>that they be non-quantitative; for infinite quantitative parts make <lb></lb>an infinite extenſion: and thus we have a <emph type="italics"></emph>Continuum<emph.end type="italics"></emph.end> compoun<lb></lb>ded of infinite Indiviſibles.</s></p><p type="main"> <s>SIMP. </s> <s>But if we may continually proſecute the diviſion in <lb></lb>quantitative parts, what need have we, for ſuch reſpect, to intro<lb></lb>duce the non-quantitative?</s></p><p type="main"> <s>SALV. </s> <s>The very poſſibility of perpetually proſecuting the di<lb></lb>viſion in quantitative parts induceth the neceſſity of the compoſiti<lb></lb>on of infinite non-quantitative. </s> <s>Therefore, coming cloſer to you, <lb></lb>I demand you to tell me reſolutely, whether the quantitative parts <lb></lb>in <emph type="italics"></emph>Continuum<emph.end type="italics"></emph.end> 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></lb>in Power, and Finite in Act. </s> <s>Infinite in Power, that is, before the <lb></lb>Diviſion; but Finite in Act, that is, after they are divided: for the <lb></lb>parts are not actually underſtood to be in the whole, till it is di<lb></lb>vided, or at leaſt marked; otherwiſe we ſay that they are in <lb></lb>Power.</s></p><p type="main"> <s>SALV. </s> <s>So that a Line <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> twenty foot long, is not ſaid to <lb></lb>contain twenty Lines of one foot a piece, actually, but only after <lb></lb>it is divided into twenty equal parts: but is till then ſaid to contain <lb></lb>them only in power. </s> <s>Now be it as you pleaſe; and tell me whe<lb></lb>ther, when the actual Diviſion of ſuch parts is made, that firſt <lb></lb>whole encreaſeth or diminiſheth, or elſe continueth of the ſame <lb></lb>bigneſs?</s></p><p type="main"> <s>SIMP. </s> <s>It neither encreaſeth, nor diminiſheth.</s></p><p type="main"> <s>SALV. </s> <s>So I think alſo. </s> <s>Therefore the quantitative parts in <emph type="italics"></emph>Con<lb></lb>tinuum<emph.end type="italics"></emph.end> quantity, be they in Act, or be they in Power, make not its <lb></lb>quantity bigger or leſſer: but it is very plain that theſe quantita<lb></lb>tive parts, actually contained in their whole, if they be infinite, <lb></lb>make it an infinite Magnitude; therefore quantitative parts, <lb></lb>though infinite only in power, cannot be contained, but only in an <lb></lb>infinite Magnitude: therefore in a finite Magnitude infinite quan<lb></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"></emph>Continuum<emph.end type="italics"></emph.end> may be <lb></lb>inceſſantly divided into parts ſtill capable of new diviſions?</s></p><p type="main"> <s>SALV. </s> <s>It ſeems that that diſtinction of Power, and Act, makes <lb></lb>that feaſible one way, which another way would be impoſſible. <lb></lb></s> <s>But I will ſee to adjuſt theſe matters by making another account: <pb xlink:href="040/01/721.jpg" pagenum="29"></pb>And to the Queſtion, which was put, Whether the quantitative <lb></lb>parts in a terminated <emph type="italics"></emph>Continuum<emph.end type="italics"></emph.end> be finite or infinite; I will anſwer <lb></lb>directly contrary to that which <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> replied, namely, that <lb></lb>they be neither finite, nor infinite.</s></p><p type="main"> <s>SIMP. </s> <s>I ſhould never have found ſuch an anſwer, not imagi<lb></lb>ning that there was any mean term between finite and infinite; <lb></lb>ſo that the diviſion or diſtinction which makes a thing to be either <lb></lb>Finite, or Infinite, is imperfect and deficient.</s></p><p type="main"> <s>SALV. </s> <s>In my opinion it is; and ſpeaking of ^{*} Diſcrete Quan</s></p><p type="main"> <s><arrow.to.target n="marg1025"></arrow.to.target><lb></lb>tities, me thinks that there is a third mean term between Finite and <lb></lb>Infinite, which is that which anſwereth to every aſſigned Number: <lb></lb>So that being demanded in our preſent caſe, Whether the quanti<lb></lb>tative parts in <emph type="italics"></emph>Continuum<emph.end type="italics"></emph.end> be Finite, or Infinite, the moſt congru<lb></lb>ous reply is to ſay, that they are neither Finite, nor Infinite, but ſo <lb></lb>many, as that they <emph type="italics"></emph>Anſwer<emph.end type="italics"></emph.end> to any number aſſigned: the which to <lb></lb>do, it is neceſſary that they be not comprehended in a limited <lb></lb>Number, for then they would not anſwer to a greater: nor, again, <lb></lb>is it neceſſary, that they be infinite, for no aſſigned Number is infi<lb></lb>nite. </s> <s>And thus at the pleaſure of the Demander, a Line being <lb></lb>propounded, we may be able to aſſign in it an hundred quantita<lb></lb>tive parts, or a thouſand, or an hundred thouſand, according to <lb></lb>the number which he beſt likes; ſo that it be not divided into in<lb></lb>finite. </s> <s>I grant therefore to the Philoſophers, that <emph type="italics"></emph>Continuum<emph.end type="italics"></emph.end> con<lb></lb>taineth as many quantitative parts as they pleaſe, and grant them <lb></lb>that it containeth the ſame either in Act, or in Power, which they <lb></lb>beſt like: but this I add again, that in like manner, as in a Line of <lb></lb>ten yards, there are contained ten Lines of one yard a piece, and <lb></lb>thirty Lines of a foot a piece, and three hundred and ſixty Lines <lb></lb>of an inch a piece, ſo it contains infinite Points; denominate them <lb></lb>in Act, or in Power, as you will: and I remit my ſelf in this matter <lb></lb>to your opinion and judgment, <emph type="italics"></emph>Simplicius.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1025"></margin.target><emph type="italics"></emph>Quantitative parts <lb></lb>in Diſcrete Quan<lb></lb>tity are neither fi<lb></lb>nite nor infinite, <lb></lb>but anſwerable to <lb></lb>every given Num<lb></lb>ber.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SIMP. </s> <s>I cannot but commend your Diſcourſe: but am great<lb></lb>ly afraid, that this parity of the Points, being contained in the like <lb></lb>manner as the quantitative parts, will not agree with abſolute ex<lb></lb>actneſs; nor ſhall it be ſo eaſie a matter for you to divide the gi<lb></lb>ven Line into infinite Points, as for thoſe Philoſophers to divide it <lb></lb>into ten yards, or thirty feet, nay, I hold it wholly impoſſible to <lb></lb>effect ſuch a diviſion: ſo that this will be one of thoſe Powers that <lb></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></lb>thing is not feaſible, render it not impoſſible; for I think alſo, that <lb></lb>you cannot ſo eaſily effect a diviſion to be made of a Line into a <lb></lb>thouſand parts; and much leſs being to divide it into 937, or ſome <lb></lb>other great Prime Number. </s> <s>But if I diſpatch this, which you, it may <lb></lb>be, judge an impoſſible diviſion, in as ſhort a time, as another <pb xlink:href="040/01/722.jpg" pagenum="30"></pb>would require to divide it into forty, you will be content more <lb></lb>willingly to admit of it in our future Diſcourſe?</s></p><p type="main"> <s>SIMP. </s> <s>I am pleaſed with your way of arguing, as you now do <lb></lb>mix it with ſome pleaſantneſs: and to your queſtion I reply, that <lb></lb>the facility would ſeem more than ſufficient, if the reſolving it into <lb></lb>Points were but as eaſie, as to divide it into a thouſand parts.</s></p><p type="main"> <s>SALV. </s> <s>Here I will tell you a thing, which haply will make you <lb></lb>wonder in this matter of going about, or being able to reſolve the <lb></lb>Line into its Infinites, keeping that order which others obſerve in <lb></lb>dividing it into forty, ſixty, or an hundred parts; namely, by di<lb></lb>viding it firſt into two, then into four: in which order he that <lb></lb>ſhould think to find its infinite Points would groſly delude himſelf; <lb></lb>for by that progreſſion, though continued to eternity, he ſhould <lb></lb>never arrive to the diviſion of all its quantitative parts: yea, he is <lb></lb>in that way ſo far from being able to arrive at the intended term <lb></lb>of Indiviſibility, that he rather goeth farther from it; and whilſt <lb></lb>he thinks by continuing the diviſion, and multiplying the multi<lb></lb>tudes of the parts, to approach to Infinite, I am of opinion, that he <lb></lb>more and more removes from it: and my reaſon is this; In the <lb></lb>Diſcourſe, we had even now, we concluded, that, in an infinite <lb></lb>Number, there was, of neceſſity, as many Square, or Cube Num<lb></lb>bers, as there were Numbers; ſince that thoſe and theſe were as ma<lb></lb>ny as their Roots, and Roots comprehend all Numbers: Next we <lb></lb>did ſee, that the greater the Numbers were that were taken, the <lb></lb>ſeldomer are their Squares to be found in them, and ſeldomer yet <lb></lb>their Cubes: Therefore it is manifeſt, that the greater the Number <lb></lb>is to which you paſs, the farther you remove from Infinite Num<lb></lb>ber: from whence it followeth, that turning backwards, (ſeeing <lb></lb>that ſuch a progreſſion more removes us from the deſired term) if <lb></lb><arrow.to.target n="marg1026"></arrow.to.target><lb></lb>any number may be ſaid to be infinite it is the Unite: and, indeed, <lb></lb>there are in it thoſe conditions, and neceſſary qualities of the Infi<lb></lb>nite Number, I mean, of containing in it as many Squares as Cubes, <lb></lb>and as Numbers.</s></p><p type="margin"> <s><margin.target id="marg1026"></margin.target><emph type="italics"></emph>The Unite of all <lb></lb>Numbers may <lb></lb>moſt properly be <lb></lb>ſaid to be Infinite.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SIMP. </s> <s>I do not apprehend very well, how this buſineſs ſhould <lb></lb>be underſtood.</s></p><p type="main"> <s>SALV. </s> <s>The thing hath no difficulty at all in it, for the Unite <lb></lb>is a Square, a Cube, a Squared Square, and all other Powers; nor <lb></lb>is there any particular whatſoever eſſential to the Square, or to the <lb></lb>Cube, which doth not agree with the Unite; as <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> one proper<lb></lb>ty of two Square-numbers is to have between them a Number <lb></lb>mean-proportional; take any Square number for one of the terms, <lb></lb>and the Unite for the other, and you ſhall likewiſe ever find be<lb></lb>tween them a Number Mean-proportional. </s> <s>Let the two Square <lb></lb>Numbers be 9 and 4, you ſee that between 9 and 1 the Mean<lb></lb>proportional is 3, and between 4 and 1 the Mean-proportional <pb xlink:href="040/01/723.jpg" pagenum="31"></pb>is 2, and between the two Squares 9 and 4, 6 is the Mean. </s> <s>The <lb></lb>property of Cubes is to have neceſſarily between them two Num<lb></lb>bers Mean-proportional. </s> <s>Suppoſe 8, and 27, the Means between <lb></lb>them are 12 and 18; and between the Unite and 8 the Means <lb></lb>are 2 and 4; betwixt the Unite and 27 there are 3, and 9. We <lb></lb>therefore conclude, <emph type="italics"></emph>That there is no other Infinite Number but the <lb></lb>Vnite.<emph.end type="italics"></emph.end> And theſe be ſome of thoſe Wonders, that ſurmount the <lb></lb>comprehenſion of our Imagination, and that advertize us how ex<lb></lb>ceedingly they err, who diſcourſe about Infinites with thoſe very <lb></lb>Attributes, that are uſed about Finites; the Natures of which have <lb></lb>no congruity with each other. </s> <s>In which affair I will not conceal <lb></lb>from you an admirable accident, that I met with ſome time ſince, <lb></lb>explaining the vaſt difference, yea, repugnance and contrariety of <lb></lb>Nature, that a terminate quantity would incur by changing or paſ<lb></lb>ſing into Infinite. </s> <s>We aſſign this Right Line A B, of any length at <lb></lb>pleaſure, and any point in the ſame, as C being taken, dividing it <lb></lb>into two unequal parts: I ſay, that many couples Lines, (hold<lb></lb>ing the ſame proportion between themſelves as have the parts <lb></lb>A C, and B C,) departing from the terms A and B to meet with <lb></lb>one another; the points of their Interſection ſhall all fall in the <lb></lb>Circumference of one and the ſame Circle: as for example, A L <lb></lb>and B L departing [or <emph type="italics"></emph>being drawn<emph.end type="italics"></emph.end>] from the Points A and B, and <lb></lb>having between themſelves the ſame proportion, as have the parts <lb></lb>A C and B C, and concurring in the point L: and the ſame pro<lb></lb>portion being between two others A K, and B K, concurring in K, <lb></lb>alſo others as A I, and B I; A H, and B H; A G, and B G; A F, <lb></lb>and B F; A E, and B E: I ſay, that the points of their Interſecti<lb></lb>on L, K, I, H, G, F, E, do all fall in the Circumference of one <lb></lb>and the ſame Semi-circle: ſo that we ſhould imagine the point <lb></lb>C to mve conti<lb></lb><figure id="id.040.01.723.1.jpg" xlink:href="040/01/723/1.jpg"></figure><lb></lb>nuallyafter ſuch <lb></lb>a ſort, that the <lb></lb>Lines produced <lb></lb>from it to the fix<lb></lb>ed terms A and <lb></lb>B retain alwaies <lb></lb>the ſame propor<lb></lb>tion that is be<lb></lb>tween the firſt <lb></lb>parts A C and C B, that point C ſhall decribe the Circumference <lb></lb>of a Circle, as we ſhall ſhew you preſently. </s> <s>And the Circle in ſuch <lb></lb>ſort deſcribed ſhall be alwaies greater and greater ſucceſſively, <lb></lb>according as the point C is taken nearer to the middle point <lb></lb>which is O; and the Circle ſhall be leſſer which ſhall be deſcribed <lb></lb>from a point nearer to the extremity B, inſomuch, that from the <pb xlink:href="040/01/724.jpg" pagenum="32"></pb>infinite Points which may be taken in the Line O B, there may be <lb></lb>deſcribed Circles (moving them in ſuch ſort as above is preſcri<lb></lb>bed) of any Magnitude; leſſer than the Pupil of the eye of a <lb></lb>Flea, and bigger than the Equinoctial of the <emph type="italics"></emph>Primum Mobile.<emph.end type="italics"></emph.end><lb></lb>Now, if raiſing any of the Points comprehended betwixt the terms <lb></lb>O and B, from every one we may deſcribe Circles, and vaſt ones <lb></lb>from the Points nearer to O; then if we raiſe the Point O it ſelf, <lb></lb>and continue to move it in ſuch ſort as aforeſaid, that is, that the <lb></lb>Lines drawn from it to the terms A and B keep the ſame proporti<lb></lb>on as have the firſt Lines A O, and O B, what Line ſhall be deſcri<lb></lb>bed? </s> <s>There would be deſcribed the Circumference of a Circle, <lb></lb>but of a Circle bigger than the biggeſt of all Circles, therefore of <lb></lb>a Circle that is infinite: but it doth alſo deſcribe a Right Line, and <lb></lb>perpendicular upon A B, erected from the Point O, and produced <lb></lb><emph type="italics"></emph>in infinitum<emph.end type="italics"></emph.end> without ever turning to reunite its laſt term with the <lb></lb>firſt, as the others did; for the limited motion of the Point C, after <lb></lb>it had deſigned the upper Semi-circle C H E, continued to de<lb></lb>ſcribe the Lower E M C, reuniting its extream terms in the point <lb></lb>C: But the Point O being moved to deſign (as all the other Points <lb></lb>of the Line A B, for the Points taken in the other part O A <lb></lb>ſhall deſign their Circles, and thoſe Points neareſt to O the <lb></lb>greateſt) its Circle; to make it the biggeſt of all, and conſe<lb></lb>quently infinite, it can never return any more to its firſt term, and <lb></lb><arrow.to.target n="marg1027"></arrow.to.target><lb></lb>in a word deſigneth an Infinite Right-Line for the Circumference <lb></lb>of its Infinite Circle. </s> <s>Conſider now, what difference there is be<lb></lb>tween a finite Circle, and an infinite; ſeeing that this in ſuch man<lb></lb>ner changeth its being that it wholly loſeth both its being, and <lb></lb>power of being; for we have already well comprehended, that <lb></lb>there cannot be aſſigned an infinite Circle; by which we may <lb></lb>conſequently know that there can be no infinite Sphære, or other <lb></lb>Body, or figured Superficies. </s> <s>Now what ſhall we ſay to this Meta<lb></lb>morphoſis in paſſing from Finite to Infinite? </s> <s>And why ſhould we <lb></lb>find greater repugnance, whilſt ſeeking Infinity in Numbers, we <lb></lb><arrow.to.target n="marg1028"></arrow.to.target><lb></lb>come to conclude it to be in the Unite? </s> <s>And whilſt that breaking <lb></lb>a Solid into many pieces, and purſuing to reduce it into very ſmall <lb></lb>powder, it were reſolved into its infinite Atomes, admitting no far<lb></lb>ther diviſion, why may we not ſay that it is returned into one ſole <lb></lb><emph type="italics"></emph>Continuum,<emph.end type="italics"></emph.end> but perhaps fluid, as the Water, or Quickſilver, or <lb></lb>other Metall melted? </s> <s>And do we not ſee Stones liquified into <lb></lb>Glaſs, and Glaſs it ſelf with much Fire to become more fluid than <lb></lb>Water?</s></p><p type="margin"> <s><margin.target id="marg1027"></margin.target><emph type="italics"></emph>The difference be<lb></lb>twixt a finite and <lb></lb>infinite Circle.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1028"></margin.target><emph type="italics"></emph>Vnity participates <lb></lb>of Infinity.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>Should we therefore think Fluids to be ſo called, be<lb></lb>cauſe they are reſolved into their firſt, infinite, indiviſible com<lb></lb>pounding parts?</s></p><p type="main"> <s>SALV. </s> <s>I know not how to find a better anſwer to reſolve cer<pb xlink:href="040/01/725.jpg" pagenum="33"></pb>tain ſenſible appearances, amongſt which this is one: When I take <lb></lb>a hard Body, be it either Stone, or Metal, and with a Hammer, or <lb></lb>very fine File, endeavour to divide it, as much as is poſſible, into <lb></lb>its moſt minute and impalpable powder; it is very clear, that its <lb></lb>leaſt Atomes, albeit for their ſmalneſs they are imperceptible, one by <lb></lb>one, to our ſight and touch; yet are they quantitative, figured, and <lb></lb>numerable: and it happens in them, that being accumulated to<lb></lb>gether, they continue in heap; and being laid hollow, or with a <lb></lb>pit in the midſt, the hollowneſs or pit remains, the parts heaped <lb></lb>about it not returning to fill it up; and being ſtirr'd, or ſhaken, <lb></lb>they ſuddenly ſettle ſo ſoon as their external mover leaves them, <lb></lb>And the like effects are ſeen in all the Aggregates of ſmall Bodies, <lb></lb>bigger, and bigger, and of any kind of Figure, although Sphærical; <lb></lb>as we ſee in heaps of Peaſe, Wheat, Bird ſhot, and other matters. </s> <s>But <lb></lb>if we try to find the like accidents in Water, you will meet with <lb></lb>none of them; but, being raiſed, it inſtantly returns to a level, if <lb></lb>it be not by a veſſel, or ſome other external ſtay upheld; being <lb></lb>made hollow, it preſently diffuſeth to fill up the Cavity; and be<lb></lb>ing long moved, it continually undulates, and ſpreads its waves very <lb></lb>far. </s> <s>From this, I think, we may very rationally infer, that the minute <lb></lb><arrow.to.target n="marg1029"></arrow.to.target><lb></lb>parts of Water, into which it ſeemeth to be reſolved, (ſince it hath <lb></lb>leſs conſiſtence than any the fineſt powder, yea, hath no conſi<lb></lb>ſtence at all) are vaſtly differing from Atomes quantitative and <lb></lb>diviſible; nor know I how to find any other difference therein <lb></lb>than that of being indiviſible. </s> <s>Methinks, alſo, that its moſt exqui<lb></lb>ſite tranſparency, affords us ſufficient grounds to conjecture there<lb></lb>of; for if we take the moſt diaphanous Chriſtal that is, and begin <lb></lb>to break, and pound it to powder, when it is in powder it loſeth <lb></lb>its tranſparency, and ſo much the more, the ſmaller it is pounded; <lb></lb>but yet Water which is ground to the higheſt degree, hath alſo the <lb></lb>higheſt degree of Diaphaneity Gold and Silver, reduced by <emph type="italics"></emph>Aqua<lb></lb>fortis<emph.end type="italics"></emph.end> into a ſmaller Powder than any File can make, yet they con<lb></lb>tinue powder, and become not fluid; nor do they liquifie till the <lb></lb>Indiviſibles of the Fire, or of the Sun-beams diſſolve them, as, I be<lb></lb>lieve, into their firſt and higheſt infinite and indiviſible compoun<lb></lb>ding parts.</s></p><p type="margin"> <s><margin.target id="marg1029"></margin.target><emph type="italics"></emph>Fluid Bodies are <lb></lb>ſuch, for that they <lb></lb>are reſolved into <lb></lb>their firſt Indiviſi<lb></lb>ble Atomes.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>This which you have hinted of the Light I have many <lb></lb>times obſerved with admiration: I have ſeen, I ſay, a burning<lb></lb>Glaſs, of a foot Diameter, liquifie or melt lead in an inſtant; <lb></lb>whence I came to be of opinion, that if the Glaſſes were very big, <lb></lb>and very polite, and of Parabolical Figure, they would no leſs melt <lb></lb>every other Metal in a very ſhort time; ſeeing that that, not very <lb></lb>big, nor very clear, and of a Sphærical Concave, with ſuch force <lb></lb>melted Lead, and burnt every combuſtible matter: effects, that <lb></lb>make the wonders, reported of the Burning-glaſſes of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end><lb></lb>credible to me.<pb xlink:href="040/01/726.jpg" pagenum="34"></pb><arrow.to.target n="marg1030"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1030"></margin.target>Archimedes <emph type="italics"></emph>his <lb></lb>Burning — Glaſſes <lb></lb>admirable.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>Touching the Effects of the Glaſſes, invented by <emph type="italics"></emph>Ar<lb></lb>chimedes,<emph.end type="italics"></emph.end> all the Miracles, that ſeveral Writers record of them, <lb></lb>are to me rendred credible by the reading of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> his own <lb></lb>Books, which I have with infinite amazement peruſed and ſtudied: <lb></lb>and if any doubts had been left me; that which laſt of all Father </s></p><p type="main"> <s><arrow.to.target n="marg1031"></arrow.to.target><lb></lb><emph type="italics"></emph>Buonaventura Cavalieri<emph.end type="italics"></emph.end> hath publiſhed, touching <emph type="italics"></emph>Lo Specehio <lb></lb>Vſtorio,<emph.end type="italics"></emph.end> (or the Burning glaſs) and which I have read with ad<lb></lb>miration, is ſufficient to reſolve them all.</s></p><p type="margin"> <s><margin.target id="marg1031"></margin.target>Buonaventura <lb></lb>Cavalieri, <emph type="italics"></emph>the Je<lb></lb>ſuate, a famous <lb></lb>Mathematician, <lb></lb>and his Book en<lb></lb>titled,<emph.end type="italics"></emph.end> Lo Spec<lb></lb>chio Uſtorio.</s></p><p type="main"> <s>SAGR. </s> <s>I have alſo ſeen that Tract, and peruſed it with much <lb></lb>delight and wonder; and becauſe I formerly had knowledge of <lb></lb>the Author, I was confirmed in the opinion which I had conceived <lb></lb>of him, that he was like to prove one of the principal Mathemati<lb></lb>cians of our Age. </s> <s>But returning to the admirable effects of the <lb></lb>Sun-Beams in melting of Metals, are we to believe that ſuch, and <lb></lb>ſo violent an operation is without Motion, or elſe that it is with <lb></lb>Motion, but extream ſwift?<lb></lb><arrow.to.target n="marg1032"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1032"></margin.target><emph type="italics"></emph>Burnings are per<lb></lb>formed with a moſt <lb></lb>ſwift Motion.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>We ſee other burnings, and meltings to be performed <lb></lb>with Motion, and with a moſt ſwift Motion. </s> <s>Obſerve the ope<lb></lb>rations of Lightnings, of Powder in Mines, and in Petards, <lb></lb>and, in ſum, how by quickning the flame of Coles, mixt with <lb></lb>groſs and impure vapours, by Bellows, encreaſeth its force in <lb></lb>the melting of Metals: ſo that I cannot ſee how the Action of <lb></lb>Light, albeit moſt pure, can be without Motion, and that alſo ve<lb></lb>ry ſwift.</s></p><p type="main"> <s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>AGR. </s> <s>But what and how great ought we to judge this Velo<lb></lb>city of the Light? </s> <s>Is it haply <emph type="italics"></emph>Inſtantaneous,<emph.end type="italics"></emph.end> and done in a moment, <lb></lb>or, as the reſt of Motions, performed in Time? </s> <s>May we not by <lb></lb>Experiment be aſſured what it is?</s></p><p type="main"> <s>SIMP. </s> <s>Quotidian experience ſhews the expanſion of Light to <lb></lb>be <emph type="italics"></emph>Inſtantaneous<emph.end type="italics"></emph.end>; in that beholding a Cannon, let off at a great <lb></lb>diſtance, the flaſh of the fire, without interpoſition of time, is tranſ<lb></lb>mitted to our eye, but ſo is not the Report to our ear untill a con<lb></lb>ſiderable time after.</s></p><p type="main"> <s>SAGR. True, but, I pray you, what doth this obvious experi<lb></lb>ment evince; but only this, that the Report is longer in arriving at <lb></lb>our Ear, than the Flaſh at our Eye; but it aſſures me not, that the <lb></lb>tranſmiſſion of the Light is therefore <emph type="italics"></emph>Inſtantaneous<emph.end type="italics"></emph.end> rather than in <lb></lb>Time, but only moſt ſwift. </s> <s>Nor doth ſuch an obſervation con<lb></lb>clude more than that other, of ſuch who ſay, that as ſoon as the <lb></lb>Sun cometh to the Horizon, its Light arriveth at our eye: for who <lb></lb>ſhall aſſure me, that its beams arrive not at the ſaid term, afore they <lb></lb>reach our ſight?</s></p><p type="main"> <s>SALV. </s> <s>The inconcludency of theſe, and other obſervations of <lb></lb>the like Nature, made me once think of ſome other way, whereby <lb></lb>we may without errour be aſcertained whether the illumination, <pb xlink:href="040/01/727.jpg" pagenum="35"></pb>that is, whether the expanſion of the Light were really <emph type="italics"></emph>Inſtantane<lb></lb>ous<emph.end type="italics"></emph.end>; ſeeing that the very ſwift Motion of Sound, aſſureth us, that <lb></lb>that of Light cannot but be extream ſwift. </s> <s>And the experiment I </s></p><p type="main"> <s><arrow.to.target n="marg1033"></arrow.to.target><lb></lb>hit upon, was this; I would have two perſons take each of them a <lb></lb>Light, which, by holding it in a Lanthorn, or other coverture, they <lb></lb>may cover, and diſcover at pleaſure by interpoſing their hand to the <lb></lb>fight of each other; and, that placing themſelvs againſt one another, <lb></lb>ſome few paces diſtance, they may practice the ſpeedy diſcovery, <lb></lb>and occultation of their Lights from the ſight of each other: So <lb></lb>that when one ſeeth the others Light, he immediatly diſcloſe his: <lb></lb>which correſpondence, after ſome Reſponſes mutually made, will <lb></lb>become ſo exactly Inſtantaneous, that, without ſenſible variation, <lb></lb>at the diſcovery of the one, the other ſhall at the ſame time ap<lb></lb>pear to the ſight of him that diſclos'd the firſt. </s> <s>Having adjuſted <lb></lb>this practice at this ſmall diſtance, let us place the two perſons with <lb></lb>two ſuch Lights at two or three miles diſtance; and by night re<lb></lb>newing the ſame experiment; Let them intenſely obſerve if the <lb></lb>Reſponſes of the diſcloſures, and occultations do follow the ſame <lb></lb>tenour which they did near hand: for if they keep the ſame pro<lb></lb>portion, it may be with certainty enough concluded, that the ex<lb></lb>panſion of Light is Inſtantaneous; but if it ſhould require time in <lb></lb>a diſtance of three miles, which importeth ſix for the going of <lb></lb>one, and return of the other, the ſtay would be ſufficiently obſer<lb></lb>vable. </s> <s>And if this Experiment be made at greater diſtances, <lb></lb>namely, at eight or ten miles, we may make uſe of the <emph type="italics"></emph>Teleſcope,<emph.end type="italics"></emph.end><lb></lb>the Obſervators accommodating each of them one at the places, <lb></lb>where by night the Lights are to be obſerved; which though not <lb></lb>very big, and ſo not viſible, at that great diſtance, to the eye at <lb></lb>large; (though eaſie to be diſcloſed, and hid) by help of the <lb></lb><emph type="italics"></emph>Teleſcopes<emph.end type="italics"></emph.end> before admitted, and fixed they may commodiouſly be <lb></lb>diſcerned.</s></p><p type="margin"> <s><margin.target id="marg1033"></margin.target><emph type="italics"></emph>The Velocity of <lb></lb>Light, how to find <lb></lb>by Experiment <lb></lb>whether it be In<lb></lb>ſtantaneosu or not.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>The Invention ſeems to me no leſs certain than ingenu<lb></lb>ous; but tell us what upon experimenting it you concluded.</s></p><p type="main"> <s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>ALV. Really, I have not tryed it, ſave only at a ſmall diſtance, <lb></lb>namely, leſs than a Mile: whereby I could come to no certainty <lb></lb>whether the apparence of the oppoſite Light was truly Inſtantane<lb></lb>ous; But if not Inſtantaneous, yet it was of exceeding great Velo<lb></lb>city, and I may ſay Momentary: and for the preſent, I would re<lb></lb>ſemble it to that Motion which we ſee a flaſh of Lightning make <lb></lb>in the Clouds ten or more Miles off: of which Light we diſtin<lb></lb>guiſh the beginning, and, I may fay, the ſource and riſe of it, in a <lb></lb>particular place in thoſe Clouds; but yet its wide expanſion imme<lb></lb>diatly ſucceeds amongſt thoſe adjacent: which to me ſeems an ar<lb></lb>gument that it is ſome ſmall time in doing; becauſe had the illu<lb></lb>mination been made all at once, and not by degrees, it feems to <pb xlink:href="040/01/728.jpg" pagenum="36"></pb>me that we could not have diſtinguiſhed its original, or rather the <lb></lb>Center of its flake, and extream Dilatations. </s> <s>But into what Oceans <lb></lb>do we by degrees engage our ſelves? </s> <s>Amongſt <emph type="italics"></emph>Vacuities, Infinites, <lb></lb>Indiviſibles,<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Instantaneous Motions<emph.end type="italics"></emph.end>; ſo that we ſhall not be <lb></lb>able by a thouſand Diſcourſes to recover the Shore?</s></p><p type="main"> <s>SAGR. </s> <s>They are things, indeed, very diſproportionate to our <lb></lb>underſtanding. </s> <s>Behold Infinite, ſought amongſt Numbers, ſeemeth <lb></lb>to determine in the Unite: From Indiviſibles ariſeth things that <lb></lb>are continually diviſible: Vacuity ſeems only to reſide indiviſibly <lb></lb>mixt with Repletion: and, in brief, theſe things ſo change the <lb></lb>nature of thoſe underſtood by us, that even the Circumference of <lb></lb>a Circle becometh an Infinite Right-Line; which, if I well re<lb></lb>member, is that Propoſition which you, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> are to mani<lb></lb>feſt by Geometrical Demonſtration. </s> <s>Therefore, if you think fit, <lb></lb>it would be well, without any more digreſſions, to make it out <lb></lb>to us.</s></p><p type="main"> <s>SALV. </s> <s>I am ready to ſerve you in demonſtrating the enſuing <lb></lb>Problem for your fuller information.</s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s><emph type="italics"></emph>A Right-Line being given, divided, according to any <lb></lb>proportion, into unequal parts, to deſcribe a Circle, to <lb></lb>the Circumference of which, at any point of the ſame, <lb></lb>two Right-Lines being produced from the terms of <lb></lb>the given Right Line, they may retain the ſame pro<lb></lb>portion that the parts of the ſaid Line given have to <lb></lb>one another, ſo that thoſe be Homologous which de<lb></lb>part ſrom the ſame terms.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the given Right-Line be AB, unequally divided ac<lb></lb>cording to any proportion in the point C; it is required to <lb></lb>deſcribe a Circle at any point of whoſe Circumference two <lb></lb>Right Lines, produced from the terms A and B, concurring, have <lb></lb>the ſame proportion to each other, that A C, hath to B C, ſo that <lb></lb>thoſe be Homologous which depart from the ſame term. </s> <s>Upon <lb></lb>the Center C, at the diſtance of the leſſer part C B, let a Circle be <lb></lb>ſuppoſed to be deſcribed, to the Circumference of which from the <lb></lb>point A the Right-line A D is made a Tangent, and indetermi<lb></lb>nately prolonged towards E: and let the Contact be in D, and <lb></lb>draw a Line from C to D, which ſhall be perpendicular to A E; <lb></lb>and let B E be perpendicular to B A, which produced, ſhall inter<pb xlink:href="040/01/729.jpg" pagenum="37"></pb>ſect A E, the Angle A being acute: Let the interſection be in E, <lb></lb>from whence let fall a Perpendicular to A E, which produced, will <lb></lb>meet with A B infinitely prolonged in F. </s> <s>I ſay, firſt, that the <lb></lb>Right-lines F E, and F C are equal: ſo that drawing the Line <lb></lb>E C, we ſhall, in the <lb></lb><figure id="id.040.01.729.1.jpg" xlink:href="040/01/729/1.jpg"></figure><lb></lb>two Triangles D E C, <lb></lb>B E C, have the two <lb></lb>Sides of the one, D E, <lb></lb>and C E, equal to the <lb></lb>two Sides of the other <lb></lb>B E, and E C; the <lb></lb>two Sides, D E, and <lb></lb>E B, being Tangents <lb></lb>to the Circle D B, <lb></lb>and the Baſes D C, <lb></lb>and C B, are likewiſe <lb></lb>equal: wherefore the <lb></lb>two Angles D E C, <lb></lb>and B E C, ſhall be <lb></lb>equal. </s> <s>And becauſe the Angle B C E wanteth of being a Right<lb></lb>Angle, as much as the Angle B E C; and the Angle C E F, to <lb></lb>make it a Right-Angle, wants the Angle C E D, thoſe Supple<lb></lb>ments being equal, the Angles F C E, and F E C ſhall be equal, <lb></lb>and ſo conſequently the Sides F E, and F C; wherefore making <lb></lb>the point F a Center, and at the diſtance F E, deſcribing a Circle, <lb></lb>it ſhall paſs by the point C. </s> <s>Deſcribe it, and let it be C E G. </s> <s>I ſay, <lb></lb>that this is the Circle required, by any point of the Circumfe<lb></lb>rence of which, any two Lines that ſhall interſect, departing from <lb></lb>the terms A and B, ſhall be in proportion to each other, as are the <lb></lb>two parts A C, and B C, which beſore did concur in the point C. <lb></lb></s> <s>This is manifeſt in the two that concur or interſect in the point E, <lb></lb>that is A E, and B E; the Angle E of the Triangle A E B being <lb></lb>divided in the midſt by C E; ſo that as A C is to C B, ſo is A E <lb></lb>to B E. </s> <s>The ſame we prove in the two A G, and B G, determined <lb></lb>in the point G. </s> <s>Therefore being (by the Similitude of the Tri<lb></lb>angles A F E, and E F B) that as A F is to E F, ſo is E F to F B; <lb></lb>that is, as A F is to F C, ſo is C F to F B: So by Diviſion; as A C <lb></lb>is to C F, (that is, to F G) ſo is C B to B F; and the whole A B <lb></lb>is to the whole B G, as the part C B to the part B F: and by Com<lb></lb>poſition; as A G is to G B, ſo is C F to F B; that is, as E F to <lb></lb>F B, that is, as A E to E B, and A C to C B: Which was to be de<lb></lb>monſtrated. </s> <s>Again, let any other Point be taken in the Circum<lb></lb>ference, as H; in which the two Lines A H and B H concur. </s> <s>I ſay, in <lb></lb>like manner as before, that as A C is to C B, ſo is A H to B H. <lb></lb></s> <s>Continue H B untill it interſect the Circumference in I, and draw <pb xlink:href="040/01/730.jpg" pagenum="38"></pb>a Line joyning I to F. </s> <s>And becauſe it hath been proved already <lb></lb>that as A B is to B G, ſo is C B to B F, the Rectangle A B F ſhall be <lb></lb>equall to the Rectangle C B G, that is I B H: and therefore, as <lb></lb>A B is to B H, ſo is I B to B F, and the Angles at B are equal: <lb></lb>Therefore A H is to H B, as I F, that is E F, to F B, and as A E <lb></lb>to E B.</s></p><p type="main"> <s>I ſay moreover, that it is impoſſible, that the Lines, which have <lb></lb>this ſame proportion, departing from the terms A and B, ſhould <lb></lb>meet in any point, either within or without the ſaid Circle: For<lb></lb>aſmuch as if it be poſſible that two Lines ſhould concur in the <lb></lb>point L, placed without; let them be A L, and B L; and continue <lb></lb>L B to the Circumference in M, and conjoyn M to F. </s> <s>If therefore <lb></lb>A L is to B L, as A C to B C, that is, as M F to F B, we ſhall have <lb></lb>two Triangles A L B, and M F B, which about the two Angles <lb></lb>A L B and M F B have their Sides proportional, their upper Angles <lb></lb>in the point B equal, and the two remaining Angles F M B and <lb></lb>L A B leſs than Right Angles (for that the Right-angle at the <lb></lb>point M hath for its Baſe the whole Diameter C G, and not the <lb></lb>ſole part B F, and the other at the point A is acute by reaſon the <lb></lb>Line A L Homologous to A C, is greater than B L Homologous to <lb></lb>B C) Therefore the Triangles A B L, and M B F are like: and <lb></lb>therefore as A B is to B L, ſo is M B to B F; Wherefore the <lb></lb>Rectangle A B F ſhall be equall to the Rectangle M B L. </s> <s>But the <lb></lb>Rectangle A B F hath been demonſtrated to be equal to that of <lb></lb>C B G: Therefore the Rectangle M B L is equal to the Rectangle <lb></lb>C B G, which is impoſſible: Therefore the Concourſe of the Lines <lb></lb>cannot fall without the Circle. </s> <s>And in like manner it may be de<lb></lb>monſtrated that it cannot fall within; Therefore all the Concour<lb></lb>ſes fall in the Circumference it ſelf.</s></p><p type="main"> <s>But it is time that we return to give ſatisfaction to the Intreaty <lb></lb>of <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> ſhewing him that the reſolving the Line into its in<lb></lb>finite Points is not only not impoſſible, but that it hath in it no <lb></lb>more difficulty than to diſtinguiſh its quantitative parts; preſup<lb></lb>poſing one thing (notwithſtanding) which I think, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end><lb></lb>you will not deny me, and that is this; that you will not require me <lb></lb>to ſever the Points one from another, and ſhew you them one by <lb></lb>one diſtinctly upon this paper: for I my ſelfe ſhould be content, <lb></lb>if without enjoyning to pull the four or ſix parts of a Line from <lb></lb>one another, you ſhould but ſhew me its diviſions marked, or at <lb></lb>moſt inclined to Angles, framing them into a Square, or a Hexa<lb></lb>gon; therefore I perſwade my ſelf, that for the preſent you will <lb></lb>grant them then ſufficiently, and actually diſtinguiſhed.</s></p><p type="main"> <s>SIMP. </s> <s>I ſhall indeed.</s></p><p type="main"> <s>SALV. </s> <s>Now if the inclining of a Line to Angles, framing <lb></lb><arrow.to.target n="marg1034"></arrow.to.target><lb></lb>therewith ſometimes a Square ſometimes an Octagon, ſometimes <pb xlink:href="040/01/731.jpg" pagenum="39"></pb>a Poligon of Forty, of an <emph type="italics"></emph>H<emph.end type="italics"></emph.end>undred, of a Thouſand Angles be a <lb></lb>mutation ſufficient to reduce into Act thoſe four, eight, forty, <lb></lb>hundred, or thouſand parts, which were, as you ſay, Potentially <lb></lb>in the ſaid Line at firſt: if I make thereof a Poligon of infinite <lb></lb>Sides, namely, when I bend it into the Circumference of a Circle, <lb></lb>may not I, with the like leave, ſay, that I have reduced thoſe infi<lb></lb>nite parts into Act, which you before, whilſt it was ſtraight, ſaid <lb></lb>were Potentially contained in it? </s> <s>Nor may ſuch a Reſolution be <lb></lb>denied to be made into its Infinite Points, as well as that of its four <lb></lb>parts in forming thereof a Square, or into its thouſand parts in <lb></lb>forming thereof a Mill-angular Figure; by reaſon that there wants <lb></lb>not in it any of the Conditions found in the Poligon of a thou<lb></lb>ſand, or of an hundred thouſand Sides. </s> <s>This applied or layed to a <lb></lb>Right-Line covereth it, touching it with one of its Sides, that is, <lb></lb>with one of its hundred thouſandth parts; the Circle, which is a <lb></lb>Poligon of infinite Sides, toucheth the ſaid Right-line with one of <lb></lb>its Sides, that is one ſingle Point divers from all its Colaterals, and <lb></lb>therefore divided, and diſtinct from them, no leſs than a Side of <lb></lb>the Poligon from its Conterminals. </s> <s>And as the Poligon turned <lb></lb>round upon a Plane deſcribes, with the conſequent tacts of its Sides, <lb></lb>a Right-line equal to its Perimeter: ſo the Circle, rowled upon <lb></lb>ſuch a Plane, deſcribes or ſtamps upon it, by its infinite ſucceſſive <lb></lb>Contacts, a Right-line, equall to its own Circumference. </s> <s>I know <lb></lb>not at preſent, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> whether or no the Peripateticks, (to <lb></lb>whom I grant, as a thing moſt certain, that <emph type="italics"></emph>Continuum<emph.end type="italics"></emph.end> may be di<lb></lb>vided into parts alwaies diviſible, ſo that continuing the diviſion <lb></lb>and ſubdiviſion there can be no end thereof) will be content to <lb></lb>yield to me, that none of thoſe diviſions are the ultimate, as in<lb></lb>deed they be not, ſince that there alwaies remains another; but <lb></lb>that only to be the laſt, which reſolves it into infinite Indiviſibles; <lb></lb>to which I yield we can never attain, dividing and ſubdividing it <lb></lb>ſucceſſively into a greater, and greater multitude of parts: but <lb></lb>making uſe of the way which I propound to diſtinguiſh and re<lb></lb>ſolve all the infinite parts at one only draught, (an Artifice which <lb></lb>ought not to be denied me) I could perſwade my ſelf they <lb></lb>would ſatisfie themſelves, and admit this compoſition of <emph type="italics"></emph>Continu-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1035"></arrow.to.target><lb></lb><emph type="italics"></emph>um<emph.end type="italics"></emph.end> to conſiſt of Atomes abſolutely indiviſible: And eſpecially, <lb></lb>this one path being more current than any other to extricate us <lb></lb>out of very intricate Laberinths; ſuch as are, (beſides that alrea<lb></lb>dy touched of the Coherence of the parts of Solids) the concei<lb></lb>ving the buſineſs of Rarefaction and Condenſation, without <lb></lb>running into the inconvenience of being forced to admit forth of <lb></lb>void Spaces or Vacuities; and for this a Penetration of Bodies: in<lb></lb>conveniences, which both, in my opinion, may eaſily be avoided, <lb></lb>by granting the foreſaid Compoſition of Indiviſibles.</s></p><pb xlink:href="040/01/732.jpg" pagenum="40"></pb><p type="margin"> <s><margin.target id="marg1034"></margin.target><emph type="italics"></emph>How infinite points <lb></lb>are aſſigned in a <lb></lb>finite Line.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1035"></margin.target>Continuum <emph type="italics"></emph>com<lb></lb>pounded of Indivi<lb></lb>ſibles.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SIMP. </s> <s>I know not what the Peripateticks would ſay, in regard <lb></lb>that the Conſiderations you have propoſed would be, for the moſt <lb></lb>part, new unto them, and as ſuch, it is requiſite that they be exa<lb></lb>mined: and it may be, that they would find you anſwers, and <lb></lb>powerful Solutions, to unty theſe knots, which I, by reaſon of the <lb></lb>want of time and ingenuity proportionate, cannot for the preſent <lb></lb>reſolve. </s> <s>Therefore, ſuſpending this particular for this time, I <lb></lb>would gladly underſtand how the introduction of theſe Indiviſi<lb></lb>bles facilitateth the knowledge of Condenſation, and Rarefa<lb></lb>ction, avoiding at the ſame time a <emph type="italics"></emph>Vacuum,<emph.end type="italics"></emph.end> and the Penetration of <lb></lb>Bodies.</s></p><p type="main"> <s>SAGR. </s> <s>I alſo much long to underſtand the ſame, it being to <lb></lb>my Capacity ſo obſcure: with this <emph type="italics"></emph>proviſo,<emph.end type="italics"></emph.end> that I be not couzen<lb></lb>ed of hearing (as <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> ſaid but even now) the Reaſons of <lb></lb><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in confutation of a <emph type="italics"></emph>Vacuum,<emph.end type="italics"></emph.end> and conſequently the Solu<lb></lb>tions which you bring, as ought to be done, whilſt that you ad<lb></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 firſt <lb></lb>it's neceſſary, that like as in favour of Rarefaction, we make uſe of <lb></lb>the Line deſcribed by the leſſer Circle bigger than its own Cir<lb></lb>cumference, whilſt it was moved at the Revolution of the greater; <lb></lb>ſo, for the underſtanding of Condenſation, we ſhall ſhew, how that, <lb></lb>at the converſion made by the leſſer Circle, the greater deſcribeth <lb></lb>a Right-line leſs than its Circumference; for the clearer explicati<lb></lb>on of which, let us ſet before us the conſideration of that which <lb></lb>befalls in the Poligons. </s> <s>In a deſcription like to that other; ſup<lb></lb>poſe two Hexagons about the common Center L, which let be <lb></lb>A B C, and H I K, with the Parallel-lines H O M, and A B C, up<lb></lb>on which they are to make their Revolutions; and the Angle I, of <lb></lb>the leſſer Poligon, reſting at a ſtay, turn the ſaid Poligon till ſuch <lb></lb>time as I K fall upon the Parallel, in which motion the point K <lb></lb>ſhall deſcribe the Arch K M, and the Side K I, ſhall unite with the <lb></lb>part I M; while this is in doing, you muſt obſerve what the Side <lb></lb>C B of the greater Poligon will do. </s> <s>And becauſe the Revolution <lb></lb>is made upon the Point I, the Line I B with its term B ſhall de<lb></lb>ſcribe, turning backward the Arch B b, below the Parallel c A, ſo <lb></lb>that when the Side K I ſhall fall upon the Line M I, the Line B C <lb></lb>ſhall fall upon the Line b c, advancing forwards only ſo much as <lb></lb>is the Line B c, and retiring back the part ſubtended by the Arch <lb></lb>B b, which falls upon the Line B A, and intending to continue af<lb></lb>ter the ſame manner the Revolution of the leſſer Poligon, this will <lb></lb>deſcribe, and paſs upon its Parallel, a Line equal to its Perimeter; <lb></lb>but the greater ſhall paſs a Line leſs than its Perimeter, the quan<lb></lb>tity of ſo many of the lines <emph type="italics"></emph>B<emph.end type="italics"></emph.end> b as it hath Sides, wanting one; <lb></lb>and that ſame line ſhall be very near equal to that deſcribed by <pb xlink:href="040/01/733.jpg" pagenum="41"></pb>the leſſer Poligon, exceeding it only the quantity of b B. </s> <s>Here <lb></lb>then, without the leaſt repugnance the cauſe is ſeen, why the grea<lb></lb>ter Poligon paſſeth or moveth not (being carried by the leſs) <lb></lb>with its Sides a greater Line than that paſſed by the leſs; that is, <lb></lb>becauſe that one part of each of them falleth upon its next coter<lb></lb>minal and precedent.</s></p><p type="main"> <s>But if we ſhould conſider the two Circles about the Center A, <lb></lb>reſting upon their Parallels, the leſſer touching his in the point B, <lb></lb>and the greater his in the <lb></lb><figure id="id.040.01.733.1.jpg" xlink:href="040/01/733/1.jpg"></figure><lb></lb>point C; here, in begin<lb></lb>ning to make the Revolu<lb></lb>tion of the leſs, it ſhall not <lb></lb>occur as before, that the <lb></lb>point B reſt for ſome time <lb></lb>immoveable, ſo that the <lb></lb>Line B C giving back, <lb></lb>carry with it the point C, <lb></lb>as it befell in the Poligons, <lb></lb>which reſting fixed in the <lb></lb>point I till that the Side <lb></lb>K I falling upon the Line <lb></lb>I M, the Line I B carried <lb></lb>back B, the term of the <lb></lb>Side C B, as far as b, by <lb></lb>which means the Side B C <lb></lb>fell on b c, ſuper-poſing or <lb></lb>reſting the part B b upon <lb></lb>the Line B A, and advancing forwards only the part <emph type="italics"></emph>B<emph.end type="italics"></emph.end> c, equal to <lb></lb>I M, that is to one Side of the leſſer Poligon: by which ſuperpoſi<lb></lb>tions, which are the exceſſes of the greater Sides above the leſs, the <lb></lb>advancements which remain equal to the Sides of the leſſer Poli<lb></lb>gon come to compoſe in the whole Revolution the Right-line <lb></lb>equal to that traced, and meaſured by the leſſer Poligon. </s> <s>But <lb></lb><arrow.to.target n="marg1036"></arrow.to.target><lb></lb>now, I ſay, that if we would apply this ſame diſcourſe to the ef<lb></lb>fect of the Circles, it will be requiſite to confeſs, that whereas the <lb></lb>Sides of whatſoever Poligon are comprehended by ſome Number, <lb></lb>the Sides of the Circle are infinite; thoſe are quantitative and di<lb></lb>viſible, theſe non-quantitative and Indiviſible: the terms of the <lb></lb>Sides of a Poligon in the Revolution ſtand ſtill for ſome time, that <lb></lb>is, each ſuch part of the time of an entire Converſion, as it is of <lb></lb>the whole Perimeter: in the Circles likewiſe the ſtay oſ the terms <lb></lb><arrow.to.target n="marg1037"></arrow.to.target><lb></lb>of its infinite Sides are momentary, for a Moment is ſuch part of a <lb></lb>limited Time, as a Point is of a Line, which containeth infinite of <lb></lb>them; the regreſſions made by the Sides of the greater Poligon, are <lb></lb>not of the whole Side, but only of its exceſs above the Side of the <pb xlink:href="040/01/734.jpg" pagenum="42"></pb>leſſer, getting forwards as much ſpace as the ſaid leſſer Side: in <lb></lb>Circles, the Point, or Side C in the inſtantaneous reſt of B recedeth <lb></lb>as much as is its exceſs above the Side B, advancing forward as <lb></lb>much as the quantity of the ſame B: And in ſhort, the infinite <lb></lb>indiviſible Sides of the greater Circle with their infinite indiviſible <lb></lb>Regreſſions, made in the infinite inſtantaneous ſtaies of the infi<lb></lb>nite terms of the infinite Sides of the leſſer Circle, and with their <lb></lb>infinite Progreſſes, equal to the infinite Sides of the ſaid leſſer <lb></lb>Circle, they compoſe and meaſure a Line equall to that deſcribed <lb></lb>by the leſſer Circle, containing in it ſelf infinite ſuperpoſitious <lb></lb>non-quantitative, which make a Conſtipation and Condenſation <lb></lb>without any penctration of quantitative parts: which cannot be <lb></lb>contrived to be done in the Line divided into quantitative parts, <lb></lb>as is the Perimeter of any Poligon, which being diſtended in a <lb></lb>Right-line at length, cannot be reduced to a leſſer length, unleſs <lb></lb>the Sides fall upon and Penetrate one the other. </s> <s>This Conſtipati<lb></lb>on of parts non-quantitative, but infinite without Penetration of <lb></lb>quantitative parts, and the former Diſtraction above declared of <lb></lb><arrow.to.target n="marg1038"></arrow.to.target><lb></lb>infinite Indiviſibles by the interpoſition of indiviſible Vacui<lb></lb>ties, I believe, is the moſt that can be ſaid for the Condenſation <lb></lb>and Rarefaction of Bodies, without being driven to introduce Pe<lb></lb>netration of Bodies, or quantitative Void Spaces. </s> <s>If there be any <lb></lb>thing therein that pleaſeth you, make uſe of it, if not, account it <lb></lb><arrow.to.target n="marg1039"></arrow.to.target><lb></lb>vain, and my diſcourſe alſo; and ſeek out ſome other explanation <lb></lb>that may better ſatisfie your Judgment. </s> <s>Only theſe two words <lb></lb>by the way, let us remember that we are amongſt Infinites, and In<lb></lb>diviſibles.</s></p><p type="margin"> <s><margin.target id="marg1036"></margin.target><emph type="italics"></emph>A Circle is a Poli<lb></lb>gon of infinite in<lb></lb>diviſible quantita<lb></lb>tive Sides.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1037"></margin.target><emph type="italics"></emph>An Inſtant or Mo<lb></lb>ment of quantita<lb></lb>tive Time, is the <lb></lb>ſame as a Point of <lb></lb>a quantitative <lb></lb>Line.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1038"></margin.target><emph type="italics"></emph>Rarefaction is the <lb></lb>diſtraction of infi<lb></lb>nite Indiviſibles <lb></lb>by the interpoſition <lb></lb>of infinite indiviſi<lb></lb>ble Vaeuities.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1039"></margin.target><emph type="italics"></emph>Condenſation, ac<lb></lb>cording to the ope<lb></lb>ration of the Au<lb></lb>thor, proceeds from <lb></lb>the Conſtipation of <lb></lb>quantitative and <lb></lb>indiviſible parts.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>That the Conceit is ingenious, and to my eares wholly <lb></lb>new, and ſtrange, I freely confeſs, but whether or no Nature pro<lb></lb>ceed in this order, I know not how to reſolve; Truth is, that till <lb></lb>ſuch time as I hear ſomething that may better ſatisfie me, that I <lb></lb>may not ſtand ſilent, I will adhere to this. </s> <s>But haply <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end><lb></lb>may have ſomwhat, which I have not yet met with, to explicate <lb></lb>the explication, which is produced by Philoſophers in ſo abſtruce <lb></lb>a matter; for, indeed, what I have hitherto read about Condenſa<lb></lb>tion, is to me ſo denſe, and that of Rarefaction ſo ſubtill, that <lb></lb>my weak ſight neither penetrates the one, nor comprehends the <lb></lb>other.</s></p><p type="main"> <s>SIMP. </s> <s>I am full of confuſion, and find great Rubbs in the one <lb></lb>path, and in the other, and more particularly in this new one: for <lb></lb>according to this Rule, an Ounce of Gold might be rarefied and <lb></lb>drawn forth into a Maſs bigger than the whole Earth, and the <lb></lb>whole Earth condenſed and reduced into a leſs Maſs than a Nut; <lb></lb>which I neither believe, nor think that you your ſelf do believe: <lb></lb>and the Conſiderations and Demonſtrations by you hitherto de<pb xlink:href="040/01/735.jpg" pagenum="43"></pb>livered, as they are things Mathematical, abſtract and ſeparate <lb></lb>from Senſible Matter, I believe, that when they come to be apply<lb></lb>ed to Matters Phyſical and Natural, they will not exactly comply <lb></lb>with theſe Rules.</s></p><p type="main"> <s>SALV. </s> <s>It is not in my power, nor, as I believe, do you deſire, <lb></lb>that I ſhould make that viſible which is inviſible; but as to ſuch <lb></lb>things as may be comprehended by our Senſes, in regard that you <lb></lb><arrow.to.target n="marg1040"></arrow.to.target><lb></lb>have inſtanced in Gold, do we not ſee an immenſe extenſion to <lb></lb>be made of its parts? </s> <s>I know not whether you may have ſeen the <lb></lb>Method that Wyer-drawers obſerve in diſgroſſing Gold Wyer: <lb></lb>which in reality is not Gold, ſave only in the Superficies, for the <lb></lb>internal ſubſtance is Silver; and the way of diſgroſſing it is this. <lb></lb></s> <s>They take a Cylinder, or, if you will, Ingot of Silver, about half <lb></lb>a yard long, and about three or four Inches thick, and this they <lb></lb><arrow.to.target n="marg1041"></arrow.to.target><lb></lb>gild or over-lay with Leaves of beaten Gold, which, you know, <lb></lb>is ſo thin that the Wind will blow it to and again, and of theſe <lb></lb>Leaves they lay on eight or ten, and no more. </s> <s>So ſoon as it is <lb></lb>gilded, they begin to draw it forth with extraordinary force, ma<lb></lb>king it to paſs thorow the hole of the Drawing Iron, and then <lb></lb>reiterate this forceable diſgroſsment again and again thorow holes <lb></lb>ſucceſſively narrower, ſo that, after ſeveral of theſe diſgroſments, <lb></lb>they bring it to the ſmalneſs of the hair of a womans head, if not <lb></lb>ſmaller, and yet it ſtill continueth gilded in its Superficies or out<lb></lb>ſide: Now I leave you to conſider to what a fineneſs and diſtenſi<lb></lb>on the ſubſtance of the Gold is brought.</s></p><p type="margin"> <s><margin.target id="marg1040"></margin.target><emph type="italics"></emph>Gold in the gilding <lb></lb>of Silver is drawn <lb></lb>forth and diſgroſ<lb></lb>ſed immenſly.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1041"></margin.target>* Or Thumb<lb></lb>breadths.</s></p><p type="main"> <s>SIMP. </s> <s>I do not ſee how it can be inferred from this Experi<lb></lb>ment, that there may be a diſgroſment of the matter of the Gold <lb></lb>ſufficient to effect thoſe wonders which you ſpeak of: Firſt, For <lb></lb>that the firſt gilding was with ten Leaves of Gold, which make a <lb></lb>conſiderable thickneſs: Secondly, howbeit in the extenſion and <lb></lb>diſgroſment that Silver encreaſeth in length, it yet withall dimi<lb></lb>niſheth ſo much in thickneſs, that compenſating the one dimenſi<lb></lb>on with the other, the Superficies doth not ſo enlarge, as that for <lb></lb>overlaying the Silver with Gold, the ſaid Gold need to be reduced <lb></lb>to a greater thinneſs than that of its firſt Leaves.</s></p><p type="main"> <s>SALV. </s> <s>You much deceive your ſelf, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> for the en<lb></lb>creaſe of the Superficies is Subduple to the extenſion in length, as <lb></lb>I could Geometrically demonſtrate to you.</s></p><p type="main"> <s>SAGR. </s> <s>I beſeech you, both in the behalf of my ſelf, and of <lb></lb><emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> to favour us with that Demonſtration, if ſo be you <lb></lb>think that we can comprehend it.</s></p><p type="main"> <s>SALV. </s> <s>I will ſee whether I can, thus upon the ſudden, recall <lb></lb>it to mind. </s> <s>It is already manifeſt, that that ſame firſt groſs Cylin<lb></lb>der of Silver, and the Wyer diſtended to ſo great a length are two <lb></lb>equal Cylinders, in regard that they are the ſame Silver; ſo that <pb xlink:href="040/01/736.jpg" pagenum="44"></pb>if I ſhall ſhew you what proportion the Superficies of equall Cy<lb></lb>linders have to one another, we ſhall obtain our deſire. </s> <s>I ſay there<lb></lb>fore, that</s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s><emph type="italics"></emph>The Superficies of Equal Cylinders, their Baſes being <lb></lb>ſubſtracted, are to one another in ſubduple proportion <lb></lb>of their lengths.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Take two equall Cylinders, the heights of which let be A B, <lb></lb>and C D: and let the Line E be a Mean-proportional <lb></lb>between them. </s> <s>I ſay, the Superficies of the Cylinder A B, <lb></lb>the Baſes ſubſtracted, hath the ſame proportion to the Superficies <lb></lb>of the Cylinder C D, the Baſes in like manner ſubſtracted, as the <lb></lb>Line A B hath to the Line E, which is ſubduple of the proportion <lb></lb>of A B to C D. </s> <s>Cut the part of the Cylinder A B in F, and let the <lb></lb>height A F be equal to C D: And becauſe the Baſes of equal Cy<lb></lb>linders anſwer Reciprocally to their heights, the Circle, Baſe of <lb></lb>the Cylinder C D, to the Circle, Baſe of the <lb></lb><figure id="id.040.01.736.1.jpg" xlink:href="040/01/736/1.jpg"></figure><lb></lb>Cylinder A B, ſhall be as the height B A to <lb></lb>D C: And becauſe Circles are to one ano<lb></lb>ther as the Squares of their Diameters, the <lb></lb>ſaid Squares ſhall have the ſame proportion, <lb></lb>that B A hath to C D: But as B A, is to <lb></lb>C D, ſo is the Square B A to the Square of <lb></lb>E: Therefore thoſe four Squares are Pro<lb></lb>portionals: And therefore their Sides ſhall <lb></lb>be Proportionals. </s> <s>And as the Line A B is to <lb></lb>E, ſo is the Diameter of the Circle C to the <lb></lb>Diameter of the Circle A: But as are the <lb></lb>Diameters, ſo are the Circumferences; and <lb></lb>as are the Circumferences, ſo likewiſe are the Superficies of Cylin<lb></lb>ders equal in Height. </s> <s>Therefore as the Line A B is to E, ſo is the <lb></lb>Superficies of the Cylinder C D to the Superficies of the Cylinder <lb></lb>A F. </s> <s>Becauſe therefore the height A F to the height A B, is as the <lb></lb>Superficies A F to the Superficies A B: And as is the height A B <lb></lb>to the Line E, ſo is the Superficies C D to the Superficies A F: <lb></lb>Therefore by Perturbation of Proportion as the height A F is to <lb></lb>E, ſo is the Superficies C D to the Superficies A B: And, by Con<lb></lb>verſion, as the Superficies of the Cylinder A B is to the Superficies <lb></lb>of the Cylinder C D, ſo is the Line E to the Line A F; that is, to <lb></lb>the Line C D: or as A B to E: Which is in ſubduple proportion <lb></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"></pb><p type="main"> <s>Now if we apply this, that hath been demonſtrated, to our <lb></lb>purpoſe; preſuppoſing that that ſame Cylinder of Silver, that was <lb></lb>gilded whilſt it was no more than half a yard long, and four or five <lb></lb>Inches thick, being diſgroſſed to the ſineneſs of an hair, is prolon<lb></lb>ged unto the extenſion of twenty thouſand yards (for its length <lb></lb>would be much greater) we ſhall find its Superficies augmented <lb></lb>to two hundred times its former greatneſs: and conſequently, thoſe <lb></lb>Leaves of Gold, which were laid on ten in number, being diſten<lb></lb>ded on a Superficies two hundred times bigger, aſſure us that the <lb></lb>Gold which covereth the Superficies of the ſo many yards of Wyer <lb></lb>is left of no greater thickneſs than the twentieth part of a Leaf of <lb></lb>ordinary Beaten-Gold. </s> <s>Conſider, now, how great its thinneſs is, and <lb></lb>whether it is poſſible to imagine it done without an immenſe di<lb></lb>ſtention of its parts: and whether this ſeem to you an Experi<lb></lb>ment, that tendeth likewiſe towards a compoſition of infinite In<lb></lb>diviſibles in Phyſical Matters: Howbeit there want not other more <lb></lb>ſtrong and neceſſary proofs of the ſame.</s></p><p type="main"> <s>SAGR. </s> <s>The Demonſtration ſeemeth to me ſo ingenuous, that <lb></lb>although it ſhould not be of force enough to prove that firſt intent <lb></lb>for which it was produced, (and yet, in my opinion, it plainly <lb></lb>makes it out) yet nevertheleſs that ſhort ſpace of time was well <lb></lb>ſpent which hath been employed in hearing of it.</s></p><p type="main"> <s>SALV. </s> <s>In regard I ſee, that you are ſo well pleaſed with theſe <lb></lb>Geometrical Demonſtrations, which bring with them certain pro. <lb></lb></s> <s>fit, I will give you the fellow to this, which ſatisfieth to a very cu<lb></lb>rious Queſtion. </s> <s>In the former we have that which hapneth in <lb></lb>Cylinders that are equall, but of different heights or lengths: it <lb></lb>will be convenient, that you alſo hear that which occurreth in Cy<lb></lb>linders equal in Superficies, but unequal in heights; my meaning <lb></lb>alwaies is, in thoſe Superficies only that encompaſs them about, <lb></lb>that is, not comprehending the two Baſes ſuperiour and inferiour. <lb></lb></s> <s>I ſay, therefore, that</s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s><emph type="italics"></emph>Upon Cylinders, the Superficies of which the Baſes be<lb></lb>ing ſubſtracted are equal, have the ſame proportion <lb></lb>to one another as their heights Reciprocally taken.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the Superficies of the two Cylinders A E and C F be <lb></lb>equall; but the height of this C D greater than the height <lb></lb>of the other A B. </s> <s>I ſay, that the Cylinder A E hath the <lb></lb>ſame proportion to the Cylinder C F, that the height C D hath <lb></lb>to A B. </s> <s>Becauſe therefore the Superficies C F is equall to the <pb xlink:href="040/01/738.jpg" pagenum="46"></pb>ſuperficies A E, the Cylinder C F ſhall be leſſe than A E: For <lb></lb>if they were equal, its Superficies, by the laſt Propoſition would <lb></lb>be greater than the Superficies A E, and <lb></lb><figure id="id.040.01.738.1.jpg" xlink:href="040/01/738/1.jpg"></figure><lb></lb>much the more, if the ſaid Cylinder C F <lb></lb>were greater than A E. </s> <s>Let the Cylinder <lb></lb>I D be ſuppoſed equal to A E: There<lb></lb>fore, by the precedent Propoſition, the <lb></lb>Superficies of the Cylinder I D ſhall be <lb></lb>to the Superficies A E, as the height I F <lb></lb>to the Mean-proportional betwixt I F & <lb></lb>A B. </s> <s>But the Superficies A E being by <lb></lb>Suppoſition equal to C F and I D, ha<lb></lb>ving the ſame proportion to C F that the <lb></lb>height I F hath to C D: Therefore <lb></lb>C D is the Mean-Proportional between <lb></lb>I F and A B. Moreover, the Cylinder <lb></lb>I D being equal to the Cylinder A E, <lb></lb>they ſhall both have the ſame proporti<lb></lb>on to the Cylinder C F: But I D is to <lb></lb>C F, as the height I F is to C D: Therefore the Cylinder A E <lb></lb>ſhall have the ſame proportion to the Cylinder C F, that the line <lb></lb>I F hath to C D; that is, that C D hath to A B: Which was to be <lb></lb>demonſtrated.<lb></lb><arrow.to.target n="marg1042"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1042"></margin.target><emph type="italics"></emph>Of Corn-ſacks <lb></lb>with a Board at <lb></lb>the Bottom, made <lb></lb>of the ſame Stuffe, <lb></lb>but different in <lb></lb>height, which are <lb></lb>the more capa<lb></lb>cious.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>From hence is collected the Cauſe of an Accident, which the <lb></lb>Vulgar do not hearken to without admiration; and it is, how it <lb></lb>is poſſible that the ſame piece of ^{*}Cloth, being longer one way than <lb></lb>another, if a Sack be made thereof to hold Corn, as the uſual <lb></lb>manner is, with a Board at the bottom, will hold more, making <lb></lb>uſe of the leſſer 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></lb>and with the other encompaſſing the Board at the bottom, than if <lb></lb>it be made up the other way: As if for Example, the Cloth were <lb></lb>one way ſix foot, and the other way twelve, it will hold more, <lb></lb>when with the length of twelve one encompaſſeth the Board at the <lb></lb>bottom, the Sack being ſix foot high, than if it encompaſſed a <lb></lb>bottom of ſix foot, having twelve for its height. </s> <s>Now, by what <lb></lb>hath been demonſtrated, there is added to the Knowledge in ge<lb></lb>neral that it holds more that way than this, the Specifick, and <lb></lb>particular Knowledge of how much it holdeth more: which is, <lb></lb>That it will hold more in proportion as it is lower, and leſſer, as <lb></lb>it is higher. </s> <s>And thus in the meaſures afore taken, the Cloth be<lb></lb>ing twice as long as broad, when it is ſewed the length-ways it will <lb></lb>hold but half ſo much, as it will do the other way. </s> <s>And likewiſe <lb></lb><arrow.to.target n="marg1044"></arrow.to.target><lb></lb>having a Mat to make a ^{*} Frale or Basket twenty five foot long, <lb></lb>and ſuppoſe ſeven broad; made up the long-way it will hold but <lb></lb>onely ſeven of thoſe meaſures, whereof the other way it will hold <lb></lb>five and twenty.</s></p><pb xlink:href="040/01/739.jpg" pagenum="47"></pb><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></lb>Veſſel made of <lb></lb>Rushes or Wick<lb></lb>er.</s></p><p type="main"> <s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>AGR. </s> <s>And thus to our particular content we continually diſ<lb></lb>cover new Notions of great Curioſity, and not unaccompanyed <lb></lb>with Utility. </s> <s>But in the particular glanced at but even now, I <lb></lb>really believe, that amongſt ſuch as are altogether void of the <lb></lb>knowledge of Geometry, there would not be found one in twen<lb></lb>ty, but at the firſt daſh would not be miſtaken, and wonder <lb></lb>that thoſe Bodies that are contained within equal Superficies, <lb></lb>ſhould not likewiſe be in every reſpect equal; like as they run in<lb></lb>to the ſame errour, ſpeaking of the Superficies, when for deter<lb></lb>mining, as it frequently falls out, of the ampleneſſe of ſeveral <lb></lb>Cities, they think they have obtained their deſire ſo ſoon as they <lb></lb>know the ſpace of their Circuits, not knowing that one Circuit <lb></lb>may be equal to another, and yet the place conteined by this <lb></lb>much larger than the place of that: which befalleth not onely in <lb></lb>irregular Superficies, but in the regular; amongſt which thoſe <lb></lb>of more Sides are alwayes more capacious than thoſe of fewer; <lb></lb>ſo that in fine, the Circle, as being a Poligon of infinite Sides, is <lb></lb>more capacious than all other Poligons of equal Perimeter; of <lb></lb>which I remember, that I with particular delight ſaw the Demon<lb></lb>ſtration on a time when I ſtudied the Sphere of <emph type="italics"></emph>Sacroboſco,<emph.end type="italics"></emph.end> with <lb></lb>a very learned Commentary upon the ſame.</s></p><p type="main"> <s>SALV. </s> <s>It is moſt certain; and I having likewiſe light upon <lb></lb>that very place, it gave me occaſion to inveſtigate, how it may <lb></lb>with one ſole Demonſtration be concluded, that the Circle is <lb></lb>greater than all the reſt of regular Iſoperemitral Figures, and of <lb></lb>others, thoſe of more Sides bigger than thoſe of fewer.</s></p><p type="main"> <s>SAGR. </s> <s>And I that take great pleaſure in certain ſelect and no<lb></lb>wiſe-trivial Demonſtrations, entreat you with all importunity to <lb></lb>make me a partaker therein.</s></p><p type="main"> <s>SALV. </s> <s>I ſhall diſpatch the ſame in few words, demonſtrating <lb></lb>the following Theorem, namely;</s></p><pb xlink:href="040/01/740.jpg" pagenum="48"></pb><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s><emph type="italics"></emph>The Circle is a Mean-Proportional betwixt any two <lb></lb>Regular Homogeneal Poligons, one of which is cir<lb></lb>cumſcribed about it, and the other Iſoperimetral to <lb></lb>it: Moreover, it being leſſe than all the circumſcri<lb></lb>bed, it is, on the contrary, bigger than all the Iſoperi<lb></lb>metral. </s> <s>And, again of the circumſcribed, thoſe that <lb></lb>have more angles are leſſer than thoſe that have <lb></lb>fewer; and on the other ſide of the Iſoperimetral, <lb></lb>thoſe of more angles are bigger.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Of the two like Poligons A and B, let A be circumſcribed <lb></lb>about the Circle A, and let the other B, be Iſoperime<lb></lb>tral to the ſaid Circle: I ſay, that the Circle is the Mean<lb></lb>proportional betwixt them. </s> <s>For that (having drawn the Semidi<lb></lb>ameter A C) the Circle being equal to that Right-angled Trian<lb></lb>gle, of whoſe Sides including the Right angle, the one is equal <lb></lb><figure id="id.040.01.740.1.jpg" xlink:href="040/01/740/1.jpg"></figure><lb></lb>to the Semidiameter A C, and the other to the Circumference: <lb></lb>And likewiſe the Poligon A being equal to the right angled Tri<lb></lb>angle, that about the right angle hath one of its Sides equal to <lb></lb>the ſaid right line A C, and the other to the Perimeter of the ſaid <lb></lb>Poligon: It is manifeſt, that the circumſcribed Poligon hath the <lb></lb>ſame proportion to the Circle, that its Perimeter hath to the Cir<lb></lb>cumference of the ſaid Circle; that is, to the Perimeter of the <lb></lb>Poligon B, which is ſuppoſed equal to the ſaid Circumference: <lb></lb>But the Poligon A hath a proportion to the Poligon B, double to <lb></lb>that of its Perimeter, to the Perimeter of B (they being like Fi<lb></lb>gures:) Therefore the Circle A is the Mean-proportional be<lb></lb>tween the two Poligons A and B. </s> <s>And the Poligon A being <lb></lb>bigger than the Circle A, it is manifeſt that the ſaid Circle <lb></lb>A is bigger than the Poligon B, its Iſoperimetral, and conſe<lb></lb>quently the greateſt of all Regular Poligons that are Iſoperimetral <pb xlink:href="040/01/741.jpg" pagenum="49"></pb>to it. </s> <s>As to the other particular, that is to prove, that of the <lb></lb>Poligons circumſcribed about the ſame Circle, that of fewer <lb></lb>Sides is bigger than that of more Sides; but that, on the contrary, of <lb></lb>the Iſoperimetral Poligons, that of more Sides is bigger than that <lb></lb>of fewer Sides, we will thus demonſtrate. </s> <s>In the Circle whoſe <lb></lb>Center is O, and Semidiameter O A, let there be a Tangent <lb></lb>A D, and in it let it be ſuppoſed, for example, that A D is the <lb></lb>half of the Side of the Pentagon circumſcribed, and A C the half <lb></lb>of the Side of the Heptagon, and draw the right lines O G C, <lb></lb>and O F D; and on the Center O, at the diſtance O C, draw the <lb></lb>Arch E C I: And becauſe the Triangle D O C is greater than the <lb></lb>Sector E O C, and the Sector C O I greater than the Triangle <lb></lb>C O A; the Triangle D O C ſhall have greater proportion to <lb></lb>the Triangle C O A, than the Sector E O C, to the Secant C O I, <lb></lb>that is, than the Secant F O G to the Secant G O A. And, by <lb></lb>Compoſition, Permutation of Proportion, the Triangle D O A <lb></lb>ſhall have greater proportion to the Secant F O A, than the Tri<lb></lb>angle C O A to the Secant G O A: And ten Triangles D O A <lb></lb>ſhall have greater proportion to ten Secants F O A, than four<lb></lb>teen Triangles C O A to fourteen Sectors G O A: That is the <lb></lb>circumſcribed Pentagon ſhall have greater proportion to the Cir<lb></lb>cle, than hath the Heptagon: And therefore the Pentagon ſhall <lb></lb>be greater than the Heptagon. </s> <s>Let us now ſuppoſe an Hep<lb></lb>tagon and a Pentagon Iſoperimetral to the ſame Circle. </s> <s>I ſay, that <lb></lb>the Heptagon is bigger than the Pentagon. </s> <s>For that the ſaid Cir<lb></lb>cle being the Mean proportional between the Pentagon circum<lb></lb>ſcribed and the Pentagon its Iſoperimetral, and likewiſe the Mean <lb></lb>between the Circumſcribed and Iſoperimetral Heptagon: It ha<lb></lb>ving been proved that the Circumſcribed Pentagon is greater then <lb></lb>the Circumſcribed Heptagon, the ſaid Pentagon ſhall have greater <lb></lb>proportion to the Circle, than the Heptagon: that is, the Circle <lb></lb>ſhall have greater proportion to its Iſoperimetral Pentagon, than <lb></lb>to its Iſoperimetral Heptagon: Therefore the Pentagon is leſſer <lb></lb>than the Iſoperimetral Heptagon. </s> <s>Which was to be demon<lb></lb>ſtrated</s></p><p type="main"> <s>SAGR. </s> <s>A moſt ingenious Demonſtration, and very acute. </s> <s>But <lb></lb>whither are we run to ingulph our ſelves in Geometry, when as <lb></lb>we were about to conſider the Difficulties propoſed by <emph type="italics"></emph>Simpli<lb></lb>cius,<emph.end type="italics"></emph.end> which indeed are very conſiderable, and in particular, that <lb></lb>of Condenſation, is in my opinion, very abſtruce.</s></p><p type="main"> <s>SALV. </s> <s>If Condenſation and Rarefaction are oppoſite Motions, <lb></lb>where there is ſeen an immenſe Rarefaction, one cannot deny an <lb></lb>extraordinary Condenſation: but immenſe Rarefactions, and, <lb></lb>which encreaſeth the wonder, almoſt Momentary, we ſee every <lb></lb>day: for what a boundleſſe Rarefaction is that of a little quan<pb xlink:href="040/01/742.jpg" pagenum="50"></pb><arrow.to.target n="marg1045"></arrow.to.target><lb></lb>tity of Gunpowder reſolved into a vaſt maſſe of Fire? </s> <s>And what, <lb></lb>beyond this, the (I could almoſt ſay) indeterminate Expanſion <lb></lb>of its Light? </s> <s>And if that Fire and this Light ſhould reunite toge<lb></lb>ther, which yet is no impoſſibility, in regard, that at the firſt <lb></lb>they lay in that little room, what a Condenſation would this be? <lb></lb></s> <s>If you ſtudy for them, you will find hundreds of ſuch Rarefacti<lb></lb>ons, which are much more readily obſerved, than Condenſati<lb></lb>ons: for Denſe matters are more tractable, and ſubject to our <lb></lb>Senſes. </s> <s>For we can eaſily order Wood at pleaſure, and we ſee <lb></lb>it reſolved into Fire, and into Light, but we do not in the ſame <lb></lb>manner ſee the Fire and the Light Condenſe to the making of <lb></lb>Wood: We ſee Fruits, Flowers, and many other ſolid matters <lb></lb>reſolved in a great meaſure into Odors, but we do not after the <lb></lb>ſame manner ſee the odoriferous Atomes concurre to the conſtitu<lb></lb>tion of the Oderate Solids; but where Senſible Obſervation is <lb></lb>wanting, we are to ſupply it with Reaſon, which will ſuffice to <lb></lb>make us apprehenſive, no leſſe of the Motion to the Rarefaction <lb></lb>and reſolution of Solids, than, to the Condenſation of rare and <lb></lb>moſt tenuous Subſtances. </s> <s>Moreover, we queſtion how to effect <lb></lb>the Condenſation and Rarefaction of the Bodies which may be <lb></lb>rarefied and condenſed, ſtudying in what manner it may be done <lb></lb>without introducing of a <emph type="italics"></emph>Vacuum,<emph.end type="italics"></emph.end> and Penetration of Bodies; <lb></lb>which doth not hinder, but that in Nature there may be matters <lb></lb>which admit no ſuch accidents, and conſequently do not allow <lb></lb>roome for thoſe things which you phraſe inconvenient and im<lb></lb>poſſible. </s> <s>And laſtly, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> I have on the the ſcore of ſatis<lb></lb>fying you, and thoſe Philoſophers that hold with you, taken <lb></lb>ſome pains in conſidering how Condenſation and Rarefaction <lb></lb>may be underſtood to be performed without admitting Penetra<lb></lb>tion of Bodies, and introducing the Void Spaces called Vacuities, <lb></lb>Effects which you deny and abhorre: for if you would but grant <lb></lb>them, I would no longer ſo reſolutely contradict you. </s> <s>There<lb></lb>fore either admit theſe Inconveniences, or accept of my Spe<lb></lb>culations, or elſe finde out others more conducing to the <lb></lb>purpoſe.</s></p><p type="margin"> <s><margin.target id="marg1045"></margin.target><emph type="italics"></emph>Rarefaction im<lb></lb>minſe is that of <lb></lb>a little Gunpow<lb></lb>der into a vaſt <lb></lb>maſs of Fire.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>As to the denying of Penetration, I am wholly of opi<lb></lb>nion with the Peripatetick Philoſophers; as to that of a <emph type="italics"></emph>Vacuum,<emph.end type="italics"></emph.end><lb></lb>I would ſee the Demonſtration of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> thorowly examined, <lb></lb>wherewith he oppoſeth the ſame, and what you, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> will <lb></lb>anſwer to it. <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> ſhall do me the favour punctually to <lb></lb>recite the proof of the Philoſopher; and you, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> to an<lb></lb>ſwer it.</s></p><p type="main"> <s>SIMP. <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> as neer as I can remember, breaks out againſt <lb></lb>certain of the Ancients, who introduced Vacuity, as neceſſary <lb></lb>to Motion, ſaying, that this without that could not be effected; <pb xlink:href="040/01/743.jpg" pagenum="51"></pb>to this <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> making oppoſition, demonſtrateth, that on the <lb></lb>contrary, the effecting of Motion (as we ſee) deſtroyeth the Poſiti<lb></lb>on of <emph type="italics"></emph>Vacuum<emph.end type="italics"></emph.end>; and his method therein is this. </s> <s>He maketh two <lb></lb>Suppoſitions, one is touching Moveables different in Gravity <lb></lb>moved in the ſame <emph type="italics"></emph>Medium:<emph.end type="italics"></emph.end> the other is concerning the ſame <lb></lb>Moveable moved in ſeveral <emph type="italics"></emph>Medium's.<emph.end type="italics"></emph.end> As to the firſt, he ſuppo<lb></lb>ſeth that Moveables different in Gravity, move in the ſame <lb></lb><emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> with unequal Velocities, which bear to each other the <lb></lb>ſame proportion as their Gravities: ſo that, for example, a Move<lb></lb>able ten times heavier than another, moveth ten times more ſwift<lb></lb>ly. </s> <s>In the other Poſition he aſſumes, that the Velocity of the <lb></lb>ſame Moveable in different <emph type="italics"></emph>Medium's<emph.end type="italics"></emph.end> are in Reciprocal to that of <lb></lb>the thickneſſe or Denſity of the ſaid <emph type="italics"></emph>Medium's<emph.end type="italics"></emph.end>: ſo that ſuppo<lb></lb>ſing <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> that the Craſſitude of the Water was ten times as great <lb></lb>as that of the Air, he will have the Velocity in the Air to be <lb></lb>ten times more than the Velocity in the Water. </s> <s>And from this ſe<lb></lb>cond Aſſumption he draweth his Demonſtration in this manner. <lb></lb></s> <s>Becauſe the tenuity of <emph type="italics"></emph>Vacuum<emph.end type="italics"></emph.end> infinitely ſurpaſſeth the corpu<lb></lb>lence, though never ſo ſubtil, of any whatever Replete <emph type="italics"></emph>Medi<lb></lb>um,<emph.end type="italics"></emph.end> every Moveable that in the Replete <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> moveth a cer<lb></lb>tain ſpace in a certain time, in a <emph type="italics"></emph>Vacuum<emph.end type="italics"></emph.end> would paſſe the ſame <lb></lb>in an inſtant: But to make a Motion in an inſtant is impoſſible: <lb></lb>Therefore to introduce Vacuity in the accompt of Motion is im<lb></lb>poſſible.</s></p><p type="main"> <s>SALV. </s> <s>The Argument one may ſee to be <emph type="italics"></emph>ad hominem,<emph.end type="italics"></emph.end> that is, <lb></lb><arrow.to.target n="marg1046"></arrow.to.target><lb></lb>againſt thoſe who would make a <emph type="italics"></emph>Vacuum<emph.end type="italics"></emph.end> neceſſary to Motion; <lb></lb>but if I ſhall admit of the Argument as concludent, granting <lb></lb>withal, that in Vacuity there would be no Motion; yet the Poſi<lb></lb>tion of Vacuity taken abſolutely, and not in relation to Motion, <lb></lb>is not thereby overthrown. </s> <s>But to tell you what thoſe Ancients, <lb></lb>peradventure, might anſwer, that ſo we may the better diſcover <lb></lb>how far the Demonſtration of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> holds good, methinks that <lb></lb>one might oppoſe his Aſſumptions, denying them both. </s> <s>And as <lb></lb>to the firſt: I greatly doubt that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> never experimented <lb></lb>how true it is, that two ſtones, one ten times heavier than the o<lb></lb>ther, let fall in the ſame inſtant from an height, <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> of an hun<lb></lb>dred yards, were ſo different in their Velocity, that upon the <lb></lb>arrival of the greater to the ground, the other was found not to <lb></lb>have deſcended ſo much as ten yards.</s></p><p type="margin"> <s><margin.target id="marg1046"></margin.target>Ariſtotle's <emph type="italics"></emph>Argu<lb></lb>ment againſt a<emph.end type="italics"></emph.end><lb></lb>Vacuum <emph type="italics"></emph>is<emph.end type="italics"></emph.end> ad <lb></lb>hominem.</s></p><p type="main"> <s>SIMP. Why, it may be ſeen by his own words, that he confeſ<lb></lb>ſeth he had made the Experiment, for he ſaith, [<emph type="italics"></emph>We ſee the more <lb></lb>grave<emph.end type="italics"></emph.end>] now that <emph type="italics"></emph>Seeing<emph.end type="italics"></emph.end> implieth that he had tried the Experi<lb></lb>ment.</s></p><p type="main"> <s>SAGR. </s> <s>But I, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that have made proof thereof, do aſ<lb></lb>ſure you, that a Cannon bullet that weigheth one hundred, rwo <pb xlink:href="040/01/744.jpg" pagenum="52"></pb>hundred, and more pounds, will not one Palme anticipate the ar<lb></lb>rival of a Musket-bullet to the ground, that weigheth but half <lb></lb>a pound, falling likewiſe from an height of two hundred yards.</s></p><p type="main"> <s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>ALV. </s> <s>But without any other Experiments, we may by ſhort <lb></lb>and neceſſary Demonſtrations cleerly prove, that it is not true that <lb></lb>a Moveable more grave moveth more ſwiftly than another leſſe <lb></lb>grave, confining our meaning ſtill to Moveables of the ſame Mat<lb></lb>ter; and, in ſhort, to thoſe of which <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſpeaketh. </s> <s>For tell <lb></lb>me, <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> whether you admit, that to every cadent grave <lb></lb>Body there belongeth by nature one determinate Velocity; ſo <lb></lb>as that it cannot be encreaſed or diminiſhed in it without uſing vi<lb></lb>olence to it, or impoſing ſome impediment upon it?</s></p><p type="main"> <s>SIMP. </s> <s>It cannot be doubted, but that the ſame Moveable in <lb></lb>the ſame <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> hath one eſtabliſhed and by-nature-determinate <lb></lb>Velocity, which cannot be increaſed, unleſſe with new <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end><lb></lb>conferred on it, or diminiſhed, ſave onely by ſome impediment <lb></lb>that retards it.</s></p><p type="main"> <s>SALV. </s> <s>If therefore we had two Moveables, the natural Velo<lb></lb>cities of which were unequal, it is manifeſt, that if we joyned the <lb></lb>ſlower with the ſwifter, this would be in part retarded by the <lb></lb>ſlower, and that in part accelerated by the other more ſwift. </s> <s>Do <lb></lb>not you concur with me in this opinion?</s></p><p type="main"> <s>SIMP. </s> <s>I think that it ought undoubtedly ſo to ſucceed.</s></p><p type="main"> <s>SALV. </s> <s>But if this be ſo, and, it be likewiſe true that a great <lb></lb>Stone moveth with (ſuppoſe) eight degrees of Velocity, and a leſ<lb></lb>ſer with fewer, then joyning them both together, the compound <lb></lb>of them will move with a Velocity leſſe than eight Degrees: But <lb></lb>the two Stones joyned together make one Stone greater than <lb></lb>that before, which moved with eight degrees of Velocity: There<lb></lb>fore this greater Stone moveth leſſe ſwiftly than the leſſer, which <lb></lb>is contrary to your Suppoſition. </s> <s>You ſee therefore, that from the <lb></lb>ſuppoſing that the more grave Moveable moveth more ſwiftly <lb></lb>than the leſſe grave, I prove unto you that the more grave mo<lb></lb>veth leſſe ſwiftly.</s></p><p type="main"> <s>SIMP. </s> <s>I find my ſelf at a loſſe, for the truth is, that the leſ<lb></lb>ſer Stone being joyned to the greater, weight is added unto it, and <lb></lb>weight being added to it, I cannot ſee why there ſhould not Ve<lb></lb>locity be added to it, or at leaſt why it ſhould be diminiſhed <lb></lb>in it.</s></p><p type="main"> <s>SALV. </s> <s>Here you run into another errour, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> for it <lb></lb>is not true, that that ſame leſſer Stone encreaſeth the weight of <lb></lb>the greater.</s></p><p type="main"> <s>SIMP. </s> <s>Oh wonderful! this quite ſurpaſſeth my apprehenſion.</s></p><p type="main"> <s>SALV. </s> <s>Not at all, if you will but ſtay till I have diſcovered <lb></lb>to you the Equivokes, of which you are in doubt: Therefore <pb xlink:href="040/01/745.jpg" pagenum="53"></pb>you muſt know that it is neceſſary to diſtinguiſh betwixt grave <lb></lb>Bodies ſet on Moving, and the ſame conſtituted in Reſt; a Stone <lb></lb>put into the Ballance not onely acquireth greater weight, by lay<lb></lb>ing another Stone upon it, but alſo the addition of, a Flake of <lb></lb>Hemp will make it weigh more by thoſe ſix or ten ounces that <lb></lb>the Hemp ſhall weigh; but if you ſhould freely let fall the Stone <lb></lb>tied to the Hemp from an high place, do you think that in the <lb></lb>Motion the Hemp weigheth down the Stone, ſo as to accelerate <lb></lb>its Motion; or elſe do you believe that it will retard it, ſuſtain<lb></lb>ing it in part? </s> <s>We indeed feel our ſhoulders laden, ſo long as we <lb></lb>will oppoſe the Motion that the weight would make which lyeth <lb></lb>upon our backs; but if we ſhould deſcend with the ſame Velocity <lb></lb>wherewith that ſame grave Body would naturally deſcend, in what <lb></lb>manner will you that it preſſe or bear upon us? </s> <s>Do not you ſee <lb></lb>that this would be a wounding one with a Lance that runneth <lb></lb>before you, with as much or more ſpeed than you purſue him. <lb></lb></s> <s>You may conclude therefore that in the free and natural fall, the <lb></lb>leſſer Stone doth not bear upon the greater, and conſequently doth <lb></lb>not encreaſe their weight, as it doth in Reſt.</s></p><p type="main"> <s>SIMP. </s> <s>But what if the greater was put upon the leſſer?</s></p><p type="main"> <s>SALV. </s> <s>It would encreaſe their weight, in caſe its Motion were <lb></lb>more ſwift; but it hath been already concluded, that in caſe the <lb></lb>leſſer ſhould be more ſlow it would in part retard the Velocity of <lb></lb>the greater, ſo that there Compound would move leſſe ſwiftly; <lb></lb>being greater than the other, which is contrary to your Aſſumpti<lb></lb>on: Let us conclude therefore, that great Moveables, and like<lb></lb>wiſe little, being of the ſame Specifical Gravity, move with like <lb></lb>Velocity.</s></p><p type="main"> <s>SIMP. </s> <s>Your diſcourſe really is full of ingenuity, yet methinks <lb></lb>it is hard to conceive that a drop of Bird-ſhot, ſhould move as <lb></lb>ſwiftly as a Canon-bullet.</s></p><p type="main"> <s>SALV. </s> <s>You may ſay a grain of Sand as faſt as a Mill-ſtone. <lb></lb></s> <s>I would not have you, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> to do as ſome others are wont <lb></lb>to do, and diverting the diſcourſe from the principal deſign, fa<lb></lb>ſten upon ſome one ſaying of mine that may want an hairs-breadth <lb></lb>of the truth, and under this hair hide a defect of another man as <lb></lb>big as the Cable of a Ship. <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> ſaith, a Ball of Iron of an <lb></lb>hundred pounds weight falling, from an height of an hundred yards, <lb></lb>commeth to the ground before that one of one pound is deſcended <lb></lb>one ſole yard: I ſay, that they arrive at the earth both in the ſame <lb></lb>time: You find, that the bigger anticipates the leſſer two Inches, <lb></lb>that is to ſay, that when the great one falls to the ground, the o<lb></lb>ther is diſtant from it two inches: you go about to hide under <lb></lb>theſe two inches the ninety nine yards of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> and ſpeaking <lb></lb>onely to my ſmall errour, paſſe over in ſilence the other great one. <pb xlink:href="040/01/746.jpg" pagenum="54"></pb><emph type="italics"></emph>Ariſtotlee<emph.end type="italics"></emph.end> affirmeth, that Moveables of different Gravities in the <lb></lb>ſame <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> move (as far as concerneth Gravity) with Veloci<lb></lb>ties proportionate to their Weights; and exemplifieth it by <lb></lb>Moveables, wherein one may diſcover the pure and abſolute effect <lb></lb>of Weight, omitting the other Conſiderations, as well of Figures, <lb></lb>as of the minute Motions; which things receive great alteration <lb></lb>from the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> which altereth the ſimple effect of the ſole <lb></lb>Gravity; wherefore we ſee Gold, that is heavier than any other <lb></lb>matter, being reduced into a very thin Leaf, to go flying to and <lb></lb>again through the Air, the like do Stones beaten to very ſmall <lb></lb>Powder. </s> <s>But if you would maintain the Univerſal Propoſition, it <lb></lb>is requiſite that you ſhew the proportion of the Velocities to be <lb></lb>obſerved in all grave Bodies, and that a Stone of twenty pounds <lb></lb>moveth ten times ſwifter than one of two: which, I tell you, is <lb></lb>falſe, and that falling from an height of fifty or an hundred yards, <lb></lb>they come to the ground in the ſame inſtant.</s></p><p type="main"> <s>SIMP. </s> <s>Perhaps in very great heights of Thouſands of yards <lb></lb>that would happen, which is not ſeen to occur in theſe leſſer <lb></lb>heights.</s></p><p type="main"> <s>SALV. </s> <s>If this was the Meaning of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> you have in<lb></lb>volved him in another Errour, which will be found a Lie; for <lb></lb>there being no ſuch perpendicular altitudes found on the Earth, <lb></lb>its a clear caſe, that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> was not able to have made an Experi<lb></lb>ment thereof; and yet would perſwade us that he had, whilſt he <lb></lb>ſaith, that the ſaid effect is <emph type="italics"></emph>ſeen.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SIMP. <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> indeed makes no uſe of this Principle, but of <lb></lb>that other, which I believe is not obnoxious to theſe doubts.</s></p><p type="main"> <s>SALV. </s> <s>Why that alſo is no leſſe falſe than this; and I admire <lb></lb>that you do not of your ſelf perceive the fallacy, and diſcern, that <lb></lb>ſhould it be true, that the ſame Moveable in <emph type="italics"></emph>Medium's<emph.end type="italics"></emph.end> of dif<lb></lb>ferent Subtilty and Rarity, and, in a word, of different Ceſſion, <lb></lb>ſuch, for example, as are Water and Air, move with a greater <lb></lb>Velocity in the Air than in the Water, according to the propor<lb></lb>tion of the Airs Rarity to the Rarity of the Water, it would <lb></lb>follow that every Moveable that deſcendeth in the Air would <lb></lb>deſcend alſo in the Water: Which is ſo falſe, that very many <lb></lb>Bodies deſcend in the Air, that in the Water do not onely not <lb></lb>deſcend, but alſo riſe upwards.</s></p><p type="main"> <s>SIMP I do not underſtand the neceſſity of your Conſequence: <lb></lb>and I will ſay farther, that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſpeaketh of thoſe Grave<lb></lb>bodies that deſcend in the one <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> and in the other, and not <lb></lb>of thoſe that deſcend in the Air and aſcend in the Water.</s></p><p type="main"> <s>SALV. </s> <s>You produce for the Philſopher ſuch Pleas as he, with<lb></lb>out all doubt, would never alledge, for that they aggravate the <lb></lb>firſt miſtake. </s> <s>Therefore tell me, if the Craſsitude of the Water, <pb xlink:href="040/01/747.jpg" pagenum="55"></pb>or whatever it be that retardeth the Motion, hath any proporti<lb></lb>on to the Craſſitude of the Air that leſſe retards it; and if it have; <lb></lb>do you aſſign it us, at pleaſure.</s></p><p type="main"> <s>SIMP. </s> <s>It hath ſuch a proportion, and we will ſuppoſe it to be <lb></lb>decuple; and that therefore the Velocity of a Grave Body, that <lb></lb>deſcends in both the Elements, ſhall be ten times ſlower in the Wa<lb></lb>ter than in the Air.</s></p><p type="main"> <s>SALV. </s> <s>I will take one of thoſe Grave-Bodies that deſcend in <lb></lb>the Air, but not in the Water; as for inſtance, a Ball of Wood, <lb></lb>and deſire that you will aſſign it what Velocity you pleaſe, whilſt it <lb></lb>deſcends through the Air.</s></p><p type="main"> <s>SIMP. </s> <s>Suppoſe we, that it move with twenty degrees of Velo<lb></lb>city.</s></p><p type="main"> <s>SALV. </s> <s>Very well: And it is manifeſt, that that Velocity to <lb></lb>ſome other leſſer, may have the ſame proportion, that the Craſſi<lb></lb>tude of the Water hath to that of the Air; and that this ſhall be <lb></lb>the Velocity of the two only degrees: ſo that exactly to an hair, <lb></lb>and in direct conformity to the Aſſumption of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> it ſhould <lb></lb>be concluded, That the Ball of Wood, which in the Air, ten times <lb></lb>more yielding, moveth deſcending with twenty degrees of Veloci<lb></lb>ty, in the Water ſhould deſcend with two, and not return from the <lb></lb>bottom to flote a-top, as it doth: unleſs you will ſay, that the <lb></lb>aſcending of the Wood to the top is the ſame in the Water, as its <lb></lb>ſinking to the bottom with two degrees of Velocity; which I do <lb></lb>not believe. </s> <s>But ſeeing that the Ball of Wood deſcends not to the <lb></lb>bottom, I rather think that you will grant me, that ſome other Ball, <lb></lb>of other matter different from Wood, might be found that deſcends <lb></lb>in the Water with two degrees of Velocity.</s></p><p type="main"> <s>SIMP. </s> <s>Queſtionleſſe there might; but it muſt be of a matter <lb></lb>conſiderably more grave than Wood.</s></p><p type="main"> <s>SALV. </s> <s>This is that which I deſired to know. </s> <s>But this ſecond <lb></lb>Ball, which in the Water deſcendeth with two degrees of Velocity, <lb></lb>with what Velocity will it deſcend in the Air? </s> <s>It is requiſite (if <lb></lb>you will maintain <emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> Rule) that you anſwer that it will <lb></lb>move with twenty degrees: But you your ſelf have aſſigned twen<lb></lb>ty degrees of Velocity to the Ball of Wood; Therefore this, and <lb></lb>the other that is much more grave, will move thorow the Air with <lb></lb>equall Velocity. </s> <s>Now how doth the Philoſopher reconcile this <lb></lb>Concluſion with that other of his, that the Moveables of different <lb></lb>Gravity, move in the ſame <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> with different Velocities, and <lb></lb>ſo different as are their Gravities? </s> <s>But, without any deep ſtudies, <lb></lb>how comes it to paſs that you have not obſerved very frequent, <lb></lb>and very palpable Accidents, and not conſidered two Bodies, that in <lb></lb>the Water will move one an hundred times more ſwiftly than the <lb></lb>other, but that again in the Air that ſwifter one will not out-go the <pb xlink:href="040/01/748.jpg" pagenum="56"></pb>other, one ſole Centeſm? </s> <s>As for example, an Egge of Marble will <lb></lb>deſcend in the Water an hundred times faſter than one of an Hen, <lb></lb>when as in the Air, at the height of twenty Yards it will not anti<lb></lb>cipate it four Inches: and, in a word, ſuch a certain Grave Body <lb></lb>will ſink to the bottom in three hours in ten fathom Water, that <lb></lb>in the Air will paſs the ſame ſpace in one or two pulſes, and ſuch <lb></lb>another (as for inſtance a Ball of Lead) will paſs that number of <lb></lb>fathoms with eaſe in leſs than double the time. </s> <s>And here I ſee <lb></lb>plainly, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that you find, that herein there is no place left <lb></lb>for any diſtinction, or reply. </s> <s>Conclude we therefore, that that <lb></lb>ſame Argument concludeth nothing againſt <emph type="italics"></emph>Vacuum<emph.end type="italics"></emph.end>; and if it <lb></lb>ſhould, it would only overthrow Spaces conſiderably great, which <lb></lb>neither I, nor, as I take it, thoſe <emph type="italics"></emph>Ancients<emph.end type="italics"></emph.end> did ſuppoſe to be natu<lb></lb>rally allowed, though, perhaps, with violence they may be effe<lb></lb>cted, as, me thinks, one may collect from ſeveral Experiments, which <lb></lb>it would be two tedious to go about at preſent to produce.</s></p><p type="main"> <s>SAGR. </s> <s>Seeing that <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> is ſilent, I will take leave to ſay <lb></lb>ſomething. </s> <s>In regard you have with ſufficient plainneſſe demon<lb></lb>ſtrated, that it is not true, That Moveables unequally grave move in <lb></lb>the ſame <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> with Velocities proportionate to their Gravities, <lb></lb>but with equal: deſiring to be underſtood to ſpeak of Bodies of the <lb></lb>ſame Matter, or of the ſame Specifick Gravity, but not (as I con<lb></lb>ceive) of Gravities different <emph type="italics"></emph>in Spetie,<emph.end type="italics"></emph.end> (for I do not think that <lb></lb>you intend to prove unto us, that a Ball of Cork moveth with like <lb></lb>Velocity to one of Lead;) and having moreover very manifeſtly <lb></lb>demonſtrated, that it is not true, That the ſame Moveable in <emph type="italics"></emph>Me<lb></lb>diums<emph.end type="italics"></emph.end> of different Reſiſtances retain in their Velocities and Tardi<lb></lb>ties the ſame proportion as have their Reſiſtances: to me it would <lb></lb>be a very pleaſing thing to hear, what thoſe be which are obſerved <lb></lb>as well in the one caſe as in the other.</s></p><p type="main"> <s>SALV. </s> <s>The Queſtions are ingenuous, and I have many times <lb></lb>thought of them: I will relate unto you the Contemplations made <lb></lb>upon them, and what at length I did from thence infer. </s> <s>After I <lb></lb>had aſſured my ſelf that it was not true, That the ſame Moveable <lb></lb>in <emph type="italics"></emph>Medium's<emph.end type="italics"></emph.end> of different Reſiſtance obſerveth in its Velocity the <lb></lb>proportion of the Ceſſion of thoſe <emph type="italics"></emph>Media<emph.end type="italics"></emph.end>; nor yet, again, That in <lb></lb>the ſame <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> Moveables of different Gravity retain in their <lb></lb>Velocities the proportion of thoſe Gravities (ſpeaking alwaies of <lb></lb>Gravitles different <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end>) I began to put both theſe Accidents <lb></lb>together, obſerving that which befell the Moveables different in <lb></lb>Gravity put into <emph type="italics"></emph>Mediums<emph.end type="italics"></emph.end> of different Reſiſtance, and I perceived <lb></lb>that the inequality of the Velocities were found to be alwaies <lb></lb>greater in the more reſiſting <emph type="italics"></emph>Medium's,<emph.end type="italics"></emph.end> than in the more yielding; <lb></lb>and that with ſuch a diverſity, that of two Moveables that, de<lb></lb>ſcending thorow the Air, differ very little in Velocity of Motion, <pb xlink:href="040/01/749.jpg" pagenum="57"></pb>one will, in the Water, move ten times faſter than the other; <lb></lb>yea: that ſuch, as in the Air do ſwiftly deſcend, in the Water not <lb></lb>only will not deſcend, but will be wholly deprived of Motion, <lb></lb>and, which is yet more, will move upwards: for one ſhall ſome<lb></lb>times find ſome kind of Wood, or ſome knot, or root of the ſame, <lb></lb>that in the Water will lye ſtill, when as in the Air it will ſwiftly <lb></lb>deſcend.</s></p><p type="main"> <s>SAGR. </s> <s>I have many times ſet my ſelf with an extream patience <lb></lb>to ſee if I could reduce a Ball of Wax, (which of it ſelf doth not <lb></lb>go to the bottom) by adding to it grains of ſand, to ſuch a degree <lb></lb>of Gravity like to the Water, as to make it ſtand ſtill in the <lb></lb>midſt of that Element; but I could never, by all the care I <lb></lb>uſed, ſucceed in my attempt; ſo that I cannot tell, whether any <lb></lb>Solid matter may be found ſo naturally alike in Gravity to Wa<lb></lb>ter, as that being put into any place of the ſame, it can reſt or lye <lb></lb>ſtill.</s></p><p type="main"> <s>SALV. </s> <s>In this, as well as in a thouſand other actions, many <lb></lb>Animals are more ingenuous than we. </s> <s>And, in this caſe, Fiſhes <lb></lb><arrow.to.target n="marg1047"></arrow.to.target><lb></lb>would have been able to have given you ſome light, being in this <lb></lb>affair ſo skilful, that at their pleaſure they ^{*} equilibrate themſelves, <lb></lb><arrow.to.target n="marg1048"></arrow.to.target><lb></lb>not only with one kind of Water, but with ſuch, as, either of their <lb></lb>own nature, or by means of ſome ſupervenient muddineſs, or for <lb></lb>their ſaltneſs (which maketh a great alteration) are very diffe<lb></lb>rent; equilibrate themſelves, I ſay, ſo exactly, that without ſtir<lb></lb>ring in the leaſt they lye ſtill in every place: and this, in my opi<lb></lb>nion, they do, by making uſe of the Inſtrument given them by Na<lb></lb>ture to that end, <emph type="italics"></emph>ſcilicet,<emph.end type="italics"></emph.end> of that Bladder which they have in their <lb></lb>Bodies, which by a very narrow neck anſwereth to their mouth; <lb></lb>and by that they either, when they would ſtand ſtill, ſend forth <lb></lb>part of the Air that is contained in the ſaid Bladders, or, ſwimming <lb></lb>to the top they draw in more, making themſelves by that art one <lb></lb>while more, another while leſs heavy than the Water, and at their <lb></lb>pleaſures equilibrating themſelves to the ſame.</s></p><p type="margin"> <s><margin.target id="marg1047"></margin.target><emph type="italics"></emph>Fiſhes equilibrate <lb></lb>themſelves admi<lb></lb>rably in the Water.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1048"></margin.target>* Or poiſe.</s></p><p type="main"> <s>SAGR I deceived ſome of my Friends with another device; <lb></lb>for I had made my boaſt unto them, that I would reduce that Ball <lb></lb>of Wax to an exact <emph type="italics"></emph>equilibrium<emph.end type="italics"></emph.end> with the Water, and having put <lb></lb>ſome ſalt Water in the bottom of the Veſſel, and a-top of that ſome <lb></lb>freſh, I ſhewed them the Ball, which in the midſt of the Water <lb></lb>ſtood ſtill, and being thruſt to the bottom, or to the top, ſtaid nei<lb></lb>ther in this nor that ſcituation, but returned to the midſt.</s></p><p type="main"> <s>SALV. </s> <s>This ſame Experiment is not void of utility; for Phyſi<lb></lb><arrow.to.target n="marg1049"></arrow.to.target><lb></lb>cians, in particular, treating of ſundry qualities of Waters, and <lb></lb>amongſt other things, principally of the more or leſs Gravity or <lb></lb>Levity of this or that: by ſuch a Ball, in ſuch manner poiſed and <lb></lb>adjuſted that it may reſt ambiguous, if I may ſo ſay, between <pb xlink:href="040/01/750.jpg" pagenum="58"></pb>aſcending and deſcending in a Water, upon the leaſt difference <lb></lb>of weight between two Waters, if that Ball ſhall deſcend in the <lb></lb>one; in the other, that is more grave, it ſhall aſcend. </s> <s>And the <lb></lb>Experiment is ſo exact, that the addition of but only two grains <lb></lb>of Salt, put into ſix pounds of Water, ſhall make that Ball to <lb></lb>aſcend from the bottom to the ſurface, which was but a little be<lb></lb><arrow.to.target n="marg1050"></arrow.to.target><lb></lb>fore deſcended thither. </s> <s>And moreover, I will tell you this in con<lb></lb>firmation of the exactneſs of this Experiment, and withall for a <lb></lb>clear proof of the Non-reſiſtance of Water to diviſion, that not <lb></lb>only the ingravitating it with the mixture of ſome matter heavier <lb></lb>than it, maketh that ſo notable difference, but the warming or <lb></lb>cooling of it a little produceth the ſame effect, and with ſo ſubtil <lb></lb>an operation, that the infuſing four diops of other Water, a lit<lb></lb>tle warmer, or a little colder, than the ſix pounds, ſhall cauſe the <lb></lb>Ball to riſe or ſink in the ſame; to ſink in it upon the infuſion of <lb></lb>the warm, and to riſe at the infuſion of the cold. </s> <s>Now ſee how <lb></lb>much thoſe Philoſophers are deceived, who would introduce in <lb></lb>Water viſcoſity, or other conjunction of parts which make it to <lb></lb>reſiſt Diviſion or Penetration.</s></p><p type="margin"> <s><margin.target id="marg1049"></margin.target><emph type="italics"></emph>A Ball of Wax <lb></lb>prepared to make <lb></lb>the Experiment of <lb></lb>the different Gra<lb></lb>vities of Waters.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1050"></margin.target><emph type="italics"></emph>Water bath no <lb></lb>Reſiſtance to Di<lb></lb>viſion.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>I have ſeen many Convincing Diſcourſes touching <lb></lb><arrow.to.target n="marg1051"></arrow.to.target><lb></lb>this Argument in a ^{*} Treatiſe of our <emph type="italics"></emph>Accademick<emph.end type="italics"></emph.end>; yet never the leſs <lb></lb>there is reſting in me a ſtrong ſcruple, which I know not how to <lb></lb>remove: For if nothing of Tenacity, or Coherence reſides amongſt <lb></lb>the parts of Water, how can it bear it ſelf up in reaſonable big <lb></lb>and high Tumours; in particular, upon the leaves of Cole-worts <lb></lb>without diſperſing or levelling?</s></p><p type="margin"> <s><margin.target id="marg1051"></margin.target>* The Tract cited <lb></lb>in this place is <lb></lb>that which we <lb></lb>diſpoſe firſt in <lb></lb>Order, in the <lb></lb>firſt part of this <lb></lb>Tome,</s></p><p type="main"> <s>SALV. </s> <s>Although it be true, that he who is Maſter of a true <lb></lb>Concluſion, may reſolve all Objections that can be brought againſt <lb></lb>it, yet will not I arrogate to my ſelf the power ſo to do; nor <lb></lb>ought my inſufficiency becloud the ſplendour of Truth. </s> <s>Firſt, <lb></lb>therefore, I confeſs that I know not how it cometh to paſs, that <lb></lb>thoſe Globes of Water ſuſtain themſelves at ſuch an height and <lb></lb>bigneſs, albeit I certainly know that it doth not proceed from any <lb></lb><arrow.to.target n="marg1052"></arrow.to.target><lb></lb>internal Tenacity that is between its parts; ſo that it remaineth <lb></lb>neœſſary, that the Cauſe of that Effect do reſide without. </s> <s>That it <lb></lb>is not Internal, beſides thoſe Experiments already ſhewn you, I can <lb></lb>prove by another moſt convincing one. </s> <s>If the parts of that Wa<lb></lb>ter, which conſerveth it ſelf in a Globe or Tumour whilſt it is en<lb></lb>compaſſed by the Air, had an internal Cauſe for ſo doing, they <lb></lb>would much better ſuſtain themſelves being environed by a <emph type="italics"></emph>Medi<lb></lb>um,<emph.end type="italics"></emph.end> in which they had leſs propenſion to deſcend, than they have <lb></lb>in the Ambient Air: But every Fluid Body more grave than the <lb></lb>Air would be ſuch a <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end>; as, for inſtance, Wine: And there<lb></lb>fore, infuſing Wine about that Globe of Water, it might raiſe it <lb></lb>ſelf on every ſide, and yet the parts of the Water, conglutinated <pb xlink:href="040/01/751.jpg" pagenum="59"></pb>by the internal Viſcoſity, never diſſolve: But it doth not happen <lb></lb>ſo; nay, no ſooner doth the circumfuſed liquor approach thereto, <lb></lb>but, without ſtaying till it riſe much about it, the little globes of <lb></lb>Water will diſſolve and become flat, reſting under the Wine, if it <lb></lb>was red. </s> <s>The Cauſe therefore of this Effect is External, and per<lb></lb>haps in the Ambient Air: and, indeed, one may obſerve a great <lb></lb>diſſention between the Air and Water; which I have obſerved <lb></lb>in another Experiment; and this it is: If I fill a ^{*} Ball of Chriſtal, <lb></lb><arrow.to.target n="marg1053"></arrow.to.target><lb></lb>that hath a mouth as narrow as the hollow of a ſtraw, with water, <lb></lb>and when it is thus full, turn it with its mouth downwards, yet will <lb></lb>not the Water, although very heavy, and prone to deſcend tho<lb></lb>row the Air, nor the Air, as much diſpoſed on the other hand, as <lb></lb>being very light, to aſcend thorow the Waters, yet will they not <lb></lb>(I ſay) agree that that ſhould deſcend, iſſuing out at the mouth, <lb></lb>and this aſcend, entering in at the ſame: but they both continue <lb></lb>averſe and contumacious. </s> <s>Again, on the contrary, if I preſent to <lb></lb>that mouth a veſſel of red Wine, which is almoſt inſenſibly leſs <lb></lb>grave than Water, we ſhall ſee it in an inſtant gently to aſcend by <lb></lb>red ſtreams thorow the Water, and the Water with like Tardity to <lb></lb>deſcend through the Wine, without ever mixing with each other, <lb></lb>till that in the end, the Ball will be full of Wine, and the Water <lb></lb>Will all ſink unto the bottom of the Veſſel underneath. </s> <s>Now <lb></lb>what are we to ſay, or what are we to infer, but a diſagreement <lb></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"></emph>Water formed into <lb></lb>great drops upon <lb></lb>the Leaves of Col<lb></lb>worts, how they <lb></lb>conſiſt.<emph.end type="italics"></emph.end></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 ſcarce refrain my laughter to ſee the great Anti<lb></lb>pathy that <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> hath to Antipathy, ſo that he will not ſo much <lb></lb>as name it, and yet it is ſo accommodate to reſolve the doubt.</s></p><p type="main"> <s>SALV. </s> <s>Now let this, for the ſake of <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> be the ſoluti<lb></lb>on of our ſcruple; and leaving the Digreſſion, let us return to our <lb></lb>purpoſe. </s> <s>Seeing that the difference of Velocity in Moveables of <lb></lb>divers Gravities is found to be more and more, as the <emph type="italics"></emph>Mediums<emph.end type="italics"></emph.end> are <lb></lb>more and more Reſiſting: And withall, that in a <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> of <lb></lb>Quickſilver, Gold doth not only go to the bottom more ſwiftly <lb></lb>than Lead, but it alone deſcends in it, and all other Metals and <lb></lb>Stones move upwards therein, and flote thereon; whereas between <lb></lb>Balls of Gold, Lead, Braſs, Porphiry, or other grave matters, the in<lb></lb>equality of motion in the Air ſhall be almoſt wholly inſenſible, for <lb></lb>it is certain, that a Ball of Gold in the end of the deſcent of an <lb></lb><arrow.to.target n="marg1054"></arrow.to.target><lb></lb>hundred yards ſhall not out-ſtrip one of Braſs four Inches: ſeeing <lb></lb>this, I ſay, I have thought, that if we wholly took away the <lb></lb>Reſiſtance of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> all Matters would deſcend with equall <lb></lb>Velocity.</s></p><p type="margin"> <s><margin.target id="marg1054"></margin.target><emph type="italics"></emph>Reſiſtance of the<emph.end type="italics"></emph.end><lb></lb>Medium <emph type="italics"></emph>remo<lb></lb>ved, all Matters, <lb></lb>though of different <lb></lb>Gravities would <lb></lb>move with like <lb></lb>Velocity.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SIMP. </s> <s>This is a bold ſpeech, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> I ſhall never believe <lb></lb>that in <emph type="italics"></emph>Vacuity<emph.end type="italics"></emph.end> it ſelf, if ſo be one ſhould allow Motion in it, a lock <lb></lb>of Wooll would move as ſwiftly as a piece of Lead.</s></p><pb xlink:href="040/01/752.jpg" pagenum="60"></pb><p type="main"> <s>SALV. </s> <s>Fair and ſoftly, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> your ſcruple is not ſo ab<lb></lb>ſtruce, nor I ſo incautelous, that you ſhould need to think that I <lb></lb>was not adviſed of it, and that conſequently I have not found a re<lb></lb>ply to it. </s> <s>Therefore, for my explanation, and your information, <lb></lb>hearken to what I ſhall ſay. </s> <s>We are upon the examination of <lb></lb>what would befall Moveables exceeding different in weight in a <lb></lb><emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> in caſe it ſhould have no Reſiſtance, ſo that all the diffe<lb></lb>rence of Velocity that is found between the ſaid Moveables ought <lb></lb>to be referred to the ſole inequality of Weight. </s> <s>And becauſe on<lb></lb>ly a Space altogether void of Air, and of every other, though te<lb></lb>nuous and yielding Body, would be apt ſenſibly to ſhew us what <lb></lb>we ſeek, ſince we want ſuch a Space, let us ſucceſſively obſerve that <lb></lb>which happeneth in the more ſubtill and leſſe reſiſting <emph type="italics"></emph>Mediums,<emph.end type="italics"></emph.end><lb></lb>in compariſon of that which we ſee to happen in others leſſe ſubtill <lb></lb>and more reſiſting: for if we ſhould really find the Moveables <lb></lb>different in Gravity to differ leſſe and leſſe in Velocity, according <lb></lb>as the <emph type="italics"></emph>Mediums<emph.end type="italics"></emph.end> are found more and more yielding; and that, <lb></lb>finally, although extreamly unequal in weight, in a <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> more <lb></lb>tenuous than any other, though not void, the difference of Velo<lb></lb>city diſcovers it ſelf to be very ſmall, and almoſt unobſervable, I <lb></lb>conceive that we may, and that upon very probable conjecture, <lb></lb>believe, that in a <emph type="italics"></emph>Vacuum<emph.end type="italics"></emph.end> their Velocities would be exactly equal. <lb></lb></s> <s>Therefore let us conſider that which hapneth in the Air; wherein <lb></lb>to have a Figure of an uniform Superficies, and very light Matter, <lb></lb>I will that we take a blown Bladder, in which the included Air <lb></lb>will weigh little or nothing in a <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> of the Air it ſelf, becauſe <lb></lb>it can make but very ſmall Compreſſion therein, ſo that the Gravi<lb></lb>ty is only that little of the ſaid film, which would not be the thou<lb></lb>ſandth part of the weight of a lump of Lead of the bigneſs of <lb></lb>the ſaid Bladder when blown. </s> <s>Theſe, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> being let fall <lb></lb>from the height of four or ſix yards, how great a ſpace, do you <lb></lb>judge, that the Lead would anticipate the Bladder in its deſcent? <lb></lb></s> <s>Aſſure your ſelf that would not move thrice, no nor twice as faſt, <lb></lb>although even now you would have had it to have been a thou<lb></lb>ſand times more ſwift.</s></p><p type="main"> <s>SIMP. </s> <s>It is poſſible that at the beginning of the Motion, that <lb></lb>is, in the firſt five or ſix yards this might happen that you ſay; but <lb></lb>in the progreſſe, and in a long continuation I believe, that the Lead <lb></lb>would leave it behind, not only ſix, but alſo eight and ten parts of <lb></lb>twelve.</s></p><p type="main"> <s>SALV. </s> <s>And I alſo believe the ſame: and make no queſtion, <lb></lb>but that in very great diſtances the Lead will have paſſed an hun<lb></lb>dred miles of <emph type="italics"></emph>way,<emph.end type="italics"></emph.end> ere the Bladder will have paſſed ſo much as one. <lb></lb></s> <s>But this, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> which you propound, as an effect contrary to <lb></lb>my Aſſertion, is that which moſt eſpecially confirmeth it. </s> <s>It is (I <pb xlink:href="040/01/753.jpg" pagenum="61"></pb>once more tell you) my intent to declare, That the difference of <lb></lb>Gravity is in no wiſe the cauſe of the divers velocities of Movea<lb></lb>bles of different Gravity, but that the ſame dependeth on exteri<lb></lb>our accidents, & in particular, on the Reſiſtance of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> ſo <lb></lb>that, this being removed, all Moveables move with the ſame de<lb></lb>grees of Velocity. </s> <s>And this I chiefly deduce from that which but <lb></lb>now you your ſelf did admit, and which is very true, namely, that <lb></lb>of two Moveables, very different in weight, the Velocities more and <lb></lb>more differ, according as the ^{*} Spaces are greater and greater that <lb></lb><arrow.to.target n="marg1055"></arrow.to.target><lb></lb>they paſſe: an Effect which would not follow, if it did depend on <lb></lb>the different Gravities: for they being alwaies the ſame, the pro<lb></lb>portion betwixt the Spaces would likewiſe alwaies continue the <lb></lb>ſame, which proportion we ſee ſtill ſucceſſively to encreaſe in the <lb></lb>continuance of the Motion; for that the heavieſt Moveable in the <lb></lb>deſcent of one yard will not anticipate the lighteſt the tenth part <lb></lb>of that Space or Way, but in the fall of twelve yards will out-go <lb></lb>it a third part, in that of an hundred will outſtrip 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 ſtep by ſtep, if the dif<lb></lb>ference of weight in Moveables of different Gravities cannot <lb></lb>cauſe the difference of proportion in their Velocities, for that the <lb></lb>Gravities do not alter; neither then can the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> which is <lb></lb>ſuppoſed alwaies to continue the ſame, cauſe any alteration in the <lb></lb>proportion of the Velocities.</s></p><p type="main"> <s>SALV. </s> <s>You wittily bring an inſtance againſt my Poſition, that <lb></lb><arrow.to.target n="marg1056"></arrow.to.target><lb></lb>it is very neceſſary to remove. </s> <s>I ſay therefore, that a Grave Body <lb></lb>hath, by Nature, an intrinſick Principle of moving towards the <lb></lb>Common Center of heavy things, that is to that of our Terreſtrial <lb></lb>Globe, with a Motion continually accelerated, and accelerated <lb></lb>alwaies equally, <emph type="italics"></emph>ſcilicet,<emph.end type="italics"></emph.end> that in equal times there are made equal <lb></lb>^{*} additions of new Moments, and degrees of Velocities: and this <lb></lb>ought to be underſtood to hold true at all times when all acciden<lb></lb><arrow.to.target n="marg1057"></arrow.to.target><lb></lb>tal and external impediments are removed; amongſt which there <lb></lb>is one that we cannot obviate, that is the Impediment of the <emph type="italics"></emph>Me<lb></lb>dium,<emph.end type="italics"></emph.end> which is Repleat, when as it ſhould be opened and latterally <lb></lb>moved by the falling Moveable, to which tranſverſe Motion the <lb></lb><emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> though fluid, yielding and tranquile, oppoſeth it ſelf <lb></lb>with a Reſiſtance one while leſſer, and another while greater and <lb></lb>greater, according as it is more ſlowly or haſtily to open to give <lb></lb>paſſage to the Moveable, which, becauſe, as I have ſaid, it goeth <lb></lb>of its own nature continually accelerating, it cometh of conſe<lb></lb>quence to encounter continually greater Reſiſtance in the <emph type="italics"></emph>Medi<lb></lb>um,<emph.end type="italics"></emph.end> and therefore Retardment, and diminution in the acquiſt of <lb></lb>new degrees of Velocity; ſo that in the end, the Velocity arriveth <lb></lb>to that ſwiftneſſe, and the Reſiſtance of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> to that <lb></lb>ſtrength, that ballancing each other, they take away all further <pb xlink:href="040/01/754.jpg" pagenum="62"></pb>Acceleration, and reduce the Moveable to an Equable and Uni<lb></lb>form Motion, in which it afterwards continually abides. </s> <s>There is <lb></lb>therefore in the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> augmentation of Reſiſtance, not becauſe <lb></lb>it changeth its Eſſence, but becauſe the Velocity altereth where<lb></lb>with it ought to open, and laterally move, to give paſſage to the <lb></lb>falling Body, which goeth continually accelerating. </s> <s>Now the <lb></lb>obſerving, that the Reſiſtance of the Air to the ſmall Moment or <lb></lb><emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the Bladder is very great, and to the great weight of <lb></lb>the Lead is very ſmall, makes me hold for certain, that if one ſhould <lb></lb>wholly remove it, by adding to the Bladder great aſſiſtance, and <lb></lb>but very little to the Lead, their Velocities would equalize each <lb></lb>other. </s> <s>Taking this Principle therefore for granted, That in the <lb></lb><emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> wherein, either by reaſon of Vacuity, or otherwiſe, there <lb></lb>were no Reſiſtance that might abate the Velocity of the Motion, <lb></lb>ſo that of all Moveables the Velocities were alike, we might con<lb></lb><arrow.to.target n="marg1058"></arrow.to.target><lb></lb>gruouſly enough aſſign the proportions of the Velocities of like <lb></lb>and unlike Moveables, in the ſame and in different, Replear, and <lb></lb>therefore Reſiſting <emph type="italics"></emph>Medium's.<emph.end type="italics"></emph.end> And this we might effect by ſtudy<lb></lb>ing how much the Gravity of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> abateth from the Gra<lb></lb>vity of the Moveable, which Gravity is the Inſtrument wherewith <lb></lb>the Moveable makes its Way, repelling the parts of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end><lb></lb>on each Side: an operation that doth not occur in void <emph type="italics"></emph>Mediums<emph.end type="italics"></emph.end>; <lb></lb>and therefore there is no difference to be expected from the di<lb></lb>verſe Gravity: and becauſe it is manifeſt, that the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> abateth <lb></lb>from the Gravity of the Body by it contained, as much as is the <lb></lb>weight of ſuch another maſs of its own Matter, if the Velocities of <lb></lb>the Moveables that in a non-reſiſting <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> would be (as hath <lb></lb>been ſuppoſed) equal, ſhould diminiſh in that proportion, we <lb></lb>ſhould have what we deſired. </s> <s>As for example; ſuppoſing that <lb></lb>Lead be ten thouſand times more grave than Air, but Ebony a <lb></lb>thouſand times only; of the Velocities of theſe two Matters, which <lb></lb>abſolutely taken, that is, all Reſiſtance being removed, would be <lb></lb>equal, the Air ſubſtracts from the ten thouſand degrees of the <lb></lb>Lead one, and from the thouſand degrees of the Ebony likewiſe <lb></lb>abateth one, or, if you will, of its ten thouſand, ten. </s> <s>If there<lb></lb>fore the Lead and the Ebony ſhall deſcend thorow the Air from <lb></lb>any height, which, the retardment of the Air removed, they would <lb></lb>have paſſed in the ſame time, the Air will abate from the ten <lb></lb>thouſand degrees of the Leads Velocity one, but from the ten <lb></lb>thouſand degrees of Ebony's Velocity it will abate ten: which is <lb></lb>as much as to ſay, that dividing that Altitude, from which thoſe <lb></lb>Moveables departed into ten thouſand parts, the Lead will arrive <lb></lb>at the Earth, the Ebony being left behind, ten, nay, nine of thoſe <lb></lb>ſame ten thouſand parts. </s> <s>And what elſe is this, but that a Ball of <lb></lb>Lead, falling from a Tower two hundred yards high, to find how <pb xlink:href="040/01/755.jpg" pagenum="63"></pb>much it will anticipate one of Ebony of leſſe than four Inches? <lb></lb></s> <s>The Ebony weigheth a thouſand times more than the Air, but that <lb></lb>Bladder ſo blown, weigheth only four times ſo much; the Air <lb></lb>therefore from the intrinſick and natural Velocity of the Ebony <lb></lb>ſubducteth one degree of a thouſand, but from that, which alſo in <lb></lb>the Bladder would abſolutely have been the ſame, the Air ſub<lb></lb>ducts one part of four: ſo that by that time the Ball of Ebony <lb></lb>falling from the Tower, ſhall come to the ground, the Bladder <lb></lb>ſhall have paſſed but three quarters of that height. </s> <s>Lead is twelve <lb></lb>times heavier than Water, but Ivory only twice as heavy; the <lb></lb>Water therefore, from their abſolute Velocities which would be <lb></lb>equal, ſhall abate in the Lead the twelfth part, but in the Ivory <lb></lb>the half: when therefore, in the Water, the Lead ſhall have de<lb></lb>ſcended eleven fathom, the Ivory ſhall have deſcended ſix. </s> <s>And, <lb></lb>arguing by this Rule, I believe, that we ſhall find the Experiment <lb></lb>much more exactly agree with this ſame Computation, than with <lb></lb>that of <emph type="italics"></emph>Ariſtotle.<emph.end type="italics"></emph.end> By the like method we might find the Veloci<lb></lb>ties of the ſame Moveable in different fluid <emph type="italics"></emph>Mediums,<emph.end type="italics"></emph.end> not compa<lb></lb>ring the different Reſiſtances of the <emph type="italics"></emph>Mediums,<emph.end type="italics"></emph.end> but conſidering the <lb></lb>exceſſes of the Gravity of the Moveable over and above the Gra<lb></lb>vities of the <emph type="italics"></emph>Mediums: v. </s> <s>gr.<emph.end type="italics"></emph.end> ^{*} Tin is a thouſand times heavier than <lb></lb><arrow.to.target n="marg1059"></arrow.to.target><lb></lb>Air, and ten times heavier than Water; therefore dividing the ab<lb></lb>ſolute Velocity of the Tin into a thouſand degrees, it ſhall move <lb></lb>in the Air, (which deducteth from it the thouſandth part,) with nine <lb></lb>hundred ninety nine, but in the Water with nine hundred only; <lb></lb>being that the Water abateth the tenth part of its Gravity, and <lb></lb>the Air the thouſandth part. </s> <s>Take a Solid ſomewhat heavier than <lb></lb>Water, as for inſtance, the Wood called Oake, a Ball of which <lb></lb>weighing, as we will ſuppoſe, a thouſand drams, a like quantity <lb></lb>of Water will weigh nine hundred and fifty, but ſo much Air will <lb></lb>weigh but two drams,: it is manifeſt, that ſuppoſing that its abſo<lb></lb>lute Velocity were of a thouſand degrees, in Air there would re<lb></lb>main nine hundred ninety eight, but in the Water only fifty; be<lb></lb>cauſe that the Water of the thouſand degrees of Gravity taketh <lb></lb>away nine hundred and fifty, and leaves fifty only; that Solid there<lb></lb>fore would move well-near twenty times as faſt in the Air as Wa<lb></lb>ter; like as the exceſſe of its Gravity above that of the Water is <lb></lb>the twentieth part of its own. </s> <s>And here I deſire that we may con<lb></lb>ſider, that no matters, having a power to move downwards in the <lb></lb>Water, but ſuch as are more grave in Species than it; and conſe<lb></lb>quently many hundreds of times, more grave than the Air, in <lb></lb>ſeeking what the proportions of their Velocities are in the Air and <lb></lb>Water, we may, without any conſiderable errour, make account <lb></lb>that the Air doth not deduct any thing of moment from the abſo<lb></lb>lute Gravity, and conſequently, from the abſolute Velocity of ſuch <pb xlink:href="040/01/756.jpg" pagenum="66"></pb>matters: ſo that having eaſily found the exceſſe of their Gravi<lb></lb>ty above the Gravity of the Water, we may ſay that their Velo<lb></lb>city in the Air, to their Velocity in the Water hath the ſame propor<lb></lb>tion, that their total Gravity hath to the exceſſe of this above <lb></lb>the Gravity of the Water. </s> <s>For example, a Ball of Ivory weigh<lb></lb>eth twenty ounces, a like quantity of Water weigheth ſeventeen <lb></lb>ounces: therefore the Velocity of the Ivory in Air, to its Velocity <lb></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"></emph>The Velocity of <lb></lb>Grave Bodies de<lb></lb>ſcending Natural<lb></lb>ly to the Center do <lb></lb>go continually en<lb></lb>creaſing till that <lb></lb>by the encreaſe of <lb></lb>the Reſiſtance of <lb></lb>the<emph.end type="italics"></emph.end> Medium <emph type="italics"></emph>it <lb></lb>becometh uniform.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1057"></margin.target>* Or aquiſts.</s></p><p type="margin"> <s><margin.target id="marg1058"></margin.target><emph type="italics"></emph>To find the Pro<lb></lb>portions of the Ve<lb></lb>locities of different <lb></lb>Moveables in the <lb></lb>ſame, and in diffe<lb></lb>rent<emph.end type="italics"></emph.end> 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 acquiſt in a buſineſſe of it ſelf cu<lb></lb>rious, and in which, but without any benefit, I have many times <lb></lb>wearied my-thoughts: nor would there any thing be wanting for <lb></lb>the putting theſe Speculations in practice, ſave onely the way <lb></lb>how one ſhould come to know of what Gravity the Air, is in com<lb></lb>pariſon to the Water, and conſequently to other heavy matters.</s></p><p type="main"> <s>SIMP. </s> <s>But in caſe one ſhould finde, that the Air inſtead of <lb></lb>Gravity had Levity, what ought one to ſay of the foregoing diſ<lb></lb>courſes, otherwiſe very ingenuous?</s></p><p type="main"> <s>SALV. </s> <s>It would be neceſſary to confeſſe that they were truly <lb></lb>Aerial, Light, and Vain. </s> <s>But will you queſtion whether the Air <lb></lb>be heavy, having the expreſſe <emph type="italics"></emph>Text<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> that affirmeth it, <lb></lb>ſaying, That all the Elements have Gravity, even the Air it ſelf; <lb></lb><arrow.to.target n="marg1060"></arrow.to.target><lb></lb>a ſigne of which (ſubjoyns he) we have in that a ^{*} Bladder blown, <lb></lb>weigheth heavier than unſwell'd.</s></p><p type="margin"> <s><margin.target id="marg1060"></margin.target>* Or <emph type="italics"></emph>Boracho<emph.end type="italics"></emph.end>; a <lb></lb>bottle made of a <lb></lb>Goat skin, uſed <lb></lb>to hold wine and <lb></lb>other Liquids.</s></p><p type="main"> <s>SIMP. </s> <s>That a <emph type="italics"></emph>Boracho,<emph.end type="italics"></emph.end> or Bladder blown, weigheth more, <lb></lb>might proceed, as I could ſuppoſe, not from the Gravity that is <lb></lb>in the Air, but in the many groſſe Vapours intermixed with it in <lb></lb>theſe our lower Regions; by means whereof I might ſay, that the <lb></lb>Gravity of the Bladder, or <emph type="italics"></emph>Boracho<emph.end type="italics"></emph.end> encreaſeth.</s></p><p type="main"> <s>SALV. </s> <s>I would not have you ſay it, and much leſſe that you <lb></lb>ſhould make <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> ſpeak it, for he treating of the Elements, <lb></lb>and deſiring to perſwade me that the Element of Air is grave, <lb></lb>making me to ſee it by an Experement: if in comming to the proof <lb></lb>he ſhould ſay: Take a Bladder, and fill it with groſſe Vapours; <lb></lb>and obſerve that its weight will encreaſe; I would tell him that <lb></lb>it would weigh yet more if one ſhould fill it with bran; but would <lb></lb>afterwards adde; that thoſe Experiments prove, that bran, and <lb></lb>groſſe Vapours are grave: but as to the Element of Air, I ſhould <lb></lb>be left in the ſame doubt as before. </s> <s>The Experiment of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end><lb></lb>therefore is good, and the Propoſition true. </s> <s>But I will not ſay ſo <lb></lb>much, for a certain other reaſon taken expreſly out of a Philoſo<lb></lb>pher whoſe name I do not remember, but am ſure that I have read <lb></lb>it, who argueth the Air to be more grave than light, becauſe it <lb></lb>more eaſily carrieth grave Bodies downwards, than the light up<lb></lb>wards.</s></p><p type="main"> <s>SAGR. </s> <s>Good i-faith. </s> <s>By this reaſon then, the Air ſhall be <pb xlink:href="040/01/757.jpg" pagenum="65"></pb>much heavier than the Water, ſince, that all Bodies are carried <lb></lb>more eaſily downwards thorow the Air than thorow the Water, <lb></lb>and all light Bodies more eaſily upwards in this than in that: nay, <lb></lb>infinite matters aſcend in the Water, that in the Air deſcend. <lb></lb></s> <s>But be the Gravity of the Bladder, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> either by reaſon of <lb></lb>the groſſe Vapours, or pure Air, this nothing concerns our pur<lb></lb>poſe, for we ſeek that which happeneth to Moveables that move <lb></lb>in this our Vaporous Region. </s> <s>Therefore, returning to that which <lb></lb>more concerneth me, I would for a full and abſolute informati<lb></lb>on in the preſent buſineſſe, not onely be aſſured that the Air is <lb></lb>grave, as I hold for certain, but I would, if it be poſſible, know <lb></lb>what its Gravity is. </s> <s>Therefore, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> if you have wherewith <lb></lb>to ſatisfie me in this alſo, I entreat you to favour me with the <lb></lb>ſame.</s></p><p type="main"> <s>SALV. </s> <s>That there reſideth in the Air poſitive Gravity, and <lb></lb><arrow.to.target n="marg1061"></arrow.to.target><lb></lb>not, as ſome have thought, Levity, which haply is in no Mat<lb></lb>ter to be found, the Experiment of the Blown-Bladder, alledged <lb></lb>by <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> affordeth us a ſufficiently-convincing Argument; for <lb></lb>if the quality of abſolute and poſitive Levity were in the Air, <lb></lb>then the Air being multiplied and compreſſed, the Levity would <lb></lb>encreaſe, and conſequently the propenſion of going upwards: <lb></lb>but Experience ſhews the contrary. </s> <s>As to the other demand, that <lb></lb><arrow.to.target n="marg1062"></arrow.to.target><lb></lb>is, of the Method how to inveſtigate its Gravity, I have tried to <lb></lb>do it in this manner: I have taken a pretty bigge Glaſſe ^{*} Bottle, <lb></lb><arrow.to.target n="marg1063"></arrow.to.target><lb></lb>with its neck bended, and a Finger-ſtall of Leather faſt about <lb></lb>it, having in the top of the ſaid Finger-ſtall inſerted and fa<lb></lb>ſtened a Valve of Leather, by which with a Siringe I have made <lb></lb>paſſe into the Bottle by force a great quantity of Air, of which, <lb></lb>becauſe it admits of great Condenſation, it may take in two or <lb></lb>three other Bottles-ful over and above that which is naturally con<lb></lb>tained therein. </s> <s>Then I have in an exact Ballance very preciſely <lb></lb>weighed that Bottle with the Air compreſſed within it, adjuſting <lb></lb>the weight with ſmall Sands. </s> <s>Afterwards, the Valve being opened, <lb></lb>and the Air let out, that was violently conteined in the Veſſel, I <lb></lb>have put it again into the Scales, and finding it notably aleviated, <lb></lb>I have by degrees taken ſo much Sand from the other Scale, keep<lb></lb>ing it by it ſelf, that the Ballance hath at laſt ſtood <emph type="italics"></emph>in Equilibrio<emph.end type="italics"></emph.end><lb></lb>with the remaining counter-poiſe, that is with the Bottle. </s> <s>And <lb></lb>here there is no queſtion, but that the weight of the reſerved Sand <lb></lb>is that of the Air that was forceably driven into the Bottle, and <lb></lb>which is at laſt gone out thence. </s> <s>But this Experiment hitherto aſ<lb></lb>ſureth me of no more but this, that the Air violently deteined in <lb></lb>the Veſſel, weigheth as much as the reſerved Sand, but how much <lb></lb>the Air reſolutely and determinately weigheth in reſpect of the <lb></lb>Water, or other grave matter, I do not as yet know, nor can <pb xlink:href="040/01/758.jpg" pagenum="66"></pb>I tell, unleſſe I meaſure the quantity of the Air compreſſed: and <lb></lb>for the diſcovering of this a Rule is neceſſary, which I have <lb></lb>found may be performed two manner of wayes, one of which <lb></lb>is to take ſuch another Bottle or Flask as the former, and in like <lb></lb>manner bended, with a Finger-ſtall of Leather, the end of which <lb></lb>may cloſely imbrace the Volve of the other, and let it be very <lb></lb>faſt tied about it. </s> <s>It's requiſite, that this ſecond Bottle be bored in <lb></lb>the bottom, ſo that as by that hole we may thruſt in a Wier, <lb></lb>wherewith we may, at pleaſure, open the ſaid Volve, to let out <lb></lb>the ſuperfluous Air of the other Veſſel, after it hath been weighed: <lb></lb>but this ſecond Bottle ought to be full of Water. </s> <s>All being pre<lb></lb>pared in the manner aforeſaid, and with the Wier opening the <lb></lb>Volve, the Air iſſuing out with impetuoſity, and paſſing into the <lb></lb>Veſſel of Water, ſhall drive it out by the hole at the Bottom: <lb></lb>and it is manifeſt, that the quantity of Water which ſhall be <lb></lb>thruſt out, is equal to the Maſſe and quantity of Air that ſhall <lb></lb>have iſſued from th'other Veſſel: that Water therefore being <lb></lb>kept, and returning to weigh the Veſſel lightned of the Air com<lb></lb>preſſed (which I ſuppoſe to have been weighed likewiſe firſt with <lb></lb>the ſaid forced Air) and the ſuperfluous ſand being laid by, as I <lb></lb>directed before; it is manifeſt, that this is the juſt weight of ſo <lb></lb>much Air in maſſe, as is the maſſe of the expulſed and reſerved <lb></lb>Water; which we are to weigh, and ſee how many times its <lb></lb>weight ſhall contain the weight of the reſerved ſand: and we may <lb></lb>without errour affirme, that the Water is ſo many times heavier <lb></lb>than Air; which ſhall not be ten times, as it ſeemeth <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end><lb></lb>held, but very neer four hundred, as the ſaid Experiment ſheweth.</s></p><p type="margin"> <s><margin.target id="marg1061"></margin.target><emph type="italics"></emph>The Air hath Po<lb></lb>ſitive Gravity.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1062"></margin.target><emph type="italics"></emph>How that Gravity <lb></lb>may be computed.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1063"></margin.target>* <emph type="italics"></emph>Un Fiaſco,<emph.end type="italics"></emph.end> thoſe <lb></lb>long-neckt glaſſe <lb></lb>bottles in which <lb></lb>we have our <lb></lb><emph type="italics"></emph>Florence<emph.end type="italics"></emph.end> Wine <lb></lb>brought to us.</s></p><p type="main"> <s>The other way is more expeditious, and it may be done with <lb></lb>one Veſſel onely, that is with the firſt accomodated after the man<lb></lb>ner before directed, into which I will not that any other Air be <lb></lb>put, more than that which naturally is found therein; but I will, <lb></lb>that we inject Water without ſuffering any Air to come out, <lb></lb>which being forced to yield to the ſupervenient Water muſt of <lb></lb>neceſſity be compreſſed: having gotten in, therefore, as much <lb></lb>Water as is poſſible, (but yet without great violence one cannot get <lb></lb>in three quarters of what the Bottle will hold) put it into the <lb></lb>Scales, and very carefully weigh it: which done, holding the <lb></lb>Veſſel with the neck upwards, open the Volve, letting out the <lb></lb>Air, of which there will preciſely iſſue forth ſo much as there is <lb></lb>Water in the Bottle. </s> <s>The Air being gone out, put the Veſſel again <lb></lb>into the Scales, which by the departure of the Air will be found <lb></lb>lightened, and abating from the oppoſite Scale the ſuperfluous <lb></lb>weight, it ſhall give us the weight of as much Air as there is <lb></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"></pb>feſſed to be witty and very ingenuous, but whilſt, me thinks, they <lb></lb>fully ſatisfie my underſtanding, they another way occaſion in <lb></lb>me much Confuſion, for it being undoubtedly true that the Ele<lb></lb>ments in their proper Region are neither heavy nor light, I can<lb></lb>not comprehend, how and which way that portion of Air, which <lb></lb>ſeemeth to have weighed <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> four drams of ſand, ſhould af<lb></lb>terwards have that ſame Gravity in the Air, in which the ſand is <lb></lb>contained that weigheth againſt it: and therefore me thinks that <lb></lb>the Experiment ought not to be practiced in the Element of Air, <lb></lb>but in a <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> in which the Air it ſelf might exerciſe its quality <lb></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"></emph>Simplicius<emph.end type="italics"></emph.end> is very acute, <lb></lb>and therefore its neceſſary, either that it be unanſwerable, or that <lb></lb>the Solution be no leſſe acute. </s> <s>That that Air, which compreſ<lb></lb>ſed, appeared to weigh as much as that ſand, left at liberty in its <lb></lb>Element is no longer to weigh any thing as the Sand doth, is a thing <lb></lb>manifeſt: and therefore for making of ſuch an Experiment, its <lb></lb>requiſite to chooſe a place and <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> wherein the Air as well as <lb></lb>the Sand might weigh: for, as hath ſeveral times been ſaid, the <lb></lb><emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> ſubſtracts from the Weight of every Matter that is im<lb></lb>merged therein, ſo much, as ſuch another quantity of the ſaid <lb></lb><emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> as is that of the maſſe immerſed, weigheth: ſo that <lb></lb>the Air depriveth the Air of all its Gravity. </s> <s>The operation, there<lb></lb><arrow.to.target n="marg1064"></arrow.to.target><lb></lb>fore, to the end it were made exactly, ought to be tried in a <emph type="italics"></emph>Va<lb></lb>cuum,<emph.end type="italics"></emph.end> wherein every grave Body would exerciſe its Moment <lb></lb>without any diminution. </s> <s>In caſe therefore, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that we <lb></lb>ſhould weigh a portion of Air in a <emph type="italics"></emph>Vacuum,<emph.end type="italics"></emph.end> would you then be <lb></lb>convinced and aſſured of the buſineſſe?</s></p><p type="margin"> <s><margin.target id="marg1064"></margin.target><emph type="italics"></emph>The Air compreſ<lb></lb>ſed and violently <lb></lb>pent up, weigheth in <lb></lb>a<emph.end type="italics"></emph.end> Vacuum; <emph type="italics"></emph>and <lb></lb>how its weight is to <lb></lb>be eſtimated.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SIMP. </s> <s>Verily I ſhould: but this is to defire, or enjoyn that <lb></lb>which is impoſſible.</s></p><p type="main"> <s>SALV. </s> <s>And therefore the obligation muſt needs be great that <lb></lb>you owe to me, when ever I ſhall for your ſake effect an impoſſibi<lb></lb>lity: but I will not ſell you that which I have already given you: <lb></lb>for we, in the foregoing Experiment, weigh the Air in a <emph type="italics"></emph>Vacuum,<emph.end type="italics"></emph.end><lb></lb>and not in the Air, or in any other Replete <emph type="italics"></emph>Medium.<emph.end type="italics"></emph.end> That from <lb></lb>the Maſs, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that in the fluid <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> is immerged certain <lb></lb>Gravity is ſubſtracted by the ſaid <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> this commeth to paſs <lb></lb>by reaſon that it reſiſteth its being opened, driven back, and in a <lb></lb>word commoved; a ſign of which is its proneneſs to return inſtant<lb></lb>ly to fill the Space up again, that the immerſed maſs occupied in it, <lb></lb>as ſoon as ever it departeth thence; for if it ſuffered not by that <lb></lb>immerſion, it would not operate againſt the ſame. </s> <s>Now tell me, <lb></lb>when you have in the Air the Bottle before filled with the ſame Air <lb></lb>naturally contained therein, what diviſion, repulſe, or, in ſhort, <lb></lb>what mutation doth the external ambient Air receive from the ſe<pb xlink:href="040/01/760.jpg" pagenum="68"></pb>cond Air that was newly infuſed with force into the Veſſel? </s> <s>Doth <lb></lb>it enlarge the Bottle, whereupon the Ambient ought the more to <lb></lb>retire it ſelf to make room for it? </s> <s>Certainly no: And therefore <lb></lb>we may ſay, that the ſecond Air is not immerſed in the Ambient, <lb></lb>not occupying any Space therein; but is as if it was in a <emph type="italics"></emph>Vacuum,<emph.end type="italics"></emph.end><lb></lb>nay more, is really conſtituted in it, and is placed in Vacuities that <lb></lb>were not repleted by the former un-condenſed Air. </s> <s>And, really, I <lb></lb>know not how to diſcern any difference between the two Conſti <lb></lb>tutions of Incloſed and <emph type="italics"></emph>Ambient,<emph.end type="italics"></emph.end> whilſt in this the <emph type="italics"></emph>Ambient<emph.end type="italics"></emph.end> doth <lb></lb>no-ways preſs the Incloſed, and in that the Incloſed doth not re<lb></lb>repulſe the <emph type="italics"></emph>Ambient<emph.end type="italics"></emph.end>: and ſuch is the placing of any matter in a <lb></lb><emph type="italics"></emph>Vacuum,<emph.end type="italics"></emph.end> and the ſecond Air compreſsed in the Flask. </s> <s>The weight <lb></lb>therefore that is found in that ſame condenſed Air, is the ſame that <lb></lb>it would have, were it freely diſtended in a <emph type="italics"></emph>Vacuum.<emph.end type="italics"></emph.end> Tis true in<lb></lb>deed, that the weight of the Sand that weigheth againſt it, as ha<lb></lb>ving been in the open Air, would in a <emph type="italics"></emph>Vacuum<emph.end type="italics"></emph.end> have been a little <lb></lb>more than juſt ſo heavy; and therefore it is neceſſary to ſay, that <lb></lb>the weighed Air is in reality ſomewhat leſſe heavy than the Sand <lb></lb>that counterpoiſeth it, that is, ſo much, by how much the like <lb></lb>quantity of Air would weigh in a <emph type="italics"></emph>Vacuum.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SIMP. </s> <s>I had thought that there was ſomething to have been <lb></lb>wiſhed for in the Experiments before produced; but now I am <lb></lb>thorowly ſatisfied.<lb></lb><arrow.to.target n="marg1065"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1065"></margin.target><emph type="italics"></emph>The difference, <lb></lb>though very great, <lb></lb>of the Gravity of <lb></lb>Moveables hath <lb></lb>no part in differer<lb></lb>cing their Veloci<lb></lb>ties.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>The things by me hitherto alledged, and in particular, <lb></lb>this, That the difference of Gravity, although exceeding great, <lb></lb>hath no part in diverſifying the Velocities of Moveables, ſo that, <lb></lb>notwithſtanding any thing depending on that, they would all <lb></lb>move with equal Celerity, is ſo new, and at the firſt apprehenſi<lb></lb>on ſo remote from probability, that, were there not a way to de<lb></lb>lucidate it, and make it as clear as the Sun, it would be better <lb></lb>to paſſe it over in ſilence, than to divulge it: therefore ſeeing <lb></lb>that I have let it eſcape from me, its fit that I omit neither Expe<lb></lb>riment nor Reaſon that may corroborate it.</s></p><p type="main"> <s>SAGR. </s> <s>Not onely this, but many other alſo of your Aſſerti<lb></lb>ons are ſo remote from the Opinions and Doctrines commonly <lb></lb>received, that ſending them abroad, you would ſtir up a great <lb></lb>number of Antagoniſts: in regard, that the innate Diſpoſition of <lb></lb>Men doth not ſee with good eyes, when others in their Studies <lb></lb>diſcover Truths or Fallacies, that were not diſcovered by them<lb></lb>ſelves: and with the title of Innovators of Doctrines, little plea<lb></lb>ſing to the ears of many, they ſtudy to cut thoſe knots which <lb></lb>they cannot untie, and with ſub-terranean Mines to blow up <lb></lb>thoſe Structures, which have been with the ordinary Tools by <lb></lb>patient Architects erected: but with us here, who are far from <lb></lb>any ſuch thoughts, your Experiments and Arguments are <pb xlink:href="040/01/761.jpg" pagenum="69"></pb>ſufficient to give full ſatisfaction: yet nevertheleſſe, if ſo be you <lb></lb>have other more palpable Experiments, and more convincing <lb></lb>Reaſons we would very gladly hear them.</s></p><p type="main"> <s>SALV. </s> <s>The Experiment made with two Moveables, as different <lb></lb>in weight as may be, by letting them deſcend from a place on <lb></lb>high, thereby to ſee whether their Velocity be equal, meets with <lb></lb>ſome difficulty: for if the height ſhall be great, the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end><lb></lb>which is to be opened and laterally repelled by the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the <lb></lb>cadent Body, ſhall be of much greater prejudice to the ſmall Mo<lb></lb>ment of the light Moveable, than to the violence of the heavy <lb></lb>one; whereupon in a long way the light one will be left behind: <lb></lb>and in a little altitude it might be doubted whether there were <lb></lb>really any difference, or if there were, whether it would be <lb></lb>ſenſible. </s> <s>Therefore I have oft been thinking to reiterate the de<lb></lb>ſcent ſo many times from ſmall heights, and to accumulate toge<lb></lb>ther ſo many of thoſe minute differences of time, as might inter<lb></lb>cede between the arrival or fall of the heavy Body to the ground, <lb></lb>and the arrival of the light one, which ſo conjoyned, would make <lb></lb>a time not onely obſervable, but obſervable with much facility <lb></lb>Moreover, that I might help my ſelf with Motions as ſlow as poſ<lb></lb>ſible may be, in which the Reſiſtance of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> operates <lb></lb>leſſe in altering the effect that dependeth on ſimple Gravity, I <lb></lb>have had thoughts to cauſe the Moveable to deſcend upon a de<lb></lb>clining Plane, not much raiſed above the Plane of the Horizon; <lb></lb>for upon this, no leſſe than in perpendicularity, we may diſcover <lb></lb>that which is done by Grave Bodies different in weight: and pro<lb></lb>ceeding farther, I have deſired to free my ſelf from any whatſo<lb></lb>ever impediment, that might ariſe from the Contact of the ſaid <lb></lb>Moveables upon the ſaid declining Plane: and laſtly, I have ta<lb></lb>ken two Balls, one of Lead, and one of Cork, that above an hun<lb></lb>dred times more grave than this, and have faſtened them to two <lb></lb>ſmall threads, each equally four or five yards long, tyed on <lb></lb>high: and having removed aſwel the one as the other Ball from <lb></lb>the ſtate of Perpendicularity, I have let them both go in the ſame <lb></lb>Moment, and they deſcending by the Circumferences of Circles <lb></lb>deſcribed by the equal Strings their Semidiameters, and having <lb></lb>paſſed beyond the Perpendicular, they afterwards by the ſame <lb></lb>way returned back, and reiterating theſe Vibrations, and re<lb></lb>turns of themſelves neer an hundred times, they have ſhewn ve<lb></lb>ry ſenſibly, that the grave <emph type="italics"></emph>Pendulum<emph.end type="italics"></emph.end> moveth ſo exactly under the <lb></lb>time of the light one, that it doth not in an hundred, no nor in a <lb></lb>thouſand Vibrations, anticipate the time of one ſmall moment, <lb></lb>but that they keep an equal paſſe in their Recurſions. </s> <s>They alſo <lb></lb>ſhew the Operation of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> which conferring ſome im<lb></lb>pediment on the Motion, doth much more diminiſh the Vibrati<pb xlink:href="040/01/762.jpg" pagenum="70"></pb>ons of the Cork, than that of the Lead: not that it maketh them <lb></lb>more or leſſe frequent, nay, when the Arches paſſed by the Cork <lb></lb>were not of above five or ſix degrees, and thoſe of the Lead fif<lb></lb>ty, they did paſs them under the ſame times.</s></p><p type="main"> <s>SIMP. </s> <s>If this be ſo, how is it then that the Velocity of the <lb></lb>Lead is not greater than that of the Cork? </s> <s>that paſſing a jour<lb></lb>ney of ſixty degrees, in the time that this paſseth hardly ſix?</s></p><p type="main"> <s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>ALV. </s> <s>But what would you ſay, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> in caſe they <lb></lb>ſhould both diſpatch their Recurſions in the ſame time, when the <lb></lb>Cork being removed thirty degrees from the Perpendicular, <lb></lb>ſhould paſs an arch of ſixty, and the Lead removed from the <lb></lb>ſame middle point onely two degrees, ſhould run an arch of four? <lb></lb></s> <s>would not then the Cork be ſo much more ſwift than the Lead? <lb></lb></s> <s>and yet Experience ſhews that ſo it happeneth: therefore obſerve, <lb></lb>The <emph type="italics"></emph>Pendulum<emph.end type="italics"></emph.end> of Lead being carried <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> fifty degrees from the <lb></lb>Perpendicular, and thence let go, ſwingeth, and paſſing beyond <lb></lb>the Perpendicular, neer fifty more degrees, deſcribeth an arch <lb></lb>of well neer an hundred degrees; and returning of its ſelf back <lb></lb>again, it deſcribeth another arch, not much leſſe than the former, <lb></lb>and continuing its Vibrations, after a great number of them, it <lb></lb>finally returneth to Reſt: Each of thoſe Vibrations are made un<lb></lb>der equal times aſwel thoſe of ninety degrees, as thoſe of fifty, <lb></lb>twenty, ten, or four; ſo that by conſequence, the Velocity of the <lb></lb>Moveable doth ſucceſſively languiſh and abate, in regard, that <lb></lb>under equal times it doth ſucceſſively paſſe arches continually <lb></lb>leſſer and leſſer. </s> <s>The like, yea the ſelf ſame effect is performed <lb></lb>by the Cork, hanging by a ſtring of the like length, ſave that <lb></lb>in a leſſe number of Vibracions it returneth to Reſt, as being leſs <lb></lb>apt, by means of its Levity, to overcome the obſtacle of the Air: <lb></lb>and yet nevertheleſs all the Vibrations, both great and ſmall, are <lb></lb>made under times equal to one another, and equal alſo to the <lb></lb>times of the times of the Vibrations of the Lead. </s> <s>Whereupon it <lb></lb>is true, that if whilſt the Lead paſſeth an arch of fifty degrees, <lb></lb>the Cork paſseth one but of ten, the Cork is then more ſlow <lb></lb>than the Lead: but it will alſo happen on the other ſide, that the <lb></lb>Cork paſseth the arch of fifty degrees, when the Lead paſseth <lb></lb>but that of ten or ſix; and ſo in ſeveral times the Lead ſhall be <lb></lb>ſwifter onewhile, and the Cork another while: but if the ſame <lb></lb>Moveables ſhall alſo under the ſame equal times, paſs arches that <lb></lb>are equal, one may then very ſafely ſay, that their Velocities are <lb></lb>equal.</s></p><p type="main"> <s>SIMP. </s> <s>This diſcourſe ſeems to me concluding, and not con<lb></lb>cluding, and I finde in my thoughts ſuch a Confuſion, ariſing <lb></lb>from the one-while ſwift, another-while ſlow, another-while ex<lb></lb>treme ſlow motion of both the one and other Moveable; as that <pb xlink:href="040/01/763.jpg" pagenum="71"></pb>it permits me not to diſcern clearly, whether it be true, That their <lb></lb>Velocities are alwaies equal.</s></p><p type="main"> <s>SAGR. </s> <s>Give me leave, I pray you, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> to interpoſe two <lb></lb>words. </s> <s>And tell me, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> whether you admit, that it may be <lb></lb>ſaid with abſolute verity that the Velocities of the Cork and of <lb></lb>the Lead are equal, in caſe, that both of them departing at the <lb></lb>ſame moment from Reſt, and moving by the ſame declivities, they <lb></lb>ſhould alwaies paſſe 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></lb>paſſeth now ſixty degrees, now fifty, now thirty, now ten, now <lb></lb>eight, four, and two; and when each of them paſſeth the Arch of <lb></lb>ſixty degrees they paſſe it in the ſame time; in the Arch of fifty the <lb></lb>ſame time is ſpent by both the one and the other Moveable; ſo in <lb></lb>the Arch of thirty, of ten, and of the reſt: and therefore it is con<lb></lb>cluded, that the Velocity of the Lead in the Arch of ſixty degrees, <lb></lb>is equal to the Velocity of the Cork in the ſame Arch of ſixty de<lb></lb>grees: and that the Velocities in the Arch of fifty, are likewiſe <lb></lb>equal to one the other, and ſo in the reſt. </s> <s>But it is not ſaid, that the <lb></lb>Velocity that is exerciſed in the Arch of ſixty is equal to the Ve<lb></lb>locity that is exerciſed in the Arch of fifty, nor this to that of the <lb></lb>Arch of thirty. </s> <s>But the Velocities are alwaies leſſer, in the leſſer <lb></lb>Arches. </s> <s>And this is collected from our ſenſibly ſeeing the ſame <lb></lb>Moveable conſume as much time in paſſing the great Arch of ſixty <lb></lb>degrees, as in paſſing the leſſer of fifty, or the leaſt of ten: and, in a <lb></lb>word, in their being all paſſed alwaies under equal times. </s> <s>It is true <lb></lb>therefore, that both the Lead and the Cork ſucceſſively retard the <lb></lb>Motion, according to the Diminution of the Arches, but yet do <lb></lb>not alter their harmony in keeping the equality of Velocity in all <lb></lb>the ſame Arches by them paſſed. </s> <s>I deſired to ſay thus much, more <lb></lb>to try whether I have rightly apprehended the Conceit of <emph type="italics"></emph>Salvia<lb></lb>tus,<emph.end type="italics"></emph.end> than out of any neceſſity that I thought <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> to ſtand in <lb></lb>of a more plain Explanation than that of <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> which is, as <lb></lb>in all other things, extreamly clear, and ſuch, that, it being fre<lb></lb>quent with him to reſolve Queſtions, in appearance not only ob<lb></lb>ſcure, but repugnant to Nature, and to the Truth, with Reaſons, <lb></lb>or Obſervations, or Experiments very trite and familiar to every <lb></lb>one, it hath (as I have underſtood from divers) given occaſion to <lb></lb>one of the moſt eſteemed Profeſſors of our Age to put the leſſe <lb></lb>eſteem upon his Novelties, holding them to have as much of Sor<lb></lb>didneſſe, for that they depend on over low and popular Funda<lb></lb>mentals: as if the moſt admirable and moſt-to-be-prized Proper<lb></lb>ty of the Demonſtrative Sciences, were not to ſpring and ariſe <lb></lb>from Principles known, underſtood, and granted by every one. <lb></lb></s> <s>But let us, for all that, continue to banquet our ſelves with this diet <pb xlink:href="040/01/764.jpg" pagenum="72"></pb>that is ſo light of digeſtion; and ſuppoſing that <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> is fully <lb></lb>ſatisfied in underſtanding and admitting, That the intern Gravity <lb></lb>of different Moveables hath no ſhare in differencing their Veloci<lb></lb>ties, ſo that all of them, for ought that dependeth on that, would <lb></lb>move with the ſame Velocities; tell us, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> in what you <lb></lb>place the ſenſible and apparent inequalities of Motion; and an<lb></lb>ſwer to that Inſtance that <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> produceth, and which I like<lb></lb>wiſe confirm, I mean, of ſeeing a Cannon Bullet move more ſwift<lb></lb>ly than a drop of Bird-ſhot, for the difference of Velocity ſhall be <lb></lb>but ſmall, in reſpect of that which I object againſt you of Movea<lb></lb>bles of the ſame matter, of which ſome of the greater will deſcend <lb></lb>in a <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> in leſſe than one beat of the Pulſe, that ſpace, that <lb></lb>others which are leſſer will not paſſe in an hour, nor in four, nor in <lb></lb>twenty; ſuch are pebbles and minute gravel-ſtones, eſpecially, <lb></lb>that ſmall ſand which muddieth the Water; in which <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end><lb></lb>they will not deſcend in many hours ſo much as two fathoms, <lb></lb>which Stones, and thoſe of no great bigneſſe, do paſſe in one beat <lb></lb>of the Pulſe.</s></p><p type="main"> <s>SALV. </s> <s>That which the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> operates, in retarding Movea<lb></lb>bles, the more according as they are compared to one another, leſs <lb></lb>grave <emph type="italics"></emph>in ſpecie,<emph.end type="italics"></emph.end> hath been already declared, ſhewing that it pro<lb></lb>ceeds from the ſubſtraction of weight. </s> <s>But how one and the ſame <lb></lb><emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> can with ſo great difference diminiſh the Velocity in <lb></lb>Moveables that differ only in Magnitude, although they are of <lb></lb>the ſame Matter, and of the ſame Figure, requireth for its expli<lb></lb>cation a more ſubtil diſcourſe, than that which ſufficeth for under<lb></lb>ſtanding how the more dilated Figure of the Moveable, or the <lb></lb>Motion of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> that is made contrary to the Moveable, re</s></p><p type="main"> <s><arrow.to.target n="marg1066"></arrow.to.target><lb></lb>tardeth the Velocity of the ſaid Moveable. </s> <s>I reduce the cauſe of <lb></lb>the ſaid Problem to the Scabroſity, and Poroſity, that is common<lb></lb>ly, and, for the moſt part, neceſſarily found in the Superficies of <lb></lb>Solid Bodies, the which Scabroſities, in their Motion, go repulſing <lb></lb>and commoving the Air, or other Ambient <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end>: of which we <lb></lb>have an evident teſtimony, in that we hear the Bodies, though made <lb></lb>as round as is poſſible for them to be, to hum whilſt they paſſe ve<lb></lb>ry ſwiftly thorow the Air; and they are not only heard to hum, but <lb></lb>to whir and whiſtle, if there be but in them ſome more than ordi<lb></lb>nary cavity or prominency. </s> <s>We ſee alſo, that in turning round <lb></lb>every rotund Solid maketh a little wind: And what need more? <lb></lb></s> <s>Do we not hear a notable whirring, and in a very ſharp Accent, <lb></lb>made by a Top, while it turneth round on the ground with great <lb></lb>Celerity? </s> <s>The ſhrilneſs of which whizzing groweth flatter accor<lb></lb>ding as the Velocity of the <emph type="italics"></emph>Vertigo<emph.end type="italics"></emph.end> doth by degrees more and <lb></lb>more ſlacken: a neceſſary Argument likewiſe of the commotion <lb></lb>and percuſſion of the Air by thoſe (though very ſmall) Scabroſi<pb xlink:href="040/01/765.jpg" pagenum="73"></pb>ties of their Superficies. </s> <s>It is not to be doubted, but that theſe in the <lb></lb>deſcent of Moveables, grating upon, and repulſing the fluid Am<lb></lb>bient, procure retardment in the Velocity, and ſo much the greater, <lb></lb>by how much the Superficies ſhall be greater, as is that of leſſer <lb></lb>Solids compared to bigger.</s></p><p type="margin"> <s><margin.target id="marg1066"></margin.target><emph type="italics"></emph>The greater or leſs <lb></lb>Scabroſity and Po<lb></lb>roſity of the Super<lb></lb>ficies of Movea<lb></lb>bles, a probable <lb></lb>cauſe of their grea<lb></lb>ter or leſſer Retar<lb></lb>dation.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SIMP. Stay, I pray you, for here I begin to be at a loſſe: for <lb></lb>though I underſtand and admit, that the Confrication of the <emph type="italics"></emph>Medi<lb></lb>um<emph.end type="italics"></emph.end> with the Superficies of the Moveable retardeth the Motion, <lb></lb>and that it more retardeth it where <emph type="italics"></emph>(ceteris paribus)<emph.end type="italics"></emph.end> the Superficies <lb></lb>is greater, yet do I not comprehend upon what ground you call the <lb></lb>Superficies of leſſer Solids greater: & farthermore if, as you affirm, the <lb></lb>greater Superficies ought to cauſe greater retardment, the greater <lb></lb>Solids ought to be the ſlower, which is not ſo: but this Objection <lb></lb>may eaſily be removed, by ſaying, that although the greater hath <lb></lb>a greater Superficies, it hath alſo a greater Gravity, upon which <lb></lb>the impediment of the greater Superficies hath not ſo much more <lb></lb>prevalent influence, than the impediment of the leſſer Superficies <lb></lb>hath upon the leſſer Gravity, as that the Velocity of the greater <lb></lb>Solid ſhould become the leſſer. </s> <s>And therefore I ſee no reaſon why <lb></lb>one ſhould alter the equality of the Velocities, whilſt, that looking <lb></lb>how much the Moving Gravity diminiſheth, the faculty of the Re<lb></lb>tarding Superficies doth diminiſh at the ſame rate.</s></p><p type="main"> <s>SALV. </s> <s>I will reſolve all that which you object in one word. <lb></lb></s> <s>Therefore, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> you will without controverſie admit, that <lb></lb>when, of two equal Moveables of the ſame Matter, and alike in Fi<lb></lb>gure (which undoubtedly would move with equal ſwiftneſſe) as <lb></lb>well the Gravity, as the Superficies of one of them diminiſheth, <lb></lb>(yet ſtill retaining the ſimilitude of Figure) the Velocity like<lb></lb>wiſe, for the ſame reaſon, would not be diminiſhed in that which <lb></lb>was leſſened.</s></p><p type="main"> <s>SIMP. Really, I think, that it ought ſo to follow as you ſay, <lb></lb>granting the preſent Doctrine with a <emph type="italics"></emph>ſalvo<emph.end type="italics"></emph.end> ſtill to our Doctrine, <lb></lb>which teacheth, that the greater or leſſer Gravity hath no operati<lb></lb>on in accelerating or retarding Motion.</s></p><p type="main"> <s>SALV. </s> <s>And this I confirm; and grant you likewiſe your Po<lb></lb>ſition, from whence, in my opinion, may be inferred, That in caſe <lb></lb>the Gravity diminiſheth more than the Superficies, there may be <lb></lb>introduced in the Moveable, in that manner diminiſhed, ſome re<lb></lb>tardment of Motion, and that greater and greater, by how much in <lb></lb>proportion, the diminution of the Weight was greater than the di<lb></lb>minution of the Superficies</s></p><p type="main"> <s>SIMP. </s> <s>I make not the leaſt queſtion of it.<lb></lb><arrow.to.target n="marg1067"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1067"></margin.target><emph type="italics"></emph>Solids cannot be <lb></lb>diminiſhed at the <lb></lb>ſame rate in Super<lb></lb>ficies as in Weight, <lb></lb>retaining the ſimi<lb></lb>litude of the Fi<lb></lb>gures.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>Now know, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that in Solids one cannot di<lb></lb>miniſh the Superficies ſo much as the Weight keeping the ſimili<lb></lb>tude of Figure. </s> <s>For it being manifeſt, that in diminiſhing of grave <pb xlink:href="040/01/766.jpg" pagenum="74"></pb>Solids, the Weight leſſeneth as much as the Bulk, when ever the <lb></lb>Bulk happens to be diminiſhed more than the Superficies, (care <lb></lb>being had to retain the ſimilitude of Figure) the Gravity likewiſe <lb></lb>would come to be more diminiſhed than the Superficies. </s> <s>But <emph type="italics"></emph>Geo<lb></lb>metry<emph.end type="italics"></emph.end> teacheth us, that there is much greater proportion between <lb></lb>the Bulk and the Bulk in like Solids, than between their Superfi<lb></lb>cies. </s> <s>Which for your better underſtanding, I ſhall explain in ſome <lb></lb>particular caſe. </s> <s>Therefore fancy to your ſelf, for example, a Dye, <lb></lb>one of the Sides of which is <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> two Inches long, ſo that one of <lb></lb>its Surfaces ſhall be four Square Inches, and all ſix, that is, all its <lb></lb>Superficies twenty four Square Inches. </s> <s>Then ſuppoſe the ſame <lb></lb>Dye at three ſawings cut into eight ſmall Dice, the Side of every <lb></lb>one of which will be one Inch, and one of its Surfaces an Inch <lb></lb>Square, and its whole Superficies ſix Square Inches, of which the <lb></lb>whole Dye contained twenty four in its Superficial content. </s> <s>Now, <lb></lb>you ſee, that the Superficial content of the little Dye is the fourth <lb></lb>part of the Superficial content of the great one, (for ſix is the <lb></lb>fourth part of twenty four) but the Solid content of the ſaid Dye <lb></lb>is only the eighth part: therefore the Bulk, and conſequently the <lb></lb>Weight, doth much more diminiſh than the Superficies. </s> <s>And if <lb></lb>you ſubdivide the little Dye into eight others, we ſhall have for <lb></lb>the whole Superficial content of one of theſe, one and an half <lb></lb>Square Inches, which is the ſixteenth part of the Superficies of the <lb></lb>firſt Dye; but its Bulk, or Maſs, is only the ſixty fourth part of that. <lb></lb></s> <s>You ſee therefore, how that in only theſe two diviſions the Bulks <lb></lb>decreaſe four times faſter than their Superficies: and if we ſhould <lb></lb>proſecute the Subdiviſion, untill that we had reduced the firſt So<lb></lb>lid into a ſmall powder, we ſhould find the Gravity of the minute <lb></lb>Atomes to be leſſened an hundred and an hundred times more <lb></lb>than their Superficies. </s> <s>And this which I have exemplified in <lb></lb>Cubes, hapneth in all like Solids, the Bulks of which are in Seſ<lb></lb>quialter proportion of their Superficies. </s> <s>You ſee, therefore, in how <lb></lb>much greater proportion the Impediment of the Contact of the <lb></lb>Superficies of the Moveable with the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> encreaſeth in ſmall <lb></lb>Moveables, than in greater: and if we ſhould add, that the Sca<lb></lb>broſities in the very ſmall Superficies of the minute Atomes are <lb></lb>not happily leſſer than thoſe of the Superficies of greater Solids, <lb></lb>that are diligently poliſhed, obſerve how fluid, and void of all Re<lb></lb>ſiſtance being opened, the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> is required to be, when it is to <lb></lb>give paſſage to ſo feeble a Virtue. </s> <s>And therefore take notice, <emph type="italics"></emph>Sim<lb></lb>plicius,<emph.end type="italics"></emph.end> that I did not equivocate, when even now I ſaid, That the <lb></lb>Superficies of leſſer Solids is greater, in compariſon of that of <lb></lb>bigger.</s></p><p type="main"> <s>SIMP. </s> <s>I am wholly ſatisfied: and I verily believe, that if I were <lb></lb>to begin my Studies again, I ſhould follow the Counſel of <emph type="italics"></emph>Plato,<emph.end type="italics"></emph.end><pb xlink:href="040/01/767.jpg" pagenum="75"></pb>and enter my ſelf firſt in the Mathematicks, which I ſee to proceed <lb></lb>very ſcrupulouſly, and refuſe to admit any thing for certain, ſave <lb></lb>that which they neceſſarily demonſtrate.</s></p><p type="main"> <s>SAGR. </s> <s>I have taken great delight in this Diſcourſe; but, be<lb></lb>fore we paſſe any further, I would be glad to be ſatisfied in one <lb></lb>particular, which newly came into my thoughts, when but juſt <lb></lb>now you ſaid, that Like-Solids are in Seſquialter proportion to <lb></lb>their Superficies for I have ſeen, and underſtood the Propoſition </s></p><p type="main"> <s><arrow.to.target n="marg1068"></arrow.to.target><lb></lb>with its Demonſtration, in which it is proved, That the Superficies <lb></lb>of Like-Solids are in duplicate proportion of their Sides; and ano<lb></lb>ther that proveth the ſame Solids to be in triple proportion of the <lb></lb>ſame Sides; but the proportion of Solids to their Superficies, I do <lb></lb>not remember that I ever ſo much as heard it mentioned.</s></p><p type="margin"> <s><margin.target id="marg1068"></margin.target><emph type="italics"></emph>Solids are to each <lb></lb>other in Seſquial<lb></lb>ter proportion to <lb></lb>their Superficies.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>You your ſelf have anſwered and declared the doubt. <lb></lb></s> <s>For that which is triple of a thing of which another is double, doth <lb></lb>it not come to be Seſquialter of this double? </s> <s>Yes doubtleſſe. </s> <s>Now, <lb></lb>if Superficies are in double proportion of the Lines, of which the <lb></lb>Solids are in triple proportion, may not we ſay, That the Solids are <lb></lb>in Seſquialter proportion of their Superficies?</s></p><p type="main"> <s>SAGR. </s> <s>I underſtand you very well. </s> <s>And although other par<lb></lb>ticulars, pertaining to the matter of which we have treated, do re<lb></lb>main for me to ask, yet if we ſhould thus run from one Digreſſion <lb></lb>to another, it will be late before we ſhould come to the Queſtions <lb></lb>principally intended, which concern the diverſities of the Acci<lb></lb>dents of the Reſiſtances of Solids againſt Fraction; and therefore, <lb></lb>if you ſo pleaſe, we may return to the firſt Theme, which we pro<lb></lb>poſed in the beginning.</s></p><p type="main"> <s>SALV. </s> <s>You ſay very well; but the ſo many, and ſo different <lb></lb>things that have been examined, have ſtoln ſo much of our time, <lb></lb>that there is but little of it left in this day to ſpend in our other <lb></lb>principal Argument, which is full of Geometrical Demonſtrati<lb></lb>ons that are to be conſidered with attention: ſo that I ſhould think <lb></lb>it were better to adjourn our meeting till to morrow, as well for <lb></lb>this which I have told you, as alſo becauſe I might bring with me <lb></lb>ſome Papers, on which I have, in order, ſet down the Theorems and <lb></lb>Problems, in which are propoſed and demonſtrated the different <lb></lb>Paſſions of this Subject, which, it may be, would not otherwiſe <lb></lb>with requiſite Method come into my mind.</s></p><p type="main"> <s>SAGR. </s> <s>I very gladly comply with your advice, and ſo much the <lb></lb>more willingly, in regard that, for a Concluſion of this daies Con<lb></lb>ference, I ſhall have time to hear you reſolve ſome doubts that I <lb></lb>find in my mind concerning the Point laſt handled. </s> <s>Of which one <lb></lb>is, Whether we are to hold, that the Impediment of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end><lb></lb>may be ſufficient to aſſign bounds to the Acceleration of Bodies of <lb></lb>very grave Matter, that are of great Bulk, and of a Spherical Figure: <pb xlink:href="040/01/768.jpg" pagenum="76"></pb>and I inſtance in the Spherical Figure, that I might take that which <lb></lb>is contained under the leaſt Superficies, and therefore leſſe ſubject <lb></lb>to Retardment. </s> <s>Another ſhall be, touching the Vibrations of Pen<lb></lb>dulums, and this hath many heads: One ſhall be, Whether all, <lb></lb>both Great, Mean, and Little, are made really and preciſely under <lb></lb>equal Times: And another, What is the proportion of the Times <lb></lb>of Moveables, ſuſpended at unequal ſtrings, of the Times of their <lb></lb>Vibrations I mean.</s></p><p type="main"> <s>SALV. </s> <s>The Queſtions are ingenious, and, like as it is incident <lb></lb>to all Truths, I ſuppoſe, that, which ever of them we handle, it will <lb></lb>draw after it ſo many other Truths, and curious Conſequences, <lb></lb>that I cannot tell whether the remainder of this day may ſuffice <lb></lb>for the diſcuſſing of them all.</s></p><p type="main"> <s>SAGR. </s> <s>If they ſhall be but as delightful as the precedent, it <lb></lb>would be more grateful for me to employ as many daies, not to ſay, <lb></lb>hours, as it is unto night, and I believe that <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> will not be <lb></lb>cloy'd with ſuch Argumentations as theſe.</s></p><p type="main"> <s>SIMP. </s> <s>No certainly: and eſpecially, when the Queſtions trea<lb></lb>ted of are Phyſical, touching which we read not the Opinions or <lb></lb>Diſcourſes of other Philoſophers.<lb></lb><arrow.to.target n="marg1069"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1069"></margin.target><emph type="italics"></emph>Any Body, of any <lb></lb>Figure, Greatneſs, <lb></lb>and Gravity, is <lb></lb>checked by the Re<lb></lb>nitence of the<emph.end type="italics"></emph.end> Me<lb></lb>dium, <emph type="italics"></emph>though ne<lb></lb>ver ſo tenuous, in <lb></lb>ſuch ſort, that the <lb></lb>Motion continuing, <lb></lb>it is reduced to <lb></lb>equability.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>I come therefore to the firſt, affirming without any <lb></lb>hæſitation, that there is not a Sphere ſo big, nor of Matter ſo grave, <lb></lb>but that the Renitence of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> though very tenuous, checks <lb></lb>its Acceleration, and in the continuation of the Motion reduceth <lb></lb>it to Equability, of which we may draw a very clear Argument <lb></lb>from Experience it ſelf. </s> <s>For if any falling Moveable were able in <lb></lb>its continuation of Motion to attain any degree of Velocity, no <lb></lb>Velocity that ſhould be conferred upon it, could be ſo great but <lb></lb>that it would depoſe it, and free it ſelf of it by help of the Impe<lb></lb>diment of the <emph type="italics"></emph>Medium.<emph.end type="italics"></emph.end> And thus, a Cannon-bullet, that had de <lb></lb>ſcended through the Air, <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> four yards, and had, for example, <lb></lb>acquired ten degrees of Velocity, and that with theſe ſhould enter <lb></lb>into the Water, in caſe the Impediment of the Water were not <lb></lb>able to prohibit ſuch a certain <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> in the Ball, it would en<lb></lb>creaſe it, or at leaſt would continue it unto the bottom; which is <lb></lb>not obſerved to enſue: nay, the Water, although it were but a few <lb></lb>fathoms in depth, would impede and debilitate it in ſuch a man<lb></lb>ner, that it will make but a ſmall impreſſion in the bottom of the <lb></lb>River or Lake. </s> <s>It is therefore manifeſt, that that Velocity, of <lb></lb>which the Water had ability to deprive it in a very ſhort way, <lb></lb>would never be permitted to be acquired by it, though in a depth <lb></lb>of a thouſand Fathoms. </s> <s>And why ſhould it be permitted to gain <lb></lb>it in a thouſand, to be taken from it again in four? </s> <s>What need we <lb></lb>more? </s> <s>Do we not ſee the immenſe <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the Ball, ſhot from <lb></lb>the Cannon it ſelf, to be in ſuch a manner flatted by the interpo<pb xlink:href="040/01/769.jpg" pagenum="77"></pb>ſition of a few Fathom of Water, that without any harm to the <lb></lb>Ship, it but very hardly reacheth to make a dent in it? </s> <s>The Air al<lb></lb>ſo, though very yielding, doth nevertheleſſe repreſſe the Velocity <lb></lb>of the falling Moveable, although it be very heavy, as we may by <lb></lb>ſuch like Experiments collect; for if from the top of a very high <lb></lb>Tower we ſhould diſcharge a Muſquet downwards, this will make <lb></lb>a leſſer impreſſion on the ground, than if we ſhould diſcharge the <lb></lb>Muſquet at the height of four or ſix yards above the Plane: an <lb></lb>evident ſign, that the <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> wherewith the Bullet iſſueth from <lb></lb>the Gun, diſcharged on the top of the Tower, doth gradually di<lb></lb>miniſh in deſcending thorow the Air: therefore the deſcending <lb></lb>from any whatſoever great height will not ſuffice to make it ac<lb></lb>quire that <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> of which the Reſiſtance of the Air deprived <lb></lb>it, when it had in any manner been conferred upon it. </s> <s>The batte<lb></lb>ry likewiſe that the force of a Bullet, ſhot from a Culverin, ſhall <lb></lb>make in a Wall at the diſtance of twenty Paces, would not, I be<lb></lb>lieve, be ſo great, if the Bullet was ſhot perpendicularly from any <lb></lb>immenſe Altitude. </s> <s>I believe, therefore, that there is a Bound or <lb></lb>term belonging to the Acceleration of every Natural Moveable <lb></lb>that departs from Reſt, and that the Impediment of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> in <lb></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></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></lb>the purpoſe: nor doth any thing remain, unleſſe the Adverſary <lb></lb>ſhould fortifie himſelf, by denying, that they will hold true in great <lb></lb>and ponderous Maſſes, and that a Cannon-bullet coming from the <lb></lb>Concave of the Moon, or from the upper Region of the Air, <lb></lb>would make a greater percuſſion than coming from the Cannon.</s></p><p type="main"> <s>SALV. </s> <s>There is no queſtion, but that many things may be <lb></lb>objected, and that they may not be all ſalved by Experiments; ne<lb></lb>vertheleſſe in this contradiction, me thinks, there is ſomething that <lb></lb>may fall under conſideration; <emph type="italics"></emph>ſcilicet,<emph.end type="italics"></emph.end> that it is very probable, <lb></lb><arrow.to.target n="marg1071"></arrow.to.target><lb></lb>that the Grave Body, falling from an Altitude, acquireth ſo much <lb></lb><emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> at its arrival to the ground, as would ſuffice to return it <lb></lb>to that height, as is plainly ſeen in a <emph type="italics"></emph>Pendulum<emph.end type="italics"></emph.end> reaſonable weighty, <lb></lb>that being removed fifty or ſixty degrees from the Perpendicular, <lb></lb>gaineth that Velocity and Virtue which exactly ſufficeth to force it <lb></lb>to the like Recurſion, that little abated, which is taken from it by <lb></lb>the Impediment of the Air. </s> <s>To conſtitute, therefore, the Cannon<lb></lb>bullet in ſuch an Altitude as may ſuffice for the acquiſt of an <emph type="italics"></emph>Impe<lb></lb>tus,<emph.end type="italics"></emph.end> as great as that which the Fire giveth it in its iſſuing from the <lb></lb>Piece, it would ſuffice to ſhoot it upwards perpendicularly with <lb></lb>the ſaid Cannon, and then obſerving, whether in its fall it maketh <lb></lb>an impreſſion equal to that of the percuſſion made near at hand in <lb></lb>its iſſuing forth; but, indeed, I believe, that it would not be any <pb xlink:href="040/01/770.jpg" pagenum="78"></pb>whit near ſo forcible. </s> <s>And therefore I hold that the Velocity, <lb></lb>which the Bullet hath near to its going out of the Piece, would <lb></lb>be one of thoſe that the Impediment of the Air would never ſuffer <lb></lb>it to acquire, whilſt it ſhould with a natural Motion deſcend, leaving <lb></lb>the ſtate of Reſt, from any great height. </s> <s>I come now to the other <lb></lb>Queſtions belonging to <emph type="italics"></emph>Pendulums,<emph.end type="italics"></emph.end> matters which to many would <lb></lb>ſeem very frivolous, and more eſpecially to thoſe Philoſophers that <lb></lb>are continually buſied in the more profound Queſtions of Natural <lb></lb>Philoſophy: yet, notwithſtanding, will not I contemn them, being <lb></lb>encouraged by the Example of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> himſelf, in whom I admire <lb></lb>this above all things; that he hath not, as one may ſay, omitted any <lb></lb>matter that any waies merited conſideration, which he hath not <lb></lb>ſpoken of: and now upon the Queſtions you propounded, I think <lb></lb>I can tell you a certain conceit of mine upon ſome Problems con<lb></lb>cerning Muſick, a noble Subject, of which ſo many famous men, <lb></lb>and <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> himſelf, have written; and touching it, he conſide<lb></lb>reth many curious Problems: ſo that if I likewiſe ſhall from ſo fa<lb></lb>miliar and ſenſible Experiments, draw Reaſons of admirable acci<lb></lb>dents on the Argument of Sounds, I may hope that my diſcourſes <lb></lb>will be accepted by you.</s></p><p type="margin"> <s><margin.target id="marg1071"></margin.target><emph type="italics"></emph>A Grave Body, <lb></lb>falling from an <lb></lb>Altitude, acqui<lb></lb>reth ſo much<emph.end type="italics"></emph.end> Im<lb></lb>petus <emph type="italics"></emph>at its arri<lb></lb>val to the ground, <lb></lb>as in all probabili<lb></lb>ty, would ſuffice to <lb></lb>recarry it to the <lb></lb>ſame height from <lb></lb>whence it fell.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR Not only accepted, but by me, in particular, moſt paſ<lb></lb>ſionately deſired, in regard that I taking a great delight in all Mu<lb></lb>ſical Inſtruments, and being reaſonably well inſtructed concerning <lb></lb>Conſonances, have alwaies been ignorant and perplexed with <lb></lb>endeavouring to know, whence it cometh that one ſhould more <lb></lb>pleaſe and delight me than another; and that ſome not only pro<lb></lb>cure me no delight, but highly diſpleaſe me: the trite Ptoblem al<lb></lb>ſo of the two Chords ſet to an Uniſon, one of which moveth and <lb></lb>actually ſoundeth at the touching of the other, I alſo am unreſol<lb></lb>ved in: nor am I very clearly informed concerning the Forms of <lb></lb>Conſonances, and other particularities.</s></p><p type="main"> <s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>ALV. </s> <s>We will ſee, if from theſe our <emph type="italics"></emph>Peudulums<emph.end type="italics"></emph.end> one may ga<lb></lb>ther any ſatisfaction in all theſe Doubts. </s> <s>And as to the firſt Que<lb></lb>ſtion, that is, Whether the ſame <emph type="italics"></emph>Pendulum<emph.end type="italics"></emph.end> doth really and punctu<lb></lb>ally perform all its Vibrations, great, leſſer, and leaſt, under Times <lb></lb>preciſely equal; I refer my ſelf to that which I have heretofore <lb></lb>learnt from our <emph type="italics"></emph>Academian,<emph.end type="italics"></emph.end> who plainly demonſtrateth, that the <lb></lb><arrow.to.target n="marg1072"></arrow.to.target><lb></lb>Moveable that ſhould deſcend along the Chords, that are Subten<lb></lb>ſes to any Arch, would neceſſarily paſſe them all in equal Times, <lb></lb>as well the Subtenſe under an hundred and eighty degrees, (that <lb></lb>is, the whole Diameter) as the Subtenſes of an hundred, ſixty, ten, <lb></lb>two, or half a degree, or of four minutes: ſtill ſuppoſing that they <lb></lb>all determine in the loweſt Point touching the Horizontal Plane. <lb></lb></s> <s>Next as to the deſcendents by the Arches of the ſame Chords eli<lb></lb>vated above the Horizon, and that are not greater than a Qua<pb xlink:href="040/01/771.jpg" pagenum="79"></pb>drant, that is, than ninety degrees, Experience likewiſe ſhews, that <lb></lb><arrow.to.target n="marg1073"></arrow.to.target><lb></lb>they paſſe all in Times equal, but yet ſhorter than the Times of <lb></lb>the paſſages by the Chords: an effect which hath ſo much of won<lb></lb>der in it, by how much at the firſt apprehenſion one would think <lb></lb>the contrary ought to follow: For the terms of the beginning, <lb></lb>and the end of the Motion being common, and the Right-Line be<lb></lb>ing the ſhorteſt, that can be comprehended between the ſaid <lb></lb>Terms, it ſeemeth reaſonable, that the Motion made by it ſhould <lb></lb>be finiſhed in the ſhorteſt Time, which yet is not ſo: but the ſhor<lb></lb>teſt Time, and conſequently, the ſwifteſt Motion, is that made by <lb></lb>the Arch of which the ſaid Right-Line is Chord. </s> <s>In the next <lb></lb><arrow.to.target n="marg1074"></arrow.to.target><lb></lb>place, as to the Times of the Vibrations of Moveables, ſuſpended <lb></lb>by ſtrings of different lengths, thoſe Times are in Subduple pro<lb></lb>portion to the lengths of the ſtrings, or, if you will, the lengths <lb></lb>are in duplicate proportion to the Times, that is, are as the Squares <lb></lb>of the Times: ſo that if, for example, the Time of a Vibration <lb></lb>of one <emph type="italics"></emph>Pendulum<emph.end type="italics"></emph.end> is double to the Time of a Vibration of another, <lb></lb>it followeth, that the length of the ſtring of that is quadruple to <lb></lb>the length of the ſtring of this. </s> <s>And in the Time of one Vibration <lb></lb>of that, another ſhall then make three Vibrations, when the ſtring <lb></lb>of that ſhall be nine times as long as the other. </s> <s>From whence doth <lb></lb>follow, that the length of the ſtrings have to each other the ſame <lb></lb>proportion, that the Squares of the Numbers of the Vibrations that <lb></lb>are made in the ſame Times have.</s></p><p type="margin"> <s><margin.target id="marg1072"></margin.target><emph type="italics"></emph>Moveables deſcen<lb></lb>ding along the <lb></lb>Chords, that are <lb></lb>Subtenſes to any <lb></lb>Arch of a Circle, <lb></lb>paſſe as well the <lb></lb>greater as the leſ<lb></lb>ſer Chords in equal <lb></lb>Times.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1073"></margin.target><emph type="italics"></emph>Moveables and<emph.end type="italics"></emph.end><lb></lb>Pendula <emph type="italics"></emph>deſcend<lb></lb>ing along the Ar<lb></lb>ches of the ſame <lb></lb>Chords, elivated as <lb></lb>far as 90 deg. </s> <s>paſs <lb></lb>the ſaid Arches in <lb></lb>Times equal, but <lb></lb>that are ſhorter <lb></lb>than the tranſiti<lb></lb>ons along the <lb></lb>Chords.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1074"></margin.target><emph type="italics"></emph>The Times of the <lb></lb>Vibrations of Mo<lb></lb>vables, hanging at <lb></lb>alonger or ſhorter <lb></lb>thread, are to one <lb></lb>another in propor<lb></lb>tion ſubduple the <lb></lb>lengths of the <lb></lb>ſtrings, at which <lb></lb>they hang.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. Then, if I have rightly underſtood you, I may eaſily <lb></lb><arrow.to.target n="marg1075"></arrow.to.target><lb></lb>know the length of a ſtring, hanging at any never-ſo-great height, <lb></lb>although the ſublime term of the ſuſpenſion were inviſible to me, <lb></lb>and I only ſaw the other lower extream. </s> <s>For if I ſhall faſten a <lb></lb>weight of ſufficient Gravity to the ſaid ſtring here below, and ſet <lb></lb>it on vibrating to and again, and a friend telling ſome of its Recur<lb></lb>ſions, and I at the ſame time tell the Recurſions of another Movea<lb></lb>ble, ſuſpended at a ſtring that is preciſely a yard long, by the <lb></lb>Numbers of the Vibrations of theſe <emph type="italics"></emph>Pendula,<emph.end type="italics"></emph.end> made in the ſame <lb></lb>Time, I will find the length of the ſtring. </s> <s>As for example, ſuppoſe <lb></lb>that in the time that my friend hath counted twenty Recurſions of <lb></lb>the long ſtring, I had told two hundred and forty of my ſtring, <lb></lb>that is one yard long: ſquaring the two numbers twenty and two <lb></lb>hundred and forty, which are 400, and 57600, I will ſay, that the <lb></lb>long ſtring containeth 57600 of thoſe Meaſures, of which my <lb></lb>ſtring containeth 400. and becauſe the ſtring is one ſole yard, I will <lb></lb>divide 57600 by 400, and the quotient will be 144, and I will af<lb></lb>firm that ſtring to be 144 yards long.</s></p><p type="margin"> <s><margin.target id="marg1075"></margin.target><emph type="italics"></emph>To find the Length <lb></lb>of any Rope, or <lb></lb>ſtring, at which a <lb></lb>Moveable hang<lb></lb>eth, by the frequen<lb></lb>cy of its Vibrations<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>Nor will you be miſtaken one Inch; and eſpecially, if <lb></lb>you take a great Number of Vibrations.</s></p><p type="main"> <s>SAGR. </s> <s>You give me frequent occaſion to admire the Riches, <pb xlink:href="040/01/772.jpg" pagenum="80"></pb>and withal the extraordinary bounty of Nature, whil'ſt by things <lb></lb>ſo common, and, I might in a certain ſence ſay, vile, you go col<lb></lb>lecting of Notions very curious, new, and oftentimes, remote <lb></lb>from all imagination. </s> <s>I have an hundred times conſidered the Vi<lb></lb>brations, in particular, of the Lamps in ſome Churches, hanging <lb></lb>by very long ropes, when they have been unawares ſtirred by <lb></lb>any one: but the moſt that I inferred from that ſame Obſervati<lb></lb>on, was the improbability of the Opinion of thoſe who hold, <lb></lb>that ſuch-like Motions are maintained and continued by the <emph type="italics"></emph>Medi<lb></lb>um,<emph.end type="italics"></emph.end> that is by the Air: for it ſhould ſeem to me, that the Air had <lb></lb>a great judgment, and withal but little buſineſſe to ſpend ſo ma<lb></lb>ny hours time in vibrating an hanging Weight with ſo much Regu<lb></lb>larity: but that I ſhould have learnt, that that ſame Moveable, <lb></lb>ſuſpended at a ſtring of an hundred yards long, being removed <lb></lb>from Perpendicularity one while ninety degrees, and another <lb></lb>while one degree onely, or half a degree, ſhould ſpend as much time <lb></lb>in paſſing this little, as in paſſing that great Arch, certainly would <lb></lb>never have come into my head, for I ſtill think, that it bordereth <lb></lb>upon Impoſsibility. </s> <s>Now I am in expectation to hear that theſe <lb></lb>petty Notions will aſsign me ſuch Reaſons of thoſe Muſical Pro<lb></lb>blems, as may, in part at leaſt, give me ſatisfaction.<lb></lb><arrow.to.target n="marg1076"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1076"></margin.target><emph type="italics"></emph>Every<emph.end type="italics"></emph.end> Pendulum <lb></lb><emph type="italics"></emph>hath the Time of <lb></lb>its Vibration ſo li<lb></lb>mited; that it is <lb></lb>not poſſible to make <lb></lb>it move under any <lb></lb>other Period.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>Above all things, you are to know, that every <emph type="italics"></emph>Pendu<lb></lb>lum<emph.end type="italics"></emph.end> hath the Time of its Vibrations ſo limited, and prefixed, that <lb></lb>it is impoſſible to make it move under any other Period, than that <lb></lb>onely one, which is natural unto it. </s> <s>Let any one take the ſtring in <lb></lb>hand, to which the Weight is faſtened, and trie all the wayes <lb></lb>he can to encreaſe or decreaſe the frequency of its Vibrations, <lb></lb>and he ſhall finde it labour in vain: but we may, on the contrary, <lb></lb>on a <emph type="italics"></emph>Pendulum,<emph.end type="italics"></emph.end> though grave and at reſt, by onely blowing up<lb></lb>on it, conferre a Motion, and a Motion conſiderably great, by <lb></lb>reiterating the blaſts, but under the Time that is properly be<lb></lb>longing to its Vibrations: for if at the firſt blaſt we ſhould have re<lb></lb>moved it from Perpendicularity half an Inch, adding a ſecond, <lb></lb>after that it being returned towards us, is ready to begin the ſe<lb></lb>cond Vibration, we ſhould conferre new Motion on it, and ſo <lb></lb>ſucceſſively with other blaſts, but given in Time, and not when <lb></lb>the <emph type="italics"></emph>Pendulum<emph.end type="italics"></emph.end> is comming towards us (for ſo we ſhould impede; <lb></lb>and not help the Motion) and ſo continuing with many Impul<lb></lb>ſes, we ſhould confer upon it ſuch an <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> that a greater <lb></lb>force by much than that of a blaſt of our breath, will be required <lb></lb>to ſtay it.</s></p><p type="main"> <s>SAGR. </s> <s>I have, from my childhood, obſerved, that one man a<lb></lb>lone, by means of theſe Impulſes, given in Time, hath been able <lb></lb>to towl a very great Bell, and when it was to ceaſe, I have ſeen <lb></lb>four or ſix men more lay hold on the Bell-rope, and they have all <pb xlink:href="040/01/773.jpg" pagenum="81"></pb>been raiſed from the ground: ſo many together being unable to <lb></lb>arreſt that <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> which one alone, with regular Pulls, had con<lb></lb>ferred upon the Bell.</s></p><p type="main"> <s>SALV. </s> <s>An example, that declareth my meaning with no leſſe </s></p><p type="main"> <s><arrow.to.target n="marg1077"></arrow.to.target><lb></lb>propriety than this that I have premiſed, doth ſute to render the <lb></lb>reaſon of the admirable Problem of the Chord of the Lute or Viol, <lb></lb>which moveth, and maketh not onely that really to ſound, which <lb></lb>is tuned to the Uniſon, but that alſo which is ſet to an Eighth <lb></lb>and a Fifth. </s> <s>The Chord being toucht, its Vibrations begin, and <lb></lb>continue all the Time that its Sound is heard to endure: theſe <lb></lb>Vibrations make the Air neer adjacent to vibrate and tremble, <lb></lb>whoſe tremblings and quaverings diſtend themſelves a great way, <lb></lb>and ſtrike upon all the Chords of the Inſtrument, and alſo of o<lb></lb><arrow.to.target n="marg1078"></arrow.to.target><lb></lb>thers neer unto it: the Chord that is ſet to an Uniſon, with that <lb></lb>which is toucht, being diſpoſed to make its Vibrations ^{*} in the <lb></lb>ſame Time, beginneth at the firſt impulſe to move a little, and <lb></lb><arrow.to.target n="marg1079"></arrow.to.target><lb></lb>a ſecond, a third, a twentieth, and many more, overtaking it, all <lb></lb>in juſt and Periodick Times, it receiveth at laſt, the ſame Tre<lb></lb>mulation, with that firſt touched, and one may clearly ſee it go, <lb></lb>dilating its Vibrations exactly according to the Pace of its Mo<lb></lb>ver. </s> <s>This Undulation that diſtendeth it ſelf thorow the Air, mo<lb></lb>veth, and makes to vibrate, not onely the Chords, but likewiſe <lb></lb>any other Body diſpoſed to trembling, and to vibrate in the very <lb></lb>Time of the trembling Chord: ſo that if we fix in the Sides of <lb></lb>the Inſtrument ſeveral ſmall pieces of Briſtles, or of other flexible <lb></lb>matters, you ſhall ſee upon the ſounding of the Viol, now one, <lb></lb>now another of thoſe Corpuſcles tremble, according as that <lb></lb>Chord is toucht, whoſe Vibrations return in the ſame Time: the <lb></lb>others will not move at the ſtriking of this Chord, nor will that <lb></lb>Briſtle tremble at the ſtriking of another Chord. </s> <s>If with the Bow <lb></lb>one ſmartly ſtrike the Baſe-Chord of a Viol, and ſet a drinking <lb></lb>Glaſſe, thin and ſmooth, neer unto it, if the Tone of the Chord <lb></lb>be an Uniſon to the Tone of the Glaſſe, the Glaſſe ſhall dance, <lb></lb>and ſenſibly re-ſound. </s> <s>Again, the ample dilating of the Tremor <lb></lb>or Undulation of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> about the Body reſounding, is ap<lb></lb>parently ſeen in making the Glaſſe to ſound, by putting a little <lb></lb>Water in it, and then chafing the brim or edge of it with the tip <lb></lb>of the finger: for the included Water is obſerved to undulate in <lb></lb>a moſt regular order: and the ſame effect will be yet more clearly <lb></lb>ſeen, by ſetting the foot of the Glaſſe in the bottom of a reaſo<lb></lb>nable large Veſſel, in which there is Water as high almoſt as to <lb></lb>the brim of the Glaſſe, for making it to ſound, as before, with <lb></lb>the Confrication of the finger, we ſhall ſee the trembling of the <lb></lb>Water to diffuſe it ſelf moſt regularly, and with great Velocity, <lb></lb>to a great diſtance round about the Glaſſe; and it hath many <pb xlink:href="040/01/774.jpg" pagenum="82"></pb>times been my fortune, in making a reaſonable big Glaſſe, almoſt <lb></lb>full of Water, to ſound as aforeſaid, to ſee the Waves in the <lb></lb>Water, at firſt formed with an exact equality; and it hapning <lb></lb>ſometimes, that the Tone of the Glaſſe riſeth an Eighth higher, at <lb></lb>the ſame inſtant, I have ſeen every one of the ſaid Waves to divide <lb></lb>themſelves in two: an accident that very clearly proveth the <lb></lb>forme of the Octave to be the double.</s></p><p type="margin"> <s><margin.target id="marg1077"></margin.target><emph type="italics"></emph>The Chord of a <lb></lb>Muſical Inſtru<lb></lb>ment touched, mo<lb></lb>veth, and maketh <lb></lb>the Chords ſet to an <lb></lb>Uniſon, Fifth and <lb></lb>Eighth, with it to <lb></lb>ſound; and why.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1078"></margin.target><emph type="italics"></emph>Sundry Problems <lb></lb>touching Muſical <lb></lb>Proportions, and <lb></lb>their Solutions.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1079"></margin.target>* Or under.</s></p><p type="main"> <s>SAGR. </s> <s>The ſame hath alſo befaln me more than once, to my <lb></lb>delight, and alſo benefit: for I ſtood a long time perplexed a<lb></lb>bout theſe Forms of Conſonants, not conceiving, that the Rea<lb></lb>ſon, commonly given thereof by the Authours that have hither<lb></lb>to written learnedly of Muſick, were ſufficiently convincing, <lb></lb>they tell us, that the Diapaſon, that is the Eighth, is contained <lb></lb>by the double, the Diapente, which we call the Fifth, by the <lb></lb>Seſquialter: for a Chord being diſtended on the ^{*} Monochord, <lb></lb><arrow.to.target n="marg1080"></arrow.to.target><lb></lb>ſtriking it all; and afterwards ſtriking but the half of it, by pla<lb></lb>cing a Bridge in the middle, one heareth an Eighth; and if the <lb></lb>Bridge be placed at a third of the whole Chord, touching the <lb></lb>whole, and then the two thirds, it ſoundeth a Fifth; whereupon <lb></lb>they infer, that the Eighth is contained between two and one, and <lb></lb>the Fifth between three and two. </s> <s>This Reaſon, I ſay, ſeemed to <lb></lb>me not neceſſarily concluding for the aſſigning juſtly the double <lb></lb>and the Seſquialter, for the natural Forms of the Diapaſon and <lb></lb>the Diapente. </s> <s>And that which moved me ſo to think, was this. <lb></lb></s> <s>There are three ways, by which we may ſharpen the Tone of a <lb></lb>Chord: one is, by making it ſhorter, the other is by diſtending; <lb></lb>or making it more tenſe; and the third is by making it thinner. </s> <s>If, <lb></lb>retaining the ſame Tention and thickneſſe, we would hear an <lb></lb>Eighth, it is neceſſary to ſhorten it to one half, which is done by <lb></lb>ſtriking it all, and then half. </s> <s>But if, retaining the ſame length <lb></lb>and thickneſſe, we would have it riſe to an Eighth, by ſcrewing <lb></lb>it higher, it will not ſuffice to ſtretch it double as much, but we <lb></lb>ſhall need the quadruple, ſo that, if before it was ſtretched by a <lb></lb>Weight of one pound, it will be needful to faſten four pound <lb></lb>to it to ſharpen it to an Eighth. </s> <s>And laſtly, if, keeping the ſame <lb></lb>length and Tention, we would have a Chord, that by being ſmal<lb></lb>ler, rendereth an Eighth, it will be neceſſary, that it retain onely <lb></lb>a fourth part of the thickneſſe of the other more Grave. </s> <s>And this <lb></lb>which I ſpeak of the Eighth, that is, that its form taken from the <lb></lb>Tention, or from the thickneſſe of the Chord, is in duplicate <lb></lb>proportion to that which it receiveth from the length, is to be <lb></lb>underſtoood of all other Muſical Intervals: for that which the <lb></lb>length giveth us in a Seſquialter proportion, <emph type="italics"></emph>i. </s> <s>e.<emph.end type="italics"></emph.end> by ſtriking it all, <lb></lb>and then the two thirds, if you would have it proceed from the <lb></lb>Tention, or from the diſgroſſing, you muſt double the Seſqui<pb xlink:href="040/01/775.jpg" pagenum="83"></pb>alter proportion, taking the double Seſquiquartan: and if the <lb></lb>Grave Chord were ſtretched by four pound weight, faſten to the <lb></lb>Acute not ſix, but nine: and, as to the thickneſſe, make the Grave <lb></lb>Chord thicker than the Acute, according to the proportion of <lb></lb>nine to four, to have the Fifth. </s> <s>Theſe being moſt exact Experi<lb></lb>ments, I thought, that I ſaw no reaſon, why theſe Sage Philoſo<lb></lb>phers ſhould eſtabliſh the form of the Eighth to be rather the dou<lb></lb>ble, than quadruple; and the Form of the Fifth to be rather the <lb></lb>Seſquialter, than the double Seſquiquartan. </s> <s>But becauſe the <lb></lb>numbring of the Vibrations of a Chord, which in giving a ſound, <lb></lb>are extreme frequent, is altogether impoſſible, I ſhould always <lb></lb>have been in doubt, whether or no it were true, that the more <lb></lb>Acute Chord of the Eighth, made in the ſame time, double the <lb></lb>number of the Vibrations of the more Grave, if the Waves, <lb></lb>which may be continued as long as you pleaſe, by making the <lb></lb>Glaſs to ſound and vibrate, had not ſenſibly ſhewn me, that in <lb></lb>the ſelf ſame moment that (ſometimes) the Sound is heard to riſe <lb></lb>to an Eighth, there are ſeen to ariſe other Waves more minute, <lb></lb>which with infinite ſmoothneſs cut in the middle each of thoſe <lb></lb>firſt.</s></p><p type="margin"> <s><margin.target id="marg1080"></margin.target>* An Inſtrument <lb></lb>of but one ſtring; <lb></lb>called by <emph type="italics"></emph>Mar<lb></lb>ſennus la Tromper<lb></lb>te Marine.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>An excellent Obſervation for diſtinguiſhing one by <lb></lb>one the Undulations ariſing from the Tremulation of the re<lb></lb>ſounding Body: which are thoſe that diffuſing themſelves tho<lb></lb>row the Air, make the titillation upon the Drum of our Ear, that <lb></lb>in our Soul becommeth a Sound: But whereas beholding and ob<lb></lb>ſerving them in the Water, endure no longer than the confrica<lb></lb>tion of the finger laſteth, and alſo in that time they are not per<lb></lb>manent, but are continually made and diſſolved, would it not <lb></lb>be an ingenious undertaking, if one could make, with much <lb></lb>exquiſiteneſſe, ſuch, as would continue a long time; I mean <lb></lb>Moneths and Years, ſo as to give a man opportunity meaſure, <lb></lb>and with eaſe to number them?</s></p><p type="main"> <s>SAGR. </s> <s>I aſſure you I ſhould highly value ſuch an Invention.</s></p><p type="main"> <s>SALV. </s> <s>The diſcovery was accidental, and the Obſervation <lb></lb>and applicative improvement of it onely were mine, and I hold <lb></lb>it to be a Circumſtance of noble Contemplation, althongh a buſi<lb></lb>neſſe in its ſelf ſufficiently homely. </s> <s>Scraping a Braſſe Plate with <lb></lb>an Iron Chizzel to fetch out ſome Spots, in moving the Chizzel to <lb></lb>and again upon it pretty quick, I heard it (once or twice amongſt <lb></lb>many gratings) to Sibilate and ſend forth a whiſtling noiſe, very <lb></lb>ſhrill and audible: and looking upon the Plate, I ſaw a long <lb></lb>row of ſmall ſtreaks, parallel to one another, and diſtant from <lb></lb>one another by moſt equal Intervals: returning to my ſcraping <lb></lb>again, I perceived by ſeveral trials, that in thoſe ſcrapings, and <lb></lb>thoſe onely that whiſtled, the Chizzel left the ſtreaks upon the <pb xlink:href="040/01/776.jpg" pagenum="84"></pb>Plate: but when the Scraping paſſed without any Sibilation, <lb></lb>there was not ſo much as the leaſt ſign of any ſuch ſtreaks. </s> <s>Re<lb></lb>peating the Experiment ſeveral times afterwards, ſcraping now <lb></lb>with greater, now with leſſe velocity, the Sibilation hapned to <lb></lb>be of a Tone ſometimes acuter, ſometimes graver; and I obſerved <lb></lb>the marks made in the more acute ſounds to be cloſer together, <lb></lb>and thoſe of the more grave farther aſunder: and ſometimes alſo, <lb></lb>according as the ſelf ſame ſcrape was made towards the end, with <lb></lb>greater velocity than at the beginning, the ſound was heard to <lb></lb>grow ſharper, and the ſtreaks were obſerved to ſtand thicker, <lb></lb>but ever with extream neatneſſe, and marked with exact equidi<lb></lb>ſtance: and farther-more, in the Sibilating ſcrapes; I felt the <lb></lb>Chizzel to ſhake or tremulate in my hand, and a certain chilneſſe <lb></lb>to run along my arm; and in ſhort, I ſaw the ſame effected upon <lb></lb>the Toole, which we uſe to obſerve in whiſpering, and after<lb></lb>wards ſpeaking aloud, for ſending forth the breath without <lb></lb>forming a ſound, we do not perceive any moving in the throat <lb></lb>and mouth, in compariſon of that which we diſcern to be in the <lb></lb>Wind-pipe and Throat of every one, in ſending forth the voice; <lb></lb>and eſpecially in grave and loud Tones. </s> <s>I have likewiſe ſome<lb></lb>times amongſt the Chords of the Viols, obſerved two that were <lb></lb>Uniſons to the Sibilations made by ſcraping after the manner I <lb></lb>told you, and that were moſt different in Tone, from which two <lb></lb>they preciſely were diſtant a perfect Fifth, and then meaſuring <lb></lb>the intervals of the ſtreaks of both the Scrapes, I ſaw the di<lb></lb>ſtance that conteined forty five ſpaces of the one, conteined <lb></lb>thirty of the other: which, indeed, is the Form attributed to the <lb></lb>Diapente. </s> <s>But here, before I proceed any farther, I will tell you, <lb></lb>that of the three manners of rendring a Sound Acute, that which <lb></lb>you refer to the ſlenderneſſe or fineneſſe of the Chord, may <lb></lb>with more truth be aſcribed to the Weight. </s> <s>For the alteration ta<lb></lb>ken from the thickneſſe, anſwereth, when the Chords are of the <lb></lb>ſame matter; and ſo a Gut-ſtring to make an Eighth, ought to be <lb></lb>four times thicker than the other Gut-ſtring; and one of Wier four <lb></lb>times thicker than another of Wier. </s> <s>But if I would make an Eighth <lb></lb>with one of Wier to one of Gut-ſtring, I am not to make it four <lb></lb>times thicker, but four times graver, ſo that, as to thickneſſe, <lb></lb>this of Wier ſhall not be four times thicker, but quadruple in <lb></lb>Gravity, for ſome times it ſhall be more ſmall than its reſpon<lb></lb>dent to the Acuter Eighth, that is of Gut-ſtring. </s> <s>Hence it com<lb></lb>meth to paſſe that, ſtringing an Inſtrument with Chords of Gold, <lb></lb>and another with Chords of Braſſe, if they ſhall be of the ſame <lb></lb>length, thickneſſe, and Tention, Gold being almoſt twice as <lb></lb>heavy, the Strings ſhall prove about a Fifth more Grave. </s> <s>And <lb></lb>here it is to be noted, that the Gravity of the Moveable more re<pb xlink:href="040/01/777.jpg" pagenum="85"></pb>ſiſteth the Velocity, than the thickneſſe doth; contrary to what <lb></lb>others at the firſt would think: for indeed, in appearance, its more <lb></lb>reaſonable, that the Velocity ſhould be retarded by the Reſiſtance <lb></lb>of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> againſt Opening in a Moveable thick and light, <lb></lb>than in one grave and ſlender: and yet in this caſe it happeneth <lb></lb>quite contrary. </s> <s>But purſuing our firſt Intent, I ſay, That the <lb></lb>ncereſt and immediate reaſons of the Forms of Muſical Intervals, <lb></lb>is neither the length of the Chord, nor the Tention, nor the <lb></lb>thickneſſe, but the proportion of the numbers of the Vibrations, <lb></lb>and Percuſſions of the Undulations of the Air that beat upon the <lb></lb>Drum of our Ear, which it ſelf alſo doth tremulate under the <lb></lb>ſame meaſures of Time. </s> <s>Having eſtabliſhed this Point, we may, <lb></lb>perhaps, aſſign a very apt reaſon, whence it commeth, that of <lb></lb>thoſe Sounds that are different in Tone, ſome Couples are re<lb></lb>ceived with great delight by our Sence, others with leſs, and <lb></lb>others occaſion in us a very great diſturbance; which is to ſeek a <lb></lb>reaſon of the Conſonances more or leſſe perfect, and of Diſlo<lb></lb>nances. </s> <s>The moleſtation and harſhneſſe of theſe proceeds, as I <lb></lb>believe, from the diſcordant Pulſations of two different Tones, <lb></lb>which diſproportionally ſtrike the Drum of our Ear: and the <lb></lb>Diſſonances ſhall be extreme harſh, in caſe the Times of the Vi<lb></lb>brations were incommenſurable. </s> <s>For one of which take that, <lb></lb>when of two Chords ſet to an Uniſon, one is ſounded, and ſuch <lb></lb>a part of another, as is the Side of the Square of its Diameter; <lb></lb>a Diſſonance like to the ^{*} Tritone, or Semi-diapente. </s> <s>Conſonan<lb></lb><arrow.to.target n="marg1081"></arrow.to.target><lb></lb>ces, and with pleaſure received, ſhall thoſe Couples of Sounds <lb></lb>be, that ſhall ſtrike in ſome order upon the Drum; which order <lb></lb>requireth, firſt, that the Pulſations made in the ſame Time be <lb></lb>commenſurable in number, to the end, the Cartillage of the Drum, <lb></lb>may not ſtand in the perpetual Torment of a double inflection of <lb></lb>allowing and obeying the ever diſagreeing Percuſſions. </s> <s>Therefore <lb></lb>the firſt and moſt grateful Conſonance ſhall be the Eighth, being, <lb></lb>that for every ſtroke, that the Grave-ſtring or Chord giveth upon <lb></lb>the Drum, the Acute giveth, two; ſo that both beat together <lb></lb>in every ſecond Vibration of the Acute Chord; and ſo of the <lb></lb>whole number of ſtrokes, the one half accord to ſtrike together, <lb></lb>but the ſtrokes of the Chords that are Uniſons, alwayes joyn <lb></lb>both together, and therefore they are, as if they were of the <lb></lb>ſame Chord, nor make they a Conſonance. </s> <s>The Fifth delighteth <lb></lb>likewiſe, in regard, that for every two ſtroaks of the Grave <lb></lb>Chord, the Acute giveth three: from whence it followeth, that <lb></lb>numbering the Vibrations of the Acute Chord, the third part of <lb></lb>that number will agree to beat together; that is, two Solitary ones <lb></lb>interpoſe between every couple of Conſonances; and in the Di<lb></lb>ateſſeron there interpoſe three. </s> <s>In the ſecond, that is in the <emph type="italics"></emph>Seſ-<emph.end type="italics"></emph.end><pb xlink:href="040/01/778.jpg" pagenum="86"></pb><emph type="italics"></emph>quioctave<emph.end type="italics"></emph.end> Tone for every nine Pulſations, one onely ſtrikes in Con<lb></lb>ſort with the other of the Graver Chord; all the reſt are Diſcords, <lb></lb>and received upon the Drum with regret, and are judged Diſſo<lb></lb>nances by the Ear.</s></p><p type="margin"> <s><margin.target id="marg1081"></margin.target>* Or a falſe Fifth.</s></p><p type="main"> <s>SIMP. </s> <s>I could wiſh this Diſcourſe were a little explained.</s></p><p type="main"> <s>SALV. </s> <s>Suppoſe this line A B the Space, and dilating of a Vi<lb></lb>bration of the Grave Chord; and the line C D that of the Acute <lb></lb>Chord, which with the other giveth the Eighth: and let A B be <lb></lb>divided in the midſt in E. </s> <s>It is manifeſt, that the Chords begin<lb></lb>ing to move at the terms A and C, by that time the Acute Vibra<lb></lb>tion ſhall be come to the term D, the other <lb></lb><figure id="id.040.01.778.1.jpg" xlink:href="040/01/778/1.jpg"></figure><lb></lb>ſhall be diſtended onely to the half E, which <lb></lb>not being the bound or term of the Motion, <lb></lb>it ſtrikes not: but yet a ſtroak is made in D. <lb></lb></s> <s>The Vibrations afterwards returning from D <lb></lb>to C, the other paſſeth from E to B, where<lb></lb>upon the two Percuſſions of B and C ſtrike <lb></lb>both together upon the Drum: and ſo con<lb></lb>tinuing to reiterate the like ſubſequent Vi<lb></lb>brations; one ſhall ſee, that the union of the <lb></lb>Percuſſions of the Vibrations C D with thoſe of A B, happen al<lb></lb>ternately every other time: but the Pullations of the terms A B <lb></lb>are alwayes accompanied with one of C D, and that alwayes the <lb></lb>ſame: which is manifeſt, for ſuppoſing that A and C ſtrike to<lb></lb>gether; in the time that A is paſſing to B, C goeth to D, and <lb></lb>returneth back to C: ſo that the ſtroaks at B and C are alſo <lb></lb>together. </s> <s>But now let the two Vibrations A B and C D be thoſe <lb></lb>that produce the Diapente, the times of which are in proportion <lb></lb>Seſquialter, and divide A B of the Grave Chord, in three equal <lb></lb>parts in E and O; And ſuppoſe the Vibrations to begin at the <lb></lb>ſame moment from the terms A and C: It is manifeſt, that at the <lb></lb>ſtroke that ſhall be made in D, the Vibration of A B ſhall have <lb></lb>got no farther than O, the Drum therefore receiveth the Pulſa<lb></lb>tion D onely: again in the return from D to C, the other Vibra<lb></lb>tion paſſeth from O to B, and returneth to O, making the Pul<lb></lb>ſation in B, which likewiſe is ſolitary, and in Counter-time, (an <lb></lb>accident to be conſidered:) for we having ſuppoſed the firſt <lb></lb>Pulſations to be made at the ſame moment in the terms A and C, <lb></lb>the ſecond, which was onely by the term D, was made as long after <lb></lb>as the time of the tranſition C D, that is A O, imports; but <lb></lb>that which followeth, made in B, is diſtant from the other one<lb></lb>ly ſo much as is the time O B, which is the half: afterwards con<lb></lb>tinuing the Recurſion from O to A, whilſt the other goeth from <lb></lb>C to D, the two Pulſations come to be made both at once in A <lb></lb>and D. </s> <s>There afterwards follow other Periods like to theſe, that <pb xlink:href="040/01/779.jpg" pagenum="87"></pb>is, with the interpoſition of two ſingle and ſolitary Pulſations of <lb></lb>the Acute Chord, and one of the Grave Chord, likewiſe ſolita<lb></lb>ry, is interpoſed between the two ſolitary ſtrokes of the Acute. </s> <s>So <lb></lb>that if we did but ſuppoſe the Time divided into Moments, that is, <lb></lb>into ſmall equal Particles: ſuppoſing that in the two firſt moments, <lb></lb>I paſſed from the Concordant Pulſations made in A and C to O <lb></lb>and D, and that in D, I make a Percuſſion: and that in the third <lb></lb>and fourth moment I return from D to C, ſtriking in C, and <lb></lb>that from O, I paſt to B, and returned to O, ſtriking in B; and <lb></lb>that laſtly in the fifth and ſixth moment from O and C, I paſt to <lb></lb>A and D ſtriking in both: we ſhall have the Pulſations diſtributed <lb></lb>with ſuch order upon the Drum, that ſuppoſing the Pulſations of <lb></lb>the two Chords in the ſame inſtant, it ſhall two moments after <lb></lb>receive a ſolitary Percuſſion, in the third moment anothor, ſoli<lb></lb>tary likewiſe, in the fourth another ſingle one, and two moments <lb></lb>after, that is, in the ſixth, two together; and here ends the <lb></lb>Period, and, if I may ſo ſay, Anomaly; which Period is oft-times <lb></lb>afterwards replicated.</s></p><p type="main"> <s>SAGR. </s> <s>I can hold no longer, but muſt needs expreſſe the con<lb></lb>tent I take in hearing reaſons ſo appoſitely aſſigned of effects that <lb></lb>have ſo long time held me in darkneſſe and blindneſſe. </s> <s>Now I <lb></lb>know why the Uniſon differeth not at all from a ſingle Tone: I <lb></lb>ſee why the Eighth is the principal Conſonance, but withal ſo <lb></lb>like to an Uniſon, that, as an Uniſon, it is taken and cojoyned <lb></lb>with others: it reſembleth an Uniſon, for that whereas the Pul<lb></lb>ſations of Chords ſet to an Uniſon, keep time in ſtriking, theſe <lb></lb>of the Grave Chord in an Eighth alwayes keep time with thoſe <lb></lb>of the Acute, and of theſe one interpoſeth alone, and in equal <lb></lb>diſtances, and as, one may ſay, without any variety, whereupon <lb></lb>that Conſonance is over ſweet. </s> <s>But the Fifth, with thoſe its <lb></lb>Counter-times, and with the interpoſures of two ſolitary Pulſa<lb></lb>tions of the Acute Chord, and one of the Grave Chord, <lb></lb>between the Couples of Diſcordant Pulſations, and thoſe <lb></lb>three ſolitary ones, with an interval of time, as great as the half of <lb></lb>that which interpoſeth between each Couple, and the ſolitary <lb></lb>Percuſſions of the Acute Chord, maketh ſuch a Titillation and <lb></lb>Tickling upon the Cartillage of the Drum of the Ear, that al<lb></lb>laying the Dulcity with a mixture of Acrimony, it ſeemeth at <lb></lb>one and the ſame time to kiſſe and bite.</s></p><p type="main"> <s>SALV. </s> <s>It is convenient, in regard I ſee, that you take ſuch de<lb></lb>light in theſe Novelties, that I ſhew you the way whereby the Eye <lb></lb>alſo, and not the Ear alone, may recreate it ſelf in beholding <lb></lb>the ſame ſports that the Ear feeleth. </s> <s>Suſpend Balls of Lead or o<lb></lb>ther heavy matter on three ſtrings of different lengths, but in <lb></lb>ſuch proportion, that while the longer maketh two Vibrations, <pb xlink:href="040/01/780.jpg" pagenum="88"></pb>the ſhorter may make four, and the middle one three; which <lb></lb>will happen, when the longeſt containeth ſixteen feet, or other <lb></lb>meaſures, of which the middle one containeth nine, and the <lb></lb>ſhorteſt four: and removing them all together from Perpendi<lb></lb>cularity, and then letting them go, you ſhall ſee a pleaſing In<lb></lb>termixtion of the ſaid <emph type="italics"></emph>Pendulums<emph.end type="italics"></emph.end> with various encounters, but <lb></lb>ſuch, that, at every fourth Vibration of the longeſt, all the three <lb></lb>will concurre in one and the ſame term together, and then again <lb></lb>will depart from it, reiterating anew the ſame Period: the which <lb></lb>commixture of Vibrations, is the ſame, that being made by the <lb></lb>Chords, preſents to the Ear an Eighth, with a Fifth in the midſt. <lb></lb></s> <s>And if you qualifie the length of other ſtrings in the like diſpo<lb></lb>ſure, ſo that their Vibrations anſwer to thoſe of other Muſical, <lb></lb>but Conſonant Intervals, you ſhall ſee other and other Inter<lb></lb>weavings, and alwaies ſuch, that in determinate times, and after <lb></lb>determinate numbers of Vibrations, all the ſtrings (be they three, <lb></lb>or be they four) will agree to joyn in the ſame moment, in the <lb></lb>term of their Recurſions, and from thence to begin ſuch another <lb></lb>Period: but if the Vibrations of two or more ſtrings are either <lb></lb>Incommenſurable, ſo, that they never return harmoniouſly to ter<lb></lb>minate determinate numbers of Vibrations, or though they be <lb></lb>not Incommenſurable, yet if they return not till after a long time, <lb></lb>and after a great number of Vibrations, then the ſight is con<lb></lb>founded in the diſorderly order of irregular Intermixtures, and <lb></lb>the Ear with wearineſſe and regret receiveth the intemperate Im<lb></lb>pulſes of the Airs Tremulations, that without Order or Rule, <lb></lb>ſucceſſively beat upon its Drum.</s></p><p type="main"> <s>But whither, my Maſters, have we been tranſported for ſo <lb></lb>many hours by various Problems, and unlook't for Diſcourſes? <lb></lb></s> <s>We have made it Night, and yet we have handled few or none of <lb></lb>the points propounded; nay we have ſo loſt our way, that I <lb></lb>ſcarſe remember our firſt entrance, and that ſmall Introduction, <lb></lb>which we laid down, as the Hypotheſis and beginning of the fu<lb></lb>ture Demonſtrations.</s></p><p type="main"> <s>SAGR It will be convenient, therefore, that we break up our <lb></lb>Conference for this time, giving our Minds leave to compoſe <lb></lb>themſelves in the Nights Repoſe, that we may to Morrow (if <lb></lb>you pleaſe ſo far to favour us) reaſſume the Diſcourſes deſired, <lb></lb>and chiefly intended.</s></p><p type="main"> <s>SALV. </s> <s>I ſhall not fail to be here to Morrow at the uſual <lb></lb>hour, to ſerve and enjoy you.</s></p><p type="head"> <s><emph type="italics"></emph>The End of the Firſt Dialogue.<emph.end type="italics"></emph.end></s></p></chap><chap><pb xlink:href="040/01/781.jpg" pagenum="89"></pb><p type="head"> <s>GALILEUS, <lb></lb>HIS <lb></lb>DIALOGUES <lb></lb>OF <lb></lb>MOTION.</s></p><p type="head"> <s>The Second Dialogue.</s></p><p type="head"> <s><emph type="italics"></emph>INTERLOCUTORS,<emph.end type="italics"></emph.end></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"></emph>Simplicius,<emph.end type="italics"></emph.end> and I, ſtaid expecting your com<lb></lb>ing, and we have been trying to recall to <lb></lb>memory our laſt Conſideration, which, as <lb></lb>the Principle and Suppoſition, on which <lb></lb>you ground the Concluſions that you in<lb></lb>tended to Demonſtrate to us, was that <lb></lb>Reſiſtance, that all Bodies have to <emph type="italics"></emph>Fracti<lb></lb>on,<emph.end type="italics"></emph.end> depending on that Cement, that con<lb></lb>nects and glutinates the parts, ſo, as that <lb></lb>they do not ſeparate and divide without a powerful attraction: <lb></lb>and our enquiry hath been, what might be the Cauſe of that <lb></lb>Coherence, which in ſome Solids is very vigorous; propounding <lb></lb>that of <emph type="italics"></emph>Vacuum<emph.end type="italics"></emph.end> for the principal, which afterwards occaſioned ſo <lb></lb>many Digreſſions as held us the whole day, and far from the <pb xlink:href="040/01/782.jpg" pagenum="90"></pb>matter at firſt propoſed, which was the Contemplation of the Re<lb></lb>ſiſtances of Solids to Fraction.</s></p><p type="main"> <s>SALV. </s> <s>I remember all that hath been ſaid, and returning to <lb></lb>our begun diſcourſe; What ever this Reſiſtance of Solids to brea<lb></lb>king by a violent attraction, is ſuppoſed to be, it is ſufficient, that it <lb></lb>is to be found in them: which, though it be very great againſt the <lb></lb>ſtrength of one that draweth them ſtreight out, it is obſerved to be <lb></lb>leſſe in forcing them tranſverſely, or ſidewaies: and thus we ſee, <lb></lb>for example, a rod of Steel, or Glaſſe to ſuſtain the length-waies a <lb></lb>weight of a thouſand pounds, which, faſtned at Right-Angles in<lb></lb>to a Wall, will break if you hang upon it but only fifty. </s> <s>And of <lb></lb>this ſecond Reſiſtance we are to ſpeak, enquiring, according to <lb></lb>what proportions it is found in Priſmes, and Cylinders of like and <lb></lb>unlike figure, length, and thickneſs, and, withal, of the ſame mat<lb></lb>ter. </s> <s>In which Speculation, I take for a known Principle, that which <lb></lb>in the Mechanicks is demonſtrated amongſt the Paſſions of the <lb></lb>Vectis, which we call the Leaver: namely, That in that uſe of the <lb></lb>Leaver, the Force is to the Reſiſtance in Reciprocal proportion, <lb></lb>as the Diſtances from the Fulciment to the ſaid Force and the Re<lb></lb>ſiſtance.</s></p><p type="main"> <s>SIMP. </s> <s>This <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> in his Mechanicks, demonſtrated before <lb></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></lb>for the firmneſſe oſ Demonſtration, I think, that <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end><lb></lb>ought to be preferred far before him, on one ſole Propoſition of <lb></lb>whom, by him demonſtrated in his Book, <emph type="italics"></emph>De Equiponderantium,<emph.end type="italics"></emph.end><lb></lb>depend the Reaſons, not only of the Leaver, but of the greater <lb></lb>part of the other Mechanick Inſtruments.</s></p><p type="main"> <s>SAGR. </s> <s>But ſince that this Principle is the foundation of all <lb></lb>that which you intend to demonſtrate to us, it would be very re<lb></lb>quiſite, that you produce us the proof of this ſame Suppoſition, <lb></lb>if it be not too long a work, giving us a full and perfect informati<lb></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></lb>you into the field of all our future Speculations, by an enterance <lb></lb>ſomewhat different from that of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end>; and that, ſuppo<lb></lb>ſing no more, but only that equal Weights, put into a Ballance of <lb></lb>equal Arms, make an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> (a Principle likewiſe ſuppoſed <lb></lb>by <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> himſelf.) I come, in the next place, to demon<lb></lb>ſtrate to you, that not only it is as true as the other, That unequal <lb></lb>Weights make an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> in a Stiliard of Armes unequal, ac<lb></lb>cording to the proportion of thoſe Weights Reciprocally ſuſpen<lb></lb>ded, but that it is one and the ſame thing to place equal Weights <lb></lb>at equal diſtances, as to place unequal Weights at diſtances that <lb></lb>are in Reciprocal Proportion to the Weights. </s> <s>Now for a plain <pb xlink:href="040/01/783.jpg" pagenum="91"></pb>Demonſtration of what I ſay, deſcribe a Solid Priſm or Cylinder <lb></lb>A B, [<emph type="italics"></emph>as in<emph.end type="italics"></emph.end> Figure 1. <emph type="italics"></emph>at the end of this Dialogue,<emph.end type="italics"></emph.end>] ſuſpended by <lb></lb>its ends at the Line H I, and ſuſtained by two Cords, H A, and I B. <lb></lb></s> <s>It is manifeſt, that if I ſuſpend the whole by the Cord C, placed <lb></lb>in the middle of the Beam or Ballance H I, the Priſm A B will be <lb></lb>equilibrated, one half of its weight, being on one ſide, and the other <lb></lb>half on the other ſide of the Point of Suſpenſion C by the Princi<lb></lb>ple that we preſuppoſed. </s> <s>Now let the Priſm be divided into un<lb></lb>equal parts by the Line D, and let the part D A be grea<lb></lb>ter, and D B leſſer; and to the end, that ſuch diviſion being made, <lb></lb>the Parts of the Priſm may reſt in the ſame ſcituation and conſti<lb></lb>tution, in reſpect of the Line H I, let us help it with a Cord E D, <lb></lb>which, being faſtened in the Point E, ſuſtaineth the parts A D, and <lb></lb>D B: It is not to be doubted, but that there being no local muta<lb></lb>tion in the Priſm, in reſpect of the Ballance H I, it ſhall remain in <lb></lb>the ſame ſtate of Equilibration. </s> <s>But it will reſt in the ſame Con<lb></lb>ſtitution likewiſe, if the Part of the Priſm, that is now ſuſpended at <lb></lb>the two extreams, or ends with Cords A H and D E, be hanged at <lb></lb>one ſole Cord G L, placed in the midſt: and likewiſe the other <lb></lb>part D B, will not change ſtate, if ſuſpended by the middle, and <lb></lb>ſuſtained by the Cord F M. </s> <s>So that the Cords H A, E D, and I B <lb></lb>being untied, and only the two Cords G L, and F M being left, the <lb></lb><emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> will ſtill remain, the Suſpenſion being ſtill made at <lb></lb>the Point C. Now, here let us confider, that we have two Grave <lb></lb>Bodies A D, and D B, hanging at the terms G and F of a Beam <lb></lb>G F, in which the <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> is made at the Point C: in ſuch <lb></lb>manner, that the diſtance of the ſuſpenſion of the Weight A D <lb></lb>from the Point C, is the Line C G, and the other part C F, is the <lb></lb>diſtance at which the other Weight D B hangeth. </s> <s>It remaineth, <lb></lb>therefore, only to be demonſtrated, that thoſe Diſtances have the <lb></lb>ſame proportion to one another, as the Weights themſelves have, <lb></lb>but reciprocally taken: that is, that the diſtance G C is to the di<lb></lb>ſtance C F, as the Priſm D B to the Priſm D A, which we prove <lb></lb>thus. </s> <s>The Line G E being the half of E H, and E F the half of <lb></lb>E I, all G F ſhall be equall to all H I, and therefore equal to C I: <lb></lb>and taking away the common part C F, the remainder G C ſhall <lb></lb>be equal to the remainder F I, that is, to F E: and C E taken in <lb></lb>common, the two Lines G E and C F ſhall be equal: and, there<lb></lb>fore, as G E, is to E F, ſo is F C, to C G: but as G C is to E F, ſo is <lb></lb>the double to the double; that is H E to E I; that is, the Priſm <lb></lb>A D to the Priſm D B. </s> <s>Therefore by Equality of proportion, <lb></lb>and by Converſion, as the diſtance G C is to the diſtance C F, ſo <lb></lb>is the Weight B D to the Weight D A: which is that that I was to <lb></lb>demonſtrate. </s> <s>If you underſtand this, I believe that you will not <lb></lb>ſcruple to admit, that the two Priſmes A D, and D B make an <pb xlink:href="040/01/784.jpg" pagenum="92"></pb><emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> in th Point C, for the half of the whole Solid A B is <lb></lb>on the right hand of the Suſpenſion C, and the other half on the <lb></lb>left; and that in this manner there are repreſented two equal <lb></lb>Weights, diſpoſed and diſtended at two equal diſtances. </s> <s>Again, <lb></lb>that the two Priſmes A D, and D B, being reduced into two Dice, <lb></lb>or two Balls, or into any two other Figures, (provided that they <lb></lb>keep the ſame Suſpenſions G and F) do continue to make their <lb></lb><emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> in the Point C, I believe none can deny, for that it is <lb></lb>moſt manifeſt, that Figures change not weight, where the ſame <lb></lb>quantity of matter is retained. </s> <s>From which we may gather the <lb></lb>general Concluſion, That two Weights, whatever they be, make <lb></lb>an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> at Diſtances reciprocally anſwering to their Gra<lb></lb>vities. </s> <s>This Principle, therefore, being eſtabliſhed, before we paſs <lb></lb>any farther, I am to propoſe to Conſideration, how theſe Forces, <lb></lb>Reſiſtances, Moments, Figures, may be conſidered in Abſtract, <lb></lb>and ſeparate from Matter, as alſo in Concrete and conjoyned <lb></lb>with Matter; and in this manner thoſe Accidents that agree with <lb></lb>Figures, conſidered as Immaterial, ſhall receive certain Modifica<lb></lb>tions, when we ſhall come to add Matter to them, and conſequent<lb></lb>ly Gravity. </s> <s>As for example, if we take a Leaver, as for inſtance <lb></lb>B A [<emph type="italics"></emph>as in<emph.end type="italics"></emph.end> Fig. </s> <s>2.] which, reſting upon the Fulciment E, we ap<lb></lb>ply to raiſe the heavy Stone D: It is manifeſt by the Principle de<lb></lb>monſtrated, that the Force placed at the end B, ſhall ſuffice to <lb></lb>equal the Reſiſtance of the Weight D, if ſo be, that its Moment <lb></lb>have the ſame proportion to the Moment of the ſaid D, that the <lb></lb>Diſtance A C hath to the Diſtance C B: and this is true, if we <lb></lb>confider no other Moments than thoſe of the ſimple Force in B, <lb></lb>and of the Reſiſtance in D, as if the ſaid Leaver were immaterial, <lb></lb>and void of Gravity. </s> <s>But if we bring to account the Gravity alſo <lb></lb>of the Inſtrument or Leaver it ſelf, which hapneth ſometimes to be <lb></lb>of Wood, and ſometimes of Iron; it is manifeſt, that the weight <lb></lb>of the Leaver, being added to the Force in B, it will alter the pro<lb></lb>portion, which it will be requiſite to deliver in other terms. </s> <s>And <lb></lb>therefore before we paſſe any farther, it is neceſſary, that we di<lb></lb>ſtinguiſh between theſe two waies of Conſideration, calling that a <lb></lb>taking it abſolutely, when we ſuppoſe the Inſtrument to be taken <lb></lb>in Abſtract, that is, disjunct from the Gravity of its own Matter; <lb></lb>but conjoyning the Matter, as alſo the Gravity, with ſimple and <lb></lb>abſolute Figures, we will phraſe the Figures conjoyn'd with the <lb></lb>Matter, Moment, or Force compounded.</s></p><p type="main"> <s>SAGR I muſt of neceſſity break the Reſolution I had taken, <lb></lb>not to give occaſion of digreſſing, for I ſhould not be able to ſet <lb></lb>my ſelf to hear what remaines with attention, if a certain ſcruple <lb></lb>were not removed that cometh into my head; and it is this, That <lb></lb>I gueſſe you make compariſon between the Force placed in B, and <pb xlink:href="040/01/785.jpg" pagenum="93"></pb>the total Gravity of the Stone D, of which Gravity me thinks, that <lb></lb>one, and that, very probably, the greater part, reſteth upon the <lb></lb>Plane of the Horizon: ſo that----</s></p><p type="main"> <s>SALV. </s> <s>I have rightly apprehended you, ſo that you need ſay <lb></lb>no more, but only take notice, that I named not the total Gravity <lb></lb>of the Stone, but ſpake of the Moment that it hath, and exerciſeth <lb></lb>at the Point A, the extream term of the Leaver B A, which is ever <lb></lb>leſs than the entire weight of the Stone; and is variable according <lb></lb>to the Figure of the Stone, and according as it hapneth to be more <lb></lb>or leſſe elevated.</s></p><p type="main"> <s>SAGR. </s> <s>I am ſatisfied in that particular, but I have one thing <lb></lb>more to deſire, namely, that for my perfect information, you would <lb></lb>demonſtrate to me the way, if there be one, how I may find what <lb></lb>part of the total weight that is, which cometh to be born by the <lb></lb>ſubjacent Plane, and what that which gravitates upon the Leaver <lb></lb>at the extream A.</s></p><p type="main"> <s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>ALV. </s> <s>Becauſe I can give you ſatisfaction in few words, I will <lb></lb>not fail to ſerve you: therefore, deſcribing a ſlight Figure thereof, <lb></lb>be pleaſed to ſuppoſe, that the Weight, whoſe Center of Gravity is <lb></lb>A, [<emph type="italics"></emph>as in<emph.end type="italics"></emph.end> Fig. </s> <s>3.] reſteth upon the Horizon with the term B, and <lb></lb>at the other end is born up by the Leaver C G, on the Fulciment <lb></lb>N, by a Power placed in G: and that from the Center A, and term <lb></lb>C, Perpendiculars be let fall to the Horizon, A O, and C F. </s> <s>I ſay, <lb></lb>That the Moment of the whole Weight ſhall have to the Moment <lb></lb>of the whole Power in G, a proportion compounded of the Di<lb></lb>ſtance G N to the Diſtance N C, and of F B to B O. Now, as the <lb></lb>Line F B is to B O, ſo let N C be to X. </s> <s>And the whole Weight A <lb></lb>being born by the two Powers placeed in B and C, the Power B is <lb></lb>to C, as the diſtance F O to O B: and by Compoſition, the <lb></lb>two Powers B and C together, that is, the total Moment of <lb></lb>the whole Weight A, is to the Power in C, as the Line F B is <lb></lb>to the Line B O; that is, as N C to X: But the Moment of <lb></lb>the Power in C is to the Moment of the Power in G, as the Di<lb></lb>ſtance G N is to N C: Therefore, by Perturbation of proportion, <lb></lb>the whole Weight A is to the Moment of the Power in G, as G N <lb></lb>to X: But the proportion of G N to X is compounded of the pro<lb></lb>portion G N to N C, and of that of N C to X; that is, of F B to <lb></lb>B O: Therefore the Weight A is to the Power that bears it up in <lb></lb>G, in a proportion compounded of G N to N C, and of that of <lb></lb>F B to B O: which is that that was to be demonſtrated. </s> <s>Now re<lb></lb>turning to our firſt intended Argument, all things hitherto decla<lb></lb>red being underſtood, it will not be hard to know the reaſon, <lb></lb>whence it cometh to paſſe that</s></p><pb xlink:href="040/01/786.jpg" pagenum="94"></pb><p type="head"> <s>PROPOSITION I.</s></p><p type="main"> <s><emph type="italics"></emph>A Solid Priſm or Cylinder of Glaſſe, Steel, Wood, or <lb></lb>other Frangible Matter, that being ſuſpended length<lb></lb>waies, will ſuſtain a very great Weight hanged <lb></lb>Thereat, will, Sidewaies, (as we ſaid even now) be <lb></lb>broken in pieces by a far leſſer Weight, according as <lb></lb>its length ſhall exceed its thickneſs.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Wherefore let us deſcribe the Solid Priſm A B C D, <lb></lb>fixed into a Wall by the Part A B, and in the <lb></lb>other extream ſuppoſe the Force of the Weight E; <lb></lb>(alwaies underſtanding the Wall to be erect to the Horizon, <lb></lb>and the Priſm or Cylinder faſtened in the Wall at Right-An<lb></lb>gles) it is manifeſt, that being to break, it will be broken in the place <lb></lb>B, where the Mortace in the Wall ſerveth for Fulciment, and B C <lb></lb>for the part of the Leaver in which lieth the force, and the thick<lb></lb>neſſe of the Solid B A is the other part of the Leaver, in which <lb></lb>lieth the Reſiſtance, which conſiſteth in the unfaſtening, or divi<lb></lb>ding, that is to be made of the part of the Solid B D, that is with<lb></lb>out the Wall from that which is within: and by what hath been <lb></lb>declared, the Moment <lb></lb><figure id="id.040.01.786.1.jpg" xlink:href="040/01/786/1.jpg"></figure><lb></lb>of the Force placed in <lb></lb>C, is to the Moment of <lb></lb>the Reſiſtance that lieth <lb></lb>in the thickneſſe of the <lb></lb>Priſm, that is, in the <lb></lb>Connection of the Baſe <lb></lb>B A, with the parts con<lb></lb>tiguous to it, as the <lb></lb>length C B is to the half <lb></lb>of B A: And therefore <lb></lb>the abſolute Reſiſtance <lb></lb>againſt Fraction that is <lb></lb>in the Priſm B D, <lb></lb>(which abſolute Reſi<lb></lb>ſtance is that which is <lb></lb>made by drawing it <lb></lb>downwards, for at that <lb></lb>time the motion of the Mover is the ſame with that of the Body <lb></lb>Moved) againſt the fracture to be made by help of the Leaver <pb xlink:href="040/01/787.jpg" pagenum="95"></pb>B C, is as the Length B C to the half of A B in the Priſm, which <lb></lb>in the Cylinder is the Semidiameter of its Baſe. </s> <s>And this is our firſt <lb></lb>Propoſition. </s> <s>And obſerve, that what I have ſaid ought to be un<lb></lb>derſtood, when the Confideration of the proper Weight of the So<lb></lb>lid B D is removed: which Solid I have taken as weighing nothing. <lb></lb></s> <s>But in caſe we would bring its Gravity to account, conjoyning it <lb></lb>with the Weight E, we ought to add to the Weight E the half of <lb></lb>the Weight of the Solid B D: ſo that the Weight B D being <lb></lb><emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> two pounds, and the Weight of E ten pounds, we are to <lb></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"></emph>Simplicius,<emph.end type="italics"></emph.end> hanging at the term C, <lb></lb>gravitates in reſpect of B C, with all its Moment of ten pounds, <lb></lb>whereas if only B D were pendent, it would weigh with its whole <lb></lb>Moment of two pounds; but, as you ſee, that Solid is diſtributed <lb></lb>thorow all the length B C, uniformly, ſo that its parts near to the <lb></lb>extream B, gravitate leſſe than the more remote: ſo that, in a word, <lb></lb>compenſating thoſe with theſe, the weight of the whole Priſm is <lb></lb>brought to operate under the Center of its Gravity, which anſwe<lb></lb>reth to the middle of the Leaver B C: But a Weight hanging at <lb></lb>the end C, hath a Moment double to that which it would have <lb></lb>hanging at the middle: And therefore the half of the Weight of <lb></lb>the Priſm ought to be added to the Weight E, when we would uſe <lb></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 ſelf, <lb></lb>me thinks, that the Power of both the Weights B D and E, ſo placed, <lb></lb>would have the ſame Moment, as if the whole Weight of B D, and <lb></lb>the double of E were hanged in the midſt of the Leaver B C.</s></p><p type="main"> <s>SALV. </s> <s>It is exactly ſo, and you are to bear it in mind. </s> <s>Here we <lb></lb>may immediatly underſtand</s></p><p type="head"> <s>PROPOSITION II.</s></p><p type="main"> <s><emph type="italics"></emph>How, and with what proportion, a Ruler, or Priſm, <lb></lb>more broad than thick, reſiſteth Fraction, better if it <lb></lb>be forced according to its breadth, than according to <lb></lb>its thickneſſe.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>For underſtanding of which, let a Priſm be ſuppoſed A D: <lb></lb>[<emph type="italics"></emph>as in<emph.end type="italics"></emph.end> Fig. </s> <s>4.] whoſe breadth is A C, and its thickneſs much <lb></lb>leſſer C B: It is demanded, why we would attempt to break <lb></lb>it edge-waies, as in the firſt Figure it will reſiſt the great Weight <lb></lb>T, but placed flat-waies, as in the ſecond Figure, it will not reſiſt <pb xlink:href="040/01/788.jpg" pagenum="96"></pb>X, leſſer than T: Which is manifeſted, ſince we underſtand the <lb></lb>Fulciment, one while under the Line B C, and another while under <lb></lb>C A, and the Diſtances of the Forces to be alike in both Caſes, to <lb></lb>wit, the length <emph type="italics"></emph>B<emph.end type="italics"></emph.end> D. </s> <s>But in the firſt Caſe, the Diſtance of the Re<lb></lb>ſiſtance from the Fulciment, which is the half of the Line C A, is <lb></lb>greater than the Diſtance in the other Caſe, which is the half of B <lb></lb>C: Therefore the Force of the Weight T, muſt of neceſſity be grea<lb></lb>ter than X, as much as the half of the breadth C A is greater than <lb></lb>half the thichneſſe B C, the firſt ſerving for the Counter-Leaver of <lb></lb>C A, and the ſecond of C B to overcome the ſame Reſiſtance, that <lb></lb>is the quantity of the <emph type="italics"></emph>Fibres,<emph.end type="italics"></emph.end> or ſtrings of the whole Baſe A B. <lb></lb></s> <s>Conclude we therefore, that the ſaid Priſm or Ruler, which is <lb></lb>broader than it is thick, reſiſteth, bresking more the edge-waies <lb></lb>than the flat-waies, according to the Proportion of the breadth to <lb></lb>the thickneſs.</s></p><p type="main"> <s>It is requiſite that we begin in the next place</s></p><p type="head"> <s>PROPOSITION III.</s></p><p type="main"> <s><emph type="italics"></emph>To find according to what proportion the encreaſe of the <lb></lb>Moment of the proper Gravity is made in a Priſm <lb></lb>or Cylinder, in relation to the proper Reſiſtance <lb></lb>againſt Fraction, whilſt that being parallel to the <lb></lb>Horizon, it is made longer and longer: Which Mo<lb></lb>ment I find to encreaſe ſucceſsively in duplicate Pro<lb></lb>portion to that of the prolongation.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>For demonſtration whereof, deſcribe the Priſm or Cylin<lb></lb>der A D, firmly faſtned in the Wall at the end A, and let <lb></lb>it be equidiſtant from the Horizon, and let the ſame be <lb></lb>underſtood to be prolonged as far as E, adding thereto the part <lb></lb><emph type="italics"></emph>B<emph.end type="italics"></emph.end> E. </s> <s>It is manifeſt, that the prolongation of the Leaver A <emph type="italics"></emph>B<emph.end type="italics"></emph.end><lb></lb>to C encreaſeth, by it ſelf alone, that is taken abſolutely, the <lb></lb>Moment of the Force preſſing againſt the Reſiſtance of the <lb></lb>Separation and Rupture to be made in A, according to the pro<lb></lb>portion of C A to <emph type="italics"></emph>B<emph.end type="italics"></emph.end> A: but, moreover, the Weight of the Solid <lb></lb>affixed <emph type="italics"></emph>B<emph.end type="italics"></emph.end> E, encreaſeth the Moment of the preſſing Gravity of <lb></lb>the Weight of the Solid A <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> according to the Proportion of <lb></lb>the Priſm A E to the Priſm A <emph type="italics"></emph>B<emph.end type="italics"></emph.end>; which proportion is the ſame <lb></lb>as that of the length A C, to the length A <emph type="italics"></emph>B<emph.end type="italics"></emph.end>: Therefore it is clear <pb xlink:href="040/01/789.jpg" pagenum="97"></pb>that the two augmentations of the Lengths and of the Gravities <lb></lb>being put together, the Moment compounded of both is in double <lb></lb><figure id="id.040.01.789.1.jpg" xlink:href="040/01/789/1.jpg"></figure><lb></lb>proportion to ei<lb></lb>ther of them. </s> <s>We <lb></lb>conclude there<lb></lb>fore, That the Mo<lb></lb>ments of the For<lb></lb>ces of Priſmes and <lb></lb>Cylinders of equal <lb></lb>thickneſſe, but of <lb></lb>unequal length, are <lb></lb>to one another in <lb></lb>duplicate proporti<lb></lb>on to that of their <lb></lb>Lengths; that is, <lb></lb>are as the Squares of <lb></lb>their Lengths.</s></p><p type="main"> <s>We will ſhew, in <lb></lb>the ſecond place, <lb></lb>according to what proportion the Reſiſtance of Fraction in Priſmes <lb></lb>and Cylinders encreaſeth, when they continue of the ſame length, <lb></lb>and encreaſe in thickneſs. </s> <s>And here I ſay, that</s></p><p type="head"> <s>PROPOSITION IV.</s></p><p type="main"> <s><emph type="italics"></emph>In Priſmes and Cylinders of equal length, but unequal <lb></lb>thickneſs, the Reſiſtance againſt Fraction encreaſeth <lb></lb>in a proportion iriple to the Diameters of their <lb></lb>Thickneſſes, that is, of their Baſes.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the two Cylinders be theſe A and <emph type="italics"></emph>B, [as in<emph.end type="italics"></emph.end> Fig. </s> <s>5.] <lb></lb>whoſe equal lengths are D G, and F H, the unequal <emph type="italics"></emph>B<emph.end type="italics"></emph.end>aſes <lb></lb>the Circles, whoſe Diameters are C D, and E F. </s> <s>I ſay, <lb></lb>that the Reſiſtance of the Cylinder <emph type="italics"></emph>B<emph.end type="italics"></emph.end> is to the Reſiſtance of the <lb></lb>Cylinder A againſt Fraction, in a proportion triple to that which <lb></lb>the Diameter F E hath to the Diameter D C. </s> <s>For if we conſider <lb></lb>the abſolute and ſimple Reſiſtance that reſides in the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>aſes, that <lb></lb>is, in the Circles E F, and D C to breaking, offering them vio<lb></lb>lence by pulling them end-waies, without all doubt, the Reſiſtance <lb></lb>of the Cylinder <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> is ſo much greater than that of the Cylinder A, <lb></lb>by how much the Circle E F is greater than C D; for the Fibres, <lb></lb>Filaments, or tenacious parts, which hold together the Parts of the <lb></lb>Solid, are ſo many the more. <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut if we conſider, that in offering <pb xlink:href="040/01/790.jpg" pagenum="98"></pb>them violence tranſverſly we make uſe of two Leavers; of which <lb></lb>the Parts or Diſtances, at which the Forces are applied are the Lines <lb></lb>D G, and F H, the Fulciments are in the Points D and F; but the <lb></lb>other Parts or Diſtances, at which the Reſiſtances are placed, are <lb></lb>the Semidiameters of the Circles D C and E F, becauſe the Fila<lb></lb>ments diſperſed thorow the whole Superficies of the Circles are as <lb></lb>if they were all reduced into the Centers: conſidering, I ſay, thoſe <lb></lb>Leavers, we would be underſtood to intend, that the Reſiſtance in <lb></lb>the Center of the Baſe E F againſt the Force of H, is ſo much grea<lb></lb>ter than the Reſiſtance of the Baſe C D, againſt the Force placed <lb></lb>in G, (and the Forces in G and H are of equal Leavers D G, and <lb></lb>F H) as the Semidiameter F E is greater than the Semidiameter <lb></lb>D C, the Reſiſtance againſt Fraction, therefore, in the Cylinder <lb></lb>B, encreaſeth above the Reſiſtance of the Cylinder A, according <lb></lb>to both the proportions of the Circles E F and D C, and of their <lb></lb>Semidiameters, or, if you will, Diameters: <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut the proportion of <lb></lb>the Circles is double of that of the Diameters; Therefore the pro<lb></lb>portion of the Reſiſtances, which is compounded of them, is in <lb></lb>triplicate proportion of the ſaid Diameters: Which is that which <lb></lb>I was to prove. <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut becauſe alſo the Cubes are in triplicate pro<lb></lb>portion to their Sides, we may likewiſe conclude, <emph type="italics"></emph>That the Reſi<lb></lb>ſtances of Cylinders of equal Length, are to one another as the Cubes <lb></lb>of their Diameters.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>From that which we have Demonſtrated we may likewiſe con<lb></lb>clude, that</s></p><p type="head"> <s>COROLARY.</s></p><p type="main"> <s><emph type="italics"></emph>The Reſiſtances of Priſms, and Cylinders of equal length are in <lb></lb>Seſquialter proportion to that of the ſaid Cylinders.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The which is manifeſt, becauſe the Priſms and Cylinders, <lb></lb>equal in height, are to one another, in the ſame proportion as <lb></lb>their <emph type="italics"></emph>B<emph.end type="italics"></emph.end>aſes; that is, the double of the Sides or Diameters of the <lb></lb>ſaid <emph type="italics"></emph>B<emph.end type="italics"></emph.end>aſes: <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut the Reſiſtances (as hath been demonſtrated) are <lb></lb>in triplicate proportion to the ſaid Sides or Diameters: Therefore <lb></lb>the proportion of the Reſiſtances is Seſquialter to the proportion <lb></lb>of the ſaid Solids, and, conſequently, to the Weights of the ſaid <lb></lb>Solids.</s></p><p type="main"> <s>SIMP. </s> <s>It is convenient, that, before we proceed any farther, I <lb></lb>be reſolved of a certain Doubt, and this it is, That I have not hi<lb></lb>therto heard propoſed to Conſideration another certain kind of <lb></lb>Reſiſtance, that, in my opinion, is ſucceſſively diminiſhed in So<lb></lb>lids, according as they are more and more prolonged, and not on<lb></lb>ly in uſing them ſidelongs, but alſo leng thwaies, in the ſelf ſame <pb xlink:href="040/01/791.jpg" pagenum="99"></pb>manner juſt as we ſee a very long Cord to be much leſſe apt to <lb></lb>ſuſtain a great weight, than if it were ſhort: ſo that I believe, that <lb></lb>a Ruler of Wood or Iron will ſuſtain a much greater weight, if it <lb></lb>ſhall be ſhort, than if it ſhall be very long; underſtanding it al<lb></lb>waies to be uſed lengthwaies, and not tranſverſly; and alſo <lb></lb>its own weight being accounted for, which in the longer is <lb></lb>greater.</s></p><p type="main"> <s>SALV. </s> <s>I fear, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that in this Point you, with many <lb></lb>others, are deceived, if ſo be, that I have rightly apprehended your <lb></lb>meaning, ſo that you would ſay, that a Cord <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> forty yards <lb></lb>long cannot ſuſtain ſo much, as if uſe were made but of one or two <lb></lb>yards of the ſame Rope.</s></p><p type="main"> <s>SIMP. </s> <s>That is it, which I would have ſaid, and as yet it ſeemeth <lb></lb>a very probable Propoſition.</s></p><p type="main"> <s>SALV. </s> <s>But I hold it not only improbable, but falſe: and think <lb></lb>that I can very eaſily reclaim you from your Errour. </s> <s>Therefore <lb></lb>let us ſuppoſe this Rope A B, [<emph type="italics"></emph>as in<emph.end type="italics"></emph.end> Fig. </s> <s>6.] faſtned on high by <lb></lb>the end A, and by the other end let there hang the Weight C, <lb></lb>by the force of which, the ſaid Rope is to be broken. </s> <s>Do you <lb></lb>aſſign me the particular place, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> where the Rupture is <lb></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 cauſe why it ſhould break in D.</s></p><p type="main"> <s>SIMP. </s> <s>The reaſon thereof is, becauſe the Rope was not ſtrong <lb></lb>enough in that part, to ſuſtain <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> an hundred pounds of weight, <lb></lb>for ſo much is the Rope D B with the Stone C.</s></p><p type="main"> <s>SALV. </s> <s>Therefore when ever ſuch a Rope ſhall come to be vio<lb></lb>lently ſtretched by thoſe hundred pounds of weight, it ſhall break <lb></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 ſame Weight, not <lb></lb>at the end of the Rope <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> but near to the point D, as for inſtance, <lb></lb>in E, or elſe did tye the Rope not at the height A, but very near, <lb></lb>and almoſt at the Point D it ſelf, as in F, tell me, I ſay, whether <lb></lb>the Point D would feel the ſame weight of an hundred pounds.</s></p><p type="main"> <s>SIMP. </s> <s>It would ſo, ſtill joyning the piece of Rope E <emph type="italics"></emph>B<emph.end type="italics"></emph.end> to the <lb></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></lb>by the ſaid hundred pounds of weight, it will break by your con<lb></lb>ceſſion. </s> <s>And yet F E, is a ſmall piece of the length A <emph type="italics"></emph>B<emph.end type="italics"></emph.end>: why do <lb></lb>you ſay then, that the long Rope is weaker than the ſhort one? <lb></lb><emph type="italics"></emph>B<emph.end type="italics"></emph.end>e content, therefore, to ſuffer your ſelf to be reclaimed from an <lb></lb>Errour, in which you have had many Companions, and thoſe in <lb></lb>other things very knowing. </s> <s>And let us go on: and having demon<lb></lb>ſtrated, that Priſms and Cylinders encreaſe their Moments above <pb xlink:href="040/01/792.jpg" pagenum="100"></pb>their Reſiſtances, according to the Squares of their Lengths (alwaies <lb></lb>provided, that they retain the ſame thickneſſe) and that likewiſe, <lb></lb>theſe that are equally long, but different in thickneſſe, encreaſe <lb></lb>their Reſiſtances according to the proportion of the Cubes of the <lb></lb>Sides or Diameters of their Baſes, we may enquire what befal<lb></lb>leth to thoſe Solids, being different in length and thickneſs, in which <lb></lb>I obſerve, that</s></p><p type="head"> <s>PROPOSITION V.</s></p><p type="main"> <s><emph type="italics"></emph>Priſms and Cylinders, of different length and thickneſs, <lb></lb>have their Reſiſtances againſt Fraction, in a propor<lb></lb>tion compounded of the proportion of the Cubes of the <lb></lb>Diameters of their Baſes, and of the proportion of <lb></lb>their lengths reciprocally taken.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let theſe two A B C, and D E F, [<emph type="italics"></emph>as in<emph.end type="italics"></emph.end> Fig. </s> <s>7.] be ſuch Cy<lb></lb>linders. </s> <s>I ſay, the Reſiſtance of the Cylinder A C ſhall be to <lb></lb>the Reſiſtance of the Cylinder D F, in a proportion com<lb></lb>pounded of the proportion of the Cube of the Diameter A B, to <lb></lb>the Gube of the Diameter D E, and of the proportion of the <lb></lb>Length E F to the Length B C. </s> <s>Suppoſe E G equal to B C, and to <lb></lb>the Lines A B, and D E, let C H be a third proportional, and I, <lb></lb>a fourth; and as E F is to B C, ſo let I be to S. </s> <s>And becauſe the <lb></lb>Reſiſtance of the Cylinder A C is to the Reſiſtance of the Cylin<lb></lb>der D G, as the Cube A B to the Cube D E; that is, as the Line <lb></lb>A B to the Line I: and the Reſiſtance of the Cylinder G D is to <lb></lb>the Reſiſtance of the Cylinder D F, as the Length F E is to the <lb></lb>Length E G; that is, as the Line I is to S: Therefore by Equali<lb></lb>ty of proportion, as the Reſiſtance of the Cylinder A C is to the <lb></lb>Reſiſtance of the Cylinder D F, ſo is the Line A B to S: But the <lb></lb>Line A B is to S, in a proportion compounded of A B to I, and of <lb></lb>I to S: Therefore the Reſiſtance of the Cylinder A C is to the Re<lb></lb>ſiſtance of the Cylinder D F, in a proportion compounded of A B <lb></lb>to I, that is, as the Cube of A B to the Cube of D E, and of the <lb></lb>proportion of the Line I to S; that is, of the Length E F to the <lb></lb>Length B C: Which was to be demonſtrated.</s></p><p type="main"> <s>After the Propoſition laſt demonſtrated, we will conſider what <lb></lb>hapneth between like Cylinders and Priſms, of which we will de<lb></lb>monſtrate, how that</s></p><pb xlink:href="040/01/793.jpg" pagenum="101"></pb><p type="head"> <s>PROPOSITION VI.</s></p><p type="main"> <s><emph type="italics"></emph>Of like Cylinders and Priſms the Moments compoun<lb></lb>ded, that is to ſay, reſulting from their Gravities, <lb></lb>and from their Lengths, which are, as it were, Lea<lb></lb>vers, have to one another a proportion Seſquialter to <lb></lb>that which is between the Reſiſtances of their ſame <lb></lb>Baſes.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>For demonſtration of which let us deſcribe the two like Cy<lb></lb>linders A B, and C D, [<emph type="italics"></emph>as in<emph.end type="italics"></emph.end> Fig. </s> <s>8.] I ſay, that the Mo<lb></lb>ment of the Cylinder A B, to overcome the Reſiſtance of its <lb></lb>Baſe B, hath to the Moment of C D, to overcome the Reſiſtance <lb></lb>of its Baſe C, a proportion Seſquialter to that which the ſame Re<lb></lb>ſiſtance of the Baſe B, hath to the Reſiſtance of the Baſe D: <lb></lb>And becauſe the Moments of the Solids A B, and C D, to over<lb></lb>come the Reſiſtances of their Baſes B and D, are compounded of <lb></lb>their Gravities, and of the Forces of their Leavers, and the Force <lb></lb>of the Leaver A B is equal to the Force of the Leaver C D, and <lb></lb>that becauſe the length A B hath the ſame proportion to the Semi<lb></lb>diameter of the Baſe B, (by the ſimilitude of the Cylinders) that <lb></lb>the Length C D hath to the Semidiameter of the Baſe D; it re<lb></lb>maineth, that the total Moment of the Cylinder A B, be to the <lb></lb>total Moment of C D, as the ſole Gravity of the Cylinder A B is <lb></lb>to the ſole Gravity of the Cylinder C D; that is, as the ſaid Cy<lb></lb>linder A B is to the ſaid C D: But theſe are in triplicate propor<lb></lb>tion to the Diameters of their Baſes <emph type="italics"></emph>B<emph.end type="italics"></emph.end> and D; and the Reſiſtances <lb></lb>of the ſame <emph type="italics"></emph>B<emph.end type="italics"></emph.end>aſes, being to one another as the ſaid <emph type="italics"></emph>B<emph.end type="italics"></emph.end>aſes, they are <lb></lb>conſequently in duplicate proportion to their ſame <emph type="italics"></emph>B<emph.end type="italics"></emph.end>aſes: There<lb></lb>fore the Moments of Cylinders are in Seſquialter proportion to <lb></lb>the Reſiſtances of their <emph type="italics"></emph>B<emph.end type="italics"></emph.end>aſes.</s></p><p type="main"> <s>SIMP. </s> <s>This Propoſition, indeed, is not only new, but unexpe<lb></lb>cted to me, and at firſt ſight, very remote from the judgment that <lb></lb>I ſhould have conjecturally paſt upon it: for in regard, that theſe <lb></lb>Figures are in all other reſpects alike, I ſhould have thought that <lb></lb>their Moments likewiſe ſhould have retained the ſame proportion <lb></lb>towards their proper Reſiſtances.</s></p><p type="main"> <s>SAGR. </s> <s>This is the Demonſtration of that Propoſition, that in <lb></lb>the beginning of our Diſcourſes, I ſaid, I thought------I had ſome <lb></lb>glimps of.</s></p><p type="main"> <s>SALV. </s> <s>That which now befalleth, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> hapned for ſome <pb xlink:href="040/01/794.jpg" pagenum="102"></pb>time to my ſelf, believing, that the Reſiſtances of like Solids were <lb></lb>alike, till that a certain, and that no very fixed or accurate Obſer<lb></lb>vation ſeemed to repreſent unto me, that Solids do not contain <lb></lb>an equal tenure in their Toughneſs, but that the bigger are leſſe <lb></lb>apt to ſuffer violent accidents, as luſty men are more damnified by <lb></lb>their falls than little children; and, as in the begining we ſaid, we <lb></lb>ſee a great <emph type="italics"></emph>B<emph.end type="italics"></emph.end>eam or Column break to pieces falling from the ſame <lb></lb>height, and not a ſmall Priſin or little Cylinder of Marble. </s> <s>This <lb></lb>ſame Obſervation gave me the hint for finding of that which I am <lb></lb>now about to demonſtrate; a Quality truly admirable, for that <lb></lb>amongſt the infinite Solid-like Figures, there are not ſo much <lb></lb>as two, whoſe Moments retain the ſame proportion towards their <lb></lb>proper Reſiſtances.</s></p><p type="main"> <s>SIMP. </s> <s>Now you put me in mind of ſomething inſerted by <emph type="italics"></emph>Ari<lb></lb>ſtotle<emph.end type="italics"></emph.end> amongſt his Mechanical Queſtions, where he would give a <lb></lb>Reaſon, whence it is, that <emph type="italics"></emph>B<emph.end type="italics"></emph.end>eams the longer they are, they are by ſo <lb></lb>much the more weak, and bend more and more, although the ſhort <lb></lb>ones be the ſlendereſt, and the long ones thickeſt: and, if I well re<lb></lb>member, he reduceth the Reaſon to the ſimple Leaver.</s></p><p type="main"> <s>SALV. </s> <s>It is very true, and becauſe the Solution ſeemeth not <lb></lb>wholly to remove the cauſe of doubting <emph type="italics"></emph>Monſignore di Guevara,<emph.end type="italics"></emph.end><lb></lb>who, the truth is, with his moſt learned <emph type="italics"></emph>Commentaries<emph.end type="italics"></emph.end> hath highly <lb></lb>enobled and illuſtrated that Work, enlargeth himſelf with other <lb></lb>accute Speculations for the obviating all difficulties, yet himſelf <lb></lb>alſo remaining perplexed in this point, whether, the lengths and <lb></lb>thickneſſes of ſuch Solid Figures, encreaſing with the ſelf ſame <lb></lb>proportion, they ought to retain the ſame tenure in their Tough<lb></lb>neſſes and Reſiſtances againſt their breaking, and likewiſe againſt <lb></lb>their bending. </s> <s>After I had long conſidered thereon, I have, in <lb></lb>this manner found, that which I am about to tell you. </s> <s>And firſt <lb></lb>I will demonſtrate that</s></p><pb xlink:href="040/01/795.jpg" pagenum="103"></pb><p type="head"> <s>PROPOSITION VII.</s></p><p type="main"> <s><emph type="italics"></emph>Of like and heavy Priſms or Cylinders there is one only, <lb></lb>and no more, that is reduced (being charged with its <lb></lb>own weight) to the ultimate ſtate between breaking <lb></lb>and holding it ſelf together: ſothat every greater, as <lb></lb>being unable to reſiſt its own weight, will break, <lb></lb>and every leſſer reſiſteth ſome Force that is employed <lb></lb>againſt it to break, it.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the heavy Priſm be A B [<emph type="italics"></emph>as in<emph.end type="italics"></emph.end> Fig 9.] reduced to the <lb></lb>utmoſt length of its Conſiſtance, ſo that being lengthned <lb></lb>never ſo little more it will break: I ſay, that this is the only <lb></lb>one amongſt all thoſe that are like unto it, (which yet are infinite) <lb></lb>that is capable of being reduced to that dubious and tickliſh ſtate; <lb></lb>ſo that every greater being oppreſſed with its own weight will <lb></lb>break, and every leſſer not, nay, will be able to reſiſt ſome additi<lb></lb>on of a new violence, over and above that of its own weight. <lb></lb></s> <s>Firſt, take the Priſm C E, like to, and greater than A B. </s> <s>I ſay, that <lb></lb>this cannot conſiſt, but will break, being overcome by its own <lb></lb>Gravity. </s> <s>Suppoſe the part C D as long as A B. </s> <s>And becauſe the <lb></lb>Reſiſtance C D is to that of A B, as the Cube of the thickneſſe of <lb></lb>C D to the Cube of the thickneſs of A B; that is, as the Priſm <lb></lb>C E to the Priſm A B (being alike:) Therefore the Weight of <lb></lb>C E is the greateſt that can be ſuſtained at the length of the Priſm <lb></lb>C D: But the Length C E is greater: Therefore the Priſm C E <lb></lb>will break. </s> <s>But let F G be leſſet: it ſhall be demonſtrated like<lb></lb>wiſe (ſuppoſing F H equal to B A) that the Reſiſtance of F G is <lb></lb>to that of A B, as the Priſm F G is to the Priſm A B, in caſe that the <lb></lb>Diſtance A B, that is F H, were equal to F G, but it is greater: <lb></lb>Therefore the Moment of the Priſm F G, placed in G, doth not <lb></lb>ſuffice to break the Priſm F G.</s></p><p type="main"> <s>SAGR. </s> <s>A moſt manifeſt and brief Demonſtration, inferring the <lb></lb>truth and neceſſity of a Propoſition that at firſt ſight ſeemeth far <lb></lb>from probability. </s> <s>It would be requiſite, therefore, to alter much <lb></lb>the proportion betwixt the Length and Thickneſſe of the greater <lb></lb>Priſm by making it thicker or ſhorter, to the end it might be re<lb></lb>duced to that nice ſtate of indifferency between holding and brea<lb></lb>king; and the Inveſtigation of that ſame State, as I think, would <lb></lb>be no leſſe ingenuous.</s></p><p type="main"> <s>SALV. Nay, rather more, as it is alſo more laborious: and I am <pb xlink:href="040/01/796.jpg" pagenum="104"></pb>ſure I have ſpent no ſmall time to find it; and I will now impart it <lb></lb>to you: Therefore</s></p><p type="head"> <s>PROP. VIII. PROBL. I.</s></p><p type="main"> <s><emph type="italics"></emph>A Cylinder or Priſm of the utmoſt length not to be bro<lb></lb>ken by its own weight, and alſo a greaver length, be<lb></lb>ing given, to find the thickneſſe of another Cylinder <lb></lb>or Priſm that under-given length is the only one, and <lb></lb>biggeſt, that can reſiſt its own weight.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the Cylinder B C [<emph type="italics"></emph>as in<emph.end type="italics"></emph.end> Fig. </s> <s>10.] be the biggeſt that <lb></lb>can reſiſt its own weight, and let D E be a Length greater <lb></lb>than A C; it is required to find the Thickneſſe of the Cylin<lb></lb>der, that under the Length D E is the greateſt reſiſting its own <lb></lb>weight. </s> <s>Let I be a third proportional to the Lengths D E, and <lb></lb>A C; and as D E is to I, ſo let the Diameter F D be to the Dia<lb></lb>meter B A: and make the Cylinder F E. </s> <s>I ſay, that this is the big<lb></lb>geſt, and only one amongſt all that are like to it that reſiſteth its <lb></lb>own weight. </s> <s>To the Lines D C and I let M be a third propor<lb></lb>tional, and O a fourth. </s> <s>And ſuppoſe F G equal to A C. </s> <s>And be<lb></lb>cauſe the Diameter F D is to the Diameter A B, as the Line D E <lb></lb>to I, and O is a fourth proportional to D E and I, the Cube of <lb></lb>F D ſhall be to the Cube of B A as D E is to O: But as the Cube of <lb></lb>F D is to the Cube of B A, ſo is the Reſiſtance of the Cylinder <lb></lb>D G to the Reſiſtance of the Cylinder B C: Therefore the Reſi<lb></lb>ſtance of the Cylinder D G is to that of the Cylinder B C, as the <lb></lb>Line D F is to O. </s> <s>And becauſe the Moment of the Cylinder B C <lb></lb>is equal to its Reſiſtance, if we ſhew that the Moment of the Cylin<lb></lb>der F E is to the Moment of the Cylinder B C, as the Reſiſtance <lb></lb>D F to the Reſiſtance B A; that is, as the Cube of F D to the Cube <lb></lb>of B A; that is, as the Line D E to O, we ſhall have our intent: <lb></lb>that is, that the Moment of the Cylinder F E is equal to the Reſi<lb></lb>ſtance placed in F D. </s> <s>The Moment of the Cylinder F E is to the <lb></lb>Moment of the Cylinder D G, as the Square of D E is to the <lb></lb>Square of A C; that is, as the Line D E to I: But the Moment of <lb></lb>the Cylinder D G is to the Moment of the Cylinder B C, as the <lb></lb>Square D F to the Square B A; that is, as the Square of D E to the <lb></lb>Square of I; that is, as the Square of I to the Square of M; that <lb></lb>is, as I to O: Therefore, by Equality of proportion, as the Mo<lb></lb>ment of the Cylinder F E is to the Moment of the Cylinder B C, <lb></lb>ſo is the Line D E to O; that is, the Cube D F to the Cube <lb></lb>B A; that is, the Reſiſtance of the Baſe D F to the Reſiſtance <pb xlink:href="040/01/797.jpg" pagenum="105"></pb>of the Baſe B A: Which is that that was ſought.</s></p><p type="main"> <s>SAGR This, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> is a long Demonſtration, and very hard <lb></lb>to be born in mind at the firſt hearing, therefore I could wiſh, that <lb></lb>you would pleaſe to repeat it.</s></p><p type="main"> <s>SALV. </s> <s>I will do what you ſhall command; but haply it would <lb></lb>be better to produce one more conciſe and ſhort: but then it will <lb></lb>be requiſite to deſcribe a Figure ſomewhat different.</s></p><p type="main"> <s>SAGR. </s> <s>The favour will then be the greater: and beſtow upon <lb></lb>me the draught of that already explained, that I may at my leaſure <lb></lb>conſider it again.</s></p><p type="main"> <s>SALV. </s> <s>I will not fail to ſerve you. </s> <s>Now, ſuppoſe a Cylinder A, <lb></lb><arrow.to.target n="marg1082"></arrow.to.target><lb></lb>[<emph type="italics"></emph>as in<emph.end type="italics"></emph.end> Fig. </s> <s>11.] the Diameter of whoſe Baſe let be the Line D C, <lb></lb>and let this A be the greateſt that can ſuſtain it ſelf and not break, <lb></lb>than which we will find a bigger, which likewiſe ſhall be the big<lb></lb>geſt alſo, and the only one that ſuſtaineth it ſelf. </s> <s>Let us deſire one <lb></lb>like to the ſaid A, and as long as the aſſigned Line, and let this be <lb></lb><emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> E, the Diameter of whoſe Baſe let be K L; and to the two <lb></lb>Lines D C, and K L let M N be a third proportional; which let be <lb></lb>the Diameter of the Baſe of the Cylinder X, in length equal to E. <lb></lb></s> <s>I ſay, that this X is that which we ſeek. </s> <s>And becauſe the Reſi<lb></lb>ſtance D C is to the Reſiſtance K L, as the Square D C to the <lb></lb><emph type="italics"></emph>S<emph.end type="italics"></emph.end>quare K L; that is, as the Square K L to the Square M N; that <lb></lb>is, as the Cylinder E to the Cylinder X; that is, as the Moment E <lb></lb>to the Moment X: But the Reſiſtance K L is to M N, as the Cube <lb></lb>of K L is to the Cube of M N; that is, as the Cube B C to the <lb></lb>Cube K L; that is, as the Cylinder A to the Cylinder E; that is, <lb></lb>as the Moment A to the Moment E: Therefore, by Perturbation <lb></lb>of proportion, as the Reſiſtance D C is to M N, ſo is the Moment <lb></lb>A to the Moment X: Therefore the Priſm X, is in the ſame Conſti<lb></lb>tution of Moment and Reſiſtance as the Priſm A.</s></p><p type="margin"> <s><margin.target id="marg1082"></margin.target><emph type="italics"></emph>The laſt Problem <lb></lb>performed another <lb></lb>way.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>But let us make the Problem more general, and let the Propo<lb></lb>ſition be this:</s></p><p type="main"> <s><emph type="italics"></emph>The Cylinder<emph.end type="italics"></emph.end> A C <emph type="italics"></emph>being given, and its Moment to-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1083"></arrow.to.target><lb></lb><emph type="italics"></emph>wards its Reſiſtance being ſuppoſed at pleaſure, and <lb></lb>any Length<emph.end type="italics"></emph.end> D E <emph type="italics"></emph>being aſsigned, to find the Thick<lb></lb>neſſe af the Cylinder whoſe Length is<emph.end type="italics"></emph.end> D E, <emph type="italics"></emph>and whoſe <lb></lb>Moment towards its Reſiſtance retaineth the ſame <lb></lb>proportion, that the Moment of the Cylinder<emph.end type="italics"></emph.end> A C <lb></lb><emph type="italics"></emph>doth to its Reſiſtance.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/798.jpg" pagenum="106"></pb><p type="margin"> <s><margin.target id="marg1083"></margin.target><emph type="italics"></emph>The laſt Propoſi<lb></lb>tion made more ge<lb></lb>neral.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Reaſſuming the above ſaid Figure and almoſt the ſame Me<lb></lb>thod, we will ſay: Becauſe the Moment of the Cylinder <lb></lb>F E hath the ſame proportion to the Moment of the part <lb></lb>D G, that the Square E D hath to the Square F G; that is that <lb></lb>the Line D E hath to I: and becauſe the Moment of the Cylinder <lb></lb>F G is to the Moment of the Cylinder A C, as the Square F D to <lb></lb>the Square A B; that is, as the Square D E to the Square I; that <lb></lb>is, as the Square I to the Square M; that is, as the Line I to O: <lb></lb>Therefore, <emph type="italics"></emph>ex æquali,<emph.end type="italics"></emph.end> the Moment of the Cylinder F E hath the <lb></lb>ſame proportion to the Moment of the Cylinder A C, that the <lb></lb>Line D E hath to the Line O; that is, that the Cube D E hath <lb></lb>to the Cube of I; that is, that the Cube of F D hath to the <lb></lb>Cube of A B; that is, that the Reſiſtance of the Baſe F D hath to <lb></lb>the Reſiſtance of the Baſe A B: Which was to be performed.</s></p><p type="main"> <s>Now, let it be obſerved, that from the things hitherto demonſtra<lb></lb>ted, we may plainly gather, how Impoſſible it is, not only for Art, but <lb></lb><arrow.to.target n="marg1084"></arrow.to.target><lb></lb>for Nature her ſelf to encreaſe her Machines to an immenſe Vaſt<lb></lb>neſſe: ſo that it would be impoſſible by Art to build extraordina<lb></lb>ry vaſt Ships, Palaces, or Temples, whoſe ^{*} Oars, Sail-yards, Beams, <lb></lb>Iron Bolts, and, in a word, their other parts ſhould conſiſt or hold <lb></lb>together: neither again could Nature make Trees of unmeaſura<lb></lb><arrow.to.target n="marg1085"></arrow.to.target><lb></lb>ble greatneſſe, for that their Arms or Bows being oppreſſed with <lb></lb>their own weight would at laſt break: and likewiſe it would be <lb></lb>impoſſible for her to make ſtructures of Bones for men, Horſes, or <lb></lb>other Animals, that might ſubſiſt, and proportionatly perform <lb></lb>their Offices, when thoſe Animals ſhould be augmented to im<lb></lb>menſe heights, unleſſe ſhe ſhould take Matter much more hard and <lb></lb>Refiſting than that which ſhe commonly uſeth, or elſe ſhould de<lb></lb>form thoſe Bones by augmenting them beyond their due Symetry, <lb></lb>and making the Figure or ſhape of the Animal to become mon<lb></lb>ſtrouſly big: Which haply was hinted by my moſt Witty Poet, <lb></lb>where deſcribing an huge Giant, he ſaith,</s></p><p type="margin"> <s><margin.target id="marg1084"></margin.target>* Oares are uſed <lb></lb>in the Ships or <lb></lb>Gallies of the <lb></lb>Mediterrane, up<lb></lb>on which our <lb></lb>Author was a <lb></lb>Coaſter.</s></p><p type="margin"> <s><margin.target id="marg1085"></margin.target><emph type="italics"></emph>Bones of Animals <lb></lb>magnified beyond <lb></lb>their ratural ſize, <lb></lb>would not ſubſiſt, if <lb></lb>it be required to <lb></lb>retain the ſame <lb></lb>proportion of thick<lb></lb>neſs and hardneſs <lb></lb>in them that is in <lb></lb>thoſe of Natural <lb></lb>Animals.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Non ſi puo compartir quanto ſia lungo,<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Si ſmiſuratamente è tutto groſſo.<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1086"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1086"></margin.target><emph type="italics"></emph>Example of the <lb></lb>Bone of an Animal <lb></lb>enlarged to thrice <lb></lb>the Natural pro<lb></lb>portion, how much <lb></lb>thicker it ought to <lb></lb>be to perform its <lb></lb>office.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And for a ſhort example of this that I ſay, [<emph type="italics"></emph>as in<emph.end type="italics"></emph.end> Fig. </s> <s>12.] I <lb></lb>have heretofore drawn the Figure of a Bone only trebled in <lb></lb>Length, and augmented in Thickneſſe in ſuch proportion, as that <lb></lb>it may in its great Animal perform the office proportionate to that <lb></lb>of the leſſer Bone in a ſmaller Animal, and the Figures are theſe: <lb></lb>whereby you ſee what a diſproportionate Figure that of the aug<lb></lb>mented Bone becometh. </s> <s>Whence it is manifeſt, that he that would <lb></lb>in an huge Giant keep the proportions that the Members have in <pb xlink:href="040/01/799.jpg" pagenum="107"></pb>an ordinary Man, muſt either find Matter much more hard and re<lb></lb>ſiſting to make Bone of, or elſe muſt admit that its Strength is in <lb></lb>proportion much more weak than in Men of middle Stature: other<lb></lb>wiſe, encreaſing the Giant to an immeaſurable height he would be <lb></lb>oppreſſed, and fall under his own weight. </s> <s>Whereas on the con<lb></lb>trary, in diminiſhing of Bodies we do not ſee the Strength and <lb></lb>Forces to diminiſh in the ſame proportion, nay, in the leſſer the <lb></lb>Robuſtiouſneſſe encreaſeth with a great proportion. </s> <s>So that I <lb></lb>believe, that a little Dog could carry on his back two or three Dogs <lb></lb>equal to himſelf, but I do not think that an Horſe could carry ſo <lb></lb>much as one ſingle Horſe of his own ſize.</s></p><p type="main"> <s>SIMP. </s> <s>But if it be ſo, I have great reaſon to doubt the Im<lb></lb>menſe bulks that we ſee in Fiſhes, for (if I rightly underſtand <lb></lb>you) a Whale ſhall be as big as ten Elephants, and yet they ſu<lb></lb>ſtain themſelves.</s></p><p type="main"> <s>SALV. </s> <s>Your doubt, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> prompts me with another Con<lb></lb>dition which I perceived not before, which is alſo able to make <lb></lb>Giants and other very big Animals to conſiſt, and act themſelves <lb></lb>no leſſe than ſmaller, and this will happen when not only Strength <lb></lb>is added to the Bones and other Parts, whoſe office it is to ſuſtain <lb></lb>their own and the ſupervenient weight; but the ſtructure of the <lb></lb>Bones being left with the ſame proportions, the ſame Fabricks <lb></lb>would juſt in the ſame manner, yea, with much more eaſe, con<lb></lb>ſiſt, when the Gravity of the matter of thoſe Bones, or that of <lb></lb>the Fleſh, or whatever elſe is to reſt it ſelf upon the Bones is dimini<lb></lb>ſhed in that proportion: and of this ſecond Artifice, Nature hath <lb></lb>made uſe in the framing of Fiſhes, making their Bones, and Pulps, <lb></lb>not only very light, but without any Gravity.</s></p><p type="main"> <s>SIMP. </s> <s>I ſee very well, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> whither your Diſcourſe ten<lb></lb>deth: you will ſay, that becauſe the Element of Water is the Ha<lb></lb>bitation of Fiſhes, which by its Corpulence, or, as others will, by <lb></lb>its Gravity diminiſheth the weight of Bodies demerged in it, for <lb></lb>that reaſon the Matter of Fiſhes, not weighing any thing, may be <lb></lb>ſuſtained without ſurcharging their Bones: but this doth not ſuf<lb></lb>fice, for although the reſt of the ſubſtance of the Fiſh weigh not, <lb></lb>yet without doubt the matter of their Bones hath its weight: <lb></lb>and who will ſay, that the Rib of a Whale that is as big as a <lb></lb>Beam doth not weigh very much, and in Water ſinketh to the Bot<lb></lb>tom? </s> <s>Theſe therefore ſhould not be able to ſubſiſt in ſo vaſt a <lb></lb>Bulk.</s></p><p type="main"> <s>SALV. </s> <s>You argue very cunningly; and for an anſwer to your <lb></lb>Doubt, tell me, whether you have obſerved Fiſhes to ſtand im<lb></lb>moveable under water at their pleaſures, and not to deſcend to<lb></lb>wards the Bottom, or raiſe themſelves towards the top without <lb></lb>making ſome motion with their Fins?</s></p><pb xlink:href="040/01/800.jpg" pagenum="108"></pb><p type="main"> <s>SIMP. </s> <s>This is a very manifeſt Obſervation.</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"></emph>The Cauſe why <lb></lb>Fiſhes do equili<lb></lb>brate themſelves <lb></lb>in the Water.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>This power therefore that the Fiſhes have to ſtay them<lb></lb>ſelves, as if they were immoveable in the midſt of the Water, is a <lb></lb>moſt infallible argument, that the Compofition of their Corporeal <lb></lb>Maſſe equalleth the Specifick Gravity of the Water, ſo that if <lb></lb>there be found in them ſome parts that are more grave than the <lb></lb>Water, it is neceſſarily requiſite that they have others ſo much <lb></lb>leſſe grave, ſo that the <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> may be ballanced. </s> <s>If therefore <lb></lb>the Bones be more grave, it is neceſſary that the Pulps, or other <lb></lb>Matters that are in them, be more light; and theſe will with their <lb></lb>lightneſſe counterpoiſe and compenſate the weight of the Bones. <lb></lb></s> <s>So that in Aquatick Animals the quite contrary hapneth to that <lb></lb>which befals the Terreſtrial, namely, that in the latter it is the of<lb></lb>fice of the Bones to ſuſtain their own weight, and the weight of <lb></lb>the Fleſh; and in the former, the <emph type="italics"></emph>Fleſh [if one may ſo call it]<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1088"></arrow.to.target><lb></lb>beareth up its own weight, and that of the Bones. </s> <s>And therefore <lb></lb>ceaſe to wonder how there may be moſt vaſt Animals in the Wa<lb></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"></emph>Aquatick Animals <lb></lb>greater than the <lb></lb>Terreſtrial, and for <lb></lb>what Reaſon.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SIMP. </s> <s>I am ſatisfied, and moreover obſerve, that theſe which <lb></lb>we call Terreſtrial Animals, ought with more reaſon to be called <lb></lb>Aerial; becauſe in the Air they really live, and by the Air they are <lb></lb>environ'd, and of the Air they breath.</s></p><p type="main"> <s>SAGR. </s> <s>The Diſcourſe of <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> pleaſeth me, as alſo his <lb></lb>Doubt and its Solution. </s> <s>And farthermore I comprehend very ea<lb></lb>ſily, that one of theſe huge Fiſhes being haul'd on ſhore, could not <lb></lb>perchance be able to ſuſtain it ſelf for any time; but that the Con<lb></lb>nections of the Bones being relaxed, its Maſſe would be cruſh'd un<lb></lb>der its own weight.</s></p><p type="main"> <s>SALV. </s> <s>For the preſent, I encline to the ſame Opinion: nor am <lb></lb>I far from thinking that the ſame would happen to that huge Ship, <lb></lb>which floating in the Sea is not diſſolved by its weight, and the bur<lb></lb>den of its Lading and Artilery, but on dry ground, and environed <lb></lb>with Air, it perhaps would fall in pieces. </s> <s>But let us purſue our bu<lb></lb>ſineſſe, and demonſtrate, that</s></p><pb xlink:href="040/01/801.jpg" pagenum="109"></pb><p type="head"> <s>PROP. IX. PROBL. II.</s></p><p type="main"> <s><emph type="italics"></emph>A Priſme or Cylinder with its weight, and the great<lb></lb>eſt Weight ſuſtained by it being given, to find the <lb></lb>greateſt Length, beyond which being prolonged. </s> <s>it <lb></lb>would break under its own Weight.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let there be given the Priſme A C (<emph type="italics"></emph>as in<emph.end type="italics"></emph.end> Fig. </s> <s>13.) with its <lb></lb>weight, and likewiſe let the Weight D be given, the great<lb></lb>eſt that can be ſuſtained by the extreme C: it is required to <lb></lb>finde the greateſt Length unto which the ſaid Priſme may be pro<lb></lb>longed, without breaking. </s> <s>As the weight of the Priſme A C is to <lb></lb>the Compound of the weights A C, with the double of the <lb></lb>Weight D, ſo let the length C A be to C A H: between which <lb></lb>let A G be a Mean-Proportional. </s> <s>I ſay that A G is the Length <lb></lb>ſought. </s> <s>For the depreſſing Moment of the Weight D in C, is <lb></lb>equal to the Moment of the double weight D, if it be placed in <lb></lb>the middle of A C, where is alſo the Center of the Moment of <lb></lb>the Priſme A C: The Moment, therefore, of the Reſiſtance of <lb></lb>the Priſme A C, which reſides in A, is equivalent to the gravi<lb></lb>tation of the double of the Weight D with the weight A C, but <lb></lb>hanged in the midſt of A C. </s> <s>And becauſe it hath been made, <lb></lb>that as the Moment of the ſaid Weights ſo ſituated, that is, of <lb></lb>the double of D, with A C, is to the Moment of A C, ſo is H A <lb></lb>to A C, between which A G is a Mean Proportional: There<lb></lb>fore the Moment of D doubled with the Moment of A C, is to <lb></lb>the Moment A C, as the Square G A to the Square A C: But the <lb></lb>preſſing Moment of the Priſme G A, is to the Moment of A C, <lb></lb>as the Square G A to the Square A C: Therefore the Length <lb></lb>A G is the greateſt that was ſought, namely, that unto which the <lb></lb>Priſme A G being prolonged, it would ſuſtain it ſelf, but beyond <lb></lb>it would break.</s></p><p type="main"> <s>Hitherto we have conſidered the Moments and Reſiſtances of <lb></lb>ſolid Priſmes and Cylinders, one end of which is ſuppoſed im<lb></lb>moveable, and to the other onely the Force of a preſſing weight <lb></lb>is applyed, conſidering it by it ſelf alone, or joyned with the <lb></lb>Gravity of the ſame Solid, or elſe the ſole Gravity of the ſaid <lb></lb>Solid. </s> <s>Now I deſire that we may ſpeak ſomething of thoſe ſame <lb></lb>Priſmes or Cylinders, in caſe they were ſuſtained at both ends, or <lb></lb>did reſt upon one ſole point taken between the ends. </s> <s>And firſt, <lb></lb>I ſay that,</s></p><pb xlink:href="040/01/802.jpg" pagenum="110"></pb><p type="head"> <s>PROPOSITION X.</s></p><p type="main"> <s><emph type="italics"></emph>The Cylinder that being charged with its own Weight <lb></lb>ſhall be reduced to its greateſt Length, beyond which <lb></lb>it would not ſuſtain it ſelf, whether it be born up in <lb></lb>the middle by one ſole Fulciment, or elſe by two at <lb></lb>the ends, may be double in length to that which <lb></lb>ſhould be faſtned in the Wall, that is ſuſtained at but <lb></lb>one end.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Which of it ſelt is very obvious; for if we ſhall ſup<lb></lb>poſe of the Cylinder which I deſcribe A B C, its <lb></lb>half A B to be the utmoſt Length that is able to be <lb></lb>ſuſtained, being faſtened at the end B, it ſhall be ſuſtained in the <lb></lb>ſame manner, if being laid upon the Fulciment G, it ſhall be <lb></lb>counterpoiſed by its other half B C. </s> <s>And likewiſe, if of the Cy<lb></lb>linder D E F, the Length ſhall be ſuch that onely one half of it <lb></lb>can be ſuſtained, being faſtened at the end D, and conſequent<lb></lb>ly the other E F, fixed at the end F; it is manifeſt, that placing <lb></lb>the Fulciments H and I under the ends D and F, every Moment <lb></lb>of Force or of Weight that is added in E, will there make the <lb></lb>Fracture.</s></p><p type="main"> <s>That which requireth a more ſubtil Speculation is, when ſub<lb></lb>ſtracting from the proper Gravity of ſuch Solids, it were pro<lb></lb>pounded to us</s></p><p type="head"> <s>PROP. XI. PROBL. III.</s></p><p type="main"> <s><emph type="italics"></emph>To find whether that Force or weight, that being ap<lb></lb>plied to the middle of a Cylinder ſuſtained at the <lb></lb>ends, would ſuffice to break it, could do the ſame, <lb></lb>applied in any other place, neerer to one end than to <lb></lb>the other.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>As for Example, whether we deſiring to break a Staffe <lb></lb>and took it with the ends in our hands, and ſetting our <lb></lb>knee, to the midſt of it, the ſame Force that ſhould ſuf<lb></lb>fice to break it in that manner, would alſo ſuffice in caſe the knee <pb xlink:href="040/01/803.jpg" pagenum="111"></pb>were ſet, not in the midſt, 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"></emph>Ariſtotle<emph.end type="italics"></emph.end> in his <lb></lb><emph type="italics"></emph>Mechanical Queſtions.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>The Queſtion of <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> is not preciſely the ſame, <lb></lb>for he ſeeks no more, but to render a reaſon why leſſe labour is <lb></lb>required to break the Staffe, holding the hands at the ends of it, <lb></lb>that is, far diſtant from the Knee, than if we held them neerer: <lb></lb>and he giveth a general Reaſon of the ſame, reducing the cauſe <lb></lb>of it to the Leavers, which are longer when the Arms are ex<lb></lb>tended, graſping the ends. </s> <s>Our Queſtion addeth ſomething <lb></lb>more, ſeeking whether, ſetting the Knee in the midſt, or in ano<lb></lb>ther place, but alwayes keeping the hands at the ends, the ſame <lb></lb>Force ſerveth in all ſituations.</s></p><p type="main"> <s>SAGR. </s> <s>At firſt apprehenſion it ſhould ſeem that it doth, for <lb></lb>that the two Leavers retain in a certain faſhion the ſame Moment, <lb></lb>ſeeing that as the one is ſhortned, the other is lengthened.</s></p><p type="main"> <s>SALV. </s> <s>Now you ſee, how eaſie it is to make Equivocations, <lb></lb>and with what caution and circumſpection we are to walk, leaſt <lb></lb>we run into them. </s> <s>This that you ſay, and which indeed at the <lb></lb>firſt ſight carrieth with it ſo much of probability, is in the ſtrict<lb></lb>neſſe of it ſo falſe, that whether the Knee, which is the Fulci<lb></lb>ment of the two Leavers, be placed or not placed in the midſt, <lb></lb>it maketh ſuch alteration, that of that Force which would ſuffice <lb></lb>to make the Fracture in the midſt, it being to be made in ſome <lb></lb>other place, it will not ſuffice to apply four times ſo much, nor <lb></lb>ten, nor an hundred, no nor a thouſand. </s> <s>Upon this we will <lb></lb>make ſome general Conſideration, and then we will come to the <lb></lb>Specifick Determination of the Propoſition, according to which, <lb></lb>the Forces for making of Fractures gradually vary more in one <lb></lb>point than in another.</s></p><p type="main"> <s>Let us firſt deſigne this Truncheon A B to be broken in the <lb></lb>midſt upon the Fulciment C, and neer unto that let us deſigne <lb></lb>it again, but under the Characters D E, to be broken on the <lb></lb>Fulciment F, remote from the middle. </s> <s>Firſt it is manifeſt, that <lb></lb>the Diſtances A C and C B being equal, the Force ſhall be ſha<lb></lb>red equally in the ends B and A. Again, according as the Di<lb></lb>ſtance D F groweth leſſe than the Diſtance A C, the Moment <lb></lb>of the Force placed in D groweth leſſe than the Moment in A, <lb></lb>that is placed at the Diſtance C A, and leſſeneth according to <lb></lb>the proportion of the Line D F to A C; and conſequently, it is <lb></lb>requiſite to encreaſe it to equalize or exceed the Reſiſtance of F: <lb></lb>But the Diſtance D F may diminiſh <emph type="italics"></emph>in infinitum,<emph.end type="italics"></emph.end> in relation to <lb></lb>the Diſtance A C: Therefore it is requiſite, that it be poſſible for <lb></lb>the Force to be applyed in D, to encreaſe <emph type="italics"></emph>in infinitum,<emph.end type="italics"></emph.end> that it <lb></lb>may countervail the Reſiſtance in F. But, on the contrary, ac<pb xlink:href="040/01/804.jpg" pagenum="112"></pb>cording as the Diſtance F E encreaſeth above C B, it is requiſite <lb></lb>to diminiſh the Force in E, that it may compenſate the Reſi<lb></lb>ſtance in F: But the Diſtance F E in relation to C B, cannot en<lb></lb>creaſe <emph type="italics"></emph>in infinitum,<emph.end type="italics"></emph.end> by drawing the Fulciment F towards the end <lb></lb>D, no nor yet to the double: Therefore, the Force in E, that it <lb></lb>may compenſate the Reſiſtance in F, ſhall be alwayes more than <lb></lb>half of the Force in B. </s> <s>We may comprehend, therefore, the ne<lb></lb>ceſſity of augmenting the Moments of the Collected Forces in E <lb></lb>and D infinitely to equalize or exceed the Reſiſtance placed in F, <lb></lb>according as the Fulciment F ſhall approach neerer and neerer <lb></lb>to the end D.</s></p><p type="main"> <s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>AGR. </s> <s>What will <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> ſay to this? </s> <s>Muſt he not con<lb></lb>feſſe the Virtue of Geometry to be a more powerful inſtrument <lb></lb>than all others, to ſharpen the Wit, and diſpoſe it to diſcourſe <lb></lb>and ſpeculate well? </s> <s>and that <emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> had great reaſon to deſire that <lb></lb>his Scholars ſhould be well grounded in the Mathematicks? </s> <s>I <lb></lb>have very well underſtood the nature of the Leaver, and how <lb></lb>that its Length encreaſing or decreaſing, the Moment of the <lb></lb>Force and of the Reſiſtance augmented or diminiſhed, and yet in <lb></lb>the determination of the preſent Problem I deceived my ſelf, and <lb></lb>that not a little, but infinitely much.</s></p><p type="main"> <s>SIMP. </s> <s>The truth is, I begin to ſee that Logick, although it <lb></lb>be a moſt appoſite Inſtrument to regulate our Diſcourſe, doth <lb></lb>not attain, as to the prompting of the Mind with Invention, <lb></lb>unto the acuteneſſe of Geometry.</s></p><p type="main"> <s>SAGR. </s> <s>In my conceit, Logick giveth us to underſtand, whe<lb></lb>ther the Diſcourfes and Demonſtrations already made and found <lb></lb>are concluding, but that it teacheth us how to finde concluding <lb></lb>Diſcourſes and Demonſtrations; the truth is, I do not believe: <lb></lb>But it will be better, that <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> ſhew us according to what pro<lb></lb>portion the Moments of the Forces do go increaſing, to overcome <lb></lb>the Reſiſtance of the ſame Piece of Wood, according to the ſe<lb></lb>veral places of the Fracture.</s></p><p type="main"> <s>SALV. </s> <s>The proportion that you ſeek, proceedeth after ſuch <lb></lb>a manner, that</s></p><pb xlink:href="040/01/805.jpg" pagenum="113"></pb><p type="head"> <s>PROPOSITION XII.</s></p><p type="main"> <s><emph type="italics"></emph>If in the length of a Cylinder we ſhall marke two places, <lb></lb>upon which we would make the Fracture of the ſaid <lb></lb>Cylinder, the Reſiſtances of thoſe two places have <lb></lb>the ſame proportion to each other, as have the Re<lb></lb>ctangles made by the Diſtances of thoſe places <lb></lb>reciprocally taken.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the two Forces (<emph type="italics"></emph>as in<emph.end type="italics"></emph.end> Fig. </s> <s>16.) be A and B the leaſt, to <lb></lb>break in C, and E and F likewiſe the leaſt, to break in D. <lb></lb></s> <s>I ſay the Forces A and B have the ſame proportion to the <lb></lb>Forces E and F, that the Rectangle A D B hath to the Rectan<lb></lb>gle A C B. </s> <s>For the Forces A and B, have to the Forces E and F, a <lb></lb>proportion compounded of the Forces A and B, to the Force <lb></lb>B, of B to F, and of F to E and E: But as the Forces A and <lb></lb>B are to the Force B, ſo is the Length B A to A C; and as the <lb></lb>Force B is to F, ſo is the Line D B to B C; and as the Force F is <lb></lb>to F and E, ſo is the Line D A to A B: Therefore the Forces A <lb></lb>and B have to the Forces E and F a proportion compounded of <lb></lb>theſe three, namely, of B A to A C, of D B to B C, and of D A <lb></lb>A B. </s> <s>But of the two proportions D A to A B, and A B to A C, <lb></lb>is compounded the proportion of D A to A C: Therefore the <lb></lb>Forces A and B have to the Forces E and F, the proportion com<lb></lb>pounded of this D A to A C, and of the other D B to D C. <lb></lb></s> <s>But the Rectangle A D B hath to the Rectangle A C B, a pro<lb></lb>portion compounded of the ſame D A to A C, and of D B to <lb></lb>B C: Therefore the Forces A and B are to the Forces E and F, <lb></lb>as the Rectangle A D B is to the Rectangle A C B; which is as <lb></lb>much as to ſay, the Reſiſtance againſt Fraction in C, hath the <lb></lb>ſame proportion to the Reſiſtance againſt Fraction in D, that <lb></lb>the Rectangle A D B hath to the Rectangle A C B: Which was <lb></lb>to be demonſtrated.</s></p><p type="main"> <s>In conſequence of this Theorem we may reſolve a Problem of <lb></lb>great Curioſity; and it is this:</s></p><pb xlink:href="040/01/806.jpg" pagenum="114"></pb><p type="head"> <s>PROP. XIII. PROBL. IV.</s></p><p type="main"> <s><emph type="italics"></emph>There being given the greateſt Weight that can be ſup<lb></lb>ported at the middle of a Cylinder or Priſme, where <lb></lb>the Reſiſtance is leafl; and there being given a <lb></lb>Weight greater than that, to find in the ſaid Cylin<lb></lb>der, the point at which the given greater Weight may <lb></lb>be ſupporited as the greateſt Weight.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the given weight greater than the greateſt weight that <lb></lb>can be ſupported at the middle of the Cylinder A B, have <lb></lb>unto the ſaid greateſt weight, the proportion of the line E <lb></lb>to F: it is required to find the point in the Cylinder at which the <lb></lb>ſaid given weight commeth to be ſupported as the biggeſt. </s> <s>Be<lb></lb>tween E and F let G be a Mean-Proportional; and as E is to G, <lb></lb>ſo let A D be to S, S ſhall be leſſer than A D. </s> <s>Let A D be the <lb></lb>Diameter of the Semicircle A H D: in which ſuppoſe A H equal <lb></lb>to S; and joyn together H and D, and take D R equal to it. <lb></lb></s> <s>I ſay that R is the point ſought, at which the given weight, <lb></lb>greater than the greateſt that can be ſupported at the middle of the <lb></lb>Cylinder D, would become as the greateſt weight. </s> <s>On the length <lb></lb><emph type="italics"></emph>B<emph.end type="italics"></emph.end>A deſcribe the Semicircle A N B, and raiſe the Perpendicular <lb></lb>RN, and conjoyn N and <lb></lb>D: And becauſe the two <lb></lb><figure id="id.040.01.806.1.jpg" xlink:href="040/01/806/1.jpg"></figure><lb></lb>Squares N R and R D are <lb></lb>equal to the Square N D; <lb></lb>that is, to the Square A D; <lb></lb>that is, to the two A H and <lb></lb>and H D; and H D is equal <lb></lb>to the Square D R: There<lb></lb>fore the Square N R, that <lb></lb>is, the Rectangle A R B <lb></lb>ſhall be equal to the Square A H; that is, to the Square S: But <lb></lb>the Square S is to the Square A D, as F to E; that is, as the <lb></lb>greateſt ſupportable Weight at D to the given greater Weight: <lb></lb>Therefore this greater ſhall be ſupported at R, as the greateſt <lb></lb>that can be there ſuſtained. </s> <s>Which is that that we ſought.</s></p><p type="main"> <s>SAGR. </s> <s>I underſtand you very well, and am conſidering that <lb></lb>the Priſme A B having alwayes more ſtrength and reſiſtance a<lb></lb>gainſt Preſſion in the parts that more and more recede from the <lb></lb>middle, whether in very great and heavy Beams one may take <pb xlink:href="040/01/807.jpg" pagenum="115"></pb>away a pretty big part towards the end with a notable alleviation <lb></lb>of the weight; which in Beams of great Rooms would be commo<lb></lb>dious, and of no ſmall proſit. </s> <s>And it would be pretty, to find what <lb></lb>Figure that Solid ought to have, that it might have equal Reſi<lb></lb>ſtance in all its parts; ſo as that it were not with more eaſe to be <lb></lb>broken by a weight that ſhould preſſe it in the midſt, than in any <lb></lb>other place.</s></p><p type="main"> <s>SALV. </s> <s>I was juſt about to tell you a thing very notable and <lb></lb>pleaſant to this purpoſe. </s> <s>I will aſſume a brief Scheme for the bet<lb></lb>ter explanation of my meaning. </s> <s>This Figure D B is a Priſm, whoſe <lb></lb>Reſiſtance againſt Fraction in the term A D by a Force preſſing <lb></lb>at the term B, is leſſe than the Reſiſtance that would be found in <lb></lb>the place C I, by how much the length C B is leſſer than B A; as <lb></lb>hath already been demon<lb></lb>ſtrated. </s> <s>Now ſuppoſe the <lb></lb><figure id="id.040.01.807.1.jpg" xlink:href="040/01/807/1.jpg"></figure><lb></lb>ſaid Priſme to be ſawed <lb></lb>Diagonally according to the <lb></lb>Line FB, ſo that the oppo<lb></lb>ſite Surfaces may be two <lb></lb>Triangles, one of which to<lb></lb>wards us is F A B. </s> <s>This So<lb></lb>lid obtains a quality contrary to the Priſme, to wit, that it leſſe re<lb></lb>ſiſteth Fraction by the Force placed in B at the term C than at A, <lb></lb>by as much the Length C <emph type="italics"></emph>B<emph.end type="italics"></emph.end> is leſſe than <emph type="italics"></emph>B<emph.end type="italics"></emph.end> A; Which we will ea <lb></lb>ſily prove: For imagining the Section C N O parallel to the other <lb></lb>A F D, the Line <emph type="italics"></emph>F<emph.end type="italics"></emph.end> A ſhall be to C N in the Triangle F A <emph type="italics"></emph>B<emph.end type="italics"></emph.end> in the <lb></lb>ſame proportion, as the Line A <emph type="italics"></emph>B<emph.end type="italics"></emph.end> is to <emph type="italics"></emph>B<emph.end type="italics"></emph.end> C: and therefore if we <lb></lb>ſuppoſe the Fulciment of the two Leavers to be in the Points A <lb></lb>and C, whoſe Diſtances are <emph type="italics"></emph>B<emph.end type="italics"></emph.end> A, A F, <emph type="italics"></emph>B<emph.end type="italics"></emph.end> C, and C N, theſe, I ſay, <lb></lb>ſhall be like: and therefore that Moment which the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce placed <lb></lb>at <emph type="italics"></emph>B<emph.end type="italics"></emph.end> hath at the Diſtance <emph type="italics"></emph>B<emph.end type="italics"></emph.end> A above the Reſiſtance placed at the <lb></lb>Diſtance A <emph type="italics"></emph>F<emph.end type="italics"></emph.end>, the ſaid <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce at <emph type="italics"></emph>B<emph.end type="italics"></emph.end> ſhall have at the Diſtance <emph type="italics"></emph>B<emph.end type="italics"></emph.end>C <lb></lb>above the ſame Reſiſtance, were it placed at the Diſtance C N: <lb></lb><emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut the Reſiſtance to be overcome at the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>ulciment C, being pla<lb></lb>ced at the Diſtance C N, from the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce in <emph type="italics"></emph>B<emph.end type="italics"></emph.end> is leſſer than the <lb></lb>Reſiſtance in A ſo much as the Rectangle C O is leſſe than the <lb></lb>Rectangle A D; that is, ſo much as the Line C N is leſs than A <emph type="italics"></emph>F<emph.end type="italics"></emph.end>; <lb></lb>that is, C <emph type="italics"></emph>B<emph.end type="italics"></emph.end> than B A: Therefore the Reſiſtance of the part O C B <lb></lb>againſt <emph type="italics"></emph>F<emph.end type="italics"></emph.end>raction in C is ſo much leſs than the Reſiſtance of the <lb></lb>whole D A O againſt <emph type="italics"></emph>F<emph.end type="italics"></emph.end>racture in O, as the Length C B is leſs than <lb></lb>A B. </s> <s>We have therefore from the Beam or Priſme D B, taken <lb></lb>away a part, that is half, cutting it Diagonally, and left the Wedge <lb></lb>or triangular Priſm <emph type="italics"></emph>F<emph.end type="italics"></emph.end> B A; and they are two Solids of contrary <lb></lb>Qualities, namely, that more reſiſts the more it is ſhortned, and this <lb></lb>in ſhortning loſeth its toughneſs as faſt. </s> <s>Now this being granted, <pb xlink:href="040/01/808.jpg" pagenum="116"></pb>it ſeemeth very reaſonable, nay, neceſſary, that one may give it <lb></lb>a cut, by which taking away that which is ſuperfluous, there remai<lb></lb>neth a Solid of ſuch a <emph type="italics"></emph>F<emph.end type="italics"></emph.end>igure, as in all its parts hath equal Reſi<lb></lb>ſtance.</s></p><p type="main"> <s>SIMP. </s> <s>It muſt needs be ſo; for where there is a tranſition from <lb></lb>the greater to the leſſer, one meeteth alſo with the equal.</s></p><p type="main"> <s>SAGR. </s> <s>But the buſineſſe is to find how we are to guide the <lb></lb>Saw for making of this Section.</s></p><p type="main"> <s>SIMP. </s> <s>This ſeemeth to me as if it were a very eaſie buſineſſe; <lb></lb>for if in ſawing the Priſm diagonally, taking away half of it, the <lb></lb>Figure that remains retaineth a contrary quality to that of the <lb></lb>whole Priſm, ſo as that in all places wherein this acquireth ſtrength, <lb></lb>that as faſt loſeth it, me thinks, that keeping the middle way, that <lb></lb>is, taking only the half of that half, which is the fourth part of the <lb></lb>whole, the remaining Figure will not gain or loſe ſtrength in any <lb></lb>of all thoſe places wherein the loſſe and the gain of the other two <lb></lb>Figures were alwaies equal.</s></p><p type="main"> <s>SALV. </s> <s>You have not hit the mark, <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end>; and as I ſhall <lb></lb>ſhew you, it will appear in reality, that that which may be cut off <lb></lb>from the Priſm, and taken away without weakening it is not its <lb></lb>fourth part, but the third. </s> <s>Now it remaineth (which is that that <lb></lb>was hinted by <emph type="italics"></emph>Sagredus<emph.end type="italics"></emph.end>)</s></p><p type="head"> <s>PROP. XIV. PROBL. V.</s></p><p type="main"> <s><emph type="italics"></emph>To find according to what Line the Section is to be <lb></lb>made; Which I will prove to be a Parabolical <lb></lb>Line.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>But firſt it is neceſſary to demonſtrate a certain Lemma, which <lb></lb>is this:</s></p><p type="head"> <s>LEMMA I.</s></p><p type="main"> <s><emph type="italics"></emph>If there ſhall be two Ballances or Leavers divided by their Fulci<lb></lb>ments in ſuch ſort that the two Distances where at the Forces <lb></lb>are to be placed, have to each other double the proportion of <lb></lb>the Diſtances at which the Reſiſtances ſball be, which Reſi<lb></lb>ſtances are to each other as their Diſtances, the ſuſtaining <lb></lb>Powers ſhall be equal.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let A B and C D be two Leavers divided upon their Fulciments <lb></lb>E and F, in ſuch ſort that the Diſtance E B hath to F D a pro<lb></lb>portion double to that which the Diſtance E A hath to F C. </s> <s>I ſay, <pb xlink:href="040/01/809.jpg" pagenum="117"></pb>the Powers that in BD ſhall ſuſtain the Reſiſtances A and C ſhall <lb></lb>be equal to each other. </s> <s>Let E G be ſuppoſed a Mean-Proporti<lb></lb>onal between E B and F D; therefore as B E is to E G, ſo ſhall <lb></lb>G E be to F D, and A E to C <emph type="italics"></emph>F<emph.end type="italics"></emph.end>; and ſo is ſuppoſed the Reſiſtance <lb></lb>of A to the Reſiſtance of C. </s> <s>And becauſe that as E G is to <emph type="italics"></emph>F<emph.end type="italics"></emph.end> D, <lb></lb>ſo is A E to C <emph type="italics"></emph>F<emph.end type="italics"></emph.end>; by Permutation as G E is to E A, ſo ſhall D <emph type="italics"></emph>F<emph.end type="italics"></emph.end><lb></lb>be to <emph type="italics"></emph>F<emph.end type="italics"></emph.end> C: And therefore (in <lb></lb>regard that the two Leavers <lb></lb><figure id="id.040.01.809.1.jpg" xlink:href="040/01/809/1.jpg"></figure><lb></lb>D C and G A are divided pro<lb></lb>portionally in the Points <emph type="italics"></emph>F<emph.end type="italics"></emph.end> and <lb></lb>E) in caſe the Power that being <lb></lb>placed at D compenſates the <lb></lb>Reſiſtance of C were at G, it <lb></lb>would countervail the ſame Reſiſtance of C placed in A: But by <lb></lb>what hath been granted, the Reſiſtance of A hath the ſame propor<lb></lb>tion to the Reſiſtance of C, that AE hath to C <emph type="italics"></emph>F<emph.end type="italics"></emph.end>; that is, B E <lb></lb>hath to E G: Therefore the Power G, or if you will D, placed at <lb></lb>B will ſuſtain the Reſiſtance placed at A: Which was to be de<lb></lb>monſtrated.</s></p><p type="main"> <s>This being underſtood: in the Surface <emph type="italics"></emph>F<emph.end type="italics"></emph.end> B of the Priſme D B, <lb></lb>let the Parabolical Line <emph type="italics"></emph>F<emph.end type="italics"></emph.end> N B be drawn, whoſe Vertex is B, ac<lb></lb>cording to which let the ſaid Priſme be ſuppoſed to be ſawed, the <lb></lb>Solid compriſed between the Baſe A D, the Rectangular Plane <lb></lb>A G, the Bight Line B G, and the Superficies D G B <emph type="italics"></emph>F<emph.end type="italics"></emph.end> being leſt <lb></lb>incurvated according to the Curvity of the Parabolical Line <lb></lb><emph type="italics"></emph>F<emph.end type="italics"></emph.end> N B. </s> <s>I ſay, that <lb></lb>that Solid is through<lb></lb><figure id="id.040.01.809.2.jpg" xlink:href="040/01/809/2.jpg"></figure><lb></lb>out of equal Reſi<lb></lb>ſtance. </s> <s>Let it be cut <lb></lb>by the Plane C O pa<lb></lb>rallel to A D; and <lb></lb>imagine two Leavers <lb></lb>divided and ſuppor<lb></lb>ted upon the Fulciments A and C; and let the Diſtances of one <lb></lb>be B A and A F, and of the other B C, and C N. </s> <s>And becauſe in <lb></lb>the Parabola <emph type="italics"></emph>F B<emph.end type="italics"></emph.end> A, A <emph type="italics"></emph>B<emph.end type="italics"></emph.end> is to <emph type="italics"></emph>B<emph.end type="italics"></emph.end> C, as the Square of <emph type="italics"></emph>F<emph.end type="italics"></emph.end> A to the <lb></lb>Square of C N, it is manifeſt, that the Diſtance <emph type="italics"></emph>B<emph.end type="italics"></emph.end> A of one Leaver, <lb></lb>hath to the Diſtance <emph type="italics"></emph>B<emph.end type="italics"></emph.end> C of the other a proportion double to that <lb></lb>which the other Diſtance A <emph type="italics"></emph>F<emph.end type="italics"></emph.end> hath to the other C N, And be<lb></lb>cauſe the Reſiſtance that is to be equal by help of the Leaver <lb></lb><emph type="italics"></emph>B<emph.end type="italics"></emph.end> A hath the ſame proportion to the Reſiſtance that is to be <lb></lb>equal by help of the Leaver <emph type="italics"></emph>B<emph.end type="italics"></emph.end> C, that the Rectangle D A hath to <lb></lb>the Rectangle O C; which is the ſame that the Line A <emph type="italics"></emph>F<emph.end type="italics"></emph.end> hath to <lb></lb>N C, which are the other two Diſtances of the Leavers; it is ma<lb></lb>nifeſt by the fore going Lemma, that the ſame Force that being <pb xlink:href="040/01/810.jpg" pagenum="118"></pb>applyed to the Line <emph type="italics"></emph>B<emph.end type="italics"></emph.end> G will equal the Reſiſtance D A, will like<lb></lb>wiſe equal the Reſiſtance C O. </s> <s>And the ſame may be demonſtra<lb></lb>ted, if one cut the Solid in any other place: therefore that Parabo<lb></lb>lical Solid is throughout of equal Reſiſtance. </s> <s>In the next place, <lb></lb>that cutting the Priſme according to the Parabolical Line F N B, <lb></lb>the third part of it is taken away, appeareth, For that the Semi<lb></lb>Parabola F N <emph type="italics"></emph>B<emph.end type="italics"></emph.end> A and the Rectangle F <emph type="italics"></emph>B<emph.end type="italics"></emph.end> are Baſes of two Solids <lb></lb>contained between two parallel Planes, that is, between the Rect<lb></lb>angles F B and D G, whereby they retain the ſame Proportion, as <lb></lb>thoſe their Baſes: But the Rectangle F <emph type="italics"></emph>B<emph.end type="italics"></emph.end> is Seſquialter to the Se<lb></lb>miparabola F N <emph type="italics"></emph>B<emph.end type="italics"></emph.end> A: Therefore cutting the Priſine according to <lb></lb>the Parabolick Line, we take away the third part of it. </s> <s>Hence we <lb></lb>ſee, that <emph type="italics"></emph>B<emph.end type="italics"></emph.end>eams may be made with the diminution of their Weight <lb></lb>more than thirty three in the hundred, without diminiſhing their <lb></lb>Strength in the leaſt; which in great Ships, in particular, for bea<lb></lb>ring the Decks may be of no ſmall benefit; for that in ſuch kind <lb></lb>of Fabricks Lightneſſe is of infinite importance.</s></p><p type="main"> <s>SAGR. </s> <s>The Commodities are ſo many, that it would be tedi<lb></lb>ous, if not impoſſible, to mention them all. <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut I, laying aſide <lb></lb>theſe, would more gladly underſtand that the alleviation is made <lb></lb>according to the aſſigned proportions. </s> <s>That the Section, according <lb></lb>to the Diagonal Line, cuts away half of the weight I very well <lb></lb>know: but that the other Section according to the Parabolical Line <lb></lb>takes away the third part of the Priſme I can believe upon the <lb></lb>word of <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> who evermore ſpeaks the truth, but in this <lb></lb>Caſe Science would better pleaſe me than Faith.</s></p><p type="main"> <s>SALV. </s> <s>I ſee then that you would have the Demonſtration, <lb></lb>whether or no it be true, that the exceſſe of the Priſme over and <lb></lb>above this, which for this time we will call a Parabolical Solid, is <lb></lb>the third part of the whole Priſme. </s> <s>I am certain that I have for<lb></lb>merly demoſtrated it; I will try now whether I can put the <lb></lb>Demonſtration together again: to which purpoſe I do remember <lb></lb>that I made uſe of a Certain Lemma of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> inſerted by <lb></lb>him in his <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ook <emph type="italics"></emph>de Spiralibus,<emph.end type="italics"></emph.end> and it is this:</s></p><p type="head"> <s>LEMMA II.</s></p><p type="main"> <s><emph type="italics"></emph>If any number of Lines at pleaſure ſhall exceed one another equal<lb></lb>ly, and the exceſſes be equal to the leaſt of them, and there be as <lb></lb>many more, each of them equal to the greateſt; the Squares of all <lb></lb>theſe ſhall be leſſe than the triple of the Squares of thoſe that <lb></lb>exceed one another: but they ſhall be more than triple to thoſe <lb></lb>others that remain, the Square of the greateſt being ſub<lb></lb>ſtracted.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/811.jpg" pagenum="119"></pb><p type="main"> <s>This being granted: Let the Parabolick Line A <emph type="italics"></emph>B<emph.end type="italics"></emph.end> be inſcribed <lb></lb>in this Rectangle A C <emph type="italics"></emph>B<emph.end type="italics"></emph.end> P: we are to prove the Mixt Triangle <lb></lb><emph type="italics"></emph>B<emph.end type="italics"></emph.end> A P, whoſe ſides are <emph type="italics"></emph>B<emph.end type="italics"></emph.end> P and P A, and <emph type="italics"></emph>B<emph.end type="italics"></emph.end>aſe the Parabolical Line <lb></lb><emph type="italics"></emph>B<emph.end type="italics"></emph.end> A, to be the third part of the whole Rectangle C P. </s> <s>For if it be <lb></lb>not ſo, it will be either more than the third part, or leſſe. </s> <s>Let it be <lb></lb>ſuppoſed that it may be <lb></lb>leſſe, and to that which is <lb></lb><figure id="id.040.01.811.1.jpg" xlink:href="040/01/811/1.jpg"></figure><lb></lb>wanting ſuppoſe the Space <lb></lb>X to be equal. </s> <s>Then di<lb></lb>viding the Rectangle con<lb></lb>tinually into equal parts <lb></lb>with Lines parallel to the <lb></lb>Sides <emph type="italics"></emph>B<emph.end type="italics"></emph.end> P and C A, we <lb></lb>ſhall in the end arrive at <lb></lb>ſuch parts, as that one of them ſhall be leſſe than the Space X. <lb></lb></s> <s>Now let one of them be the Rectangle O <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> and by the Points <lb></lb>where the other Parallels interſect the Parabolick Line, let the Pa<lb></lb>rallels to A P paſſe: and here I will ſuppoſe a Figure to be cir<lb></lb>cumſcribed about our Mixt-Triangle, compoſed of Rectangles, <lb></lb>which are <emph type="italics"></emph>B<emph.end type="italics"></emph.end> O, I N, H M, F L, E K, G A; which Figure ſhall alſo <lb></lb>yet be leſs than the third part of the Rectangle C P, in regard that <lb></lb>the exceſſe of that Figure over and above the Mixed Triangle is <lb></lb>much leſſe than the Rectangle <emph type="italics"></emph>B<emph.end type="italics"></emph.end> O, which yet again is leſſe than <lb></lb>the Space X.</s></p><p type="main"> <s>SAGR. Softly, I pray you, for I do not ſee how the exceſſe of <lb></lb>this circumſcribed Figure above the Mixt Triangle is conſiderably <lb></lb>leſſer than the Rectangle <emph type="italics"></emph>B<emph.end type="italics"></emph.end> O.</s></p><p type="main"> <s>SALV. </s> <s>Is not the Rectangle <emph type="italics"></emph>B<emph.end type="italics"></emph.end> O equal to all theſe ſmall Rect<lb></lb>angles by which our Parabolical Line paſſeth; I mean theſe, <emph type="italics"></emph>B<emph.end type="italics"></emph.end> I, <lb></lb>I H, H F, F E, E G, and G A, of which one part only lyeth with<lb></lb>out the Mixt Triangle? </s> <s>And the Rectangle <emph type="italics"></emph>B<emph.end type="italics"></emph.end> O, is it not alſo ſup<lb></lb>poſed to be leſſe than the Space X? </s> <s>Therefore if the Triangle to<lb></lb>gether with X did, as the Adverſary ſuppoſeth, equalize the third <lb></lb>part of the Rectangle C P the circumſcribed Figure that adjoyns <lb></lb>to the Triangle ſo much leſſe than the Space X, will remain even <lb></lb>yet leſſe than the third part of the ſaid Rectangle C P. <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut this <lb></lb>cannot be, for it is more than a third part, therefore it is not true <lb></lb>that our Mixt Triangle is leſſe than one third of the Rectangle.</s></p><p type="main"> <s>SAGR. </s> <s>I underſtand the Solution of my Doubt. <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut it is <lb></lb>requiſite now to prove unto us, that the Circumſcribed Figure is <lb></lb>more than a third part of the Rectangle C P; which, I believe, will <lb></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></lb><arrow.to.target n="marg1089"></arrow.to.target><lb></lb>D E hath the ſame proportion to the Square of Z G, that the Line <pb xlink:href="040/01/812.jpg" pagenum="120"></pb>D A hath to A Z; which is the ſame that the Rectangle K E hath to <lb></lb>the Rectangle A G, their heights A K and K L being equal. </s> <s>There<lb></lb>fore the proportion that the Square E D hath to the Square Z G; <lb></lb>that is, the Square L A hath to the Square A K, the Rectangle K E <lb></lb>hath likewiſe to the Rectangle K Z. </s> <s>And in the ſelf-ſame manner <lb></lb>we might prove that the other Rectangles L F, M H, N I, O B are <lb></lb>to one another as the Squares of the Lines M A, N A, O A, P A. <lb></lb></s> <s>Conſider we in the next place, how the Circumſcribed Figure is <lb></lb>compounded of certain Spaces that are to one another as the <lb></lb>Squares of the Lines that exceed with Exceſſes equal to the leaſt, <lb></lb>and how the Rectangle C P is compounded of ſo many other Spa<lb></lb>ces each of them equal to the Greateſt, which are all the Rectan<lb></lb>gles equal to O B. Therefore, by the Lemma of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> the <lb></lb>Circumſcribed Figure is more than the third part of the Rectangle <lb></lb>C P: But it was alſo leſſe, which is impoſſible: Therefore the <lb></lb>Mixt-Triangle is not leſſe than one third of the Rectangle C P. <lb></lb></s> <s>I ſay likewiſe, that it is not more: For if it be more than one <lb></lb>third of the Rectangle C P, ſuppoſe the Space X equal to the ex<lb></lb>ceſſe of the Triangle above the third part of the ſaid Rectangle <lb></lb>C P, and the diviſion and ſubdiviſion of the Rectangle into Rect<lb></lb>angolets, but alwaies equal, being made, we ſhall meet with ſuch as <lb></lb>that one of them is leſſer than the Space X; which let be done: <lb></lb>and let the Rectangle <emph type="italics"></emph>B<emph.end type="italics"></emph.end> O be leſſer than X; and, having deſcribed <lb></lb>the Figure as before, we ſhall have inſcribed in the Mixt-Triangle <lb></lb>a Figure compounded of the Rectangles V O, T N, S M, N L, Q K, <lb></lb>which yet ſhall not be leſs <lb></lb><figure id="id.040.01.812.1.jpg" xlink:href="040/01/812/1.jpg"></figure><lb></lb>than the third part of the <lb></lb>great Rectangle C P, for <lb></lb>the Mixt Triangle doth <lb></lb>much leſſe exceed the In<lb></lb>ſcribed Figure than it doth <lb></lb>exceed the third part of <lb></lb>the Rectangle C P; Be<lb></lb>cauſe the exceſſe of the <lb></lb>Triangle above the third part of the Rectangle C P is equal to <lb></lb>the Space X which is greater than the Rectangle <emph type="italics"></emph>B<emph.end type="italics"></emph.end> O, and this al<lb></lb>ſo is conſiderably greater than the exceſſe of the Triangle above <lb></lb>the Inſcribed Figure: For to the Rectangle <emph type="italics"></emph>B<emph.end type="italics"></emph.end> O, all the Rectan<lb></lb>golets A G, G E, E <emph type="italics"></emph>F,<emph.end type="italics"></emph.end> F H, H I, I <emph type="italics"></emph>B<emph.end type="italics"></emph.end> are equal, of which the Ex<lb></lb>ceſſes of the Triangle above the Inſcribed <emph type="italics"></emph>F<emph.end type="italics"></emph.end>igure are leſſe than <lb></lb>half: And therefore the Triangle exceeding the third part of the <lb></lb>Rectangle C P, by much more (exceeding it by the Space X) <lb></lb>than it exceedeth its inſcribed <emph type="italics"></emph>F<emph.end type="italics"></emph.end>igure, that ſame <emph type="italics"></emph>F<emph.end type="italics"></emph.end>igure ſhall alſo <lb></lb>be greater than the third part of the Rectangle C P: <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut it is leſſer, <lb></lb>by the Lemma preſuppoſed: <emph type="italics"></emph>F<emph.end type="italics"></emph.end>or that the Rectangle C P, as being <pb xlink:href="040/01/813.jpg" pagenum="127"></pb>the Aggregate of all the biggeſt Rectangles, hath the ſame pro<lb></lb>portion to the Rectangles compounding the Inſcribed <emph type="italics"></emph>F<emph.end type="italics"></emph.end>igure, that <lb></lb>the Aggregate of of all the Squares of the Lines equal to the big<lb></lb>geſt, hath to the Squares of the Lines that exceed equally, ſubſtra<lb></lb>cting the Square of the biggeſt: And therefore (as it hapneth in <lb></lb>Squares) the whole Aggregate of the biggeſt (that is the Rectan<lb></lb>gle C P) is more than triple the Aggregate of the exceeding <lb></lb>ones, the biggeſt deducted, that compound the Inſcribed <emph type="italics"></emph>F<emph.end type="italics"></emph.end>i<lb></lb>gure. </s> <s>Therefore the Mixt-Triangle is neither greater nor leſſer <lb></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"></emph>The Quadrature of <lb></lb>the Parabola ſhewn <lb></lb>by one ſingle De<lb></lb>monſtration.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>A pretty and ingenuous Demonſtration: and ſo much <lb></lb>the more, in that it giveth us the Quadrature of the Parabola, ſhew<lb></lb>ing it to be <emph type="italics"></emph>Seſquitertial<emph.end type="italics"></emph.end> of the Triangle inſcribed in the ſame; <lb></lb>proving that which <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> demonſtrateth by two very diffe<lb></lb>rent, but both very admirable, methods of a great number of Pro<lb></lb>poſitions. </s> <s>As hath likewiſe been demonſtrated lately by <emph type="italics"></emph>Lucas <lb></lb>Valerius,<emph.end type="italics"></emph.end> another ſecond <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> of our Age, which Demon<lb></lb>ſtration is ſet down in the Book that he writ of the Center of the <lb></lb>Gravity of Solids.</s></p><p type="main"> <s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>ALV. </s> <s>A Treatiſe which verily is not to come behind any one <lb></lb>that hath been written by the moſt <emph type="italics"></emph>F<emph.end type="italics"></emph.end>amous Geometricians of the <lb></lb>preſent and all paſt Ages: which when it was read by our <emph type="italics"></emph>Acade<lb></lb>mick,<emph.end type="italics"></emph.end> it made him deſiſt from proſecuting his Diſcoveries that he <lb></lb>was then proceeding to write on the ſame Subject: in regard he <lb></lb>ſaw the whole buſineſs ſo happily found and demonſtrated by the <lb></lb>ſaid <emph type="italics"></emph>Valerius.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>I was informed of all theſe things by our <emph type="italics"></emph>Academick<emph.end type="italics"></emph.end>; <lb></lb>and have beſought him withall that he would one day let me ſee <lb></lb>his Demonſtrations that he had ſound at the time when he met <lb></lb>with the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ook of <emph type="italics"></emph>Valerius:<emph.end type="italics"></emph.end> but I never was ſo happy as to ſee them.</s></p><p type="main"> <s>SALV. </s> <s>I have a Copy of them, and will impart them to you, <lb></lb>for you will be much pleaſed to ſee the variety of Methods, which <lb></lb>theſe two Authors take to inveſtigate the ſame Concluſions, and <lb></lb>their Demonſtrations: wherein alſo ſome of the Concluſions have <lb></lb>different Explanations, howbeit in effect equally true.</s></p><p type="main"> <s>SAGR. </s> <s>I ſhall be very glad to ſee them, therefore when you re<lb></lb>turn to our wonted Conferences you may do me the favour to <lb></lb>bring them with you. <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut in the mean time, this ſame of the Re<lb></lb>fiſtance of the Solid taken from the Priſme by a Parabolick Secti<lb></lb>on, being an Operation no leſſe ingenuous than beneficial in many <lb></lb>Mechanical Works, it would be good that Artificers had ſome ea<lb></lb>ſie and expedite Rule how they may draw the ſaid Parabolick <lb></lb>Line upon the Plane of the Priſme.</s></p><p type="main"> <s>SALV. </s> <s>There are ſeveral waies to draw thoſe Lines, but two <lb></lb><arrow.to.target n="marg1090"></arrow.to.target><lb></lb>that are more expedite than all the reſt, I will deſcribe unto you. <pb xlink:href="040/01/814.jpg" pagenum="122"></pb>One of which is truly admirable, ſince that thereby, in leſſe time <lb></lb>than another can with Compaſſes ſlightly draw upon a paper <lb></lb>four or ſix Circles of different ſizes, I can deſign thirty or forty <lb></lb>Parabolick Lines no leſſe exact, ſmall, and ſmooth than the Cir<lb></lb>cumferences of thoſe Circles. </s> <s>I have a <emph type="italics"></emph>B<emph.end type="italics"></emph.end>all of <emph type="italics"></emph>B<emph.end type="italics"></emph.end>raſſe exquiſitely <lb></lb>round, no bigger than a Nut, this thrown upon a Steel Mirrour <lb></lb>held, not erect to the Horizon, but ſomewhat inclined, ſo that the <lb></lb><emph type="italics"></emph>B<emph.end type="italics"></emph.end>all in its motion may run along preſſing lightly upon it, leaveth <lb></lb>a Parabolical Line finely and ſmoothly deſcribed, and wider or <lb></lb>narrower according as the Projection ſhall be more or leſs elevated. <lb></lb></s> <s>Whereby alſo we have a clear and ſenſible Experiment that the <lb></lb>Motion of Projects is made by Parabolick Lines: an Effect obſer<lb></lb>ved by none before our <emph type="italics"></emph>Academick,<emph.end type="italics"></emph.end> who alſo layeth down the <lb></lb>Demonſtration of it in his <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ook of Motion, which we will joynt<lb></lb>ly peruſe at our next meeting. </s> <s>Now the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>all, that it may deſcribe <lb></lb>by its motion thoſe Parabola's, muſt be rouled a little in the hands <lb></lb>that it may be warmed, and ſomewhat moyſtned, for by this <lb></lb>means it will leave its track more apparent upon the Mirrour. </s> <s>The <lb></lb>other way to draw the Line that we deſire upon the Priſme is after <lb></lb>this manner. </s> <s>Let two Nailes be faſtned on high in a Wall, at an <lb></lb>equal diſtance from the Horizon, and remote from one another <lb></lb>twice the breadth of the Rectangle upon which we would trace the <lb></lb>Semiparabola, and to theſe two Nails tye a ſmall thread of ſuch a <lb></lb>length that its doubling may reach as far as the length of the <lb></lb>Priſme; this ſtring will hang in a Parabolick <emph type="italics"></emph>F<emph.end type="italics"></emph.end>igure: ſo that tra<lb></lb>cing out upon the Wall the way that the ſaid String maketh on it, <lb></lb>we ſhall have a whole Parabola deſcribed: which a Perpendicular <lb></lb>that hangeth in the midſt between theſe two Nailes will divide <lb></lb>into two equal parts. </s> <s>And for the transferring or ſetting off of <lb></lb>that Line afterwards upon the oppoſite Surfaces of the Priſme it is <lb></lb>not difficult at all, ſo that every indifferent Artiſt will know how <lb></lb>to do it. </s> <s>The ſame Line might be drawn upon the ſaid Sur<lb></lb>face of the Priſme by help of the Geometrical Lines delineated up<lb></lb>on the <emph type="italics"></emph>Compaſſe<emph.end type="italics"></emph.end> of our <emph type="italics"></emph>Friend,<emph.end type="italics"></emph.end> without any more ado.</s></p><p type="margin"> <s><margin.target id="marg1090"></margin.target><emph type="italics"></emph>Several waies to <lb></lb>deſcribe a Para<lb></lb>bola.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>We have hitherto demonſtrated ſo many Concluſions touching <lb></lb>the Contemplation of theſe Reſiſtances of Solids againſt Fraction <lb></lb>by having firſt opened the way unto the Science with ſuppoſing the <lb></lb>direct Reſiſtance for known, that we may in purſuance of them <lb></lb>proceed forwards to the finding of other, and other Concluſions, <lb></lb>with their Demonſtrations of thoſe which in Nature are infinite. <lb></lb></s> <s>Only at preſent, for a final concluſion of this daies Conferences, <lb></lb>I will add the Speculation of the Reſiſtances of the Hollow Solids <lb></lb>which Art, and chiefly Nature, uſeth in an hundred Operations, <lb></lb>when without encreaſing the weight ſhe greatly augmenteth the <lb></lb>ſtrength: as is ſeen in the Bones of Birds, and in many Canes that <pb xlink:href="040/01/815.jpg" pagenum="123"></pb>are light and of great Reſiſtance againſt bending and breaking. <lb></lb></s> <s>For if a Wheat Straw that ſupports an Ear that is heavier than the <lb></lb>whole Stalk, were made of the ſame quantity of matter but were <lb></lb>maſſie or ſolid, it would be much leſſe repugnant to Fraction or <lb></lb>Flection. </s> <s>And with the ſame Reaſon Art hath obſerved, and Ex<lb></lb>perience confirmed, that an hollow Cane, or a Trunk of Wood <lb></lb>or Metal, is much more firm and tough than if being of the ſame <lb></lb>weight and length it were ſolid, which conſequently would be <lb></lb>more flender, and therefore Art hath contrived to make Lances hol<lb></lb>low within when they are deſired to be ſtrong and light. </s> <s>We will <lb></lb>ſhew therefore, that</s></p><p type="head"> <s>PROPOSITION XV.</s></p><p type="main"> <s><emph type="italics"></emph>The Reſiſtances of two Cylinders, equall, and equally <lb></lb>long, one of which is Hollow, and the other Maſsie, <lb></lb>have to each other the ſame proportion, as their Dia<lb></lb>meters.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the Cane or Hollow Cylinder be A E, [<emph type="italics"></emph>as in<emph.end type="italics"></emph.end> Fig. </s> <s>17.] <lb></lb>and the Cylinder I N Maſſie, and equall in weight and length. <lb></lb></s> <s>I ſay, the Reſiſtance of the Cane A E hath the ſame propor<lb></lb>tion to the Reſiſtance of the ſolid Cylinder, as the Diameter <lb></lb>A B hath to the Diameter I L. </s> <s>Which is very manifeſt; For the <lb></lb>Cane and the Cylinder I N being equal, and of equal lengths, the <lb></lb>Circle I L that is Baſe of the Cylinder ſhall be equal to the Ring <lb></lb>A B that is Baſe of the Cane A E, (I call the Superficies that re<lb></lb>maineth when a leſſer Circle is taken out of a greater that is Con<lb></lb>centrick with it a Ring:) and therefore their Abſolute Reſiſtan<lb></lb>ces ſhall be equal: but becauſe in breaking croſſe-waies we make <lb></lb>uſe in the Cylinder I N of the length L N for a Leaver, and of the <lb></lb>point L for a Fulciment, and of the Semidiameter or Diameter L I <lb></lb>for a Counter-Leaver; and in the Cane the part of the Leaver, <lb></lb>that is the Line B E is equal to L N; but the Counter-Leaver at <lb></lb>the Fulciment B is the Diameter or Semidiameter A B: It is mani<lb></lb>feſt therefore that the Reſiſtance of the Cane exceedeth that of <lb></lb>the Solid Cylinder as much as the Diameter A B exceeds the Dia<lb></lb>meter I L; Which is that that we ſought. </s> <s>Toughneſs therefore is ac<lb></lb>quired in the hollow Cane above the Toughneſs of the ſolid Cylin<lb></lb>der according to the proportion of the Diameters: provided al<lb></lb>waies that they be both of the ſame matter, weight, and length.</s></p><p type="main"> <s>It would be well, that in conſequence of this we try to inveſtigate <lb></lb>that which hapneth in other Caſes indifferently between all Canes <lb></lb>and ſolid Cylinders of equal length, although unequal in quantity <lb></lb>of weight, and more or leſs evacuated. </s> <s>And firſt we will demon<lb></lb>ſtrate, that</s></p><pb xlink:href="040/01/816.jpg"></pb><figure id="id.040.01.816.1.jpg" xlink:href="040/01/816/1.jpg"></figure><p type="caption"> <s><emph type="italics"></emph>Place this at the end of the ſecond Dialogue pag:<emph.end type="italics"></emph.end> 124,</s></p><pb xlink:href="040/01/817.jpg" pagenum="124"></pb><p type="head"> <s>PROP. XVI. PROBL. VI.</s></p><p type="main"> <s><emph type="italics"></emph>A Trunk or Hollow Cane being given, a Solid Cylinder <lb></lb>may be found equal to it.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>This Operation is very eaſie. </s> <s>For let the Line A B, be the Dia<lb></lb>meter of the Cane, and C D the Diameter of the Hollow or <lb></lb>Cavity. </s> <s>Let the Line A E be ſet off upon the greater Circle <lb></lb>equal to the Diameter C D, and conjoyn E B. </s> <s>And becauſe in <lb></lb><figure id="id.040.01.817.1.jpg" xlink:href="040/01/817/1.jpg"></figure><lb></lb>the Semicircle A E B the Angle E is Right<lb></lb>Angle, the Circle whoſe Diameter is A B <lb></lb>ſhall be equall to the two Circles of the Di<lb></lb>ameters A E and E B: But A E is the Dia<lb></lb>meter of the Hollow of the Cane: Therefore <lb></lb>the Circle whoſe Diameter is E B, ſhall be <lb></lb>equal to the Ring A C B D: And therefore <lb></lb>the ſolid Cylinder, the Circle of whoſe Baſe <lb></lb>hath the Diameter E B ſhall be equal to the <lb></lb>Cane, they being of the ſame length. </s> <s>This demonſtrated, we may <lb></lb>preſently be able</s></p><p type="head"> <s>PROP. XVII. PROBL. VII.</s></p><p type="main"> <s><emph type="italics"></emph>To find what proportion is betwixt the Reſiſtances of <lb></lb>any whatſoever Cane and Cylinder, their lengths be<lb></lb>ing equal.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>LET the Cane A B E, and the Cylinder R S M, be of equal <lb></lb>length: it is required to find what proportion the Reſiſtances <lb></lb>have to each other. </s> <s>By the precedent let the Cylinder I L N <lb></lb>be found equal to the Cane, and of the ſame length; and to the <lb></lb>Lines I L and R S (Diameters of the Baſes of the Cylinders I N and <lb></lb><figure id="id.040.01.817.2.jpg" xlink:href="040/01/817/2.jpg"></figure><lb></lb>R M) let the Line V be a fourth <lb></lb>Proportional. </s> <s>I ſay, the Reſiſtance <lb></lb>of the Cane A E is to the Reſi<lb></lb>ſtance of the Cylinder R M, as the <lb></lb>Line A B is to V. </s> <s>For the Cane <lb></lb>A E being equal to, and of the <lb></lb>ſame length with the Cylinder <lb></lb>I N, the Reſiſtance of the Cane <lb></lb>ſhall be to the Reſiſtance of the <lb></lb>Cylinder, as the Line A B is to I L: <lb></lb>But the Reſiſtance of the Cylinder I N is to the Reſiſtance of the <lb></lb>Cylinder R M, as the Cube I L is to the Cube R S; that is, as the <lb></lb>Line I L to V: Therefore, <emph type="italics"></emph>ex æquali,<emph.end type="italics"></emph.end> the Reſiſtance of the Cane <lb></lb>A E hath the ſame proportion to the Reſiſtance of the Cylinder <lb></lb>R M, that the Line A B hath to V: Which is that that was ſought.</s></p><p type="head"> <s><emph type="italics"></emph>The End of the Second Dialogue.<emph.end type="italics"></emph.end></s></p></chap><chap><pb xlink:href="040/01/818.jpg" pagenum="125"></pb><p type="head"> <s>GALILEUS, <lb></lb>HIS <lb></lb>DIALOGUES <lb></lb>OF <lb></lb>MOTION.</s></p><p type="head"> <s>The Third Dialogue.</s></p><p type="head"> <s><emph type="italics"></emph>INTERLOCUTORS,<emph.end type="italics"></emph.end></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"></emph>We promote a very new Science, but of a very <lb></lb>old Subject. </s> <s>There is nothing in Nature more <lb></lb>antient than<emph.end type="italics"></emph.end> MOTION, <emph type="italics"></emph>of which <lb></lb>many and great Volumns have been written <lb></lb>by Philoſophers: But yet there are ſundry <lb></lb>Symptomes and Properties in it worthy of <lb></lb>our Notice, which I find not to have been hi<lb></lb>therto obſerved, much leſſe demonſtrated by <lb></lb>any. </s> <s>Some ſlight particulars have been no<lb></lb>ted: as that the Natural Motion of Grave Bodies continually accelle-<emph.end type="italics"></emph.end><pb xlink:href="040/01/819.jpg" pagenum="126"></pb><emph type="italics"></emph>rateth, as they deſcend towards their Center: but it hath not been as yet <lb></lb>declared in what proportion that Acceleration is made. </s> <s>For no man, <lb></lb>that I know, hath ever demonſtrated, That there is the ſame proportion <lb></lb>between the Spaces, thorow which a thing moveth in equal Times, as <lb></lb>there is between the Odde Numbers which follow in order after a Vnite. <lb></lb></s> <s>It hath been obſerved that Projects [or things thrown or darted with vi<lb></lb>olence] make a Line that is ſomewhat curved; but that this line is a Pa<lb></lb>rabola, none have hinted: Yet theſe, and ſundry other things, no <lb></lb>leſſe worthy of our knowledg, will I here demonſtrate: And which <lb></lb>is more, I will open a way to a moſt ample and excellent Science, <lb></lb>of which theſe our Labours ſhall be the Elements: into which more <lb></lb>ſubtil and piercing Wits than mine will be better able to dive.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>We divide this Treatiſe into three parts. </s> <s>In the firſt part we conſider <lb></lb>ſuch things as reſpect Equable or Vniforme Motion. </s> <s>In the ſecond we <lb></lb>write of Motion naturally accelerate. </s> <s>In the third we treat of Violent <lb></lb>Motion, or<emph.end type="italics"></emph.end> De Projectis.</s></p><p type="head"> <s>OF EQVABLE MOTION.</s></p><p type="main"> <s><emph type="italics"></emph>Concerning Equable or Vniform Motion we have need of onely one <lb></lb>Definition, which I thus deliver.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>DEFINITION.</s></p><p type="main"> <s>By an Equable or Uniform Motion, I underſtand that by which a <lb></lb>Moveable in all equal Times paſſeth thorow equal Spaces.</s></p><p type="head"> <s>ADVERTISEMENT.</s></p><p type="main"> <s><emph type="italics"></emph>I thought good to add to the old Definition (which ſimply termeth <lb></lb>that an Equable Motion, whereby equal Spaces are paſt in equal <lb></lb>Times) this Particle<emph.end type="italics"></emph.end> All, <emph type="italics"></emph>that is, any whatſoever Times that are equal: <lb></lb>for it may happen, that a Moveable may paſſe thorow equal Spaces in cer<lb></lb>tain equal Times, though the Spaces be not equal which it hath gone in <lb></lb>leſſer, though equal parts of the ſame Time. </s> <s>From this our Definition <lb></lb>follow theſe four Axiomes:<emph.end type="italics"></emph.end> ſcilicet,</s></p><p type="head"> <s>AXIOMEL</s></p><p type="main"> <s>In the ſame Equable Motion that Space is greater which is paſſed <lb></lb>in a longer Time, and that leſſer which is paſt in a ſhorter.</s></p><pb xlink:href="040/01/820.jpg" pagenum="127"></pb><p type="head"> <s>AXIOME II.</s></p><p type="main"> <s>In the ſame Equable Motion, the greater the Space is that hath <lb></lb>been gone thorow, the longer was the Time in which the Move<lb></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 paſſeth in any Time, is great<lb></lb>er than the Space which a leſſer Velocity paſſeth in the ſame <lb></lb>Time.</s></p><p type="head"> <s>AXIOME IV.</s></p><p type="main"> <s>The Velocity which paſſeth a greater Space, is greater than the <lb></lb>Velocity which paſſeth a leſſer Space in the ſame 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></lb>and with the ſame Velocity paſſe two ſeveral <lb></lb>Spaces, the Times of the Motion ſhall be to <lb></lb>one another as the ſaid Spaces.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Moveable by an Equable Motion with the ſame Velocity paß <lb></lb>the two Spaces A B and B C: and let D E be the Time of the Moti<lb></lb>on thorow A B; and let the Time of the Motion thorow B C be E F <lb></lb>I ſay that the Time D E to the Time E F, is as the Space A B to the <lb></lb>Space B C. </s> <s>Protract the Spaces and Times on both ſides, towards <lb></lb>G H and I K, and in A G take any number of Spaces equal to A B,<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.820.1.jpg" xlink:href="040/01/820/1.jpg"></figure><lb></lb><emph type="italics"></emph>and in D I the like number of Times equal to D E. Again, in C H take <lb></lb>any number of Spaces equal to B C, and in F K take the ſame number <lb></lb>of Times equal to the Time E F. </s> <s>This done, the Space B G will con<lb></lb>tain juſt as many Spaces equal to B A, as the Time E I containeth <lb></lb>Times equal to E D, equimultiplied according to what ever Rate; And <lb></lb>likewiſe the Space B H will contain as many Spaces equal to B C, as<emph.end type="italics"></emph.end><pb xlink:href="040/01/821.jpg" pagenum="128"></pb><emph type="italics"></emph>the Time K E containeth Times equal to F E, at what ever rate equi<lb></lb>multiplied. </s> <s>And foraſmuch as D E is the Time of the Motion thorow <lb></lb>A B, the whole Time E I, ſhall be the Time of the whole Space of the <lb></lb>Motion thorow B G, by reaſon that the Motion is Equable, and that the <lb></lb>number of the Times in E I equal to D E, is the ſame with the number <lb></lb>of Spaces in B G, equal to B A: For the ſame reaſon E K is the Time <lb></lb>of the Motion thorow H B. </s> <s>Now in regard the Motion is Equable, if the <lb></lb>Space G B were equal to H B, the Time I E would be equal to E K: <lb></lb>and if G B be greater than B H, I E ſhall likewiſe be greater than E K: <lb></lb>and if leſſer, leſſer. </s> <s>They are therefore four Magnitudes; A B the firſt, <lb></lb>B C the ſecond, D E the third, and E F the Fourth; and the firſt <lb></lb>and third, to wit, the Space A B, and Time D E, there were taken the <lb></lb>Time I E, and the Space G B equimultiple, according to any multi<lb></lb>plication; and it hath been demonſtrated that theſe do at once either <lb></lb>equal, or fall ſhort of, or elſe exceed the Time E K, and Space B H, <lb></lb>which are equimultiple of the ſecond and fourth: Therefore the firſt <lb></lb>bath to the ſecond, to wit the Space A B to the Space B C, the ſame <lb></lb>proportion that the third hath to the fourth, to wit, the Time D E to <lb></lb>the Time E F. </s> <s>Which was to be demonſtrated.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>THEOR. II. PROP. II.</s></p><p type="main"> <s>If a Moveable in equal Times paſſe thorow two <lb></lb>Spaces, the ſaid Spaces will be to each other, <lb></lb>as the Velocities. </s> <s>And if the Spaces are to each <lb></lb>other as the Velocities, the Times will be <lb></lb>equal.</s></p><p type="main"> <s><emph type="italics"></emph>Let us ſuppoſe A B and B C in the former Figure, to be two <lb></lb>Spaces paſt, by the Moveable in equal times; the Space A B with <lb></lb>the Velocity D E, and the Space B C with the Velocity E F. </s> <s>I <lb></lb>ſay, that the Space A B is to the Space B C, as the Velocity D E is to <lb></lb>the Velocity E F: and thus I prove it. </s> <s>Take as before, of the Spaces <lb></lb>and Velocities equi-multiples, accordieg to any what ever Rate, ſci<lb></lb>licet G B and I E, of A B and D E, and likewiſe H B and K E, of <lb></lb>B C and E F: It may be concluded as above, that G B and I E are <lb></lb>both at once either equal to, or fall ſhort of, or elſe exceed the equi-mul<lb></lb>tiples of D H and E K. </s> <s>Therefore the Propoſition is proved.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/822.jpg" pagenum="129"></pb><p type="head"> <s>THEOR. III. PROP. III.</s></p><p type="main"> <s>The Times in which the ſame Space is paſt tho<lb></lb>row by unequal Velocities, have the ſame pro<lb></lb>portion to each other as their Velocities contra<lb></lb>rily taken.</s></p><p type="main"> <s><emph type="italics"></emph>Let the two unequal Velocities be A the greater, and B the leſſe: <lb></lb>and according to both theſe let a Motion be made thorow the ſame <lb></lb>Space C D. </s> <s>I ſay the Time in which the Velocity A paſſeth the <lb></lb>Space C D, ſhall be to the Time in which the Velocity B paſſeth the <lb></lb>ſaid Space, as the Velocity B to the Velocity A. </s> <s>As A is to B, ſo let <lb></lb>C D be to C E: Then, by the <lb></lb>former Propoſition, the Time in<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.822.1.jpg" xlink:href="040/01/822/1.jpg"></figure><lb></lb><emph type="italics"></emph>which the Velocity A paſſeth <lb></lb>C D, ſhall be the ſame with <lb></lb>the Time in which B paſſeth <lb></lb>C E. </s> <s>But the Time in which <lb></lb>the Velocity B paſſeth C E, is <lb></lb>to the Time in which it paſſeth C D, as C E is to C D: Therefore <lb></lb>the Time in which the Velocity A paſſeth C D, is to the Time in which <lb></lb>the Velocity B paſſeth the ſame C D, as C E is to C D; that is, the Ve<lb></lb>locity B is to the Velocity A: Which was to be proved.<emph.end type="italics"></emph.end></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></lb>tion, but with unequal Velocities, the Spaces <lb></lb>which they paſſe in unequal Times, are to each <lb></lb>other in a proportion compounded of the pro<lb></lb>portion of the Velocities, and of the propor<lb></lb>tion of the Times.</s></p><p type="main"> <s><emph type="italics"></emph>Let the two Moveables moving with an Equable Motion, be E and <lb></lb>F: And let the proportion of the Velocity of the Moveable E be <lb></lb>to the Velocity of the Moveable F, as A is to B: And let the Time <lb></lb>in which E is moved, be unto the Time in which F is moved, as C is <lb></lb>to D. </s> <s>I ſay the Space paſſed by E, with the Velocity A in the Time C, is to <lb></lb>the Space paſſed by F, with the Velocity B in the Time D, in a proportion <lb></lb>compounded of the proportion of the Velocity A to the Velocity B, and of<emph.end type="italics"></emph.end><pb xlink:href="040/01/823.jpg" pagenum="130"></pb><emph type="italics"></emph>the proportion of the Time C to the Time D. </s> <s>Let the Space paſſed by the <lb></lb>Moveable E, with the Velocity A in the Time C, be G: And as the <lb></lb>Velocity A is to the Velocity B, <lb></lb><figure id="id.040.01.823.1.jpg" xlink:href="040/01/823/1.jpg"></figure><lb></lb>ſo let G be to I: And as the <lb></lb>Time C is to the Time D, ſo <lb></lb>let I be to L: It is manifeſt, <lb></lb>that I is the Space paſſed by F <lb></lb>in the ſame Time in which E <lb></lb>paſſeth thorow G; ſeeing that <lb></lb>the Spaces G and I are as the <lb></lb>Velocities A and B; and ſeeing that as the Time C is to the Time D, ſo <lb></lb>is I unto L; and ſince that I is the Space paſſed by the Moveable F in the <lb></lb>Time C: Therefore L ſhall be the Space that F paſſeth in the Time D, <lb></lb>with the Velocity B: But the proportion of G to L, is compounded of the <lb></lb>proportions of G to I, and of I to L; that is, of the proportions of the <lb></lb>Velocity A to the Velocity B, and of the Time C to the Time D: <lb></lb>Therefore the Propoſition is demonſtrated.<emph.end type="italics"></emph.end></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></lb>but with unequal Velocities, and if the Spaces <lb></lb>paſſed be alſo unequal, the Times ſhall be to <lb></lb>each other in a proportion compounded of the <lb></lb>proportion of the Spaces, and of the proporti<lb></lb>on of the Velocities contrarily taken.</s></p><p type="main"> <s><emph type="italics"></emph>Let A and B be the two Moveables, and let the Velocity of A be to <lb></lb>the Velocity of B, as V to T, and let the Spaces paſſed, be as S to <lb></lb>R. </s> <s>I ſay the proportion of the Time in which A is moved to the <lb></lb>Time in which B is moved, ſhall be compounded of the proportions of the <lb></lb>Velocity T to the Velocity V, and of the Space S to the Space R. </s> <s>Let C be <lb></lb>the Time of the Motion A;<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.823.2.jpg" xlink:href="040/01/823/2.jpg"></figure><lb></lb><emph type="italics"></emph>and as the Velocity T is to <lb></lb>the Velocity V, ſo let the <lb></lb>Time C be to the Time E: <lb></lb>And for aſmuch as C is the <lb></lb>Time in which A with <lb></lb>the Velocity V paſſeth the <lb></lb>Space S; and that the <lb></lb>Time C is to the Time E, as the Velocity T of the Moveable B is to the <lb></lb>Velocity V, E ſhall be the Time in which the Moveable B would paſſe<emph.end type="italics"></emph.end><pb xlink:href="040/01/824.jpg" pagenum="131"></pb><emph type="italics"></emph>the ſame Space S. </s> <s>Again as the Space S is to the Space R, ſo let the <lb></lb>Time E be to the Time G: Therefore G is the Time in which B would <lb></lb>paſſe the Space R. </s> <s>And becauſe the proportion of C to G is compounded <lb></lb>of the proportions of C to E, and of E to G; And ſince the proportion <lb></lb>of C to E is the ſame with that of the Velocities of the Moveables A and <lb></lb>B contrarily taken; that is, with that of T and V; And the proportion <lb></lb>of E to G is the ſame with the proportion of the Spaces S and R: There<lb></lb>fore the Propoſition is demonſtrated.<emph.end type="italics"></emph.end></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></lb>the proportion of their Velocities ſhall be com<lb></lb>pounded of the proportion of the Spaces paſ<lb></lb>ſed, and of the proportion of the Times con<lb></lb>trarily taken.</s></p><p type="main"> <s><emph type="italics"></emph>Let A and B be the two Moveables moving with an Equable <lb></lb>Motion; and let the Spaces by them paſſed, be as V to T; and <lb></lb>let the Times be as S to R. </s> <s>I ſay that the proportion of the Ve<lb></lb>locity of the Moveable A, to that of the Velocity of B, ſhall be <lb></lb>compounded of the proportions of the Space V to the Space T, and <lb></lb>of the Time R to the Time S. </s> <s>Let C be the Velocity with which the <lb></lb>Moveable A paſſeth the Space V in the Time S: And let the Velocity C <lb></lb>be to the Velo-<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.824.1.jpg" xlink:href="040/01/824/1.jpg"></figure><lb></lb><emph type="italics"></emph>city E, as the <lb></lb>Space V is to <lb></lb>the Space T; <lb></lb>And E ſhall <lb></lb>be the Veloci<lb></lb>ty with which <lb></lb>the Moveable <lb></lb>B paſſeth the Space T in the Time S: Again, let the Velocity E be to the <lb></lb>other Velocity G, as the Time R is to the Time S; And G ſhall be the <lb></lb>Velocity with which the Moveable B paſſeth the Space T in the Time R. <lb></lb></s> <s>We have therefore the Velocity C, wherewith the Moveable A paſſeth <lb></lb>the Space V in the Time S; and the Velocity G, wherewith the Move<lb></lb>able B paſſeth the Space T in the Time R: And the proportion of C to <lb></lb>G is compounded of the proportions of C to E and of E to G: But the <lb></lb>proportion of C to E, is ſuppoſed the ſame with that of the Space V to <lb></lb>the Space T; and the proportion of E to G, is the ſame with that of R <lb></lb>to S: Therefore the Propoſition is manifest.<emph.end type="italics"></emph.end><pb xlink:href="040/01/825.jpg" pagenum="132"></pb><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></lb>cademick, <emph type="italics"></emph>i. </s> <s>e. <lb></lb></s> <s>Galileus.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>This that we have read, is what our ^{*} <emph type="italics"></emph>Author<emph.end type="italics"></emph.end> hath written <lb></lb>of the Equable Motion. </s> <s>We will paſs therefore to a more ſubtil and <lb></lb>new Contemplation touching the Motion Naturally Accelerate: <lb></lb>and behold here the Title and Introduction.</s></p><p type="head"> <s>OF MOTION <lb></lb>NATVRALLY ACCELERATE.</s></p><p type="main"> <s><emph type="italics"></emph>In the former Book we have conſidered the Accidents which ac<lb></lb>company Equable Motion; we are now to treat of another kind of <lb></lb>Motion which we call Accelerate. </s> <s>And firſt it will be expedient to <lb></lb>find out and explain a Definition beſt agreeing to that which Nature <lb></lb>makes uſe of. </s> <s>For though it be not nconvenient to feign a Motion at plea<lb></lb>ſure, and then to conſider the Accidents that attend it (as thoſe have <lb></lb>done, who having framed in their imagination Helixes and Conchoi<lb></lb>des, which are Lines ariſing from certain Motions, although not uſed <lb></lb>by Nature, and upon that Suppoſition have laudably demonſtrated the <lb></lb>Symptomes thereof) yet in regard that Nature maketh uſe of a certain <lb></lb>kind of Acceleration in the deſcent of Grave Bodies, we are reſolved to <lb></lb>ſearch out and contemplate the paſſions thereof, and ſee whether the <lb></lb>Definition that we are about to produce of this our Accelerate Motion, <lb></lb>doth aptly and congruouſly ſute with the Eſſence of Motion Naturally <lb></lb>Accelerate. </s> <s>After many long and laborious Studies we have found out <lb></lb>a Definition which ſeemeth to expreſſe the true nature of this Accelerate <lb></lb>Motion, in regard that all the Natural Experiments that fall under <lb></lb>the Obſervation of our Senſes, do agree with thoſe its properties that <lb></lb>we intend anon to demonſtrate. </s> <s>In this Diſquiſition we have been aſſi<lb></lb>ſted, and as it were led by the hand by that obſervation of the uſual <lb></lb>Method and common procedure of Nature her ſelf in her other Operati<lb></lb>ons, wherein ſhe conſtantly makes uſe of the Firſt, Simpleſt, and Ea<lb></lb>ſieſt Means that are: for I believe that no man can think that Swim<lb></lb>ming or flying can be performed in a more ſimple or eaſie way, than that <lb></lb>which Fiſhes and Birds do uſe out of a Natural Inſtinct. </s> <s>Why there<lb></lb>fore ſhall not I be perſwaded, that, when I ſee a Stone to acquire conti<lb></lb>nually new additions of Velocity in its deſcending from its Reſt out of ſome <lb></lb>high place, this encreaſe made in the ſimpleſt eaſieſt and moſt obvious <lb></lb>manner that we can imagine? </s> <s>Now if we ſeriouſly examine all the ways <lb></lb>that can be deviſed, we ſhall find no encreaſes, no acquiſitions <lb></lb>leſſe intricate or more intelligible than that which ever encreaſeth or <lb></lb>makes its additions after the ſame manner. </s> <s>This appeareth by the great<emph.end type="italics"></emph.end><lb></lb>Affinity <emph type="italics"></emph>that is between Time and Motion. </s> <s>For as the Equability or <lb></lb>Vniformity of Motion is defined and expreſſed by the Equability of the<emph.end type="italics"></emph.end><pb xlink:href="040/01/826.jpg" pagenum="133"></pb><emph type="italics"></emph>Times and Spaces, (for we call that Motion or Lation Equable, by which <lb></lb>equal Spaces are paſt in equal Times) ſo by the ſame Equability of the <lb></lb>parts of Time, we may perceive, that the encreaſe of Celerity in the Natu<lb></lb>ral Motion of Grave Bodies, is made after a Simple and plain manner; <lb></lb>conceiving in our Mind that their Motion is continually accelerated uni<lb></lb>formly and at the ſame Rate, whilſt equal additions of Celerity are <lb></lb>conferred upon them in all equal Times. </s> <s>So that taking any equal par<lb></lb>ticles of Time beginning from the firſt Inſtant in which the Moveable <lb></lb>departeth from Reſt, and entereth upon its Deſcent, the Degree of <lb></lb>Velocity acquired in the firſt and ſecond Particles of Time, is double the <lb></lb>degree of Velocity that the Moveable acquired in the firſt Particle: and <lb></lb>the degree of Velocity that it acquireth in three Particles, is triple, and <lb></lb>that in four quadruple to the ſame Degree of the firſt Time: As, for <lb></lb>our better underſtanding, if a Moveable ſhould continue its Motion <lb></lb>according to the degree or moment of Velocity acquired in the firſt Parti<lb></lb>cle of Time, and ſhould extend its courſe equably with that ſame De<lb></lb>gree; this Motion would be twice as ſlow as that which it would obtain <lb></lb>according to the degree of Velocity acquired in two Particles of Time: <lb></lb>So that it will not be improper if we underſtand the Intention of the Ve<lb></lb>locity, to proceed according to the Extenſion of the Time. </s> <s>From whence <lb></lb>we may frame this Definition of the Motion of which we are about to <lb></lb>treat.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>DEFINITION.</s></p><p type="main"> <s>Motion Accelerate in an Equable or Vniform <lb></lb>Proportion, I call that which departing from <lb></lb>Reſt, ſuperaddeth equal moments of Velocity <lb></lb>in equal Times.</s></p><p type="main"> <s>SAGR. </s> <s>Though it were Irrational for me to oppoſe this or any <lb></lb>other Definition aſſigned by any whatſoever Author, they being all <lb></lb>Arbitrary, yet I may very well, without any offence, queſtion whe<lb></lb>ther this Definition, which is underſtood and admitted in Abſtract, <lb></lb>doth ſute, agree, and hold true in that ſort of Accelerate Motion, <lb></lb>which Grave Bodies deſcending naturally do exerciſe. </s> <s>And becauſe <lb></lb>the Authour ſeemeth to promiſe us, that the Natural Motion of <lb></lb>Grave Bodies is ſuch as he hath defined it, I could wiſh that ſome <lb></lb>Scruples were removed that trouble my mind; that ſo I might apply <lb></lb>my ſelf afterwards with greater attention to the Proportions and <lb></lb>Demonſtrations which are expected.</s></p><p type="main"> <s>SALV. </s> <s>I like well, that you and <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> do propound <lb></lb>Doubts as they come in the way: which I do imagine will be the <pb xlink:href="040/01/827.jpg" pagenum="134"></pb>ſame that I my ſelf did meet with when I firſt read this Treatiſe, <lb></lb>and that, either were reſolved by conferring with the Author, or <lb></lb>removed by my own conſidering of them.</s></p><p type="main"> <s>SAGR. </s> <s>Whilſt I am fancying to my ſelf a Grave Deſcending <lb></lb>Moveable to depart from Reſt, that is from the privation of all <lb></lb>Velocity, and to enter into Motion, and in that to go encrea<lb></lb>ſing, according to the proportion after which the Time encreaſeth <lb></lb>from the firſt inſtant of the Motion; and to have <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> in eight <lb></lb>Pulſations, acquired eight degrees of Velocity, of which in the <lb></lb>fourth Pulſation it had gained four, in the ſecond two, in the <lb></lb>firſt one, Time being ſubdiviſible <emph type="italics"></emph>in infinitum,<emph.end type="italics"></emph.end> it followeth, that <lb></lb>the Antecedent Velocity alwayes diminiſhing at that Rate, there <lb></lb>will bt no degree of Velocity ſo ſmall, or, if you will, of Tardity <lb></lb>ſo great, in which the ſaid Moveable is not found to be conſti<lb></lb>tuted, after its departure from infinite Tardity, that is, from <lb></lb>Reſt. </s> <s>So that if that degree of Velocity which it had at four Pul<lb></lb>ſations of Time, was ſuch, that maintaining it Equable, it would <lb></lb>have run two Miles in an hour, and with the degree of Velocity <lb></lb>that it had in the ſecond Pulſation, it would have gone one mile <lb></lb>an hour, it muſt be granted, that in the Inſtants of Time neeter <lb></lb>and neerer to its firſt Inſtant of moving from Reſt, it is ſo ſlow, <lb></lb>as that (continuing to move with that Tardity) it would not have <lb></lb>paſſed a Mile in an hour, nor in a day, nor in a year, nor in a <lb></lb>thouſand; nay, nor have gone one ſole foot in a greater time: <lb></lb>An accident to which me thinks the Imagination but very unea<lb></lb>ſily accords, ſeeing that Senſe ſheweth us, that a Grave Falling <lb></lb>Body commeth down ſuddenly, and with great Velocity.</s></p><p type="main"> <s>SALV. </s> <s>This is one of thoſe Doubts that alſo fell in my way <lb></lb>upon my firſt thinking on this affair, but not long after I remo<lb></lb>ved it: and that removal was the effect of the ſelf ſame Expe<lb></lb>riment which at preſent ſtarts it to you. </s> <s>You ſay, that in your <lb></lb>opinion, Experience ſheweth that the Moveable hath no ſooner <lb></lb>departed from Reſt, but it entereth into a very notable Velocity: <lb></lb>and I ſay, that this very Experiment proves it to us, that the firſt <lb></lb>Impetus's of the Cadent Body, although it be very heavy, are <lb></lb>moſt ſlack and ſlow. </s> <s>Lay a Grave Body upon ſome yielding mat<lb></lb>ter, and let it continue upon it till it hath preſſed into it as far as <lb></lb>it can with its ſimple Gravity; it is manifeſt, that raiſing it a yard <lb></lb>or two, and then letting it fall upon the ſame matter, it ſhall <lb></lb>with its percuſſion make a new preſſure, and greater than that <lb></lb>made at firſt by its meer weight: and the effect ſhall be cauſed <lb></lb>by the falling Moveable conjoyned with the Velocity acquired in <lb></lb>the Fall: which impreſſion ſhall be greater and greater, accord<lb></lb>ing as the Percuſſion ſhall come from a greater height; that is, <lb></lb>according as the Velocity of the Percutient ſhall be greater. </s> <s>We <pb xlink:href="040/01/828.jpg" pagenum="135"></pb>may therefore without miſtake conjecture the quantity of the Ve<lb></lb>locity of a falling heavy Body; by the quality and quantity of <lb></lb>the Percuſſion. </s> <s>But tell me Sirs, that Beetle which being let fall <lb></lb>upon a Stake from an height of four yards, driveth it into the <lb></lb>ground, <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> four inches, comming from an height of two yards, <lb></lb>ſhall drive it much leſſe, and leſſe from an height of one, and <lb></lb>leſſe from a foot; and laſtly lifting it up an inch, what will it do <lb></lb>more than if without any blow it were laid upon it? </s> <s>Certainly <lb></lb>but very little, and the operation would be wholly impercep<lb></lb>tible, if it were raiſed the thickneſſe of a leaf. </s> <s>And becauſe the <lb></lb>effect of the Percuſſion is regulated by the Velocity of the Percu<lb></lb>tient, who will queſtion but that the Motion is very ſlow, and <lb></lb>the Velocity extreme ſmall, where its operation is impercep<lb></lb>tible? </s> <s>See now of what power Truth is, ſince the ſame Experi<lb></lb>ment that ſeemed at the firſt bluſh to hold forth one thing, be<lb></lb>ing better conſidered, aſcertains us of the contrary. </s> <s>But without <lb></lb>having recourſe to that Experiment (which without doubt is moſt <lb></lb>perſwaſive) me-thinks that it is not hard to penetrate ſuch a <lb></lb>Truth as this by meer Diſcourſe. </s> <s>We have an heavy ſtone ſu<lb></lb>ſtained in the Air at Reſt: let it be diſengaged from its uphol<lb></lb>der, and ſet at liberty; and, as being more grave than the Air, it <lb></lb>goeth deſcending downwards, and that not with a Motion Equa<lb></lb>ble, but ſlow in the beginning, and continually afterwards ac<lb></lb>celerate: and ſeeing that the Velocity is Augmentable and Di<lb></lb>miniſhable <emph type="italics"></emph>in infinitum,<emph.end type="italics"></emph.end> what Reaſon ſhall perſwade me, that that <lb></lb>Moveable departing from an infinite Tardity (for ſuch is Reſt) <lb></lb>entereth immediately into ten degrees of Velocity, rather than in <lb></lb>one of four, or in this more than in one of two, of one, of half <lb></lb>one, or of the hundredth part of one; and to be ſhort, in all <lb></lb>the infinite leſſer? </s> <s>Pray you hear me. </s> <s>I do not think that you <lb></lb>would ſcruple to grant me, that the acquiſt of the Degrees of Ve<lb></lb>locity of the falling Stone may be made with the ſame Order as <lb></lb>is the Diminution and loſſe of the ſame degrees, when with an <lb></lb>impellent Virtue it is driven upwards to the ſame height: But if <lb></lb>that be ſo, I do not ſee how it can be ſuppoſed that in the diminu<lb></lb>tion of the Velocity of the aſcendent Stone, ſpending it all, it <lb></lb>can come to the ſtate of Reſt before it hath paſſed thorow all the <lb></lb>degrees of Tardity.</s></p><p type="main"> <s>SIMP. </s> <s>But if the greater and greater degrees of Tardity are <lb></lb>infinite, it ſhall never ſpend them all; ſo that the aſcendent <lb></lb>Grave will never attain to Reſt, but will move <emph type="italics"></emph>ad infinitum,<emph.end type="italics"></emph.end> ſtill <lb></lb>retarding: a thing which we ſee not to happen.</s></p><p type="main"> <s>SALV. </s> <s>This would happen, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> in caſe the Moveable <lb></lb>ſhould ſtay for ſome time in each degree: but it paſſeth thorow <lb></lb>them, without ſtaying longer than an inſtant in any of them. <pb xlink:href="040/01/829.jpg" pagenum="136"></pb>And becauſe in every quantitative Time, though never ſo ſmall, <lb></lb>there are infinite Inſtants, therefore they are ſufficient to anſwer <lb></lb>to the infinite degrees of Velocity diminiſhed. </s> <s>And that the <lb></lb>aſcendent Grave Body perſiſts not for any quantitative Time in <lb></lb>one and the ſame degree of Velocity, may thus be made out: <lb></lb>Becauſe, a certain quantitative Time being aſſigned it in the firſt <lb></lb>inſtant of that Time, and likewiſe in the laſt, the Moveable <lb></lb>ſhould be found to have one and the ſame degree of Velocity, it <lb></lb>might by this ſecond degree be likewiſe driven upwards ſuch an<lb></lb>other Space, like as from the firſt it was tranſported to the ſe<lb></lb>cond; and by the ſame reaſon it would paſſe from the ſecond to <lb></lb>the third, and, in ſhort, would continue its Motion Uniform <emph type="italics"></emph>ad <lb></lb>infinitum.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>From this Diſcourſe, as I conceive, one might derive a <lb></lb>very appoſite Reaſon of the Queſtion controverted amongſt Philo. <lb></lb></s> <s>ſophers, Touching what ſhould be the Cauſe of the acceleration <lb></lb>of the Natural Motion of Grave Moveables. </s> <s>For when I confider <lb></lb>in the Grave Body driven upwards, its continual Diminution of <lb></lb>that Virtue impreſſed upon it by the Projicient, which ſo long as <lb></lb>it was ſuperiour to that other contrary one of Gravity, forced it <lb></lb>upwards, this and that being come to an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> the Move<lb></lb>able ceaſeth to riſe any higher, and paſſeth thorow the ſtate of <lb></lb>Reſt, in which the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> impreſſed is not annihilated, but one<lb></lb>ly that exceſſe is ſpent, which it before had above the Gravity of <lb></lb>the Moveable, whereby prevailing over the ſame, it did drive <lb></lb>it upwards. </s> <s>And the Diminution of this forrein <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> continu<lb></lb>ing, and conſequently the advantage beginning to be on the part <lb></lb>of the Gravity, the Deſcent alſo beginneth but ſlow, in regard <lb></lb>of the oppoſition of the Virtue impreſſed, a conſiderable part of <lb></lb>which ſtill remaineth in the Moveable: but becauſe it doth go <lb></lb>continually diminiſhing, and is ſtill with a greater and greater <lb></lb>proportion overcome by the Gravity, hence ariſeth the continual <lb></lb>Acceleration of the Motion.</s></p><p type="main"> <s>SIMP. </s> <s>The conceit is witty, but more ſubtil than ſolid: for in <lb></lb>caſe it were concludent, it ſalveth onely thoſe Natural Motions <lb></lb>to which a Violent Motion preceded, in which part of the extern <lb></lb>Virtue ſtill remains in force: but where there is no ſuch remaining <lb></lb>impulſe, as where the Moveable departeth from a long Quieſ<lb></lb>cence, the ſtrength of your whole Diſcourſe vaniſheth.</s></p><p type="main"> <s>SAGR. </s> <s>I believe that you are in an Errour, and that this Di<lb></lb>ſtinction of Caſes which you make, is needleſſe, or, to ſay bet<lb></lb>ter, <emph type="italics"></emph>Null.<emph.end type="italics"></emph.end> Therefore tell me, whether may there be impreſſed <lb></lb>on the Project by the Projicient ſometimes much, and ſometimes <lb></lb>little Vertue; ſo as that it may be ſtricken upwards an hundred <lb></lb>yards, and alſo twenty, or four, or one?</s></p><pb xlink:href="040/01/830.jpg" pagenum="137"></pb><p type="main"> <s>SIMP. </s> <s>No doubt but there may.</s></p><p type="main"> <s>SAGR. </s> <s>And no leſſe poſſible is it, that the ſaid Virtue impreſſed <lb></lb>ſhall ſo little ſeperate the Reſiſtance of the Gravity, as not to <lb></lb>raiſe the Project above an inch: and finally the Virtue of the <lb></lb>Projicient may be onely ſo much, as juſt to equalize and com<lb></lb>penſate the Reſiſtance of the Gravity, ſo as that the Moveable <lb></lb>is not driven upwards, but onely ſuſtained. </s> <s>So that when you <lb></lb>hold a Stone in your hand, what elſe do you, but impreſſe on it <lb></lb>ſo much Virtue impelling upwards, as is the faculty of its Gra<lb></lb>vity drawing downwards? </s> <s>And this your Virtue, do you not <lb></lb>continue to keep it impreſſed on the Stone all the time that you <lb></lb>hold it in your hand? </s> <s>What ſay you, is it diminiſhed by your <lb></lb>long holding it? </s> <s>And this ſuſtention which impedeth the Stones <lb></lb>deſcent, what doth it import, whether it be made by your hand, <lb></lb>or by a Table, or by a Rope, that ſuſpends it? </s> <s>Doubtleſſe no <lb></lb>thing at all. </s> <s>Conclude with your ſelf therefore, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that <lb></lb>the precedence of a long, a ſhort, or a Momentary Reſt to the <lb></lb>Fall of the Stone, makes no alteration at all, ſo that the Stone <lb></lb>ſhould not alwaies depart affected with ſo much Virtue contrary <lb></lb>to Gravity, as did exactly ſuffice to have kept it in Reſt.</s></p><p type="main"> <s>SALV. </s> <s>I do not think it a ſeaſonable time at preſent to enter <lb></lb>upon the Diſquiſition of the Cauſe of the Acceleration of Natu<lb></lb>ral Motion: touching which ſundry Philoſophers have produced <lb></lb>ſundry opinions: ſome reducing it to the approximation unto <lb></lb>the Center others to the leſſe parts of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> ſucceſſively re<lb></lb>maining to be perforated; others to a certain Extruſion of the <lb></lb>Ambient <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> which in reuniting upon the back of the <lb></lb>Moveable, goeth driving and continually thruſting it; which <lb></lb>Fancies, and others of the like nature, it would be neceſſary to <lb></lb>examine, and with ſmall benefit to anſwer. </s> <s>It ſerveth our Au<lb></lb>thours turn at the preſent, that we underſtand that he will de<lb></lb>clare and demonſtrate to us ſome Paſſions of an Accelerate Mo<lb></lb>tion (be the Cauſe of its Acceleration what it will) ſo as that the <lb></lb>Moments of its Velocity do go encreaſing, after its departure from <lb></lb>Reſt with that moſt ſimple proportion wherewith the Continua<lb></lb>tion of the Time doth encreaſe: which is as much as to ſay, that <lb></lb>in equal Times there are made equal additaments of Velocity. <lb></lb></s> <s>And if it ſhall be found, that the Accidents that ſhall hereafter <lb></lb>be demonſtrated, do hold true in the Motion of Naturally De<lb></lb>ſcendent and Accelerate Grave Moveables, we may account, <lb></lb>that the aſſumed Definition taketh in that Motion of Grave Bo<lb></lb>dies, and that it is true, that their Acceleration doth encreaſe ac<lb></lb>cording as the Time and Duration of the Motion encreaſeth.</s></p><p type="main"> <s>SAGR. </s> <s>By what as yet is ſet before my Intellectuals, it appears <lb></lb>to me that one might with (haply) more plainneſſe define, and yet <pb xlink:href="040/01/831.jpg" pagenum="138"></pb>never alter the Conceit; ſaying that, A Motion uniformly accele<lb></lb>rate is that in which the Velocity goeth encreaſing according as <lb></lb>the Space encreaſeth that is paſſed thorow: So that, for example, <lb></lb>the degree of Velocity acquired by the Moveable in a deſcent of <lb></lb>four yards ſhould be double to that that it would have after it had <lb></lb>deſcended a Space of two, and this double to that acquired in the <lb></lb>Space of the firſt Yard. </s> <s>For I do not think that it can be doubted, <lb></lb>but that that Grave Moveable which falleth from an height of ſix <lb></lb>yards hath, and percuſſeth with an <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> double to that which <lb></lb>it had when it had deſcended three yards, and triple to that which <lb></lb>it had at two, and ſextuple to that had in the Space of one.</s></p><p type="main"> <s>SALV. </s> <s>I comfort my ſelf in that I have had ſuch a Companion <lb></lb>in my Errour: and I will tell you farther, that your Diſcourſe hath <lb></lb>ſo much of likelihood and probability in it, that our Author himſelf <lb></lb>did not deny unto me, when I propoſed it to him, that he likewiſe <lb></lb>had been for ſome time in the ſame miſtake. <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut that which I af<lb></lb>terwards extreamly wondred at, was to ſee in four plain words, <lb></lb>diſcovered, not only the falfity, but impoſſibility of two Propoſi<lb></lb>tions that carry with them ſo much of ſeeming truth, that having <lb></lb>propounded them to many, I never met with any one but did freely <lb></lb>admit them to be ſo.</s></p><p type="main"> <s>SIMP. </s> <s>Certainly I ſhould be of the number, and that the De<lb></lb>ſcendent Grave Moveable <emph type="italics"></emph>vires acquir at eundo,<emph.end type="italics"></emph.end> encreaſing its Ve<lb></lb>locity at the rate of the Space, and that the Moment of the ſame <lb></lb>Percutient is double, coming from a double height, ſeem to me Pro<lb></lb>poſitions to be granted without any hæſitation or controverſie.</s></p><p type="main"> <s>SALV. </s> <s>And yet they are as falſe and impoſſible, as that Moti<lb></lb>on is made in an inſtant. </s> <s>And hear a clear proof of the ſame. </s> <s>In <lb></lb>caſe the Velocities have the ſame proportion as the Spaces paſſed, <lb></lb>or to be paſſed, thoſe Spaces ſhall be paſſed in equal Times: if <lb></lb>therefore the Velocities with which the falling Moveable paſſeth <lb></lb>the Space of four yards, were double to the Velocities with which it <lb></lb>paſſeth the two firſt yards (like as the Space is double to the Space) <lb></lb>then the Times of thoſe Tranſitions are equal: but the ſame Move<lb></lb>able's paſſing the four yards, and the two in one and the ſame Time, <lb></lb>hath place only in Inſtantaneous Motion. <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut we ſee, that the <lb></lb>falling grave <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ody maketh its Motion in Time, and paſſeth the two <lb></lb>yards in a leſſer than it doth the four. </s> <s>Therefore it is falſe that its <lb></lb>Velocity encreaſeth as its Space. </s> <s>The other Propoſition is demon<lb></lb>ſtrated to be falſe with the ſame perſpicuity. </s> <s>For that which per<lb></lb>cuſſeth being the ſame, the difference and Moment of the Percuſſton <lb></lb>cannot be determined but by the difference of Velocity; If there<lb></lb>fore the percutient, coming from a double height, make a Percuſſi<lb></lb>on with a double Moment, it is neceſſary that it ſtrike with a dou<lb></lb>ble Velocity: <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut the double Velocity paſſeth the double Space in <pb xlink:href="040/01/832.jpg" pagenum="139"></pb>the ſame Time; and we ſee the Time of the Deſcent from the grea<lb></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></lb>wherewith you manifeſt abſtruce Concluſions: this extream eaſi<lb></lb>neſs rendreth them of leſſe value than they were whilſt they lay hid <lb></lb>under contrary appearances. </s> <s>I believe that the Generality of men <lb></lb>little preſſe thoſe Notions which are eaſily obtained, in compari<lb></lb>ſon of thoſe about which men make ſo long and inexplicable alter<lb></lb>cations.</s></p><p type="main"> <s>SALV. </s> <s>To thoſe which with great brevity and clarity ſhew the <lb></lb>fallacies of Propoſitions that have been commonly received for <lb></lb>true by the generality of people, it would be a very tolerable in<lb></lb>jury to return them only ſlighting inſtead of thanks: but there is <lb></lb>much diſpleaſure and moleſtation in another certain affection <lb></lb>ſometimes found in ſome men, that pretending in the ſame Studies <lb></lb>at leaſt Parity with any whomſoever, do ſee that they have let <lb></lb>paſs ſuch and ſuch for true Concluſions, which afterwards by <lb></lb>another, with a ſhort and eaſie diſquiſition, have been detected and <lb></lb>convicted for falſe. </s> <s>I will not call that affection Envy, that is ac<lb></lb>cuſtomed to convert in time to hatred and deſpite againſt the diſ<lb></lb>coverers of ſuch Fallacies, but I will call it an itch, and a deſire to <lb></lb>be able rather to maintain their inveterate Errours, than to per<lb></lb>mit the reception of new-diſcovered Truths. </s> <s>Which humour ſome<lb></lb>times induceth them to write in contradiction of thoſe truths <lb></lb>which are but too perfectly known unto themſelves only to keep <lb></lb>the Reputation of others low in the opinion of the numerous and <lb></lb>ill-informed Vulgar. </s> <s>Of ſuch falſe Concluſions received for true, <lb></lb>and very eaſie to be confuted, I have heard no ſmall number from <lb></lb>our <emph type="italics"></emph>Academick,<emph.end type="italics"></emph.end> of ſome of which I have kept account.</s></p><p type="main"> <s>SAGR. </s> <s>And you muſt not deprive us of them; but in due time <lb></lb>impart them to us, when a particular Meeting ſhall be appointed <lb></lb>for them. </s> <s>For the preſent, continuing the diſcourſe we are about, <lb></lb>I think that by this time we have eſtabliſhed the Definition of Mo<lb></lb>tion uniformly Accelerate, treated of in the enſuing diſcourſes, <lb></lb>and it is this;</s></p><p type="main"> <s><emph type="italics"></emph>A Motion Equable, or Vniformly Accelerate, we call that which <lb></lb>departing from Reſt ſuperadds equal Moments of Velocity in <lb></lb>equal Times.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>That Definition being confirmed, the Author asketh <lb></lb>and ſuppoſeth but one only Principle to be true, namely:</s></p><pb xlink:href="040/01/833.jpg" pagenum="140"></pb><p type="head"> <s>SVPPOSITION.</s></p><p type="main"> <s><emph type="italics"></emph>I ſuppoſe that the degrees of Velocity acquired by the <lb></lb>ſame Moveable upon Planes of different inclinations <lb></lb>are equal then, when the Elevations of the ſaid <lb></lb>Planes are equal.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>By the Elevation of an inclined Plane he meaneth the Per<lb></lb>pendicular, which from the higher term of the ſaid Plane <lb></lb>falleth upon the Horizontal Line produced along by the <lb></lb>lower term of the ſaid Plane inclined: as for better underſtanding; <lb></lb>the Line A B being parallel to the Horizon, upon which let the two <lb></lb><figure id="id.040.01.833.1.jpg" xlink:href="040/01/833/1.jpg"></figure><lb></lb>Planes C A, and C D be inclined: <lb></lb>the Perpendicular C B falling up<lb></lb>on the Horizontal Line B A the <lb></lb>Author calleth the Elevation <lb></lb>of the Planes C A and C D; <lb></lb>and ſuppoſeth that the degrees of <lb></lb>Velocity of the ſame Moveable <lb></lb>deſcending along the inclined Planes C A and C D, acqui<lb></lb>red in the Terms A and D are equal, for that their Elevation is <lb></lb>the ſame C B. </s> <s>And ſo great alſo ought the degree of Velocity be <lb></lb>underſtood to be which the ſame Moveable falling from the Point <lb></lb>C would acquire in the term B.</s></p><p type="main"> <s>SAGR. </s> <s>The truth is, this Suppoſition hath in it ſo much of pro<lb></lb>bability, that it deſerveth to be granted without diſpute, alwaies <lb></lb>preſuppoſing that all accidental and extern Impediments are re<lb></lb>moved, and that the Planes be very Solid and Terſe, and the Move<lb></lb>able in Figure moſt perfectly Rotund, ſo that neither the Plane, <lb></lb>nor the Moveable have any unevenneſs. </s> <s>All Contraſts and Im<lb></lb>pediments, I ſay, being removed, the light of Nature dictates to <lb></lb>me without any difficulty, that a Ball heavy and perfectly round <lb></lb>deſcending by the Lines C A, C D, and C B would come to the <lb></lb>terms A D, and B with equal <emph type="italics"></emph>Impetus's.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>You argue very probably; but over and above the pro<lb></lb>bability, I will by an Experiment ſo increaſe the likelihood, as that <lb></lb>it wants but little of being equal to a very neceſſary Demonſtrati<lb></lb>on. </s> <s>Imagine this leafe of Paper to be a Wall erect at Right-angles <lb></lb>to the Horizon, and at a Nail, faſtned in the ſame, hang a Ball or <lb></lb>Plummet of Lead, weighing an ounce or two, ſuſpended by the <lb></lb>ſmall thread A B, two or three yards long, perpendicular to the <lb></lb>Horizon: and on the Wall draw an Horizontal Line D C, cutting <pb xlink:href="040/01/834.jpg" pagenum="141"></pb>the Perpendicular A B at Right angles, which A B muſt hang two <lb></lb>Inches, or thereabouts, from the Wall: Then transferring the <lb></lb>ſtring A B with the Ball into C, let go the ſaid Ball; which you will <lb></lb><figure id="id.040.01.834.1.jpg" xlink:href="040/01/834/1.jpg"></figure><lb></lb>ſee firſt to deſcend <lb></lb>deſcribing C B D, and <lb></lb>to paſs ſo far beyond <lb></lb>the Term B, that run<lb></lb>ning along the Arch <lb></lb>B D it will riſe almoſt <lb></lb>as high as the deſigned <lb></lb>Parallel C D, wanting <lb></lb>but a very ſmall mat<lb></lb>ter of reaching to it, <lb></lb>the preciſe arrival thi<lb></lb>ther being denied it by <lb></lb>the Impediment of the Air, and of the Thread. </s> <s>From which we <lb></lb>may truly conclude, that the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> acquired in the point B by <lb></lb>the Ball in its deſcent along the Arch C B, was ſo much as ſufficed <lb></lb>to carry it upwards along ſuch another Arch B D unto the ſame <lb></lb>height: having made, and often reiterated this Experiment, let <lb></lb>us drive into the Wall, along which the Perpendicular A B paſſeth, <lb></lb>another Nail, as in E or in F, which is to ſtand out five or ſix In<lb></lb>ches; and this to the end that the thread A B, returning as before <lb></lb>to carry back the Ball C along the Arch C B, when it is come to <lb></lb>B, the Thread ſtopping at the Nail E may be conſtrained to move <lb></lb>along the Circumference B G, deſcribed about the Center E: by <lb></lb>which we ſhall ſee what that ſame <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> is able to do, which be<lb></lb>fore, being conceived in the ſame term B, carried the ſame Move<lb></lb>able along the Arch B D unto the height of the Horizontal Line <lb></lb>C D. Now, Sirs, you ſhall with delight ſee the Ball carried unto <lb></lb>the Horizontal Line in the Point G; and the ſame will happen if <lb></lb>the ſtop be placed lower, as in F, where the Ball would deſcribe <lb></lb>the Arch B I, evermore terminating its aſcent exactly in the Line <lb></lb>C D: and in caſe the Check were ſo low that the overplus of the <lb></lb>thread beneath it cannot reach to the height of C D, (which would <lb></lb>happen if it were nearer to the point B than to the interſection of <lb></lb>A B with the Horizontal Line C D) then the thread would <lb></lb>whirle and twine about the Nail. </s> <s>This experiment leaveth no <lb></lb>place for our doubting of the truth of the Suppoſition: for the <lb></lb>two Arches C B and D B being equall, and ſcituate alike, the <lb></lb>acquiſt of Moment made along the Deſcent in the Arch C B, is <lb></lb>the ſame with that made along the Deſcent in the Arch D B. </s> <s>But <lb></lb>the Moment acquired in <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> along the Arch C <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> is able to carry the <lb></lb>ſame Moveable upwards along the Arch <emph type="italics"></emph>B<emph.end type="italics"></emph.end> D: Therefore the Mo<lb></lb>ment acquired in the Deſcent D <emph type="italics"></emph>B<emph.end type="italics"></emph.end> is equall to that which driveth <pb xlink:href="040/01/835.jpg" pagenum="142"></pb>the ſame Moveable along the ſame Arch from <emph type="italics"></emph>B<emph.end type="italics"></emph.end> to D: So that ge<lb></lb>nerally every Moment acquired along the Deſcent of an Arch is <lb></lb>equall to that which hath power to make the ſame Moveable re<lb></lb>aſcend along the ſame Arch: <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut all the Moments that make the <lb></lb>Moveable aſcend along all the Arches <emph type="italics"></emph>B<emph.end type="italics"></emph.end> D, <emph type="italics"></emph>B<emph.end type="italics"></emph.end> G, <emph type="italics"></emph>B<emph.end type="italics"></emph.end> I are equal, <lb></lb>ſince they are made by one and the ſame Moment acquired along <lb></lb>the Deſcent C <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> as Experience ſhews: Therefore all the Moments <lb></lb>that are acquired by the Deſcents along the Arches D <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> G <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> and <lb></lb>I <emph type="italics"></emph>B<emph.end type="italics"></emph.end> are equal.</s></p><p type="main"> <s>SAGR. </s> <s>Your Diſcourſe is in my Judgment very Rational, and <lb></lb>the Experiment ſo appoſite and pertinent to verifie the <emph type="italics"></emph>Poſtulatum,<emph.end type="italics"></emph.end><lb></lb>that it very well deſerveth to be admitted as if it were Demon<lb></lb>ſtrated.</s></p><p type="main"> <s>SALV. </s> <s>I will not conſent, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> that we take more to our <lb></lb>ſelves than we ought; and the rather for that we are chiefly to <lb></lb>make uſe of this Aſſumption in Motions made upon ſtreight and <lb></lb>not curved Superficies; in which the Acceleration proceedeth with <lb></lb>degrees very different from thoſe wherewith we ſuppoſe it to pro<lb></lb>ceed in ſtreight Planes. </s> <s>Inſomuch, that although the Experiment <lb></lb>alledged ſhews us, that the deſcent along the Arch C <emph type="italics"></emph>B<emph.end type="italics"></emph.end> conferreth <lb></lb>on the Moveable ſuch a Moment, as that it is able to re-carry it <lb></lb>to the ſame height along any other Arch <emph type="italics"></emph>B<emph.end type="italics"></emph.end> C, <emph type="italics"></emph>B<emph.end type="italics"></emph.end> G, and <emph type="italics"></emph>B<emph.end type="italics"></emph.end> I, yet <lb></lb>we cannot with the like evidence ſhew, that the ſame would hap<lb></lb>pen in caſe a moſt exact <emph type="italics"></emph>B<emph.end type="italics"></emph.end>all were to deſcend by ſtreight Planes in<lb></lb>clined according to the inclinations of the Chords of theſe ſame <lb></lb>Arches: yea, it is credible, that Angles being formed by the ſaid <lb></lb>Right Planes in the term <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>all deſcended along the Declivi<lb></lb>ty according to the Chord C <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> finding a ſtop in the Planes aſcend<lb></lb>ing according to the Chords <emph type="italics"></emph>B<emph.end type="italics"></emph.end> D, <emph type="italics"></emph>B<emph.end type="italics"></emph.end> G, and <emph type="italics"></emph>B<emph.end type="italics"></emph.end> I, in juſtling againſt <lb></lb>them, would loſe of its <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> and could not be able in riſing to <lb></lb>attain the height of the Line C D. <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut the Obſtacle being remo<lb></lb>ved, which prejudiceth the Experiment, I do believe, that the un<lb></lb>derſtanding may conceive, that the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> (which in effect de<lb></lb>riveth vigour from the quantity of the Deſcent) would be able to <lb></lb>remount the Moveable to the ſame height. </s> <s>Let us therefore take <lb></lb>this at preſent for a <emph type="italics"></emph>Poſtulatum<emph.end type="italics"></emph.end> or Petition, the abſolute truth of <lb></lb>which will come to be eſtabliſhed hereafter by ſeeing other Con<lb></lb>cluſions raiſed upon this Hypotheſis to anſwer, and exactly jump <lb></lb>with the Experiment. </s> <s>The Author having ſuppoſed this only Prin<lb></lb>ciple, he paſſeth to the Propoſitions, demonſtratively proving them; <lb></lb>of which the firſt is this;</s></p><pb xlink:href="040/01/836.jpg" pagenum="143"></pb><p type="head"> <s>THEOR. I. PROP. I.</s></p><p type="main"> <s>The time in which a Space is paſſed by a Movea<lb></lb>ble with a Motion Vniformly Accelerate, out of <lb></lb>Reſt, is equal to the Time in which the ſame <lb></lb>Space would be paſt by the ſame Moveable <lb></lb>with an Equable Motion, the degree of whoſe <lb></lb>Velocity is ſubduple to the greateſt and ulti <lb></lb>mate degree of the Velocity of the former Vni<lb></lb>formly Accelerate Motion.</s></p><p type="main"> <s><emph type="italics"></emph>Let us by the extenſion A B repreſent the Time, in which the <lb></lb>Space<emph.end type="italics"></emph.end> C D <emph type="italics"></emph>is paſſed by a Moveable with a Motion Vniformly <lb></lb>Accelerate, out of Reſt in C: and let the greateſt and laſt de-<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.836.1.jpg" xlink:href="040/01/836/1.jpg"></figure><lb></lb><emph type="italics"></emph>gree of Velocity acquired in the Inſtants of the Time<emph.end type="italics"></emph.end><lb></lb>A B <emph type="italics"></emph>be repreſented by<emph.end type="italics"></emph.end> E B; <emph type="italics"></emph>and conſtitute at plea<lb></lb>ſure upon<emph.end type="italics"></emph.end> A B <emph type="italics"></emph>any number of parts, and thorow the <lb></lb>points of diviſion draw as many Lines, continued <lb></lb>out unto the Line<emph.end type="italics"></emph.end> A E, <emph type="italics"></emph>and equidiſtant to<emph.end type="italics"></emph.end> B E, <lb></lb><emph type="italics"></emph>which will repreſent the encreaſe of the degrees of <lb></lb>Velocity after the firſt Inſtant A. </s> <s>Then divide<emph.end type="italics"></emph.end> B E <lb></lb><emph type="italics"></emph>into two equall parts in<emph.end type="italics"></emph.end> F, <emph type="italics"></emph>and draw<emph.end type="italics"></emph.end> F G <emph type="italics"></emph>and<emph.end type="italics"></emph.end> A G <lb></lb><emph type="italics"></emph>parallel to B A and<emph.end type="italics"></emph.end> B F<emph type="italics"></emph>: The Parallelogram<emph.end type="italics"></emph.end> A G <lb></lb>F B <emph type="italics"></emph>ſhall be equall to the Triangle<emph.end type="italics"></emph.end> A E B, <emph type="italics"></emph>its Side<emph.end type="italics"></emph.end><lb></lb>G F <emph type="italics"></emph>dividing<emph.end type="italics"></emph.end> A E <emph type="italics"></emph>into two equall parts in I: For <lb></lb>if the Parallels of the Triangle<emph.end type="italics"></emph.end> A E <emph type="italics"></emph>B be continued <lb></lb>out unto<emph.end type="italics"></emph.end> I G F, <emph type="italics"></emph>we ſhall have the Aggregate of all <lb></lb>the Parallels contained in the Quadrilatural Figure <lb></lb>equal to the Aggregate of all the Parallels compre<lb></lb>hended in the Triangle<emph.end type="italics"></emph.end> A E <emph type="italics"></emph>B; For thoſe in the Triangle<emph.end type="italics"></emph.end> I E F <emph type="italics"></emph>are equal <lb></lb>to thoſe contained in the Triangle<emph.end type="italics"></emph.end> G I A, <emph type="italics"></emph>and thoſe that are in the<emph.end type="italics"></emph.end> Tra<lb></lb>pezium <emph type="italics"></emph>are in common. </s> <s>Now ſince all and ſingular the Inſtants of Time <lb></lb>do anſwer to all and ſingular the Points of the Line A B; and ſince the <lb></lb>Parallels contained in the Triangle<emph.end type="italics"></emph.end> A E <emph type="italics"></emph>B do repreſent the degrees of Ac<lb></lb>celeration or encreaſing Velocity, and the Parallels contained in the Pa<lb></lb>rallelogram do likewiſe repreſent as many degrees of Equable Motion or <lb></lb>unencreaſing Velocity: It appeareth, that as many Moments of Velocity <lb></lb>paſſed in the Accelerate Motion according to the encreaſing Parallels of the <lb></lb>Triangle A E B, as in the Equable Motion according to the Parallels of <lb></lb>the Parallelogram G B: Becauſe what is wanting in the firſt half of the<emph.end type="italics"></emph.end><pb xlink:href="040/01/837.jpg" pagenum="144"></pb><emph type="italics"></emph>Accelerate Motion of the Velocity of the Equable Motion (which defi<lb></lb>cient Moments are repreſented by the Parallels of the Triangle A<emph.end type="italics"></emph.end> G I) <lb></lb><emph type="italics"></emph>is made up by the moments repreſented by the Parallels of the Triangle<emph.end type="italics"></emph.end><lb></lb>I E F. <emph type="italics"></emph>It is manifeſt, therefore, that thoſe Spaces are equal which are <lb></lb>in the ſame Time by two Moveables, one whereof is moved with a Mo<lb></lb>tion uniformly Accelerated from Reſt, the other with a Motion Equable <lb></lb>according to the Moment ſubduple of that of the greateſt Velocity of the <lb></lb>Accelerated Motion: Which was to be demonſtrated.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>THEOR. II. PROP. II.</s></p><p type="main"> <s>If a <emph type="italics"></emph>M<emph.end type="italics"></emph.end>oveable deſcend out of Reſt with a <emph type="italics"></emph>M<emph.end type="italics"></emph.end>oti<lb></lb>on uniformly Accelerate, the Spaces which it <lb></lb>paſſeth in any whatſoever Times are to each <lb></lb>other in a proportion Duplicate of the ſame <lb></lb>Times; that is, they are as the Squares of <lb></lb>them.</s></p><p type="main"> <s><emph type="italics"></emph>Let<emph.end type="italics"></emph.end> A B <emph type="italics"></emph>repreſent a length of Time beginning at the firſt Inſtant A; <lb></lb>and let<emph.end type="italics"></emph.end> A D <emph type="italics"></emph>and<emph.end type="italics"></emph.end> A E <emph type="italics"></emph>repreſent any two parts of the ſaid Time; <lb></lb>and let<emph.end type="italics"></emph.end> H I <emph type="italics"></emph>be a Line in which the Moveable out of H, (as the firſt <lb></lb>beginning of the Motion) deſcendeth uniformly accelerating; and let the<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.837.1.jpg" xlink:href="040/01/837/1.jpg"></figure><lb></lb><emph type="italics"></emph>Space<emph.end type="italics"></emph.end> H L <emph type="italics"></emph>be paſſed in the firſt Time<emph.end type="italics"></emph.end> A D; <emph type="italics"></emph>and let<emph.end type="italics"></emph.end> H M <lb></lb><emph type="italics"></emph>be the Space that it ſhall deſcend in the Time<emph.end type="italics"></emph.end> A E. <emph type="italics"></emph>I ſay, <lb></lb>the Space<emph.end type="italics"></emph.end> M H <emph type="italics"></emph>is to the Space<emph.end type="italics"></emph.end> H L <emph type="italics"></emph>in duplicate propor<lb></lb>tion of that which the Time<emph.end type="italics"></emph.end> E A <emph type="italics"></emph>hath to the Time<emph.end type="italics"></emph.end> A D<emph type="italics"></emph>: <lb></lb>Or, if you will, that the Spaces<emph.end type="italics"></emph.end> M H <emph type="italics"></emph>and<emph.end type="italics"></emph.end> H L <emph type="italics"></emph>are to one <lb></lb>another in the ſame proportion as the Squares<emph.end type="italics"></emph.end> E A <emph type="italics"></emph>and<emph.end type="italics"></emph.end><lb></lb>A D. <emph type="italics"></emph>Draw the Line<emph.end type="italics"></emph.end> A C <emph type="italics"></emph>at any Angle with<emph.end type="italics"></emph.end> A B, <emph type="italics"></emph>and <lb></lb>from the points D and E draw the Parallels<emph.end type="italics"></emph.end> D O <emph type="italics"></emph>and<emph.end type="italics"></emph.end><lb></lb>P E<emph type="italics"></emph>: of which<emph.end type="italics"></emph.end> D O <emph type="italics"></emph>will repreſent the greateſt degree <lb></lb>of Velocity acquired in the Inſtant D of the Time<emph.end type="italics"></emph.end> A D; <lb></lb><emph type="italics"></emph>and<emph.end type="italics"></emph.end> P <emph type="italics"></emph>the greateſt degree of Velocity acquired in the In<lb></lb>ſtant E of the Time<emph.end type="italics"></emph.end> A E. <emph type="italics"></emph>And becauſe we have de<lb></lb>monſtrated in the laſt Propoſition concerning Spaces, that <lb></lb>thoſe are equal to one another, of which two Moveables <lb></lb>have paſt in the ſame Time, the one by a Moveable out <lb></lb>of Reſt with a Motion uniformly Accelerate, and the <lb></lb>other by the ſame Moveable with an Equable Motion, <lb></lb>whoſe Velocity is ſubduple to the greateſt acquired by the <lb></lb>Accelerate Motion: Therefore<emph.end type="italics"></emph.end> M H <emph type="italics"></emph>and<emph.end type="italics"></emph.end> H L <emph type="italics"></emph>are the Spaces that two <lb></lb>Lquable Motions, whoſe Velocities ſhould be as the half of<emph.end type="italics"></emph.end> P E, <emph type="italics"></emph>and<emph.end type="italics"></emph.end><pb xlink:href="040/01/838.jpg" pagenum="145"></pb><emph type="italics"></emph>half of<emph.end type="italics"></emph.end> O D, <emph type="italics"></emph>would paſſe in the Times<emph.end type="italics"></emph.end> E A <emph type="italics"></emph>and<emph.end type="italics"></emph.end> D A. <emph type="italics"></emph>If it be proved <lb></lb>therefore that theſe Spaces<emph.end type="italics"></emph.end> M H <emph type="italics"></emph>and<emph.end type="italics"></emph.end> L H <emph type="italics"></emph>are in duplicate proportion to <lb></lb>the Times<emph.end type="italics"></emph.end> E A <emph type="italics"></emph>and<emph.end type="italics"></emph.end> D A; <emph type="italics"></emph>We ſhall have done that which was intended. <lb></lb></s> <s>But in the fourth Propoſition of the Firſt Book we have demonſtrated: <lb></lb>That the Spaces paſt by two Moveables with an Equable Motion are <lb></lb>to each other in a proportion compounded of the proportion of the Velo<lb></lb>cities and of the proportion of the Times: But in this caſe the propor<lb></lb>tion of the Velocities and the proportion of the Times is the ſame<emph.end type="italics"></emph.end> (<emph type="italics"></emph>for <lb></lb>as the half of<emph.end type="italics"></emph.end> P E <emph type="italics"></emph>is to the half of<emph.end type="italics"></emph.end> O D, <emph type="italics"></emph>or the whole<emph.end type="italics"></emph.end> P E <emph type="italics"></emph>to the whole<emph.end type="italics"></emph.end><lb></lb>O D, <emph type="italics"></emph>ſo is<emph.end type="italics"></emph.end> A E <emph type="italics"></emph>to<emph.end type="italics"></emph.end> A D<emph type="italics"></emph>: Therefore the proportion of the Spaces paſ<lb></lb>ſed is double to the proportion of the Times. </s> <s>Which was to be demon<lb></lb>ſtrated.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Hence likewiſe it is manifeſt, that the proportion of the ſame Spaces <lb></lb>is double to the proportions of the greateſt degrees of Velocity: that is, <lb></lb>of the Lines<emph.end type="italics"></emph.end> P E <emph type="italics"></emph>and<emph.end type="italics"></emph.end> O D<emph type="italics"></emph>: becauſe<emph.end type="italics"></emph.end> P E <emph type="italics"></emph>is to<emph.end type="italics"></emph.end> O D, <emph type="italics"></emph>as<emph.end type="italics"></emph.end> E A <emph type="italics"></emph>to<emph.end type="italics"></emph.end> D A.</s></p><p type="head"> <s>COROLARY I.</s></p><p type="main"> <s><emph type="italics"></emph>Hence it is manifeſt, that if there were many equal Times taken in or<lb></lb>der from the firſt Inſtant or beginniug of the Motion, as ſuppoſe<emph.end type="italics"></emph.end><lb></lb>A D, D E, E F, F G, <emph type="italics"></emph>in which the Spaces<emph.end type="italics"></emph.end> H L, L M, M N, N I <lb></lb><emph type="italics"></emph>are paſſed, thoſe Spaces ſhall be to one another as the odd numbers <lb></lb>from an Vnite:<emph.end type="italics"></emph.end> ſcilicet, <emph type="italics"></emph>as 1, 3, 5, 7. For this is the Rate or pro<lb></lb>portion of the exceſſes of the Squares of Lines that equally exceed <lb></lb>one another, and the exceſſe of which is equal to the least of them, <lb></lb>or, if you will, of Squares that follow one another, beginning<emph.end type="italics"></emph.end> ab <lb></lb>Unitate. <emph type="italics"></emph>Whilſt therefore the degree of Velocity is encreaſed ac<lb></lb>cording to the ſimple Series of Numbers in equal Times, the Spaces <lb></lb>paſt in thoſe Times make their encreaſe according to the Series of <lb></lb>odd Numbers from an Vnite.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>Be pleaſed to ſtay your Reading, whilſt I do paraphraſe <lb></lb>touching a certain Conjecture that came into my mind <lb></lb>but even now; for the explanation of which, unto your under<lb></lb>ſtanding and my own, I will deſcribe a ſhort Scheme: in which I <lb></lb>fanſie by the Line A I the continuation of the Time after the firſt <lb></lb>Inſtant, applying the Right Line A F unto A according to any <lb></lb>Angle: and joyning together the Terms I F, I divide the Time A I <lb></lb>in half at C, and then draw C B parallel to I F. <emph type="italics"></emph>A<emph.end type="italics"></emph.end>nd then conſide<lb></lb>ring B C, as the greateſt degree of Velocity which beginning from <lb></lb>Reſt in the firſt Inſtant of the Time <emph type="italics"></emph>A<emph.end type="italics"></emph.end> goeth augmenting accord<lb></lb>ing to the encreaſe of the Parallels to B C, drawn in the Triangle <lb></lb><emph type="italics"></emph>A<emph.end type="italics"></emph.end> B C, (which is all one as to encreaſe according to the encreaſe <lb></lb>of the Time) I admit without diſpute, upon what hath been ſaid <lb></lb>already, That the Space paſt by the falling Moveable with the <pb xlink:href="040/01/839.jpg" pagenum="146"></pb>Velocity encreaſed in the manner aforeſaid would be equal to the <lb></lb>Space that the ſaid Moveable would paſſe, in caſe it were in the <lb></lb>ſame Time <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C, moved with an Uniform Motion, whoſe degree of <lb></lb>Velocity ſhould be equal to E C, the half of B C. </s> <s>I now proceed <lb></lb>farther, and imagine the Moveable; having deſcended with an <lb></lb><emph type="italics"></emph>A<emph.end type="italics"></emph.end>ccelerate Motion, to have in the Inſtant <lb></lb>C the degree of Velocity B C: It is ma<lb></lb><figure id="id.040.01.839.1.jpg" xlink:href="040/01/839/1.jpg"></figure><lb></lb>nifeſt, that if it did continue to move <lb></lb>with the ſame degree of Velocity B C, <lb></lb>without farther <emph type="italics"></emph>A<emph.end type="italics"></emph.end>cceleration, it would <lb></lb>paſſe in the following Time C I, a Space <lb></lb>double to that which it paſſed in the equal <lb></lb>Time <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C, with the degree of Uniform <lb></lb>Velocity E C, the half of the Degree B C. <lb></lb></s> <s>But becauſe the Moveable deſcendeth <lb></lb>with a Velocity encreaſed alwaies Uni<lb></lb>formly in all equal Times; it will add to <lb></lb>the degree C B in the following Time <lb></lb>C I, thoſe Tame Moments of Velocity <lb></lb>that encreaſe according to the Parallels of <lb></lb>the Triangle B F G, equal to the Triangle <lb></lb><emph type="italics"></emph>A<emph.end type="italics"></emph.end> B C. </s> <s>So that adding to the degree of <lb></lb>Velocity G I, the half of the degree F G, the greateſt of thoſe ac<lb></lb>quired in the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ccelerate Motion, and regulated by the Parallels of <lb></lb>the Triangle B F G, we ſhall have the degree of Velocity I N, with <lb></lb>which, with an Uniform Motion, it would have moved in the <lb></lb>Time C I: Which degree I N, being triple the degree E C, pro<lb></lb>veth that the Space paſſed in the ſecond Time C I ought to be tri<lb></lb>ple to that of the firſt Time C <emph type="italics"></emph>A. A<emph.end type="italics"></emph.end>nd if we ſhould ſuppoſe to be <lb></lb>added to <emph type="italics"></emph>A<emph.end type="italics"></emph.end> I another equal part of Time I O, and the Triangle to <lb></lb>be enlarged unto <emph type="italics"></emph>A<emph.end type="italics"></emph.end> P O; it is manifeſt, that if the Motion ſhould <lb></lb>continue for all the Time I O with the degree of Velocity I F, <lb></lb>acquired in the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ccelerate Motion in the Time <emph type="italics"></emph>A<emph.end type="italics"></emph.end> I, that degree <lb></lb>I F being Quadruple to E C, the Space paſſed would be Quadruple <lb></lb>to that paſſed in the equal firſt Time <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C: But continuing the <lb></lb>encreaſe of the Uniform <emph type="italics"></emph>A<emph.end type="italics"></emph.end>cceleration in the Triangle F P Q like <lb></lb>to that of the Triangle <emph type="italics"></emph>A<emph.end type="italics"></emph.end> B C, which being reduced to equable <lb></lb>Motion addeth the degree equal to E C, Q R being added, equal <lb></lb>to E C, we ſhall have the whole Equable Velocity exerciſed in the <lb></lb>Time I O, quintuple to the Equable Velocity of the firſt Time <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C, <lb></lb>and therefore the Space paſſed quintuple to that paſt in the firſt <lb></lb>Time <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C. </s> <s>We ſee therefore, even by this familiar computation, <lb></lb>That the Spaces paſſed in equal Times by a Moveable which <lb></lb>departing from Reſt goeth acquiring Velocity, according to the <lb></lb>encreaſe of the Time, are to one another as the odd Numbers <emph type="italics"></emph>ab<emph.end type="italics"></emph.end><pb xlink:href="040/01/840.jpg" pagenum="147"></pb><emph type="italics"></emph>unitate 1, 3, 5: A<emph.end type="italics"></emph.end>nd that the Spaces paſſed being conjunctly taken, <lb></lb>that paſſed in the double Time is quadruple to that paſſed in the <lb></lb>ſubduple, that paſſed in the triple Time is nonuple; and, in a word, <lb></lb>that the Spaces paſſed are in duplicate proportion to their Times; <lb></lb>that is, as the Squares of the ſaid Times.</s></p><p type="main"> <s>SIMP. </s> <s>I muſt confeſſe that I have taken more pleaſure in this <lb></lb>plain and clear diſcourſe of <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> than in the to-me-more <lb></lb>obſcure Demonſtration of the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>uthor: ſo that I am very well <lb></lb>ſatisfied, that the buſineſſe is to ſucceed as hath been ſaid, the <lb></lb>Definition of Uniformly <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ccelerate Motion being ſuppoſed, and <lb></lb>granted. </s> <s>But whether this be the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>cceleration of which Nature <lb></lb>maketh uſe in the Motion of its deſcending Grave Bodies, I yet <lb></lb>make a queſtion: and therefore for information of me, and of <lb></lb>others like unto me, me thinks it would be ſeaſonable in this place <lb></lb>to produce ſome Experiment amongſt thoſe which were ſaid to be <lb></lb>many, which in ſundry Caſes agree with the Concluſions demon<lb></lb>ſtrated.</s></p><p type="main"> <s>SALV. You, like a true <emph type="italics"></emph>A<emph.end type="italics"></emph.end>rtiſt, make a very reaſonable demand, <lb></lb>and ſo it is uſual and convenient to do in Sciences that apply <lb></lb>Mathematical Demonſtrations to Phyſical Concluſions, as we ſee <lb></lb>in the Profeſſors of Perſpection, <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ſtronomy, Mechanicks, Muſick, <lb></lb>and others, who with Senſible Experiments confirm thoſe their <lb></lb>Principles that are as the foundations of all the following Structure: <lb></lb>and therefore I deſire that it may not be thought ſuperfluous, that <lb></lb>we diſcourſe with ſome prolixity upon this firſt and grand funda<lb></lb>mental on which we lay the weight of the Immenſe Machine of <lb></lb>infinite Concluſions, of which we have but a very ſmall part ſet <lb></lb>down in this Book by our <emph type="italics"></emph>A<emph.end type="italics"></emph.end>uthor, who hath done enough to open <lb></lb>the way and door that hath been hitherto ſhut unto all Specula<lb></lb>tive Wits. </s> <s>Touching Experiments, therefore, the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>uthor hath <lb></lb>not omitted to make ſeveral; and to aſſure us, that the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ccelerati<lb></lb>on of natural-deſcending Graves hapneth in the aforeſaid propor<lb></lb>tion, I have many times in his company ſet my ſelf to make a triall <lb></lb>thereof in the following Method.</s></p><p type="main"> <s>In a priſme or Piece of Wood, about twelve yards long, and <lb></lb>half a yard broad one way, and three Inches the other, we made, <lb></lb>upon the narrow Side or edge a Groove of little more than an Inch <lb></lb>wide; we ſhot it with the Grooving Plane very ſtraight, and to <lb></lb>make it very ſmooth and ſleek, we glued upon it a piece of Vellum, <lb></lb>poliſhed and ſmoothed as exactly as can be poſſible: and in it we <lb></lb>have let a brazen Ball, very hard, round, and ſmooth, deſcend. <lb></lb></s> <s>Having placed the ſaid Priſme Pendent, raiſing one of its ends <lb></lb>above the Horizontal Plane a yard or two at pleaſure, we have let <lb></lb>the Ball (as I ſaid) deſcend along the Grove, obſerving, in the <lb></lb>manner that I ſhall tell you preſently, the Time which it ſpent in <pb xlink:href="040/01/841.jpg" pagenum="148"></pb>runing it all; repeating the ſame obſervation again and again to <lb></lb>aſſure our ſelves of the Time, in which we never found any diffe<lb></lb>rence, no not ſo much as the tenth part of one beat of the Pulſe. <lb></lb></s> <s>Having done, and preciſely ordered this buſineſſe, we made the <lb></lb>ſame Ball to deſcend only the fourth part of the length of that <lb></lb>Grove: and having meaſured the time of its deſcent, we alwaies <lb></lb>found it to be punctually half the other. </s> <s>And then making trial of <lb></lb>other parts, examining one while the Time of the whole Length <lb></lb>with the Time of half the Length, or with that of 2/3, or of 3/4, or, in <lb></lb>brief, with any whatever other Diviſion, by Experiments repeated <lb></lb>near an hundred Times, we alwaies found the Spaces to be to one <lb></lb>another as the Squares of the Times. </s> <s>And this in all Inclinations <lb></lb>of the Plane, that is, of the Grove in which the Ball was made to <lb></lb>deſcend. </s> <s>In which we obſerved moreover, that the Times of the <lb></lb>Deſcents along ſundry Inclinations did retain the ſame proportion <lb></lb>to one another, exactly, which anon you will ſee aſſigned to them, <lb></lb>and demonſtrated by the Author. </s> <s>And as to the meaſuring of the <lb></lb>Time; we had a good big Bucket full of Water hanged on high, <lb></lb>which by a very ſmall hole, pierced in the bottom, ſpirted, or, as <lb></lb>we ſay, ſpin'd forth a ſmall thread of Water, which we received <lb></lb>with a ſmall cup all the while that the Ball was deſcending in the <lb></lb>Grove, and in its parts; and then weighing from time to time the <lb></lb>ſmall parcels of Water, in that manner gathered, in an exact pair <lb></lb>of ſcales, the differences and proportions of their Weights gave <lb></lb>juſtly the differences and proportions of the Times; and this with <lb></lb>ſuch exactneſſe, that, as I ſaid before, the trials being many <lb></lb>and many times repeated, they never differed any conſiderable <lb></lb>matter.</s></p><p type="main"> <s>SIMP. </s> <s>I ſhould have received great ſatisfaction by being preſent <lb></lb>at thoſe Experiments: but being confident of your diligence in <lb></lb>making them, and veracity in relating them, I content my ſelf, and <lb></lb>admit them for true and certain.</s></p><p type="main"> <s>SALV. </s> <s>We may, then, reaſſume our Reading, and go on.</s></p><p type="head"> <s>COROLLARY II.</s></p><p type="main"> <s>It is collected in the ſecond place, that if any two Spaces are ta<lb></lb>ken from the beginning of the Motion, paſſed in any Times, <lb></lb>thoſe Times ſhall be unto each other as one of them is to a <lb></lb>Space that is the Mean proportional between them.</s></p><p type="main"> <s><emph type="italics"></emph>For taking two Spaces S T, and S V from the beginning of the Mo<lb></lb>tion S, to which S X is a Mean-proportional, the Time of the deſcent <lb></lb>along S T, ſhall be to the Time of the deſcent along S V, as S T to S X; <lb></lb>or, if you will, the Time along S V ſhall be to the Time along S T,<emph.end type="italics"></emph.end><pb xlink:href="040/01/842.jpg" pagenum="149"></pb><figure id="id.040.01.842.1.jpg" xlink:href="040/01/842/1.jpg"></figure><lb></lb><emph type="italics"></emph>as VS is to SX. </s> <s>For it is demonſtrated, that Spaces <lb></lb>paſſed are in duplicate proportion to the Times, or, (which <lb></lb>is the ſame) are as the Squares of the Times: But the pro<lb></lb>portion of the Space VS to the Space ST is double to the <lb></lb>proportion of V S to SX, or is the ſame that V S, and S X <lb></lb>ſquared have to one another: Therefore, the proportion of <lb></lb>the Times of the Motion by V S, and ST, is as the Spaces or <lb></lb>Lines V S to S X.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>SCHOLIUM.</s></p><p type="main"> <s><emph type="italics"></emph>That which is demonſtrated in Motions that are made Perpendicu<lb></lb>larly, may be underſtood alſo to hold true in the Motions made along <lb></lb>Planes of any whatever Inclination; for it is ſuppoſed, that in them <lb></lb>the degree of Acceleration encreaſeth in the ſame proportion; that <lb></lb>is, according to the encreaſe of the Time; or, if you will, according <lb></lb>to the ſimple and primary Series of Numbers.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>Here I deſire <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> that I alſo may be allowed, al<lb></lb>beit perhaps with too much tediouſneſſe in the opinion of <emph type="italics"></emph>Simplici<lb></lb>us,<emph.end type="italics"></emph.end> to defer for a little time the preſent Reading, untill I may have <lb></lb>explained what from that which hath been already ſaid and de<lb></lb>monſtrated, and alſo from the knowledge of certain Mechanical <lb></lb>Concluſions heretofore learnt of our <emph type="italics"></emph>Academick,<emph.end type="italics"></emph.end> I now remember <lb></lb>to adjoyn for the greater confirmation of the truth of the Princi<lb></lb>ple, which hath been examined by us even now with probable <lb></lb>Reaſons and Experiments: and, which is of more importance, for <lb></lb>the Geometrical proof of it, let me firſt demonſtrate one ſole Ele<lb></lb>mental <emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> in the Contemplation of <emph type="italics"></emph>Impetus's.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>If our advantage ſhall be ſuch as you promiſeus, there <lb></lb>is no time that I would not moſt willingly ſpend in diſcourſing <lb></lb>about the confirmation and thorow eſtabliſhing theſe Sciences of <lb></lb>Motion: and as to my own particular, I not only grant you liber<lb></lb>ty to ſatisfie your ſelf in this particular, but moreover entreat you <lb></lb>to gratifie, as ſoon as you can, the Curioſity which you have begot <lb></lb>in me touching the ſame: and I believe that <emph type="italics"></emph>Simplicius<emph.end type="italics"></emph.end> alſo is of the <lb></lb>ſame mind.</s></p><p type="main"> <s>SIMP. </s> <s>I cannot deny what you ſay.</s></p><p type="main"> <s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>ALV. </s> <s>Seeing then that I have your permiſſion, I will in the <lb></lb>firſt place conſider, as an Effect well known, That</s></p><pb xlink:href="040/01/843.jpg" pagenum="150"></pb><p type="head"> <s>LEMMA.</s></p><p type="main"> <s><emph type="italics"></emph>That the Moments or Velocities of the ſame Moveable are different <lb></lb>upon different Inclinations of Planes, and the greateſt is by the <lb></lb>Line elevated perpendicularly above the Horizon, and by the <lb></lb>others inclined, the ſaid Velocity diminiſheth according as they <lb></lb>more and more depart from Perpendicularity, that is, as they in<lb></lb>cline more obliquely: ſo that the Impetus, Talent, Energy, or, we <lb></lb>may ſay, Moment of deſcending is diminiſhed in the Moveable by <lb></lb>the ſubjected Plane, upon which the ſaid Moveable lyeth and <lb></lb>deſcendeth.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And the better to expreſs my ſelf, let the Line A B be perpen<lb></lb>dicularly erected upon the Horizon A C: then ſuppoſe the <lb></lb>ſame to be declined in ſundry Inclinations towards the Horizon, as <lb></lb>in A D, A E, A F, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> I ſay, that the greateſt and total <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end><lb></lb>of the Grave Body in deſcending is along the Perpendicular B A, <lb></lb>and leſs than that along D A, <lb></lb><figure id="id.040.01.843.1.jpg" xlink:href="040/01/843/1.jpg"></figure><lb></lb>and yet leſs along E A; and <lb></lb>ſucceſſively diminiſhing along <lb></lb>the more inclined F <emph type="italics"></emph>A,<emph.end type="italics"></emph.end> and fi<lb></lb>nally is wholly extinct in the <lb></lb>Horizontal C <emph type="italics"></emph>A,<emph.end type="italics"></emph.end> where the <lb></lb>Moveable is indifferent either <lb></lb>to Motion or Reſt, and hath not <lb></lb>of it ſelf any Inclination to <lb></lb>move one way or other, nor yet <lb></lb>any Reſiſtance to its being mo<lb></lb>ved: for as it is impoſſi<lb></lb>ble that a Grave Body, or a <lb></lb>Compound thereof ſhould move naturally upwards, receding from <lb></lb>the Common Center, towards which all Grave Matters conſpire <lb></lb>to go, ſo it is impoſſible that it do ſpontaneouſly move, unleſs <lb></lb>with that Motion its particular Center of Gravity do acquire Proxi<lb></lb>mity to the ſaid Common Center: ſo that upon the Horizontal <lb></lb>which here is underſtood to be a Superficies equidiſtant from the <lb></lb>ſaid Center, and therefore altogether void of Inclination, the <emph type="italics"></emph>Im<lb></lb>petus<emph.end type="italics"></emph.end> or Moment of that ſame Moveable ſhall be nothing at all. <lb></lb></s> <s>Having underſtood this mutation of <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> I am to explain that <lb></lb>which, in an old Treatiſe of the Mechanicks, written heretofore <lb></lb>in <emph type="italics"></emph>Padona<emph.end type="italics"></emph.end> by our <emph type="italics"></emph>Academick,<emph.end type="italics"></emph.end> only for the uſe of his Scholars, was <lb></lb>diffuſely and demonſtratively proved, upon the occaſion of con<lb></lb>ſidering the Original and Nature of the admirable Inſtrument cal<lb></lb>led the Screw, and it is, With what proportion that mutation of <pb xlink:href="040/01/844.jpg" pagenum="151"></pb><emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> is made along ſeveral Inclinations or Declivities of <lb></lb>Planes.</s></p><p type="main"> <s>As, for example, in the inclined Plane A F, drawing its Eleva<lb></lb>tion above the Horizontal, that is, the Line F C, along the which <lb></lb>the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of a Grave Body, and the Moment of Deſcent is the <lb></lb>greateſt; it is ſought what proportion this Moment hath to the <lb></lb>Moment of the ſame Moveable along the Declivity F A: Which <lb></lb>Proportion, I ſay, is Reciprocal to the ſaid Lengths. </s> <s>And this is <lb></lb>the <emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> that was to go before the Theorem, which I hope to be <lb></lb>able anon to Demonſtrate. </s> <s>Hence it is manifeſt, That the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end><lb></lb>of Deſcent of a Grave Body is as much as the Reſiſtance or leaſt <lb></lb>force that ſufficeth to arreſt and ſtay it. </s> <s>For this Force or Reſi<lb></lb>ſtance, and its meaſure, I will make uſe of the Gravity of another <lb></lb>Moveable. </s> <s>Let us now upon the Plane F A put the Moveable G <lb></lb>tyed to a thread which ſliding over F hath faſtned at its other end <lb></lb>the Weight H: and let us conſider that the Space of the Deſcent <lb></lb>or Aſcent of the Weight H along the Perpendicular, is alwaies <lb></lb>equal to the whole Aſcent or Deſcent of the other Moveable G <lb></lb>along the ^{*} Declivity A F, but yet not to the Aſcent or Deſcent </s></p><p type="main"> <s><arrow.to.target n="marg1092"></arrow.to.target><lb></lb>along the Perpendicular, in which only the ſaid Moveable G (like <lb></lb>as every other Moveable) exerciſeth its Reſiſtance. </s> <s>Which is <lb></lb>manifeſt: for conſidering in the Triangle AFC the Motion of <lb></lb>the Moveable G, as for example, upwards from A to F, to be com<lb></lb>poſed of the tranſverſe Horizontal Line A C, and of the Perpendi<lb></lb>cular C F: <emph type="italics"></emph>A<emph.end type="italics"></emph.end>nd in regard, that as to the Horizontal Plane along <lb></lb>which the Moveable, as hath been ſaid, hath no Reſiſtance to mo<lb></lb>ving (it not making by that Motion any loſs, nor yet acquiſt in <lb></lb>regard of its particular diſtance from the Common Center of Grave <lb></lb>Matters, which in the Horizon continueth ſtill the ſame) it remai<lb></lb>neth that the Reſiſtance be only in reſpect of the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ſcent that it is to <lb></lb>make along the Perpendicular C F. </s> <s>Whilſt therefore the Grave <lb></lb>Moveable G, moving from <emph type="italics"></emph>A<emph.end type="italics"></emph.end> to F, hath only the Perpendicular <lb></lb>Space C F to reſiſt in its <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ſcent, and whilſt the other Grave Move<lb></lb>able H deſcendeth along the Perpendicular of neceſſity as far as <lb></lb>the whole Space F <emph type="italics"></emph>A,<emph.end type="italics"></emph.end> and that the ſaid proportion of <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ſcent and <lb></lb>Deſcent maintains it ſelf alwaies the ſame, be the Motion of the <lb></lb>ſaid Moveables little or much (by reaſon they are tyed toge<lb></lb>ther) we may confidently affirm, that in caſe there were an <emph type="italics"></emph>Equi<lb></lb>librium,<emph.end type="italics"></emph.end> that is Reſt, to enſue betwixt the ſaid Moveables, the Mo<lb></lb>ments, the Velocities, or their Propenſions to Motion, that is the <lb></lb>Spaces which they would paſs in the ſame Time ſhould anſwer re<lb></lb>ciprocally to their Gravities, according to that which is demonſtra<lb></lb>ted in all caſes of Mechanick Motions: ſo that it ſhall ſuffice to <lb></lb>impede the deſcent of G, if H be but ſo much leſs grave than it, as <lb></lb>in proportion the Space C F is leſſer than the Space F <emph type="italics"></emph>A.<emph.end type="italics"></emph.end> Therefore <pb xlink:href="040/01/845.jpg" pagenum="152"></pb>ſuppoſe that the Moveable G is to the Moveable H, as F <emph type="italics"></emph>A<emph.end type="italics"></emph.end> is to <lb></lb>F C; and then the <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> ſhall follow, that is, the Moveables <lb></lb>H and G ſhall have equal Moments, and the Motion of the ſaid <lb></lb>Moveables ſhall ceaſe. <emph type="italics"></emph>A<emph.end type="italics"></emph.end>nd becauſe we ſee that the <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end><lb></lb>Energy, Moment, or Propenſion of a Moveable to Motion is the <lb></lb>ſame as is the Force or ſmalleſt Reſiſtance that ſufficeth to ſtop it; <lb></lb>and becauſe it hath been concluded, that the Grave Body H is ſuf. <lb></lb></s> <s>ficient to arreſt the Motion of <lb></lb><figure id="id.040.01.845.1.jpg" xlink:href="040/01/845/1.jpg"></figure><lb></lb>the Grave Body G: Therefore <lb></lb>the leſſer Weight H, which in <lb></lb>the Perpendicular F C imploy<lb></lb>eth its total Moment, ſhall be <lb></lb>the preciſe meaſure of the par<lb></lb>tial Moment that the greater <lb></lb>Weight G exerciſeth along the <lb></lb>inclined Plane F <emph type="italics"></emph>A<emph.end type="italics"></emph.end>: But the <lb></lb>meaſure of the total Moment of <lb></lb>the ſaid Grave Body G, is the <lb></lb>ſelf ſame, (ſince that to impede <lb></lb>the Perpendicular Deſcent of a <lb></lb>Grave Body there is required the oppoſition of ſuch another Grave <lb></lb>Body, which likewiſe is at liberty to move Perpendicularly:) <lb></lb>Therefore the partial <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> or Moment of G along the inclined <lb></lb>Plane F A ſhall be to the grand and total <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the ſame G <lb></lb>along the Perpendicular F C, as the Weight H to the Weight G: <lb></lb>that is, by Conſtruction, as the ſaid Perpendicular F C, the Eleva<lb></lb>tion of the inclined Plane, is to the ſame inclined Plane F A: <lb></lb>Which is that that by the <emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> was propoſed to be demon<lb></lb>ſtrated, and which by our Author, as we ſhall ſee, is ſuppoſed as <lb></lb>known in the ſecond part of the Sixth Propoſition of the preſent <lb></lb>Treatiſe.</s></p><p type="margin"> <s><margin.target id="marg1092"></margin.target>* Or inclined <lb></lb>Plane.</s></p><p type="main"> <s>SAGR. </s> <s>From this that you have already concluded I conceive <lb></lb>one may eaſily deduce, arguing <emph type="italics"></emph>ex æquali<emph.end type="italics"></emph.end> by perturbed Proportion, <lb></lb>that the Moments of the ſame Moveable, along Planes variouſly <lb></lb>inclined (as F A and F I) that have the ſame Elevation, are to each <lb></lb>other in Reciprocal proportion to the ſame Planes.</s></p><p type="main"> <s>SALV. <emph type="italics"></emph>A<emph.end type="italics"></emph.end> moſt certain Concluſion. </s> <s>This being agreed on, we <lb></lb>will paſs in the next place to demonſtrate the <emph type="italics"></emph>Theoreme,<emph.end type="italics"></emph.end> namely, <lb></lb>that</s></p><pb xlink:href="040/01/846.jpg" pagenum="153"></pb><p type="head"> <s>THEOREM.</s></p><p type="main"> <s><emph type="italics"></emph>The degrees of Velocity of a Moveable deſcending with a Natural <lb></lb>Motion from the ſame height along Planes in any manner inclined <lb></lb>at the arrival to the Horizon are alwaies equal, Impediments be<lb></lb>ing removed.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Here we are in the firſt place to advertiſe you, that it having <lb></lb>been proved, that in any Inclination of the Plane the Move<lb></lb>able from its receſſion from Quieſſence goeth encreaſing its Ve<lb></lb>locity, or quantity of its <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> with the proportion of the <lb></lb>Time (according to the Definition which the Author giveth of <lb></lb>Motion naturally Accelerate) whereupon, as he hath by the pre<lb></lb>cedent Propoſition demonſtrated, the Spaces paſſed are in dupli<lb></lb>cate proportion to the Times, and, conſequently, to the degrees <lb></lb>of Velocity: look what the <emph type="italics"></emph>Impetus's<emph.end type="italics"></emph.end> were in that which was firſt <lb></lb>moved, ſuch proportionally ſhall be the degrees of Velocity gai<lb></lb>ned in the ſame Time; ſeeing that both theſe and thoſe encreaſe <lb></lb>with the ſame proportion in the ſame Time.</s></p><p type="main"> <s>Now let the inclined Plane be A B, its elevation above the Ho <lb></lb>rizon the Perpendicular A C, and the Horizontal Plane C B: and <lb></lb>becauſe, as was even now concluded, the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of a Moveable <lb></lb>along the Perpendicular A C is to the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the ſame along <lb></lb>the inclined Plane A B, as A B is to A C, let there be taken in the <lb></lb>inclined Plane A B, A D a third proportional to A B and A C: <lb></lb>The <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> therefore, along A C is to the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> along A B, <lb></lb>that is along A D, as A C is to <lb></lb><figure id="id.040.01.846.1.jpg" xlink:href="040/01/846/1.jpg"></figure><lb></lb>A D: And therefore the Move<lb></lb>able in the ſame Time that it <lb></lb>would paſs the Perpendicular <lb></lb>Space AC, ſhall likewiſe paſs the <lb></lb>Space A D, in the inclined Plane <lb></lb>A B, (the Moments being as <lb></lb>the Spaces:) And the degree of Velocity in C ſhall have the ſame <lb></lb>proportion to the degree of Velocity in D, as A C hath to A D: <lb></lb>But the degree of Velocity in B is to the ſame degree in D, as the <lb></lb>Time along A B is to the Time along AD, by the definition of <lb></lb>Accelerate Motion; And the Time along AB is to the Time along <lb></lb>A D, as the ſame A C, the Mean Proportional between B A and <lb></lb>A D, is to A D, by the laſt Corollary of the ſecond Propoſition: <lb></lb>Therefore the degrees of Velocity in B and in C have to the de<lb></lb>gree in D, the ſame Proportion as A C hath to A D; and therefore <lb></lb>are equal: Which is the <emph type="italics"></emph>Theorem<emph.end type="italics"></emph.end> intended to be demonſtrated.</s></p><p type="main"> <s>By this we may more concludingly prove the enſuing third <pb xlink:href="040/01/847.jpg" pagenum="154"></pb>Propoſition of the Author, in which he makes uſe of this Princi<lb></lb>ple; and it is, That the Time along the inclined Plane, hath to the <lb></lb>Time along the Perpendicular, the ſame proportion as the ſaid In<lb></lb>clined Plane and Perpendicular. </s> <s>For if we put the caſe that BA <lb></lb>be the Time along A B, the Time along A D ſhall be the Mean <lb></lb>between them, that is A C, by the ſecond Corollary of the ſecond <lb></lb>Propoſition: But if C A be the Time along A D, it ſhall likewiſe <lb></lb>be the Time along <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C, by reaſon that <emph type="italics"></emph>A<emph.end type="italics"></emph.end> D and <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C are paſt in <lb></lb>equal Times: And therefore in caſe B <emph type="italics"></emph>A<emph.end type="italics"></emph.end> be the Time along A B, <lb></lb><emph type="italics"></emph>A<emph.end type="italics"></emph.end> C ſhall be the Time along <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C: Therefore, as <emph type="italics"></emph>A<emph.end type="italics"></emph.end> B is to A C, ſo <lb></lb>is the Time along <emph type="italics"></emph>A<emph.end type="italics"></emph.end> B to the Time along <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C.</s></p><p type="main"> <s>By the ſame diſcourſe one ſhall prove, that the Time along <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C <lb></lb>is to the Time along the inclined Plane <emph type="italics"></emph>A<emph.end type="italics"></emph.end> E, as <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C is to <emph type="italics"></emph>A<emph.end type="italics"></emph.end> E: <lb></lb>Therefore, <emph type="italics"></emph>ex æquali,<emph.end type="italics"></emph.end> the Time along the inclined Plane <emph type="italics"></emph>A B<emph.end type="italics"></emph.end> is, <lb></lb>Directly, to the Time along the inclined Plane <emph type="italics"></emph>A<emph.end type="italics"></emph.end> E as <emph type="italics"></emph>A B<emph.end type="italics"></emph.end> to <lb></lb><emph type="italics"></emph>A E, &c.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>One might alſo by the ſame application of the <emph type="italics"></emph>Theorem,<emph.end type="italics"></emph.end> as <emph type="italics"></emph>Sa<lb></lb>gredus<emph.end type="italics"></emph.end> ſhall very evidently ſee anon, immediately demonſtrate the <lb></lb>ſixth Propoſition of the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>uthor: <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut let this Digreſſion ſuffice <lb></lb>for the preſent, which he perhaps thinketh too tedious, though in<lb></lb>deed it is of ſome importance in theſe matters of Motion.</s></p><p type="main"> <s>SAGR. </s> <s>You may ſay extreamly delightful, and moſt neceſſary <lb></lb>to the perfect underſtanding 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 Reſt do move along <lb></lb>an Inclined Plane, and alſo along the Perpendi<lb></lb>cular whoſe heights are the ſame, the Times of <lb></lb>their Motions ſhall be to one another as the <lb></lb>Lengths of the ſaid Plane and Perpendicular.</s></p><p type="main"> <s><emph type="italics"></emph>Let the inclined Plane be A C, and the Perpendicular A B, <lb></lb>whoſe heights are the ſame above the Horizon C B, to wit, <lb></lb>the ſelf ſame Line B A. </s> <s>I ſay, that the Time of the Deſcent <lb></lb>of the ſame Moveable upon the Plane A C, hath the ſame Proporti<lb></lb>on to the Time of the Deſcent along the Perpendicular A B, as the <lb></lb>Length of the Plane A C hath to the Length of the ſaid Perpendi<lb></lb>cular. </s> <s>For let any number of Lines D G, E I, F L, be drawn, Paral<lb></lb>lel to the Horizon C B: It is manifeſt from the Aſſumption fore<lb></lb>going, that the degrees of Velocity of the Moveable, departing from <lb></lb>A the beginning of Motion, acquired in the Points G and D are<emph.end type="italics"></emph.end><pb xlink:href="040/01/848.jpg" pagenum="155"></pb><emph type="italics"></emph>equal, their exceſſe or elevation above the Horizon being equal; <lb></lb>and ſo the degrees in the Points I and E; as alſo the degrees in L <lb></lb>and F. </s> <s>And if not only theſe Parallels, but many more were ſup<lb></lb>poſed to be drawn from all the points imagined to be in the Line <lb></lb>A B, untill they meet the Line A C, the Mo-<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.848.1.jpg" xlink:href="040/01/848/1.jpg"></figure><lb></lb><emph type="italics"></emph>ments, or degrees of the Velocities along the <lb></lb>extreams [or ends] of every one of thoſe <lb></lb>Parallels, ſhall be alwaies equal to one ano<lb></lb>ther: Therefore the two Spaces A C and A B <lb></lb>are paſt with the ſame degree of Velocity: <lb></lb>But it hath been demonſtrated, that if two <lb></lb>Spaces be paſſed by a Moveable with one <lb></lb>and the ſame degree of Velocity, the Times <lb></lb>of the Motions have the ſame proportion as <lb></lb>thoſe Spaces: Therefore the Time of the Motion along A C is to the <lb></lb>Time along A B, as the Length of the Plane A C to the length of the <lb></lb>Perdendicular A B. </s> <s>Which was to be demonſtrated.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>It ſeemeth to me, that the ſame might very clearly and <lb></lb>conciſely be concluded, it having firſt been proved that the ſum of <lb></lb>the Accelerate Motion of the Tranſitions along A C and A B, is <lb></lb>as much as the Equable Motion, whoſe degree of Velocity is ſub<lb></lb>duple to the greateſt degree C B: Therefore the two Spaces AC <lb></lb>and A B being paſſed with the ſame Equable Motion, it hath been <lb></lb>ſhewn, by the Firſt Propoſition of the firſt, that the Times of the <lb></lb>Tranſitions ſhall be as the ſaid Spaces.</s></p><p type="head"> <s>COROLLARY.</s></p><p type="main"> <s>Hence is collected, that the Times of the Deſcents along Planes <lb></lb>of different Inclination, but of the ſame Elevation, are to <lb></lb>one another according to their Lengths.</s></p><p type="main"> <s><emph type="italics"></emph>For if we ſuppoſe another Plane A M, coming from A, and ter<lb></lb>minated by the ſame Horizontal C B; it ſhall in like manner be <lb></lb>demonſtrated, that the Time of the Deſcent along A M, is to the <lb></lb>Time along A B, as the Line A M to A B: But as the Time A B is <lb></lb>to the Time along A C, ſo is the Line A B to A C: Therefore,<emph.end type="italics"></emph.end> ex <lb></lb>æquali, <emph type="italics"></emph>as A M is to A C, ſo is the Time along A M to the Time <lb></lb>along A C.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/849.jpg" pagenum="156"></pb><p type="head"> <s>THEOR. IV. PROP. IV.</s></p><p type="main"> <s>The Times of the Motions along equal Planes, <lb></lb>but unequally inclined, are to each other in <lb></lb>ſubduple proportion of the Elevations of thoſe <lb></lb>Planes Reciprocally taken.</s></p><p type="main"> <s><emph type="italics"></emph>Let there proceed from the term B two equal Planes, but une<lb></lb>qually inclined, B A and B C, and let A E and C D be Hori<lb></lb>zontal Lines, drawn as far as the Perpendicular B D: Let the <lb></lb>Elevation of the Plane B A be B E; and let the Elevation of the <lb></lb>Plane B C be B D: And let B I be a Mean Proportional between the <lb></lb>Elevations D B and B E: It is manifeſt<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.849.1.jpg" xlink:href="040/01/849/1.jpg"></figure><lb></lb><emph type="italics"></emph>that the proportion of D B to B I, is ſub<lb></lb>duple the proportion of D B to B E. </s> <s>Now <lb></lb>I ſay, that the proportion of the Times <lb></lb>of the Deſcents or Motions along the <lb></lb>Planes B A and B C, are the ſame with <lb></lb>the proportion of D B to B I Reciprocal<lb></lb>ly taken: So that to the Time B A the <lb></lb>Elevation of the other Plane B C, that is <lb></lb>B D be Homologal; and to the Time along <lb></lb>B C, B I be Homologal: Therefore it is <lb></lb>to be demonſtrated, That the Time along B A is to the Time along <lb></lb>B C, as D B is to B I. </s> <s>Let I S be drawn equidiſtant from D C. </s> <s>And <lb></lb>becauſe it hath been demonſtrated that the Time of the Deſcent <lb></lb>along B A, is to the Time of the Deſcent along the Perpendicular <lb></lb>B E, as the ſaid B A is to B E; and the Time along B E is to the <lb></lb>Time along B D, as B E is to B I; and the Time along B D is to the <lb></lb>Time along B C, as B D to B C, or as B I to B S: Therefore,<emph.end type="italics"></emph.end> ex æqua<lb></lb>li, <emph type="italics"></emph>the Time along B A ſhall be to the Time along B C as B A to B S, <lb></lb>or as C B to BS: But C B is to B S, as D B to B I: Therefore the <lb></lb>Propoſition is manifeſt:<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/850.jpg" pagenum="157"></pb><p type="head"> <s>THEOR. V. PROP. V.</s></p><p type="main"> <s>The proportion of the Times of the Deſcents <lb></lb>along Planes that have different Inclinations <lb></lb>and Lengths, and the Elivations unequal, is <lb></lb>compounded of the proportion of the Lengths <lb></lb>of thoſe Planes, and of the ſubduple proporti<lb></lb>on of their Elevations Reciprocally taken.</s></p><p type="main"> <s><emph type="italics"></emph>Let A B and A C be Planes inclined after different manners, <lb></lb>whoſe Lengths are unequal, as alſo their Elevations. </s> <s>I ſay, <lb></lb>the proportion of the Time of the Deſcent along A C to the <lb></lb>Time along A B, is compounded of the proportion of the ſaid A C <lb></lb>to A B, and of the ſubduple proportion of their Elevation Recipro<lb></lb>cally taken. </s> <s>For let the Perpendicular A D be drawn, with which <lb></lb>let the Horizontal Lines B G and C D interſect, and let A L be a <lb></lb>Mean-proportional between C A and A E; and from the point L let <lb></lb>a Parallel be drawn to the Horizon interſecting<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.850.1.jpg" xlink:href="040/01/850/1.jpg"></figure><lb></lb><emph type="italics"></emph>the Plane A C in F; and A F ſhall be a Mean <lb></lb>proportional between C A and A E. </s> <s>And becauſe <lb></lb>the Time along A C is to the Time along A E, as <lb></lb>the Line F A to A E; and the Time along A E is <lb></lb>to the Time along A B, as the ſaid A E to the ſaid <lb></lb>A B: It is manifeſt that the Time along A C is to <lb></lb>the Time along A B, as A F to A B. </s> <s>It remaineth, <lb></lb>therefore, to be demonſtrated, that the proportion <lb></lb>of A F to A B is compounded of the proportion of <lb></lb>C A to A B, and of the proportion of G A to A L; <lb></lb>which is the ſubduple proportion of the Elevati<lb></lb>ons D A and A G Reciprocally taken. </s> <s>But that is manifeſt, C A <lb></lb>being put between F A and A B: For the proportion of F A to A C <lb></lb>is the ſame as that of L A to A D, or of G A to A L; which is ſub<lb></lb>duple of the proportion of the Elevations G A and A D; and the <lb></lb>proportion of C A to A B is the proportion of the Lengths: Therefore <lb></lb>the Propoſition is manifeſt.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/851.jpg" pagenum="158"></pb><p type="head"> <s>THEOR. VI. PROP. VI.</s></p><p type="main"> <s>If from the higheſt or loweſt part of a Circle, <lb></lb>erect upon the Horizon, certain Planes be <lb></lb>drawn inclined towards the Circumference, <lb></lb>the Times of the Deſcents along the ſame <lb></lb>ſhall be equal.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Circle be erect upon the Horizon G H, whoſe Diameter <lb></lb>recited upon the loweſt point, that is upon the contact with the <lb></lb>Horizon, let be F A, and from the higheſt point A let certain <lb></lb>Planes A B and A C incline towards the Circumference: I ſay that the <lb></lb>Times of the Deſcents along the ſame are equal. </s> <s>Let B D and C E be <lb></lb>two Perpendiculars let fall unto the Diameter; and let A I be a Mean<lb></lb>Proportional between the Altitudes<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.851.1.jpg" xlink:href="040/01/851/1.jpg"></figure><lb></lb><emph type="italics"></emph>of the Planes E A and A D. </s> <s>And <lb></lb>becauſe the Rectangles F A E and <lb></lb>F A D are equal to the Squares of <lb></lb>A C and A B; And alſo becauſe <lb></lb>that as the Rectangle F A E, is to <lb></lb>the Rectangle F A D, ſo is E A to <lb></lb>A D. </s> <s>Therefore as the Square of <lb></lb>C A is to the Square of B A, <lb></lb>ſo is the Line E A to the Line <lb></lb>A D. </s> <s>But as the Line E A is to <lb></lb>D A, ſo is the Square of I A to the Square of A D: Therefore <lb></lb>the Squares of the Lines C A and A B are to each other as the Squares <lb></lb>of the Lines I A and A D: And therefore as the Line C A is to A B, <lb></lb>ſo is I A to A D: But in the precedent Propoſition it hath been demon<lb></lb>ſtrated that the proportion of the Time of the Deſcent along A C to the <lb></lb>Time of the Deſcent by A B, is compounded of the proportions of C A <lb></lb>to A B, and of D A to A I, which is the ſame with the proportion of <lb></lb>B A to A C: Therefore the proportion of the Time of the Deſcent along <lb></lb>A C, to the Time of the Deſcent along A B, is compounded of the pro<lb></lb>portions of C A to A B, and of B A to A C: Therefore the proporti<lb></lb>on of thoſe Times is a proportion of equality: Therefore the Propoſition <lb></lb>is evident.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>The ſame is another way demonſtrated from the Mechanicks: Name<lb></lb>ly that in the enſuing Figure the Moveable paſſeth in equal Times along <lb></lb>C A and D A. </s> <s>For let B A be equal to the ſaid D A, ond let fall the <lb></lb>Perpendiculars B E and D F: It is manifeſt by the Elements of the<emph.end type="italics"></emph.end><pb xlink:href="040/01/852.jpg" pagenum="159"></pb><emph type="italics"></emph>Mechanicks: That the Moment of the Weight elevated upon the Plane <lb></lb>according to the Line A B C, is <lb></lb>to its total Moment, as B E to B A;<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.852.1.jpg" xlink:href="040/01/852/1.jpg"></figure><lb></lb><emph type="italics"></emph>And that the Moment of the ſame <lb></lb>Weight upon the Elevation A D, <lb></lb>is to its total Moment, as D F to <lb></lb>D A or B A: Therefore the Mo<lb></lb>ment of the ſaid Weight upon the <lb></lb>Plane inclined according to D A, <lb></lb>is to the Moment upon the Plane <lb></lb>inclined according to A B C, as <lb></lb>the Line D F to the Line B E: <lb></lb>Therefore the Spaces which the <lb></lb>ſaid Weight ſhall paſſe in equal <lb></lb>Times along the Inclined Planes C A and D A, ſhall be to each other as <lb></lb>the Line B E to D F; by the ſecond Propoſition of the Firſt Book: <lb></lb>But as B E is to D F, ſo A C is demonſtrated to be to D A: <lb></lb>Therefore the ſame Moveable will in equal Times paſſe the Lines <lb></lb>C A and D A.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>And that C A is to D A as B E is to D F, is thus demonſtrated.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Draw a Line from C to D; and by D and B draw the Lines <lb></lb>D G L, (cutting C A in the point I) and B H, Parallels to A F: <lb></lb>And the Angle A D I ſhall be equal to the Angle D C A, for that <lb></lb>the parts L A and A D of the Circumference ſubtending them, are <lb></lb>equal, and the Angle D A C common to them both: Therefore of <lb></lb>the equiangled Triangles C A D and D A I, the ſides about the <lb></lb>equal Angles ſhall be proportional: And as C A is to A D, ſo is <lb></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></lb>D F: Which was to be proved.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Or elſe the ſame ſhall be demonſtrated more ſpeedily thus.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Vnto the Horizon A B, let a Circle be erect, whoſe Diameter is <lb></lb>perpendicular to the Horizon: and <lb></lb>from the higheſt Term D let a Plane<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.852.2.jpg" xlink:href="040/01/852/2.jpg"></figure><lb></lb><emph type="italics"></emph>at pleaſure D F, be inclined to the <lb></lb>Circumference. </s> <s>I ſay that the De<lb></lb>ſcent along the Plane D F, and the <lb></lb>Fall along the Diameter B C, will <lb></lb>be paſſed by the ſame Moveable in <lb></lb>equal Times. </s> <s>For let F G be drawn <lb></lb>parallel to the Horizon A B, which <lb></lb>ſhall be perpendicular to the Diameter <lb></lb>D C, and let a Line conjoyn F and <lb></lb>C: and becauſe the Time of the Fall <lb></lb>along D C, is to the Time of the Fall along D G, as the Mean <lb></lb>Proportional between C D and D G, is to the ſaid D G; and the<emph.end type="italics"></emph.end><pb xlink:href="040/01/853.jpg" pagenum="160"></pb><emph type="italics"></emph>Mean between C D and D G being D F, (for that the Angle D F C <lb></lb>in the Semicircle, is a Right Angle, and F G perpendicular to D C:) <lb></lb>Therefore the Time of the Fall along D C is to the Time of the Fall <lb></lb>along D G, as the Line F D to D G: But it hath been demonſtrated <lb></lb>that the Time of the Deſcent along D F, is to the Time of the Fall <lb></lb>along D G, as the ſame Line D F is to D G: The Times, therefore, <lb></lb>of the Deſcent along D F and Fall along D C, are to the Time of the <lb></lb>Fall along the ſaid D G in the ſame proportion: Therefore they are <lb></lb>equal. </s> <s>It will likewiſe be demonſtrated, if from the loweſt Term C, <lb></lb>one ſhould raiſe the Chord C E, and draw E H parallel to the Hori<lb></lb>zon, and conjoyn E and D, that the Time of the Deſcent along E C <lb></lb>equals the Time of the Fall along the Diameter D C.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>COROLLARY I.</s></p><p type="main"> <s>Hence is collected that the Times of the Deſcents along all the <lb></lb>Chords drawn from the Terms C or D are equal to one <lb></lb>another.</s></p><p type="head"> <s>COROLLARY II.</s></p><p type="main"> <s>It is alſo collected that if the Perpendicular and inclined Plane <lb></lb>deſcend from the ſame point along which the Deſcents are <lb></lb>made in equal Times, they are in a Semicircle whoſe Dia<lb></lb>meter is the ſaid 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></lb>Planes, are then equal, where the Elevations of equal parts of <lb></lb>thoſe Planes ſhall be to one another as their Longitudes.</s></p><p type="main"> <s><emph type="italics"></emph>For it hath been ſhewn that the Times C A and D A in the laſt Fi<lb></lb>gure ſave one are equal, the Elevation of the part A B being equal <lb></lb>to A D, that is, that B E ſhall be to the Elevation D F, as C A <lb></lb>to D A.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>Pray you Sir be pleaſed to ſtay your Reading of what <lb></lb>followeth until that I have ſatisfied my ſelf in a Contemplation <lb></lb>that juſt now cometh into my mind, which if it be not a deluſi<lb></lb>on, is not far from being a pleaſing divertiſement: as are all ſuch <lb></lb>that proceed from Nature or neceſſity.</s></p><p type="main"> <s>It is manifeſt, that if from a point aſſigned in an Horizontal <lb></lb>Plane, one ſhall produce along the ſame Plane infinite right Lines <lb></lb>every way, upon each of which a point is underſtood to move with <lb></lb>an Equable Motion, all beginning to move in the ſame inſtant <pb xlink:href="040/01/854.jpg" pagenum="161"></pb>of Time from the aſſigned point, and the Velocities of them all <lb></lb>being equal, there ſhall conſequently be deſcribed by thoſe move<lb></lb>able points Circumferences of Circles alwayes bigger and bigger, <lb></lb>all concentrick about the firſt point aſſigned: juſt in the ſame <lb></lb>manner as we ſee it done in the Undulations of ſtanding Water, <lb></lb>when a ſtone is dropt into it; the percuſſion of which ſerveth to <lb></lb>give the beginning to the Motion on every ſide, and remaineth <lb></lb>as the Center of all the Circles that happen to be deſigned ſucceſ<lb></lb>ſively bigger and bigger by the ſaid Undulations. </s> <s>But if we ima<lb></lb>gine a Plane erect unto the Horizon, and a point be noted in the <lb></lb>ſame on high, from which infinite Lines are drawn inclined, ac<lb></lb>cording to all inclinations, along which we fancy grave Movea<lb></lb>bles to deſcend, each with a Motion naturally Accelerate <lb></lb>with thoſe Velocities that agree with the ſeveral Inclinations; <lb></lb>ſuppoſing that thoſe deſcending Moveables were continually viſi<lb></lb>ble, in what kind of Lines ſhould we ſee them continually diſpoſed? <lb></lb></s> <s>Hence my wonder ariſeth, ſince that the precedent Demonſtrati<lb></lb>ons aſſure me, that they ſhall all be alwayes ſeen in one and the <lb></lb>ſame Circumference of Circles ſucceſſively encreaſing, according <lb></lb>as the Moveables in deſcending go more and more ſucceſſively re<lb></lb>ceding from the higheſt point in which their Fall began: And the <lb></lb>better to declare my ſelf, let the chiefeſt point A be marked, from <lb></lb>which Lines deſcend according to any Inclinations A F, A H, and <lb></lb>the Perpendicular A B, in which taking the points C and D, de<lb></lb>ſcribe Circles about them that paſs by <lb></lb><figure id="id.040.01.854.1.jpg" xlink:href="040/01/854/1.jpg"></figure><lb></lb>the point A, interſecting the inclined <lb></lb>Lines in the points F, H, B, and E, G, <lb></lb>I. </s> <s>It is manifeſt, by the fore-going <lb></lb>Demonſtrations, that Moveables de<lb></lb>ſcendent along thoſe Lines departing <lb></lb>at the ſame Time from the term A, <lb></lb>one ſhall be in E, the other ſhall be in <lb></lb>G, and the other in I; and ſo con<lb></lb>tinuing to deſcend they ſhall arrive <lb></lb>in the ſame moment of Time at F, H, <lb></lb>and B: and theſe and infinite others continuing to move along the <lb></lb>infinite differing Inclinations, they ſhall alwayes ſucceſſively arrive <lb></lb>at the ſelf-ſame Circumferences made bigger & bigger <emph type="italics"></emph>in infinitum.<emph.end type="italics"></emph.end><lb></lb>From the two Species, therefore, of Motion of which Nature makes <lb></lb>uſe, ariſeth, with admirable harmonious variety, the generation of in<lb></lb>ſinite Circles. </s> <s>She placeth the one as in her Seat, and original be<lb></lb>ginning, in the Center of infinite concentrick Circles; the other <lb></lb>is conſtituted in the ſublime or higheſt Contact of infinite Circum<lb></lb>ferences of Circles, all excentrick to one another: Thoſe proceed <lb></lb>from Motions all equal and Equable; Theſe from Motions all al<pb xlink:href="040/01/855.jpg" pagenum="162"></pb>wayes Inequable to themſelves, and all unequal to one another, <lb></lb>that deſcend along the infinite different Inclinations. </s> <s>But we fur<lb></lb>ther adde, that if from the two points aſſigned for the Emanations, <lb></lb>we ſhall ſuppoſe Lines to proceed, not onely along two Superfi<lb></lb>cies Horizontal and Upright [or erect] but along all every ways <lb></lb>like as from thoſe, beginning at one ſole point, we paſſed to the <lb></lb>production of Circles from the leaſt to the greateſt, ſo beginning <lb></lb>from one ſole point we ſhall ſucceſſively produce inſinite Spheres, <lb></lb>or we may ſay one Sphere, that ſhall <emph type="italics"></emph>gradatim<emph.end type="italics"></emph.end> increaſe to infinite <lb></lb>bigneſſes: And this in two faſhions; that is, either with placing <lb></lb>the original in the Center, or elſe in the Circumference of thoſe <lb></lb>Spheres.</s></p><p type="main"> <s>SALV. </s> <s>The Contemplation is really ingenuous, and adequate <lb></lb>to the Wit of <emph type="italics"></emph>Sagredus.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SIMP. </s> <s>Though I am at leaſt capable of the Speculation, ac<lb></lb>cording to the two manners of the production of Circles and <lb></lb>Spheres, with the two different Natural Motions, howbeit I do <lb></lb>not perfectly underſtand the production depending on the Acce<lb></lb>lerate Motion and its Demonſtration, yet notwithſtanding that <lb></lb>licence of aſſigning for the place of that Emanation as well the <lb></lb>loweſt Center, as the higheſt Spherical Superficies, maketh me to <lb></lb>think that its poſſible that ſome great Miſtery may be contained <lb></lb>in theſe true and admirable Concluſions: ſome Miſtery I ſay <lb></lb>touching the Creation of the Univerſe, which is held to be of <lb></lb>Spherical form, and concerning the Reſidence of the Firſt <lb></lb>Cauſe.</s></p><p type="main"> <s>SALV. </s> <s>I am not unwilling to think the ſame: but ſuch pro<lb></lb>found Speculations are to be expected from Sharper Wits than <lb></lb>ours. </s> <s>And it ſhould ſuffice us, that if we be but thoſe leſſe noble <lb></lb>Workmen that diſcover and draw forth of the Quarry the <lb></lb>Marbles, in which the Induſtrious Statuaries afterwards make <lb></lb>wonderful Images appear, that lay hid under rude and miſhaped <lb></lb>Cruſts. </s> <s>Now, if you pleaſe, 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 ſhall have a pro<lb></lb>portion double to that of their Lengths, the <lb></lb>Motions in them from Reſt ſhall be finiſhed in <lb></lb>equal Times.</s></p><p type="main"> <s><emph type="italics"></emph>Let A E and A B be two unequal Planes, and unequally inclined, <lb></lb>and let their Elevations be F A and D A, and let F A have the <lb></lb>ſame proportion to D A, as A E hath to A B. </s> <s>I ſay that the Times <lb></lb>of the Motions along the Planes A E and A B, out of Reſt in A are<emph.end type="italics"></emph.end><pb xlink:href="040/01/856.jpg" pagenum="163"></pb><emph type="italics"></emph>equal. </s> <s>Draw Horizontal Parallels to the Line of Elevation E F and <lb></lb>B D, which cutteth A E in G. </s> <s>And be-<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.856.1.jpg" xlink:href="040/01/856/1.jpg"></figure><lb></lb><emph type="italics"></emph>cauſe the proportion of F A to A D, is <lb></lb>double the proportion of E A to A B; and <lb></lb>as F A to A D, ſo is E A to A G: There<lb></lb>fore the proportion of E A to A G, is dou<lb></lb>ble the proportion of E A to A B: There<lb></lb>fore A B is a Mean-Proportional between <lb></lb>E A and A G: And becauſe the Time of the <lb></lb>Deſcent along A B, is to the Time of the De<lb></lb>ſcent along A G, as A B to A G; and the <lb></lb>Time of the Deſcent along AG, is to the Time of the Deſcent along A E, as <lb></lb>A G is to the Mean-proportional between A G and A E, which is A B: <lb></lb>Therefore<emph.end type="italics"></emph.end> ex equali, <emph type="italics"></emph>the Time along A B is to the Time along A E, as A B <lb></lb>unto it ſelf: Therefore the Times are equal: Which was to be demonſtrated.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>THEOR. VIII. PROP. VIII.</s></p><p type="main"> <s>In Planes cut by the ſame Circle, erect to the <lb></lb>Horizon, in thoſe which meet with the end of <lb></lb>the erect Diameter, whether upper or lower, <lb></lb>the Times of the Motions are equal to the <lb></lb>Time of the Fall along the Diameter: and in <lb></lb>thoſe which fall ſhort of the Diameter, the <lb></lb>Times are ſhorter; and in thoſe which inter<lb></lb>ſect the Diameter, they are longer.</s></p><p type="main"> <s><emph type="italics"></emph>Let A B be the Perpendicular Diameter of the Circle erect to the <lb></lb>Horizon. </s> <s>That the Times of the Motions along the Planes pro<lb></lb>duced out of the Terms A and B unto the Circumference are equal, <lb></lb>hath already been demonſtrated: That the Time of the Deſcent along <lb></lb>the Plane D F, not reaching to the<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.856.2.jpg" xlink:href="040/01/856/2.jpg"></figure><lb></lb><emph type="italics"></emph>Diameter is ſborter, is demonſtrated <lb></lb>by drawing the Plane D B, which <lb></lb>ſhall be both longer and leſſe decli<lb></lb>ning than D F. </s> <s>Therefore the Time <lb></lb>along D F is ſhorter than the Time <lb></lb>along D B, that is, along A B. </s> <s>And <lb></lb>that the Time of the Deſcent along <lb></lb>the Plane that interſecteth the Dia<lb></lb>meter, as C O is longer, doth in the <lb></lb>ſame manner appear, for that it is <lb></lb>longer and leſſe declining than C B: Therefore the Propoſition is de<lb></lb>monſtrated.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/857.jpg" pagenum="164"></pb><p type="head"> <s>THEOR. IX. PROP. IX.</s></p><p type="main"> <s>If two Planes be inclined at pleaſure from a point <lb></lb>in a Line parallel to the Horizon, and be inter<lb></lb>ſected by a Line which may make Angles Al<lb></lb>ternately equal to the Angles contained be<lb></lb>tween the ſaid Planes and Horizontal Parallel, <lb></lb>the Motion along the parts cut off by the ſaid <lb></lb>Line, ſhall be performed in equal Times.</s></p><p type="main"> <s><emph type="italics"></emph>From off the point C of the Horizontal Line X, let any two Planes <lb></lb>be inclined at pleaſure C D and C E, and in any point of the <lb></lb>Line C D make the Angle C D F equal to the Angle X C E: <lb></lb>and let the Line D F cut the Plane C E in F, in ſuch a manner that <lb></lb>the Angles C D F and C F D may be equal to the Angles X C E, L C D <lb></lb>Alternately taken. </s> <s>I ſay, that<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.857.1.jpg" xlink:href="040/01/857/1.jpg"></figure><lb></lb><emph type="italics"></emph>the Times of the Deſcents along <lb></lb>C D and C F are equal. </s> <s>And <lb></lb>that (the Angle C D F being <lb></lb>ſuppoſed equal to the Angle <lb></lb>X C E) the Angle C F D is <lb></lb>equal to the Angle D C L, is <lb></lb>manifeſt. </s> <s>For the Common An<lb></lb>gle D C F being taken from the <lb></lb>three Angles of the Triangle <lb></lb>C D F equal to two Right An<lb></lb>gles, to which are equal all the Angles made with to the Line L X <lb></lb>at the point C, there remains in the Triangle two Angles C D F and <lb></lb>C F D, equal to the two Angles X C E and L C D: But it was ſup<lb></lb>poſed that C D F is equal to the Angle X C E: Therefore the remaining <lb></lb>Angle C F D is equal to the remaining angle D C L. </s> <s>Let the Plane <lb></lb>C E be ſuppoſed equal to the Plane C D, and from the points D and <lb></lb>E raiſe the Perpendiculars D A and E B, unto the Horizontal Paral<lb></lb>lel X L; and from C unto D F let fall the Perpendicular C G. </s> <s>And <lb></lb>becauſe the Angle C D G is equal to the Angle E C B; and becauſe <lb></lb>D G C and C B E are Right Angles; The Triangles C D G and <lb></lb>C B E ſhall be equiangled: And as D C is to C G, ſo let C E be <lb></lb>to E B: But D C is equal to C E: Therefore C G ſhall be equal to <lb></lb>E B. </s> <s>And inregard that of the Triangles D A C and C G F, the An<lb></lb>gles C and A are equal to the Angles F and G: Therefore as C D is to <lb></lb>D A, ſo ſhall F C be to C G; and Alternately, as D C is to C F, ſo<emph.end type="italics"></emph.end><pb xlink:href="040/01/858.jpg" pagenum="165"></pb><emph type="italics"></emph>is D A to C G, or B E. </s> <s>The proportion therefore of the Elevations <lb></lb>of the Planes equal to C D and C E, is the ſame with the proportion <lb></lb>of the Longitudes D C and C E: Therefore, by the firſt Corollary of <lb></lb>the precedent Sixth Propoſition, the Times of the Dcſcent along the <lb></lb>ſame ſhall be equal: Which mas to be proved.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Take the ſame another way: Draw F S perpendicular to the <lb></lb>Horizontal Parallel A S. </s> <s>Becauſe the Triangle C S F is like to <lb></lb>the Triangle D G C, it ſhall be, that as S F is to F C, ſo is G C <lb></lb>to C D. </s> <s>And becauſe the Triangle C F G is like to the Triangle <lb></lb>D C A, it ſhall be, that as F C is to C G, ſo is C D to D A: <lb></lb>Therefore,<emph.end type="italics"></emph.end> ex æquali, <emph type="italics"></emph>as <lb></lb>S F is to C G, ſo is C G to <lb></lb>D A: Thorefore C G is a<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.858.1.jpg" xlink:href="040/01/858/1.jpg"></figure><lb></lb><emph type="italics"></emph>Mean-proportional between <lb></lb>S F and D A: And as DA <lb></lb>is to S F, ſo is the Square <lb></lb>D A unto the Square C G <lb></lb>Again, the Triangle A C D <lb></lb>being like to the Triangle <lb></lb>C G F, it ſhall be, that as <lb></lb>D A is to D C, ſo is G C <lb></lb>to C F: and, Alternately, <lb></lb>as D A is to G C, ſo is D C to C F; and as the Square of D A <lb></lb>is to the Square of C G, ſo is the Square of D C to the Square of <lb></lb>C F. </s> <s>But it hath been proved that the Square D A is to the <lb></lb>Square C G as the Line D A is to the Line F S: Therefore, as the <lb></lb>Square D C is to the Square C F, ſo is the Line D E to F S: There<lb></lb>fore, by the ſeventh fore-going, in regard that the Elevations D A <lb></lb>and F S, of the Planes C D, and C F are in double proportion to <lb></lb>their Planes; the Times of the Motions along the ſame ſhall be <lb></lb>equal.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>THEOR. X. PROP. X.</s></p><p type="main"> <s>The Times of the Motions along ſeveral Inclina<lb></lb>tions of Planes whoſe Elevations are equal, <lb></lb>are unto one another as the Lengths of thoſe <lb></lb>Planes, whether the Motions be made from <lb></lb>Reſt, or there hath proceeded a Motion from <lb></lb>the ſame height.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Motions be made along A B C, and along A B D, until <lb></lb>they come to the Horizon D C, in ſuch ſort as that the Motion <lb></lb>along A B precedeth the Motions along B D and B C. </s> <s>I ſay, <lb></lb>that the Time of the Motion along B D, is to the Time along B C, as<emph.end type="italics"></emph.end><pb xlink:href="040/01/859.jpg" pagenum="166"></pb><emph type="italics"></emph>the Length B D is to B C. </s> <s>Let A F be drawn parallel to the Ho<lb></lb>rizon, to which continue out D B, meeting it in F; and let F E be <lb></lb>a Mean-proportional between D F and F B; and draw E O parallel <lb></lb>to D C, and A O ſhall be a Mean-proportional between C A and <lb></lb>A B: But if we ſuppoſe the Time <lb></lb>along A B, to be as A B, the Time a-<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.859.1.jpg" xlink:href="040/01/859/1.jpg"></figure><lb></lb><emph type="italics"></emph>long F B ſhall be as F B. </s> <s>And the <lb></lb>Time along all A C, ſhall be as the <lb></lb>Mean-proportional A O; and along <lb></lb>all F D ſhall be F E: Wherefore the <lb></lb>Time along the remainder B C ſhall <lb></lb>be B O; and along the remainder <lb></lb>B D ſhall be B E. </s> <s>But as B E is to <lb></lb>B O, ſo is B D to B C: Therefore <lb></lb>the Times along B D and B C, after the Deſcent along A B and <lb></lb>F B, or which is the ſame, along the Common part A B, ſhall be to <lb></lb>one another as the Lengths B D and B C: But that the Time along <lb></lb>B D, is to the Time along B C, out of Reſt in B, as the Length <lb></lb>B D to B C, hath already been demonſtrated. </s> <s>Therefore the Times <lb></lb>of the Motions along different Planes whoſe Elevations are equal, are <lb></lb>to one another as the Lengths of the ſaid Planes, whether the Motion <lb></lb>be made along the ſame out of Reſt, or whether another Motion of <lb></lb>the ſame Altitude do precede thoſe Motions: Which was to be de<lb></lb>monſtrated.<emph.end type="italics"></emph.end></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></lb>Reſt, be divided at pleaſure, the Time of <lb></lb>the Motion along the firſt part, is to the Time <lb></lb>of the Motion along the ſecond, as the ſaid <lb></lb>firſt part is to the exceſſe whereby the ſame <lb></lb>part ſhall be exceeded by the Mean-Propor<lb></lb>tional between the whole Plane and the ſame <lb></lb>firſt part.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Motion be along the whole Plane A B, ex quiete in A, <lb></lb>which let be divided at pleaſure in C; and let A F be a Mean <lb></lb>proportional between the whole B A and the firſt part A C; <lb></lb>C F ſhall be the exceſſe of the Mean proportional F A above the part <lb></lb>A C. </s> <s>I ſay the Time of the Motion along A C is to the Time of the <lb></lb>following Motion along C B, as A C to C F. </s> <s>Which is manifeſt;<emph.end type="italics"></emph.end><pb xlink:href="040/01/860.jpg" pagenum="167"></pb><emph type="italics"></emph>For the Time along A C is to the Time along all <lb></lb>A B, as A C to the Mean-proportional A F: There-<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.860.1.jpg" xlink:href="040/01/860/1.jpg"></figure><lb></lb><emph type="italics"></emph>fore, by Diviſion, the Time along A C, ſhall be to <lb></lb>the Time along the remainder C B as A C to C F: <lb></lb>If therefore the Time along A C be ſuppoſed to be <lb></lb>the ſaid A C, the Time along C B ſhall be C F: <lb></lb>Which was the Propoſition.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>But if the Motion be not made along the continu<lb></lb>ate Plane A C B, but by the inflected Plane A C D <lb></lb>until it come to the Horizon B D, to which from F a Parallel is <lb></lb>drawn F E. </s> <s>It ſhall in like manner be<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.860.2.jpg" xlink:href="040/01/860/2.jpg"></figure><lb></lb><emph type="italics"></emph>demonſtrated, that the Time along <lb></lb>A C is to the Time along the reflected <lb></lb>Plane C D, as A C is to C E. </s> <s>For <lb></lb>the Time along A C is to the Time a<lb></lb>long C B, as A C is to C F: But the <lb></lb>Time along C B, after A C hath been <lb></lb>demonſtrated to be to the Time along <lb></lb>C D, after the ſaid Deſoent along <lb></lb>A C, as C B is to C D; that is, as <lb></lb>C F to C E: Therefore,<emph.end type="italics"></emph.end> ex æquali, <emph type="italics"></emph>the Time along A C ſhall be to <lb></lb>the Time along C D, as the Line A C to C E.<emph.end type="italics"></emph.end></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></lb>ſure, be cut between the ſame Horizontal <lb></lb>Lines, and Mean-Proportionals between <lb></lb>them and the parts of them contained betwixt <lb></lb>the common Section and upper Horizontal <lb></lb>Line be given; the Time of the Motion a<lb></lb>long the Perpendicular ſhall have the ſame <lb></lb>proportion to the Time of the Motion along <lb></lb>the upper part of the Perpendicular, and af<lb></lb>terwards along the lower part of the interſe<lb></lb>cted Plane, as the Length of the whole Per<lb></lb>pendicular hath to the Line compounded of <lb></lb>the Mean-Proportional given upon the Per<lb></lb>pendicular, and of the exceſſe by which the <lb></lb>whole Plane exceeds its Mean-Proporttonal.</s></p><pb xlink:href="040/01/861.jpg" pagenum="168"></pb><p type="main"> <s><emph type="italics"></emph>Let the Horizontal Lines be A F the upper, and C D the low<lb></lb>er; between which let the Perpendicular A C, and inclined <lb></lb>Plane D F, be cut in B; and let A R be a Mean-Proportional <lb></lb>between the whole Perpendicular C A, and the upper part A B; and <lb></lb>let F S be a Mean-proportional between the whole Inclined Plane D F, <lb></lb>and the upper part B F. </s> <s>I ſay, that the Time of the Fall along the <lb></lb>whole Perpendicular A C hath the ſame proportion to the Time along <lb></lb>its upper part A B, with the lower of the Plane, that is, with B D, <lb></lb>as A C hath to the Mean-proporti<lb></lb>onal of the Perpendicular, that is<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.861.1.jpg" xlink:href="040/01/861/1.jpg"></figure><lb></lb><emph type="italics"></emph>A R, with S D, which is the ex<lb></lb>ceſſe of the whole Plane D F above <lb></lb>its Mean-proportional F S. </s> <s>Let a <lb></lb>Line be drawn from R to S, which <lb></lb>ſhall be parallel to the two Horizon<lb></lb>tal Lines. </s> <s>And becauſe the Time of <lb></lb>the Fall along all A C, is to the <lb></lb>Time along the part A B, as C A is <lb></lb>to the Mean proportional A R, if we ſuppoſe A C to be the Time of <lb></lb>the Fall along A C, A R ſhall be the Time of the Fall along A B, <lb></lb>and R C that along the remainder B C. </s> <s>For if the Time along A C <lb></lb>be ſuppoſed, as was done, to be A C it ſelf the Time along F D ſhall <lb></lb>be F D; and in like manner D S may be concluded to be the Time a<lb></lb>long B D, after F B, or after A B. </s> <s>The Time therefore along the <lb></lb>whole A C, is A R, with R C; And the Time along the inflected <lb></lb>Plane A B D, ſhall be A R, with S D: Which was to be proved.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>The ſame happeneth, if inſtead of the Perpendicular, another <lb></lb>Plane were taken, as ſuppoſe N O; and the Demonstration is the <lb></lb>ſame.<emph.end type="italics"></emph.end></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></lb>unto it, along which, when it hath the ſame <lb></lb>Elevation with the ſaid Perpendicular, it may <lb></lb>make a Motion after its Fall along the Per<lb></lb>pendicular in the ſame Time, as along the <lb></lb>ſame Perpendicular <emph type="italics"></emph>ex quiete.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Let the Perpendicular given be A B, to which extended to C, <lb></lb>let the part B C be equal; and draw the Horizontal Lines <lb></lb>C E and A G. </s> <s>It is required from B to inflect a Plane reach<lb></lb>ing to the Horizon C E, along which a Motion, after the Fall out<emph.end type="italics"></emph.end><pb xlink:href="040/01/862.jpg" pagenum="169"></pb><emph type="italics"></emph>of A, ſhall be made in the ſame Time, as along A B from Reſt in A. </s> <s>Let <lb></lb>C D be equal to C B, and drawing B D, let B E be applied equal to both <lb></lb>B D and D C. </s> <s>I ſay B E is the Plane required. </s> <s>Continue out E B to <lb></lb>meet the Horizontal Line A G in G;<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.862.1.jpg" xlink:href="040/01/862/1.jpg"></figure><lb></lb><emph type="italics"></emph>and let G F be a Mean-Proportional be<lb></lb>tween the ſaid E G and G B. </s> <s>E F ſhall <lb></lb>be to F B, as E G is to G F; and the <lb></lb>Square E F ſhall be to the Square F B, as <lb></lb>the Square E G is to the Square G F; <lb></lb>that is as the Line E G to G B: But <lb></lb>E G is double to G B: Therefore the <lb></lb>Square of E F is double to the Square of F B: But alſo the Square of <lb></lb>D B is double to the Square of B C: Therefore, as the Line E F is to <lb></lb>F B, ſo is D B to B C: And by Compoſition and Permutation, as E B is <lb></lb>to the two D B and B C, ſo is B F to B C: But B E is equal to the two <lb></lb>D B and B C: Therefore B F is equal to the ſaid B C, or B A. </s> <s>If there<lb></lb>fore A B be underſtood to be the Time of the Fall along A B, G B ſhall <lb></lb>be the Time along G B, and G F the Time along the whole G E: There<lb></lb>fore B F ſhall be the Time along the remainder B E, after the Fall from <lb></lb>G, or from A, which was the Propoſition.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROBL. II. PROP. XIV.</s></p><p type="main"> <s>A <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendicular and a <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane inclined to it being <lb></lb>given, to find a part in the upper <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendicu<lb></lb>lar which ſhall be paſt <emph type="italics"></emph>ex quiete<emph.end type="italics"></emph.end> in a Time <lb></lb>equal to that in which the inclined <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane is <lb></lb>paſt after the Fall along the part found in the <lb></lb>Perpendicular.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Perpendicular be D B, and the Plane inclined to it A C. </s> <s>It is <lb></lb>required in the Perpendicular A D to find a part which ſhall be <lb></lb>paſt<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in a Time equal to that in which the Plane A C is <lb></lb>paſt after the Fall along the ſaid part. </s> <s>Draw the Horizontal Line C B; <lb></lb>and as B A more twice A C is to A C, ſo let E A be to A R; And from <lb></lb>R let fall the Perpendicular R X unto D B. </s> <s>I ſay X is the point requi<lb></lb>red. </s> <s>And becauſe as B A more twice A C is to A C, ſo is C A to A E, <lb></lb>by Diviſion it ſhall be that as B A more A C is to A C, ſo is C E to E A: <lb></lb>And becauſe as B A is to A C, ſo is E A to A R, by Compoſition it ſhall <lb></lb>be that as B A more A C is to A C, ſo is E R to R A: But as B A more <lb></lb>A C is to A C, ſo is C E to E A: Therefore, as C E is to E A, ſo is E R, <lb></lb>to R A, and both the Antecedents to both the Conſequents, that is, C R<emph.end type="italics"></emph.end><pb xlink:href="040/01/863.jpg" pagenum="170"></pb><emph type="italics"></emph>to R E: Therefore C R, R E, and R A are Proportionals. </s> <s>Farther<lb></lb>more, becauſe as B A is to A C, ſo E A is ſuppoſed to be to A R, and,<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.863.1.jpg" xlink:href="040/01/863/1.jpg"></figure><lb></lb><emph type="italics"></emph>in regard of the likeneſſe of the Triangles, <lb></lb>as B A is to A C, ſo is X A to A R: There<lb></lb>fore, as E A is to A R, ſo is X A to A R: <lb></lb>Therefore E A and X A are equal. </s> <s>Now if <lb></lb>we underſtand the Time along R A to be as <lb></lb>R A, the Time along R C ſhall be R E, the <lb></lb>Mean-Proportional between C R and R A: <lb></lb>And A E ſhall be the Time along A C after <lb></lb>R A or after X A: But the Time along X A <lb></lb>is X A, ſo long as R A is the Time along R <lb></lb>A: But it hath been proved that X A and <lb></lb>A E are equal: Therefore the Propoſition is proved.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROBL. III. <emph type="italics"></emph>P<emph.end type="italics"></emph.end>RO<emph type="italics"></emph>P.<emph.end type="italics"></emph.end> XV.</s></p><p type="main"> <s>A <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendicular and a <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane inflected to it being <lb></lb>given, to find a part in the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendicular ex<lb></lb>tended downwards which ſhall be paſſed in the <lb></lb>ſame. </s> <s>Time as the inflected <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane after the Fall <lb></lb>along the given Perpendicular.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Perpendicular be A B, and the Plane Inſlected to it B C. </s> <s>It <lb></lb>is required in the Perpendicular extended downwards to find a <lb></lb>part which from the Fall out of A ſhall be paſt in the ſame Time as <lb></lb>B C is paſſed from the ſame Fall out of A. </s> <s>Draw the Horizontal Line <lb></lb>A D, with which let C B meet extended to D; and let D E be a Mean<lb></lb>proportional between C D and D B;<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.863.2.jpg" xlink:href="040/01/863/2.jpg"></figure><lb></lb><emph type="italics"></emph>and let B F be equal to B E; and let <lb></lb>A G be a third Proportional to B A and <lb></lb>A F. </s> <s>I ſay, B G is the Space that after <lb></lb>the Fall A B ſhall be paſt in the ſame <lb></lb>Time, as the Plane B C ſhall be paſt af<lb></lb>ter the ſame Fall. </s> <s>For if we ſuppoſe <lb></lb>the Time along A B to be as A B, the <lb></lb>Time along D B ſhall be as D B: And <lb></lb>becauſe D E is the Mean-proportional <lb></lb>between B D and D C, the ſame D E <lb></lb>ſhall be the Time along the whole D C, and B E the Time along the Part <lb></lb>or Remainder B C<emph.end type="italics"></emph.end> ex quiete, <emph type="italics"></emph>in D, or<emph.end type="italics"></emph.end> ^{*} ex caſu <emph type="italics"></emph>A B: And it may in<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1093"></arrow.to.target><lb></lb><emph type="italics"></emph>like manner be proved, that B F is the Time along B G, after the ſame <lb></lb>Fall: But B F is equal to B E: Which was the Propoſition to be proved.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/864.jpg" pagenum="171"></pb><p type="margin"> <s><margin.target id="marg1093"></margin.target>* From or after <lb></lb>the Fall A B.</s></p><p type="head"> <s>THEOR. XIII. <emph type="italics"></emph>P<emph.end type="italics"></emph.end>RO<emph type="italics"></emph>P.<emph.end type="italics"></emph.end> XVI.</s></p><p type="main"> <s>If the parts of an inclined <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane and <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendicu<lb></lb>lar, the Times of whoſe Motions <emph type="italics"></emph>ex quiete<emph.end type="italics"></emph.end> are <lb></lb>equal, be joyned together at the ſame point, a <lb></lb>Moveable coming out of any ſublimer Height <lb></lb>ſhall ſooner paſſe the ſaid part of the inclined <lb></lb><emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane, than that part of the Perpendicular.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Perpendicular be E B, and the Inclined Plane C E, joyned <lb></lb>at the ſame Point E, the Times of whoſe Motions from off Reſt in <lb></lb>E are equal, and in the Perpendicular continued out, let a ſublime <lb></lb>point A be taken at pleaſure, out of which the Moveables may be let <lb></lb>fall. </s> <s>I ſay, that the Inclined Plane E C ſhall be paſſed in a leſſe Time <lb></lb>than the Perpendicular E B, after the Fall A E. </s> <s>Draw a Line from C <lb></lb>to B, and having drawn the Horizontal Line A D continue out C E till <lb></lb>it meet the ſame in D; and let D F be a Mean-Proportional between <lb></lb>C D and D E; and let A G be a<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.864.1.jpg" xlink:href="040/01/864/1.jpg"></figure><lb></lb><emph type="italics"></emph>Mean-Proportional between B A and <lb></lb>A E; and draw F G and D G. </s> <s>And <lb></lb>becauſe the Time of the Motion along <lb></lb>E C and E B out of Reſt in E are <lb></lb>equal, the Angle C ſhall be a Right <lb></lb>Angle, by the ſecond Corollary of the <lb></lb>Sixth Propoſition; and A is a Right <lb></lb>Angle, and the Vertical Angles <lb></lb>at E are equal: Therefore the Tri<lb></lb>angles A E D and C E B are equian<lb></lb>gled, and the Sides about equal An<lb></lb>gles are Proportionals: Therefore as <lb></lb>B E is to E C, ſo is D E to E A. <lb></lb></s> <s>Therefore the Rectangle B E A is <lb></lb>equal to the Rectangle C E D: And <lb></lb>becauſe the Rectangle C D E ex<lb></lb>ceedeth the Rectangle C E D, by the Square E D, and the Rectangle <lb></lb>B A E doth exceed the Rectangle B E A, by the Square E A: The <lb></lb>exceſſe of the Rectangle C D E above the Rectangle B A E, that is of <lb></lb>the Square F D above the Square A G ſhall be the ſame as the exceſſe <lb></lb>of the Square D E above the Square A E; which exceſs is the <lb></lb>Square D A: Therefore the Square F D is equal to the two Squares <lb></lb>G A and A D, to which the Square G D is alſo equal: Therefore the<emph.end type="italics"></emph.end><pb xlink:href="040/01/865.jpg" pagenum="172"></pb><emph type="italics"></emph>Line D F is equal to D G, and the Angle D G F is equal to the An<lb></lb>gle D F G, and the Angle E G F is leſſc than the Angle E F G, and <lb></lb>the oppoſite Side E F leſſe than the Side E G. </s> <s>Now if we ſuppoſe <lb></lb>the Time of the Fall along A E to be as A E, the Time by D E ſhall <lb></lb>be as D E; and A G being a Mean-Proportional between B A and A E, <lb></lb>A G ſhall be the Time along the whole A B, and the part E G ſhall be <lb></lb>the Time along the Part E B<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in A. </s> <s>And it may in like man<lb></lb>ner be proved that E F is the Time along E C after the Deſcent D E, or <lb></lb>after the Fall A E: But E F is proved to be leſſer than E G: Therefore <lb></lb>the Propoſition is proved.<emph.end type="italics"></emph.end></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 paſ<lb></lb>ſed along the Perpendicular after the Fall from above in the <lb></lb>ſame Time in which the Inclined Plane is paſt, is leſſe than <lb></lb>that which is paſt in the ſame Time as in the Inclined, no fall <lb></lb>from above preceding, yet greater than the ſaid Inclined <lb></lb>Plane.</s></p><p type="main"> <s><emph type="italics"></emph>For it having been proved, but now, that of the Moveables coming <lb></lb>from the ſublime Term A the Time of the Converſion along E C is <lb></lb>ſhorter than the Time of the Progreſſion along E B; It is manifeſt that <lb></lb>the Space that is paſt along E B in a Time equal to the Time along E C <lb></lb>is leſs than the whole Space E B. </s> <s>And that the ſame Space along the <lb></lb>Perpendicular is greater than E C is mani<lb></lb>feſted by reaſſuming the Figure of the pre-<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.865.1.jpg" xlink:href="040/01/865/1.jpg"></figure><lb></lb><emph type="italics"></emph>cedent Propoſition, in which the part of the <lb></lb>Perpendicular B G hath been demonſtrated <lb></lb>to be paſſed in the ſame Time as B C after <lb></lb>the Fall A B: But that B G is greater than <lb></lb>B C is thus collected. </s> <s>Becauſe B E and F B <lb></lb>are equal, and B A leſſer than B D, F B, <lb></lb>hath greater proportion to B A, than E B <lb></lb>hath to B D: And, by Compoſition, F A <lb></lb>hath greater proportion to A B, than E D <lb></lb>to D B: But as F A is to A B, ſo is G F <lb></lb>to F B, (for A F is the Mean-Proportional <lb></lb>between B A and A G:) And in like man<lb></lb>ner, as E D is to B D, ſo is C E to E B: Therefore G B hath greater <lb></lb>proportion to B F, than C B hath to B E: Therefore G B is greater <lb></lb>than B C.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/866.jpg" pagenum="173"></pb><p type="head"> <s>PROBL. IV. <emph type="italics"></emph>P<emph.end type="italics"></emph.end>RO<emph type="italics"></emph>P.<emph.end type="italics"></emph.end> XVII.</s></p><p type="main"> <s>A <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendicular and <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane Inflected to it being <lb></lb>given, to aſſign a part in the given <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane, in <lb></lb>which after the Fall along the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendicular <lb></lb>the Motion may be made in a Time equal to <lb></lb>that in which the Moveable <emph type="italics"></emph>ex quiete<emph.end type="italics"></emph.end> paſſeth <lb></lb>the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendicular given.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Perpendicular be A B, and a Plane Inflected to it B E: It is <lb></lb>required in B E to aſſign a Space along which the Moveable af<lb></lb>ter the Fall along A B may move in a Time equal to that in which <lb></lb>the ſaid Perpendicular A B is paſſed<emph.end type="italics"></emph.end> ex quiete. <emph type="italics"></emph>Let the Line A D be <lb></lb>parallel to the Horizon, with which let the Plane prolonged meet in D; <lb></lb>and ſuppoſe F B equal to B A; and as B D <lb></lb>is to D F, ſo let F D be to D E. </s> <s>I ſay, that<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.866.1.jpg" xlink:href="040/01/866/1.jpg"></figure><lb></lb><emph type="italics"></emph>the Time along B E after the Fall along A B <lb></lb>equalleth the Time along A B, out of Reſt <lb></lb>in A. </s> <s>For if we ſuppoſe A B to be the Time <lb></lb>along A B, D B ſhall be the Time along <lb></lb>D B. </s> <s>And becauſe, as B D is to D F, ſo is <lb></lb>F D to D E, D F ſhall be the Time along <lb></lb>the whole Plane D E, and B F along the <lb></lb>part B E out of D: But the Time along <lb></lb>B E after D B, is the ſame as after A B: Therefore the Time along B E <lb></lb>after A B ſhall be B F, that is, equal to the Time<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in A: <lb></lb>Which was the Propoſition.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>P<emph.end type="italics"></emph.end>ROBL. V. PROP. XVIII.</s></p><p type="main"> <s>Any Space in the Perpendicular being given from <lb></lb>the aſſigned beginning of Motion that is <lb></lb>paſſed in a Time given, and any other leſſer <lb></lb>Time being alſo given, to find another Space in <lb></lb>the ſaid Perpendicular that may be paſſed in <lb></lb>the given leſſer Time.</s></p><pb xlink:href="040/01/867.jpg" pagenum="174"></pb><p type="main"> <s><emph type="italics"></emph>Let the Perpendicular be A D, in which let the Space aſſigned be <lb></lb>A B, whoſe Time from the beginning A let be A B: and let the <lb></lb>Horizon be C B E, and let a Time be given leſs than A B, to <lb></lb>which let B C be noted equal in the Horizon: It is required in the <lb></lb>ſaid Perpendicular to find a Space equal to the ſame A B that ſhall be <lb></lb>paſſed in the Time B C. </s> <s>Draw a Line from A to<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.867.1.jpg" xlink:href="040/01/867/1.jpg"></figure><lb></lb><emph type="italics"></emph>C. </s> <s>And becauſe B C is leſſe than B A, the Angle <lb></lb>B A C ſhall be leſſe than the Angle B C A. </s> <s>Let <lb></lb>C A E be made equal to it, and the Line A E meet <lb></lb>with the Horizon in the Point E, to which ſup<lb></lb>poſe E D a Perpendicular, cutting the Perpendi<lb></lb>cular in D, and let D F be cut equal to B A. </s> <s>I <lb></lb>ſay, that the ſaid F D is a part of the Perpendi<lb></lb>cular along which the Lation from the beginning <lb></lb>of Motion in A, the Time B C given will be ſpent. <lb></lb></s> <s>For if in the Right-angled Triangle A E D, a <lb></lb>Perpendicular to the oppoſite Side A D, be drawn <lb></lb>E B, A E ſhall be a Mean-Proportional betwixt <lb></lb>D A and A B, and B E a Mean-Proportional betwixt D B and B A, <lb></lb>or betwixt F A and A B (for F A is equal to D B.) And in regard <lb></lb>A B hath been ſuppoſed to be the Time along A B, A E, or E C ſhall be <lb></lb>the Time along the whole A D, and E B the Time along A F: There<lb></lb>fore the part B C ſhall be the Time along the part F D: Which was <lb></lb>intended.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROBL. VI. PROP. XIX.</s></p><p type="main"> <s>Any Space in the Perpendicular paſſed from the <lb></lb>beginning of the Motion being given, and the <lb></lb>Time of the Fall being aſſigned, to find the <lb></lb>Time in which another Space. </s> <s>equal to the gi<lb></lb>ven one, and taken in any part of the ſaid Per<lb></lb>pendicular, ſhall be afterwards paſt by the <lb></lb>ſame Moveable.</s></p><p type="main"> <s><emph type="italics"></emph>In the Perpendicular A B let A C be any Space taken from the be<lb></lb>ginning of the Motion in A, to which let D B be another equal Space <lb></lb>taken any where at pleaſure, and let the Time of the Motion along <lb></lb>A C be given, and let it be A C. </s> <s>It is required to ſind the Time of the<emph.end type="italics"></emph.end><pb xlink:href="040/01/868.jpg" pagenum="175"></pb><emph type="italics"></emph>Motion along D B after the Fall from A. </s> <s>About the whole A B de<lb></lb>ſcribe a Semicircle A E B, and from<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.868.1.jpg" xlink:href="040/01/868/1.jpg"></figure><lb></lb><emph type="italics"></emph>C let fall C E, a Perpendicular to A <lb></lb>B, and draw a Line from A to E; <lb></lb>which ſhall be greater than E C. <lb></lb></s> <s>Let E F be out equall to E C: I ſay, <lb></lb>that the remainder F A is the Time <lb></lb>of the Motion along D B. </s> <s>For be<lb></lb>cauſe A E is a Mean-proportional be<lb></lb>twixt B A and and A C, and A C <lb></lb>is the Time of the Fall along A C; <lb></lb>A E ſhall be the Time along the <lb></lb>Whole A B. </s> <s>And becauſe C E is a <lb></lb>Mean-proportional betwixt D A and <lb></lb>A C, (for D A is equal to B C) <lb></lb>C E, that is E F ſhall be the Time <lb></lb>along A D: Therefore the Remainder A F ſhall be the Time along the <lb></lb>Remainder B B: Which is the Propoſition.<emph.end type="italics"></emph.end></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"></emph>ex quiete<emph.end type="italics"></emph.end> be <lb></lb>as the ſaid Spaec, the Time thereof after another Space is ad<lb></lb>ded ſhall be the exceſſe of the Mean-proportional betwixt <lb></lb>the Addition and Space taken together, and the ſaid Space <lb></lb>above the Mean-proportional betwixt the firſt Space and the <lb></lb>Addition.</s></p><p type="main"> <s><emph type="italics"></emph>As for example, it being ſuppoſed that the Time along<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.868.2.jpg" xlink:href="040/01/868/2.jpg"></figure><lb></lb><emph type="italics"></emph>A B, out of Reſt in A, be A B; A S being another Space <lb></lb>added, The Time along A B after S A ſhall be the exceſſe of <lb></lb>the Mean-proportional betwixt S B and B A above the <lb></lb>Mean-proportional betwixt B A and A S.<emph.end type="italics"></emph.end></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></lb>of the Motion being given, to find another <lb></lb>part towards the end that ſhall be paſt in the <lb></lb>ſame Time as the firſt part given.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Space be C B, and let the part in it given after the begin<lb></lb>ing of the Motion in C be C D. </s> <s>It is required to find another <lb></lb>part towards the end B, which ſhall be paſt in the ſame Time as<emph.end type="italics"></emph.end><pb xlink:href="040/01/869.jpg" pagenum="176"></pb><emph type="italics"></emph>the given part C D. </s> <s>Take a Mean-proportional betwixt B C and C D, <lb></lb>to which ſuppoſe B A equal; and let C E be a third proportional be-<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.869.1.jpg" xlink:href="040/01/869/1.jpg"></figure><lb></lb><emph type="italics"></emph>tween B C and C A. </s> <s>I ſay, that E B is the Space that after <lb></lb>the Fall out of C ſhall be past in the ſame Time as the ſaid <lb></lb>C D is paſſed. </s> <s>For if we ſuppoſe the Time along C B <lb></lb>to be as C B; B A (that is the Mean-proportional betwixt <lb></lb>B C and C D) ſhall be the Time along C D. </s> <s>And becauſe <lb></lb>C A is the Mean proportional betwixt B C and C E, C A <lb></lb>ſhall be the Time along C E: But the whole B C is the <lb></lb>Time along the Whole C B: Therefore the part B A ſhall be <lb></lb>the Time along the part E B, after the Fall out of C: But <lb></lb>the ſaid B A was the Time along C D: Therefore C D and <lb></lb>E B ſhall be paſt in equal Times out of Reſt in C: Which <lb></lb>was to be done.<emph.end type="italics"></emph.end></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"></emph>ex quie<lb></lb>te,<emph.end type="italics"></emph.end> in which from the begining of the Motion <lb></lb>a part is taken at pleaſure, paſſed in any Time, <lb></lb>after which an Inflex Motion followeth along <lb></lb>any Plane however Inclined, the Space which <lb></lb>along that Plane is paſſed in a Time equal to <lb></lb>the Time of the Fall already made along the <lb></lb>Perpendicular ſhall be to the Space then paſ<lb></lb>ſed along the Perpendicular more than double, <lb></lb>and leſſe than triple.</s></p><p type="main"> <s><emph type="italics"></emph>From the Horizon A E let fall a Perpendicular A B, along which <lb></lb>from the begining A let a Fall be made, of which let a part A C <lb></lb>be taken at pleaſure; then out of C let any Plane G be inclined at <lb></lb>pleaſure: along which after the Fall along A C let the Motion be con<lb></lb>tinued. </s> <s>I ſay, the Space paſſed by that Motion along C G in a Time <lb></lb>equall to the Time of the Fall along A C, is more than double, and leſs <lb></lb>than triple that ſame Space A C. </s> <s>For ſuppoſe C F equal to A C, and <lb></lb>extending out the Plane G C as far as the Horizon in E, and as C E <lb></lb>is to E F, ſo let F E be to E G. </s> <s>If therefore we ſuppoſe the Time of<emph.end type="italics"></emph.end><pb xlink:href="040/01/870.jpg" pagenum="177"></pb><emph type="italics"></emph>the Fall along A C to be as the Line A C; C E ſhall be the Time along <lb></lb>E C, and C F or C A the Time of the Motion along C G. </s> <s>Therefore <lb></lb>it is to be proved that the<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.870.1.jpg" xlink:href="040/01/870/1.jpg"></figure><lb></lb><emph type="italics"></emph>Space C G is more than <lb></lb>double, and leſſe than <lb></lb>triple the ſaid C A. </s> <s>For <lb></lb>in regard that as C E is <lb></lb>to E F, ſo is F E to E G; <lb></lb>therefore alſo ſo is C F to <lb></lb>F G. </s> <s>But E C is leſſe <lb></lb>than E F: Therefore C F <lb></lb>ſhall be leſſe than F G, and <lb></lb>G C more than double to <lb></lb>F C or A C. </s> <s>And moreover, in regard that F E is leſſe than double to <lb></lb>E C, (for E C is greater than C A or C F) G F ſhall alſo be leſſe <lb></lb>than double to F C, and G C leſſe than triple to C F or C A: Which <lb></lb>was to be demonſtrated.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>And the ſame may be more generally propounded: for that which <lb></lb>hapneth in the Perpendicular and Inclined Plane, holdeth true alſo if <lb></lb>after the Motion a Plane ſomewhat inclined it be inflected along a more <lb></lb>inclining Plane, as is ſeen in the other Figure: And the Demonſtration <lb></lb>is the ſame.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>P<emph.end type="italics"></emph.end>ROBL. VIII. <emph type="italics"></emph>P<emph.end type="italics"></emph.end>RO<emph type="italics"></emph>P.<emph.end type="italics"></emph.end> XXII.</s></p><p type="main"> <s>Two unequall Times being given, and a Space <lb></lb>that is paſt <emph type="italics"></emph>ex quiete<emph.end type="italics"></emph.end> along the Perpendicular <lb></lb>in the ſhorteſt of thoſe given Times, to inflect <lb></lb>a Plane from the higheſt point of the Perpen<lb></lb>dicular unto the Horizon, along which the <lb></lb>Moveable may deſcend in a Time equal to the <lb></lb>longeſt of thoſe Times given.</s></p><p type="main"> <s><emph type="italics"></emph>Let the unsqual Times be A the greater, and B the leſſer; and let <lb></lb>the Space that is paſt<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>along the Perpendicular in the <lb></lb>Time B, be C D. </s> <s>It is required from the Term C to inflect<emph.end type="italics"></emph.end> [or <lb></lb><figure id="id.040.01.870.2.jpg" xlink:href="040/01/870/2.jpg"></figure><lb></lb>bend] <emph type="italics"></emph>a Plane untill it reach the Horizon that may be paſſed in the<emph.end type="italics"></emph.end><pb xlink:href="040/01/871.jpg" pagenum="178"></pb><emph type="italics"></emph>Time A. </s> <s>As B is to A, ſo let C D be to another Line, to which let C X <lb></lb>be equal that deſcendeth from C unto the Horizon: It is manifeſt that <lb></lb>the Plane C X is that along which the Moveable deſcendeth in the Gi<lb></lb>ven Time A. </s> <s>For it hath been demonſtrated, that the Time along the <lb></lb>inclined Plane hath the ſame proportion to the Time along its ^{*} Eleva-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1094"></arrow.to.target><lb></lb><emph type="italics"></emph>tion, as the Length of the Plane hath to the Length of its Elevation,. <lb></lb>The Time, therefore, along C X is to the Time along C D, as C X is to <lb></lb>C D, that is, as the Time A is to the Time B: But the Time B is that <lb></lb>in which the Perpendicular is paſt<emph.end type="italics"></emph.end> ex quiete: <emph type="italics"></emph>Therefore the Time A is <lb></lb>that in which the Plane C X is paſſed.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1094"></margin.target>* Or Perpendi<lb></lb>cular.</s></p><p type="head"> <s><emph type="italics"></emph>P<emph.end type="italics"></emph.end>ROBL. IX. PROP. XXIII.</s></p><p type="main"> <s>A Space paſt <emph type="italics"></emph>ex quiete<emph.end type="italics"></emph.end> along the Perpendicular in <lb></lb>any Time being given, to inflect a Plane from <lb></lb>the loweſt term of that Space, along which, <lb></lb>after the Fall along the Perpendicular, a Space <lb></lb>equal to any Space given may be paſſed in the <lb></lb>ſame Time: which nevertheleſſe is more than <lb></lb>double, and leſſe than triple the Space paſſed <lb></lb>along the Perpendicular.</s></p><p type="main"> <s><emph type="italics"></emph>Along the Perpendicular A S, in the Time A C, let the Space <lb></lb>A C be paſt<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in A; to which let I R be more than <lb></lb>double, and leſſe than triple. </s> <s>It is required from the Terme C <lb></lb>to inflect a Plane, along which a Moveable after the Fall along A C <lb></lb>may in the ſame Time A C paſſe a Space equal to the ſaid I R. </s> <s>Let <lb></lb>R N, and N M be equal to A C: And look what proportion the part <lb></lb>I M hath to M N, the ſame ſhall the Line A C have to another, equal <lb></lb>to which draw C E from C to<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.871.1.jpg" xlink:href="040/01/871/1.jpg"></figure><lb></lb><emph type="italics"></emph>the Horizon A E, which con<lb></lb>tinue out towards O, and take <lb></lb>C F, F G, and G O, equal to <lb></lb>the ſaid R N, N M, and M I. <lb></lb></s> <s>I ſay, that the Time along the <lb></lb>inflected Plane C O, after the <lb></lb>Fall A G, is equal to the Time <lb></lb>A C out of Reſt in A. </s> <s>For in <lb></lb>regard that as O G is to G F, <lb></lb>ſo is F C to C E by Compoſition it ſhall be that as O F is to F G or F C, <lb></lb>ſo is F E to E C; and as one of the Antecedents is to one of the Con<lb></lb>ſequents, ſo are all to all; that is, the whole O E is to E F as F E to <lb></lb>E C: Therefore O E, E F, and E C are Continual Proportionals:<emph.end type="italics"></emph.end><pb xlink:href="040/01/872.jpg" pagenum="179"></pb><emph type="italics"></emph>And ſince it was ſuppoſed that the Time along A C is as A C, C E ſhall <lb></lb>be the Time along E C; and E F the Time along the whole E O; and <lb></lb>the part C F that along the part C O: But C F is equal to the ſaid C A: <lb></lb>Therefore that is done which was required: For the Time C A is the <lb></lb>Time of the Fall along A C<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in A; and C F (which is equal <lb></lb>to C A) is the Time along C O, after the Deſcent along E C, or after <lb></lb>the Fall along A C: Which was the Propoſition.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>And here it is to be noted, that the ſame may happen if the preceding <lb></lb>Motion be not made along the Perpendicular, but along an Inclined Plane: <lb></lb>As in the following Figure, in which let the preceding Lation be made <lb></lb>along the inclined Plane A S beneath the Horizon A E: And the Demon<lb></lb>ſtration is the very ſame.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>SCHOLIUM.</s></p><p type="main"> <s>If one obſerve well, it ſhall be manifeſt, that the leſſe the given <lb></lb>Line I R wanteth of being triple to the ſaid A C, the nearer <lb></lb>ſhall the Inflected Plane, along which the ſecond Motion is <lb></lb>to be made, which ſuppoſe to be C O, come to the Perpen<lb></lb>dicular, along which in a Time equal to A C a Space ſhall <lb></lb>be paſſed triple to A C.</s></p><p type="main"> <s><emph type="italics"></emph>For in caſe I R were very near the triple of A C, I M ſhould be well<lb></lb>near equal to M N: And if, as I M is to M N by Conſtruction, ſo <lb></lb>A C is to C E, then it is evident that the ſaid C E will be found but <lb></lb>little bigger than C A, and, which followeth of conſequence, the point E <lb></lb>ſhall be found very near the point A, and C O to containe a very acute<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.872.1.jpg" xlink:href="040/01/872/1.jpg"></figure><lb></lb><emph type="italics"></emph>Angle with C S, and <lb></lb>almoſt to concur both in <lb></lb>one Line. </s> <s>And on the <lb></lb>contrary, if the ſaid I R <lb></lb>were but a very little <lb></lb>more than double the <lb></lb>ſaid A C, I M ſhould <lb></lb>be a very ſhort Line. <lb></lb></s> <s>Hence it may happen <lb></lb>alſo that A C may come <lb></lb>to be very ſhort in reſpect of C E which ſhall be very long, and ſhall ap<lb></lb>proach very near the Horizontal Parallel drawn from C. </s> <s>And from <lb></lb>hence we may collect, that if in the preſent Figure after the Deſcent along <lb></lb>the inclined Plane A C, a Reflexion be made along the Horizontal Line, <lb></lb>as<emph.end type="italics"></emph.end> v. </s> <s>gr. <emph type="italics"></emph>C T, the Space along which the Moveable afterwards moved <lb></lb>in a Time equal to the Time of the Deſcent along A C would be exactly <lb></lb>double to the Space A C. </s> <s>And it appears that the like Diſcourſe may be <lb></lb>here applied: For it is apparent by what hath been ſaid, that ſince O E<emph.end type="italics"></emph.end><pb xlink:href="040/01/873.jpg" pagenum="180"></pb><emph type="italics"></emph>is to E F, as F E is to E C, that F C determineth the Time along C O: <lb></lb>And if a part of the Horizontal Line T C double to C A be divided in <lb></lb>two equal parts in V, the extenſion towards X ſhall be prolonged<emph.end type="italics"></emph.end> in in<lb></lb>finitum, <emph type="italics"></emph>whilſt it ſeeks to meet with the prolonged Line A E: And the <lb></lb>proportion of the Infinite Line T X to the Infinite Line V X, ſhall be <lb></lb>no other than the proportion of the Infinite Line V X to the Infinite <lb></lb>Line X C.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>We may conclude the ſelf-ſame thing another way by reaſſuming the <lb></lb>ſame Reaſoning that we uſed in the Demonſtration of the firſt Propoſi<lb></lb>tion. </s> <s>For reſuming the Triangle A B C, repreſenting to us by its Pa<lb></lb>rallels to the Baſe B C the Degrees of Velocity continually encreaſed ac<lb></lb>cording to the encreaſes of the Time; from which, ſince they are infi<lb></lb>nite, like as the Points are infinite in the Line A C, and the Inſtants <lb></lb>in any Time, ſhall reſult the Superficies of that ſame Triangle, if we <lb></lb>underſtand the Motion to continue for ſuch another Time, but no far<lb></lb>ther with an Accelerate, but with an Equable Motion, according to the <lb></lb>greateſt degree of Velocity acquired, which degree is repreſented <lb></lb>by the Line B C. </s> <s>Of ſuch degrees ſhall be made up an Aggregate like to <lb></lb>a Parallelogram A D B C, which is the double of<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.873.1.jpg" xlink:href="040/01/873/1.jpg"></figure><lb></lb><emph type="italics"></emph>the Triangle A B C. </s> <s>Wherefore the Space which <lb></lb>with degrees like to thoſe ſhall be paſſed in the ſame <lb></lb>Time, ſhall be double to the Space paſt with the de<lb></lb>grees of Velocity repreſented by the Triangle A B C: <lb></lb>But along the Horizontal Plane the Motion is Equa<lb></lb>ble, for that there is no cauſe of Acceleration, or Re<lb></lb>tardation: Therefore it may be concluded that the <lb></lb>Space C D, paſſed in a Time equall to the Time A C is double to the <lb></lb>Space A C: For this Motion is made<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>Accelerate according <lb></lb>to the Parallels of the Triangle; and that according to the Parallels <lb></lb>of the Parallelogram, which, becauſe they are infinite, are donble to <lb></lb>the infinite Parallels of the Triangle.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Moreover it may farther be obſerved, that what ever degree of <lb></lb>ſwiftneſs is to be found in the Moveable, is indelibly impreſſed upon it <lb></lb>of its own nature, all external cauſes of Acceleration or Retardation <lb></lb>being removed; which hapneth only in Horizontal Planes: for in de<lb></lb>clining Planes there is cauſe of greater Acceleration, and in the riſing <lb></lb>Planes of greater Retardation. </s> <s>From whence in like manner it fol<lb></lb>loweth that the Motion along the Horizontal Plane is alſo Perpetual: <lb></lb>for if it be Equable, it can neither be weakned nor retarded, nor much <lb></lb>leſſe deſtroyed. </s> <s>Farthermore, the degree of Celerity acquired by the <lb></lb>Moveable in a Natural Deſcent, being of its own Nature Indelible and <lb></lb>Penpetual, it is worthy conſideration, that if after the Deſcent along a <lb></lb>declining Plane a Reflexion be made along another Plane that is riſing, <lb></lb>in this latter there is cauſe of Retardation, for in theſe kind of Planes<emph.end type="italics"></emph.end><pb xlink:href="040/01/874.jpg" pagenum="181"></pb><emph type="italics"></emph>the ſaid Moveable doth naturally deſcend; whereupon there reſults a <lb></lb>mixture of certain contrary Affections, to wit, that degree of Celerity <lb></lb>acquired in the precedent Deſcent, which would of it ſelf carry the Move<lb></lb>able uniformly<emph.end type="italics"></emph.end> in infinitum, <emph type="italics"></emph>and of Natural Propenſion to the Motion of <lb></lb>Deſcent according to that ſame proportion of Acceleration wherewith it <lb></lb>alwaies moveth. </s> <s>So that it will be but reaſonable, if, enquiring what <lb></lb>accidents happen when the Moveable after the Deſcent along any incli<lb></lb>ned Plane is Reflected along ſome riſing Plane, we take that greateſt de<lb></lb>gree acquired in the Deſcent to keep it ſelf perpetually the ſame in the <lb></lb>Aſcending Plane; But that there is ſuperadded to it in the Aſcent the <lb></lb>Natural Inclination downwards, that is the Motion from Reſt Accelerate <lb></lb>according to the received proportion: And leſt this ſhould, perchance, be <lb></lb>ſomewhat intricate to be underſtood, it ſhall be more clearly explained by a <lb></lb>Scheme.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Let the Deſcent therefore be ſuppoſed to be made along the Declining <lb></lb>Plane A B, from which let the Reflex Motion be continued along another <lb></lb>Riſing Plane B C: And in the firſt place let the Planes be equal, and <lb></lb>elevated at equal Angles to the Horizon G H. </s> <s>Now it is manifeſt, that <lb></lb>the Moveable<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in A deſcending along A B acquireth degrees of <lb></lb>Velocity according to the increaſe of its Time, and that the degree in B <lb></lb>is the greateſt of thoſe acquired and by Nature immutably impreſſed, I <lb></lb>mean the Cauſes of new Acceleration or Retardation being removed: <lb></lb>of Acceleration, I ſay, if it ſhould paſſe any farther along the extended <lb></lb>Plane; and of Retardation, whilſt the Reflection is making along the <lb></lb>Acclivity B C: But along the Horizontal Plane G H the Equable Mo<lb></lb>tion according to the de-<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.874.1.jpg" xlink:href="040/01/874/1.jpg"></figure><lb></lb><emph type="italics"></emph>gree of Velocity acquired <lb></lb>from A unto B would ex<lb></lb>tend<emph.end type="italics"></emph.end> in infinitum. <emph type="italics"></emph>And <lb></lb>ſuch a Velocity would <lb></lb>that be which in a Time <lb></lb>equal to the Time of the <lb></lb>Deſcent along A B would paſſe a Space in double the Horizon to the ſaid <lb></lb>A B. </s> <s>Now let us ſuppoſe the ſame Moveable to be Equably moved with <lb></lb>the ſame degree of Swiftneſſe along the Plane B C, in ſuch ſort that alſo <lb></lb>in this Time equal to the Time of the Deſcent along A B a Space may be <lb></lb>paſſed a long B C extended double to the ſaid A B. </s> <s>And let us under<lb></lb>ſtand that as ſoon as it beginneth to aſcend there naturally befalleth the <lb></lb>ſame that hapneth to it from A along the Plane A B, to wit, a certain <lb></lb>Deſcent<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>according to thoſe degrees of Acceleration, by vertue <lb></lb>of which, as it befalleth in A B, it may deſcend as much in the ſame <lb></lb>Time along the Reflected Plane as it doth along A B: It is manifeſt, that <lb></lb>by this ſame Mixture of the Equable Motion of Aſcent, and the Acce<lb></lb>lerate of Deſcent the Moveable may be carried up to the Term C along <lb></lb>the Plane B C according to thoſe degrees of Velocity, which ſhall be<emph.end type="italics"></emph.end><pb xlink:href="040/01/875.jpg" pagenum="182"></pb><emph type="italics"></emph>equal. </s> <s>And that two points at pleaſure D and E being taken, equally <lb></lb>remote from the Angle B, the Tranſition along D B is made in a Time <lb></lb>equal to the Time of the Reflection along B E, we may collect from hence: <lb></lb>Draw D F, which ſhall be Parallel to B C; for it is manifeſt that the <lb></lb>Deſcent along A D is reflected along D F: And if after D the Move<lb></lb>able paſſe along the Horizontal Plane D E, the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>in E ſhall be <lb></lb>the ſame as the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>in D: Therefore it will aſcend from E to C: <lb></lb>And therefore the degree of Velocity in D is equal to the degree in E. <lb></lb></s> <s>From theſe things, therefore, we may rationally affirm, that, if a de<lb></lb>ſcent be made along any inclined Plane, after which a Reflection may <lb></lb>follow along an elevated Plane, the Moveable may by the conceived<emph.end type="italics"></emph.end><lb></lb>Impetus <emph type="italics"></emph>aſcend untill it attain the ſame beight, or Elevation from the <lb></lb>Horizon. </s> <s>As if a Deſcent be made along A B, the Moveable would <lb></lb>paſſe along the Reflected Plane B C, untill it arrive at the Horizon <lb></lb>A C D; and that not only when the Inclinations of the Planes are <lb></lb>equal, but alſo when they are unequal, as is the Plane B D: For it was <lb></lb>first ſuppoſed, that the degrees of Velocity are equal, which are acqui<lb></lb>red upon Planes unequally inclined, ſo long as the Elevation of thoſe <lb></lb>Planes above the Horizon was the ſame: But, if there being the ſame <lb></lb>Inclination of the Planes E B and B D, the Deſcent along E B ſufficeth <lb></lb>to drive the Moveable along the Plane BD as far as D, ſeeing this Impulſe<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.875.1.jpg" xlink:href="040/01/875/1.jpg"></figure><lb></lb><emph type="italics"></emph>is made by the<emph.end type="italics"></emph.end> Impe<lb></lb>tus <emph type="italics"></emph>of Velocity in the <lb></lb>point B; and if the<emph.end type="italics"></emph.end><lb></lb>Impetus <emph type="italics"></emph>be the ſame <lb></lb>in B, whether the <lb></lb>Moveable deſcend a<lb></lb>long A B, or along E B: It is manifeſt, that the Moveable ſhall be in <lb></lb>the ſame manner driven along B D, after the Deſcent along A B, and <lb></lb>after that along E B: But it will happen that the Time of the Aſcent <lb></lb>along B D ſhall be longer than along B C, like as the Deſcent along <lb></lb>E B is made in a longer time than along A B: But the Proportion of <lb></lb>thoſe Times was before demonſtrated to be the ſame as the Lengths of <lb></lb>thoſe Planes. </s> <s>Now it follows, that we ſeek the proportion of the Spaces <lb></lb>paſt in equal Times along Planes, whoſe Inclinations are different, but <lb></lb>their Elevations the ſame; that is, which are comprehended between <lb></lb>the ſame Horizontal Parallels. </s> <s>And this hapneth according to the fol<lb></lb>lowing Propoſition.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/876.jpg" pagenum="183"></pb><p type="head"> <s>THEOR. XV. PROP. XXIV.</s></p><p type="main"> <s>There being given between the ſame Horizontal <lb></lb>Parallels a Perpendicular and a <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane eleva<lb></lb>ted from its loweſt term, the Space that a <lb></lb>Moveable after the Fall along the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendi<lb></lb>cular paſſeth along the Elevated <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane in a <lb></lb>Time equal to the Time of the Fall, is greater <lb></lb>than that <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendicular, but leſſe than double <lb></lb>the ſame.</s></p><p type="main"> <s><emph type="italics"></emph>Between the ſame Horizontal Parallels B C and H G let there <lb></lb>be the Perpendicular A E; and let the Elevated Plane be E B, <lb></lb>along which after the Fall along the Perpendicular A E out of <lb></lb>the Term E let a Reflexion be made towards B. </s> <s>I ſay, that the Space, <lb></lb>along which the Moveable aſcendeth in a Time equal to the Time of the <lb></lb>Deſcent A E, is greater than A E, but leſſe than double the ſame A E. <lb></lb></s> <s>Let E D be equal to A E, and as E B is to B D, ſo let D B be to B F. </s> <s>It <lb></lb>ſhall be proved, firſt that the point F is the Term at which the Moveable <lb></lb>with a Reflex Motion along E B arriveth in a Time equal to the Time <lb></lb>A E: And then, that E F is greater than E A, but leſſe than double the <lb></lb>ſame. </s> <s>If we ſuppoſe the Time of the Deſcent along A E to be as A E, <lb></lb>the Time of the Deſcent along B E, or Aſcent along E B ſhall be as the <lb></lb>ſame Line B E: And D B being a Mean-Proportional betwixt E B <lb></lb>and B F, and B E being the Time of Deſcent along the whole B E, B D <lb></lb>ſhall be the Time of the Deſcent along B F, and the Remaining part <lb></lb>D E the Time of the<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.876.1.jpg" xlink:href="040/01/876/1.jpg"></figure><lb></lb><emph type="italics"></emph>Deſcent along the Re<lb></lb>maining part F E: But <lb></lb>the Time along F E<emph.end type="italics"></emph.end> ex <lb></lb>quiete <emph type="italics"></emph>in B, and the <lb></lb>Time of the Aſcent a<lb></lb>long E F is the ſame, ſince that the Degree of Velocity in E was acqui<lb></lb>red along the Deſcent B E, or A E: Therefore the ſame Time D E ſhall <lb></lb>be that in which the Moveable after the Fall out of A along A E, <lb></lb>with a Reflex Motion along E B ſhall reach to the Mark F: But it hath <lb></lb>been ſuppoſed that E D is equal to the ſaid A E: Which was firſt to be <lb></lb>proved. </s> <s>And becauſe that as the whole E B is to the whole B D, ſo is the <lb></lb>part taken away D B to the part taken away B F, therefore, as the whole <lb></lb>E B is to the whole B D, ſo ſhall the Remainder E D be to D F: <lb></lb>But E B is greater than B D: Therefore E D is greater than D F, and <lb></lb>E F leſſe than double to D E or A E: Which was to be proved.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/877.jpg" pagenum="184"></pb><p type="main"> <s><emph type="italics"></emph>And the ſame alſo hapneth if the precedent Motion be not made <lb></lb>along the Perpendicular, but along an Inclined Plane; and the Demon<lb></lb>ſtration is the ſame, provided that the Reflex Plane be leſſe riſing, that is, <lb></lb>longer than the declining Plane.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>THEOR. XVI. <emph type="italics"></emph>P<emph.end type="italics"></emph.end>RO<emph type="italics"></emph>P.<emph.end type="italics"></emph.end> XXV.</s></p><p type="main"> <s>If after the Deſcent along any Inclined Plane a <lb></lb>Motion follow along the Plane of the Hori<lb></lb>zon, the Time of the Deſcent along the Incli<lb></lb>ned Plane ſhall be to the Time of the Motion <lb></lb>along any Horizontal Line; as the double <lb></lb>Length of the Inclined Plane is to the Line ta<lb></lb>ken in the Horizon.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Horizontal Line be C B, the inclined Plane A B, and after <lb></lb>the Deſcent along A B let a Motion follow along the Horizon, in <lb></lb>which take any Space B D. </s> <s>I ſay, that the Time of the Deſcent <lb></lb>along A B to the Time of the Motion along B D is as the double of A B <lb></lb>to B D. </s> <s>For B C being ſuppoſed <lb></lb>the double of A B, it is manifeſt by<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.877.1.jpg" xlink:href="040/01/877/1.jpg"></figure><lb></lb><emph type="italics"></emph>what hath already been demonſtra<lb></lb>ted that the Time of the Deſcent <lb></lb>along A B is equal to the Time of <lb></lb>the Motion along B C: But the <lb></lb>Time of the Motion along B C is to <lb></lb>the Time of the Motion along B D, as the Line C B is to the Line B D: <lb></lb>Therefore the Time of the Motion along A B is the Time along B D, as <lb></lb>the Double of A B is to B D: Which was to be proved.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROBL X. PROP. XXVI.</s></p><p type="main"> <s>A Perpendicular between two Horizontal <emph type="italics"></emph>P<emph.end type="italics"></emph.end>aral<lb></lb>lel Lines, as alſo a Space greater than the ſaid <lb></lb><emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendicular, but leſſe than double the ſame, <lb></lb>being given, to raiſe a <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane between the ſaid <lb></lb><emph type="italics"></emph>P<emph.end type="italics"></emph.end>arallels from the loweſt Term of the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>er<lb></lb>pendicular, along which the Moveable may <lb></lb>with a Reflex Motion after the Fall along the <lb></lb><emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendicular paſſe a Space equal to the Space <lb></lb>given, and in a Time equal to the Time of the <lb></lb>Fall along the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendicular.</s></p><pb xlink:href="040/01/878.jpg" pagenum="185"></pb><p type="main"> <s><emph type="italics"></emph>Let A B be a Perpendicular between the Horizontal Parallels A O <lb></lb>and B C; and let F E be greater than B A, but leſſe than double <lb></lb>the ſame. </s> <s>It is required between the ſaid Parallels from the point <lb></lb>B to raiſe a Plane, along which the Moveable after the Fall from A to <lb></lb>B may with a Reflex Motion in a Time equal to the Time of the Fall <lb></lb>along A B paſſe a Space aſcending equal to the ſaid E F. </s> <s>Suppoſe E D <lb></lb>equall to A B, the Remaining Part D F ſhall be leſſe, for that the whole <lb></lb>E F is leſſe than double to A B: Let D I be equal to D F, and as E I is <lb></lb>to I D, ſo let D F be to another Space F X, and out of B let the Right-<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.878.1.jpg" xlink:href="040/01/878/1.jpg"></figure><lb></lb><emph type="italics"></emph>Line B O be reflected, equal to E X. </s> <s>I ſay, that the Plane along B O <lb></lb>is that along which after the Fall A B a Moveable in a Time equal <lb></lb>to the Time of the Fall along A B paſſeth aſcending a Space equal to <lb></lb>the given Space E F. </s> <s>Suppoſe B R and R S equal to the ſaid E D and <lb></lb>D F. </s> <s>And becauſe that as E I is to I D, ſo is D F to F X; therefore, <lb></lb>by Compoſition, as E D is to D I, ſo ſhall D X be to X F; that is, as <lb></lb>E D is to D F, ſo ſhall D X be to X F, and E X to X D; that is, as <lb></lb>B O is to O R, ſo ſhall R O be to O S: And if we ſuppoſe the Time <lb></lb>along A B to be A B, the Time along O B ſhall be the ſame O B, and <lb></lb>R O the Time along O S, and the Remaining Part B R the Time along <lb></lb>the Remaining Part S B, deſcending from O to B: But the Time of <lb></lb>the Deſcent along S B from Rest in O, is equal to the Time of the <lb></lb>Aſcent from B to S after the Fall A B: Therefore B O is the Plane ele<lb></lb>vated from B, along which after the Fall along A B the Space B S <lb></lb>equal to the given Space E F is paſſed in the Time B R or B A: Which <lb></lb>was required to be done.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/879.jpg" pagenum="186"></pb><p type="head"> <s>THEOR. XVII. PROP. XXVII.</s></p><p type="main"> <s>If a Moveable deſcend along unequal <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lanes, <lb></lb>whoſe Elevation is the ſame, the Space that <lb></lb>ſhall be paſt along the lower part of the longeſt <lb></lb>in a Time equal to that in which the whole <lb></lb>ſhorter <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane is paſſed, is equal to the Space <lb></lb>that is compounded of the ſaid ſhorter <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane <lb></lb>and of the part to which that ſhorter <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane <lb></lb>hath the ſame <emph type="italics"></emph>P<emph.end type="italics"></emph.end>roportion that the longer <lb></lb><emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane hath to the Exceſſe by which the longeſt <lb></lb>exceedeth the ſhorteſt.</s></p><p type="main"> <s><emph type="italics"></emph>Let A C be the longer Plane, and A B the ſhorter, whoſe Elevation <lb></lb>A D is the ſame; and in the lower part of A C take the Space <lb></lb>C E, equal to the ſaid A B; and as C A is to A E, (that is to <lb></lb>the exceſſe of the Plane C A above A B) ſo let C E be to E F. </s> <s>I ſay, <lb></lb>that the Space F C is that which is paſt after the Deſcent out of A in <lb></lb>a Time equal to the Time of<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.879.1.jpg" xlink:href="040/01/879/1.jpg"></figure><lb></lb><emph type="italics"></emph>the Deſcent along A B. </s> <s>For <lb></lb>the whole C A, being to the <lb></lb>whole A E, as the part taken <lb></lb>away C E is to the part taken <lb></lb>away E F, therefore the re<lb></lb>maining part E A ſhall be to <lb></lb>the remaining part A F, as the <lb></lb>whole C A is to the whole A E: Therefore the three Spaces C A, <lb></lb>A E, and A F are three Continual proportionals. </s> <s>And if the Time <lb></lb>along A B be ſuppoſed to be as A B, the Time along A C ſhall be as <lb></lb>A C, and the Time along A F ſhall be as A E, and along the remain<lb></lb>ing part F C ſhall be as E C: But E C is equal to the ſaid A B: There<lb></lb>fore the Propoſition is manifeſt.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>THEOR. XVIII. PROP. XXVIII.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Horizontal Line A G be Tangent to a Circle, and from the <lb></lb>point of Contact let A B be the Diameter, and A E B two Chords <lb></lb>at pleaſure: We are to aſſign the proportion of the Time of the <lb></lb>Fall along A B to the Time of the Deſcent along both the Chords <lb></lb>A E B. </s> <s>Let B E be continued out till it meet the Tangent in G, and<emph.end type="italics"></emph.end><pb xlink:href="040/01/880.jpg" pagenum="187"></pb><emph type="italics"></emph>let the Angle B A E be cut in two equal parts, and draw A F. </s> <s>I ſay, <lb></lb>that the Time along A B is to the Time along A E B, as A E is to A E F. <lb></lb></s> <s>For in regard the Angle F A B is equal to the Angle F A E, and the An<lb></lb>gle E A G to the Angle A B F, the whole Angle G A F ſhall be equal to <lb></lb>the two Angles F A B, and A B F; <lb></lb>to which alſo the Angle G F A<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.880.1.jpg" xlink:href="040/01/880/1.jpg"></figure><lb></lb><emph type="italics"></emph>is equal: Therefore the Line G F <lb></lb>is equal to G A. </s> <s>And becauſe the <lb></lb>Rectangle B G E is equal to the <lb></lb>Square of G A, it ſhall likewiſe <lb></lb>be equal to the Square of G F, and <lb></lb>the three Lines B G, G F, and <lb></lb>G E ſhall be proportionals. </s> <s>And <lb></lb>if we ſuppoſe A E to be the Time <lb></lb>along A E, G E ſhall be the Time <lb></lb>along G E, and G F the Time along the whole G B, and E F the Time <lb></lb>along E B, after the Deſcent out of G, or out of A, along A E: The Time, <lb></lb>therefore, along A E, or along A B ſhall be to the Time along A E B, as <lb></lb>A E is to A E F: Which was to be determined.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>More briefly thus. </s> <s>Let G F be cut equal to G A: It is manifeſt <lb></lb>that G F is the Mean-proportional between B G, and G E. </s> <s>The reſt as <lb></lb>before.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROBL. <emph type="italics"></emph>XI. P<emph.end type="italics"></emph.end>RO<emph type="italics"></emph>P. XXIX.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Any Horizontal Space being given upon the <lb></lb>end of which a Perpendicular is erected, <lb></lb>in which a part is taken equal to half of the <lb></lb>Space given in the Horizontal a Moveable fal<lb></lb>ling from that height, and turned along the <lb></lb>Horizon, ſhall paſſe the Horizontal Space to<lb></lb>gether with the Perpendicular in a ſhorter <lb></lb>Time than any other Space of the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendi<lb></lb>cular with the ſame Horizontal Space.</s></p><p type="main"> <s><emph type="italics"></emph>Let there be an Horizontal Space in which let any Space be given <lb></lb>B C, and on B let there be a Perpendicular erected, in which let <lb></lb>B A be the half of the foreſaid B C. </s> <s>I ſay, that the Time in which <lb></lb>a Moveable let fall out of A paſſeth both the Spaces A B and B C is the <lb></lb>ſhorteſt of all Times in which the ſaid Space B C with a part of the <lb></lb>Perpendicular, whether greater or leſſer than the part A B, ſhall be paſ<lb></lb>ſed. </s> <s>Let a greater be taken, as in the ſirſt Figure, or leſſer, as in the<emph.end type="italics"></emph.end><pb xlink:href="040/01/881.jpg" pagenum="188"></pb><emph type="italics"></emph>ſecond, which let be E B. </s> <s>It is to be proved that the Time in which the <lb></lb>Spaces E B and B C are paſſed is longer than the Time in which A B <lb></lb>and B C are paſſed. </s> <s>Let the Time along A B be as A B; the ſame ſhall <lb></lb>be the Time of the Motion along the Horizontal Space B G; becauſe <lb></lb>B C is double to A B, and the Time along both the Spaces A B C ſhall <lb></lb>be double of O B A. </s> <s>Let B O<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.881.1.jpg" xlink:href="040/01/881/1.jpg"></figure><lb></lb><emph type="italics"></emph>be a Mean-proportional between <lb></lb>E B and B A. </s> <s>B O ſhall be the <lb></lb>Time of the Fall along E B. <lb></lb>Again, let the Horizontal Space <lb></lb>B D be double to the ſaid B E: <lb></lb>It is manifeſt that the Time of it <lb></lb>after the Fall E B is the ſame <lb></lb>B O. </s> <s>As D B is to B C, or as <lb></lb>E B is to B A, ſo let O B be to <lb></lb>B N: and in regard the Motion <lb></lb>along the Horizontal Plane is Equable, and O B being the Time along <lb></lb>B D after the Fall out of E, therefore N B ſhall be the Time along B C <lb></lb>after the Fall from the ſame Altitude E. </s> <s>Hence it is manifeſt, that O B, <lb></lb>together with B N is the Time along E B C; and becauſe the double of <lb></lb>B A is the Time along A B C; it remains to be proved, that O B, to<lb></lb>gether with B N is more than double B A. </s> <s>Now becauſe O B is a Mean <lb></lb>between E B and B A, the proportion of E B to B A is double the pro<lb></lb>portion of O B to B A: and, in regard that E B is to B A, as O B is to <lb></lb>B N, the proportion of O B to B N ſhall alſo be double the proportion of <lb></lb>O B to B A: But that proportion of O B to B N is compounded of the <lb></lb>proportions of O B to B A, and of A B to B N: therefore the proportion <lb></lb>of A B to B N is the ſame with that of O B to B A. </s> <s>Therefore B O, <lb></lb>B A, and B N are three continual Proportionals, and O B, together with <lb></lb>B N, are greater than double B A: Whereupon the Propoſition is ma<lb></lb>nifeſt.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/882.jpg" pagenum="189"></pb><p type="head"> <s>THEOR. <emph type="italics"></emph>XIX.<emph.end type="italics"></emph.end> PROP. <emph type="italics"></emph>XXX.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>If a Perpendicular be let fall from any point of the <lb></lb>Horizontal Line, and out of another point in <lb></lb>the ſame Horizontal Line a Plane be drawn <lb></lb>forth untill it meet the Perpendicular, along <lb></lb>which a Moveable deſcendeth in the ſhorteſt <lb></lb>time unto the ſaid Perpendicular, this Plane <lb></lb>ſhall be that which cutteth off a part equall to <lb></lb>the diſtance of the aſſigned point from the end <lb></lb>of the Perpendicular.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Perpendicular B D be let fall from the point B of the Ho<lb></lb>rizontal Line A C, in which let there be any point C, and in the <lb></lb>Perpendicular let the Diſtance B E be ſuppoſed equal to the Di<lb></lb>ſtance B C, and draw C E. </s> <s>I ſay, that of all Planes inclined out of <lb></lb>the point C till they meet the Perpendicular C E is that, along which <lb></lb>in the ſhorteſt of all Times the Deſcent<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.882.1.jpg" xlink:href="040/01/882/1.jpg"></figure><lb></lb><emph type="italics"></emph>is made unto the Perpendicular. </s> <s>For <lb></lb>let the Planes C F and C G be inclined <lb></lb>above and below, and draw I K a Tan<lb></lb>gent unto the Semidiameter B C of the <lb></lb>deſcribed Circle in C, which ſhall be <lb></lb>equidiſtant from the Perpendicular; <lb></lb>and unto the ſaid C F let E K be Paral<lb></lb>lel cutting the Circumference of the Cir<lb></lb>cle in L: It is manifeſt that the Time of <lb></lb>the Deſcent along L E is equal to the <lb></lb>Time of the Deſcent along C E: But <lb></lb>the Time along K E is longer than along <lb></lb>L E: Therefore the Time along K E is <lb></lb>longer than that along C E: But the <lb></lb>Time along K E is equal to the Time a<lb></lb>long C F, they being equal, and drawn <lb></lb>according to the ſame Inclination: Likewiſe ſince C G, and I E are <lb></lb>equal, and inclined according to the ſame Inclination, the Times of the <lb></lb>Motions along them ſhall be equal: But H E being ſhorter than I E, the <lb></lb>Time along it is alſo ſhorter than I E: Therefore the Time alſo along <lb></lb>C E, (which is equal to the Time along H E) ſhall be ſhorter than the <lb></lb>Time along I E: The Propoſition, therefore, is manifeſt.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/883.jpg" pagenum="190"></pb><p type="head"> <s>THEOR. <emph type="italics"></emph>XX.<emph.end type="italics"></emph.end> PROP. <emph type="italics"></emph>XXXI.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>If a Right-Line ſhall be in any manner inclined <lb></lb>upon the Horizontal Line, the Plane produced <lb></lb>from a given point in the Horizon untill it <lb></lb>meet with the Inclined Plane, along which <lb></lb>the Deſcent is made in the ſhorteſt of all <lb></lb>Times, is that which ſhall divide the Angle <lb></lb>contained between the two <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendiculars <lb></lb>drawn from the given <emph type="italics"></emph>P<emph.end type="italics"></emph.end>oint, the one unto the <lb></lb>Horizontal Line, the other to the Inclined <lb></lb>Line, into two equal parts.</s></p><p type="main"> <s><emph type="italics"></emph>Let C D be a Line inclined in any manner upon the Hori<lb></lb>zontal Line A B, and let any point A be given in the Hori<lb></lb>zon, and from it let A C be drawn Perpendicular to A B, <lb></lb>and A E Perpendicular to C D, and let the Line F A divide the <lb></lb>Angle C A E into two equal parts. </s> <s>I ſay, that of all Planes incli<lb></lb>ned out of any point of the Line C D to the point A that ſame pro<lb></lb>duced along F A is it along<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.883.1.jpg" xlink:href="040/01/883/1.jpg"></figure><lb></lb><emph type="italics"></emph>which the Deſcent is made in <lb></lb>the ſhorteſt of all Times. </s> <s>Let <lb></lb>F G be drawn Parallel to AE; <lb></lb>the alternate Angles G F A <lb></lb>and F A E ſhall be equal: But <lb></lb>E A F is equal to that other <lb></lb>F A G: Therefore of the Tri<lb></lb>angle the Sides F G and G A <lb></lb>ſhall be equal. </s> <s>If therefore <lb></lb>about the Center G, at the di<lb></lb>ſtance G A, a Circle be deſcri<lb></lb>bed it ſhall paſſe by F, and ſhall <lb></lb>touch the Horizontal, and the Inclined Lines in the points A and F: <lb></lb>For the Angle G F C is a Right Angle, and likewiſe G F is equidiſtant <lb></lb>to A E: Whence it is manifeſt that all Lines produced from the point <lb></lb>A unto the inclined Plane do extend beyond the Circumference, and, <lb></lb>which followeth of conſequence, that the Motions along the ſame do <lb></lb>take up more Time than along F A. </s> <s>Which was to be demonſtrated.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/884.jpg" pagenum="191"></pb><p type="head"> <s>LEMMA.</s></p><p type="main"> <s>If two Circles touch one another within, the innermoſt of which <lb></lb>toucheth ſome Right Line, and the exteriour one cutteth it, <lb></lb>three Lines produced from the Contact of the Circles unto <lb></lb>three points of the Tangent Right-Line, that is, to the Con<lb></lb>tact of the interiour Circle, and to the Sections of the exte<lb></lb>riour ſhall contain equall Angles in the Contact of the <lb></lb>Circles.</s></p><p type="main"> <s><emph type="italics"></emph>Let two Circles touch one another in the point A, of which let the <lb></lb>Centers be B, that of the leſſer, and C that of the greater; and let <lb></lb>the interiour Circle touch any Line F G in the point H, and let the grea<lb></lb>ter cut it in the points F and G, and connect the three Lines A F, A H, <lb></lb>and A G. </s> <s>I ſay, that the Angles by<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.884.1.jpg" xlink:href="040/01/884/1.jpg"></figure><lb></lb><emph type="italics"></emph>them contained F A H and G A H are <lb></lb>equal. </s> <s>Produce A H untill it meeteth <lb></lb>the Circumference in I, and from the <lb></lb>Centers draw B H and C I, and thorow <lb></lb>the ſaid Centers let B C be drawn, <lb></lb>which continued forth ſhall meet with <lb></lb>the Contact A, and with the Circum<lb></lb>ferences of the Circles in O and N. <lb></lb></s> <s>And becauſe the Angles I C N and <lb></lb>H O B are equal, for as much as either <lb></lb>of them is double to the Angle I A N, <lb></lb>the Lines B H and C I ſhall be Parallels: And becauſe B H drawn <lb></lb>from the Center to the Contact is Perpendicular to F G; C I ſhall alſo be <lb></lb>Perpendicular to the ſame, and the Arch F I equal to the Arch I G, and, <lb></lb>which followeth of conſequence, the Angle F A I to the Angle I A G: <lb></lb>Which was to be demonſtrated.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/885.jpg" pagenum="192"></pb><p type="head"> <s>THEOR. <emph type="italics"></emph>XXI.<emph.end type="italics"></emph.end> PROP. <emph type="italics"></emph>XXXII.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>If two points be taken in the Horizon, and any <lb></lb>Line ſhould be inclined from one of them to<lb></lb>wards the other, out of which a Right-Line is <lb></lb>drawn unto the Inclined Line, cutting off a <lb></lb>part thereof equal to that which is included <lb></lb>between the points of the Horizon, the De<lb></lb>ſcent along this laſt drawn ſhall be ſooner per<lb></lb>formed, than along any other Right Lines pro<lb></lb>duced from the ſame point unto the ſaid Incli<lb></lb>ned Line. </s> <s>And along other Lines which are <lb></lb>on each hand of this by equal Angles a De<lb></lb>ſcent ſhall be made in equal Times.</s></p><p type="main"> <s><emph type="italics"></emph>In the Horizon let there be two points A and B, and from B incline <lb></lb>the Right Line B C, in which from the Term B take B D equal to <lb></lb>the ſaid B A, and draw a Line from A to D. </s> <s>I ſay, that the De<lb></lb>ſcent along A D is more ſwiftly made, than along any other whatſoever <lb></lb>drawn from the point A unto the inclined Line B C. </s> <s>For out of the <lb></lb>points A and D unto B A and<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.885.1.jpg" xlink:href="040/01/885/1.jpg"></figure><lb></lb><emph type="italics"></emph>B D draw the Perpendiculars <lb></lb>A E and D E, interſecting one <lb></lb>another in E: and foraſmuch as <lb></lb>in the equicrural Triangle A B D <lb></lb>the Angles B A D and B D A <lb></lb>are equal, the remainders to the <lb></lb>Right-Angles D A E and E D A <lb></lb>ſhall be equal. </s> <s>Therefore a Circle <lb></lb>deſcribed about the Center E at <lb></lb>the diſtance A E ſhall alſo paſſe <lb></lb>by D; and the Lines B A and <lb></lb>B D will touch it in the points A <lb></lb>and D. </s> <s>And ſince A is the end of the Perpendicular A E, the Deſcent <lb></lb>along A D ſhall be ſooner performed, than along any other produced from <lb></lb>the ſame Term A unto the Line B C beyond the Circumference of the <lb></lb>Circle: Which was firſt to be proved.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>But if in the Perpendicular A E being prolonged any Center be taken as <lb></lb>F, and at the diſtance F A the Circle A G C be deſcribed cutting the <lb></lb>Tangent Line in the points G and C; drawing A G and A C they ſhall <lb></lb>make equal Angles with the middle Line A D by what hath been afore<emph.end type="italics"></emph.end><pb xlink:href="040/01/886.jpg" pagenum="193"></pb><emph type="italics"></emph>demonſtrated, and the Motions thorow them ſhall be performed in equal <lb></lb>Times ſeeing that they terminate in A unto the Circumference of the <lb></lb>Circle A G O from the higheſt point of it A.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROBL. XII. PROP. <emph type="italics"></emph>XXXIII.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>A Perpendicular and Plane inclined to it being <lb></lb>given, whoſe height is one and the ſame, as al<lb></lb>ſo the higheſt term, to find a point in the Per<lb></lb>pendicular above the common term, out of <lb></lb>which if a Moveable be demitted that ſhall <lb></lb>afterwards turn along the inclined Plane, the <lb></lb>ſaid Plane may be paſt in the ſame Time in <lb></lb>which the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendicular <emph type="italics"></emph>ex quiete<emph.end type="italics"></emph.end> would be <lb></lb>paſſed.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Perpendicular and inclined Plane, whoſe Altitude is the <lb></lb>ſame, be A B and A C. </s> <s>It is required in the Perpendicular B A, <lb></lb>continued out from the point A to find a Point out of which a <lb></lb>Moveable deſcending may paſſe the Space A C in the ſame Time in <lb></lb>which it will paſſe the ſaid Perpendicular A B out of Reſt in A. </s> <s>Draw <lb></lb>D C E at Right-Angles to A C, and let C D be cut equal to A B, and <lb></lb>draw a Line from A to D: The Angle A D C ſhall be greater than the <lb></lb>Angles C A D: (for C A is greater than A B or C D:) Let the <lb></lb>Angle D A E be equal to the Angle A D E; and to A E let E F an in<lb></lb>clined Plane be Perpen-<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.886.1.jpg" xlink:href="040/01/886/1.jpg"></figure><lb></lb><emph type="italics"></emph>dicular, and let both be<lb></lb>ing prolonged meet in F, <lb></lb>and unto both A I and <lb></lb>A G ſuppoſe C F to be <lb></lb>equal, and by G draw <lb></lb>G H equidiſtant to the <lb></lb>Horizon. </s> <s>I ſay, that H <lb></lb>is the point which is <lb></lb>ſought. </s> <s>For ſuppoſing the <lb></lb>Time of the Fall along <lb></lb>the Perpendicular A B <lb></lb>to be A B, the Time along <lb></lb>A C ex quiete in A ſhall be the ſame A C. </s> <s>And becauſe in the Right<lb></lb>angled Triangle A E F, from the Right Angle E unto the Baſe A F, <lb></lb>E C is a Perpendicular, A E ſhall be a Mean-Proportional betwixt F A <lb></lb>and A C, and C E a Mean betwixt A C and C F, that is, betwixt C A <lb></lb>and A I: and foraſmuch as the Time of A C out of A is A C, A E<emph.end type="italics"></emph.end><pb xlink:href="040/01/887.jpg" pagenum="194"></pb><emph type="italics"></emph>ſhall be the Time of the whole A F, and E C the Time of A I: And be<lb></lb>cauſe in the Equicrural Triangle A E D the Side A E is equal to the <lb></lb>Side E D, E D ſhall be the Time along A F, and E C is the Time along <lb></lb>A I: Therefore C D, that is A B ſhall be the Time along A F<emph.end type="italics"></emph.end> ex qui<lb></lb>ete <emph type="italics"></emph>in A; which is the ſame as if we ſaid, that A B is the Time along <lb></lb>A G out of G, or out of H: Which was to be done.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROBL. <emph type="italics"></emph>XIII. P<emph.end type="italics"></emph.end>RO<emph type="italics"></emph>P. XXXIV.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>An inclined <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane and Perpendicular whoſe ſub<lb></lb>lime term is the ſame being given, to find a <lb></lb>more ſublime point in the Perpendicular pro<lb></lb>longed out of which a Moveable falling, and <lb></lb>being turned along the inclined <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane, may <lb></lb>paſſe them both in the ſame Time, as it doth <lb></lb>the ſole inclined <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lane <emph type="italics"></emph>ex quiete<emph.end type="italics"></emph.end> in its ſuperi<lb></lb>our Term.</s></p><p type="main"> <s><emph type="italics"></emph>Let the inclined Plane and Perpendicular be A B and A C, whoſe <lb></lb>Term A is the ſame. </s> <s>It is required in the Perpendicular prolonged <lb></lb>from A to find a ſublime point, out of which the Moveable deſcen<lb></lb>ding, and being turned along the Plane A B, may paſſe the aſſigned part <lb></lb>of the Perpendicular and the Plane A B in the ſame Time, as it would the <lb></lb>ſole Plane A B out of Reſt in A.<emph.end type="italics"></emph.end></s></p><figure id="id.040.01.887.1.jpg" xlink:href="040/01/887/1.jpg"></figure><p type="main"> <s><emph type="italics"></emph>Let the Ho<lb></lb>rizontal Line <lb></lb>be B C, and <lb></lb>let A N be <lb></lb>cut equal to <lb></lb>A C; and as <lb></lb>A B is to B N, <lb></lb>ſo let A L be <lb></lb>to L C: and <lb></lb>unto A L let <lb></lb>A I be equal, <lb></lb>and unto A C <lb></lb>and B I let C <lb></lb>E be a third <lb></lb>proportional, <lb></lb>marked in the <lb></lb>Perpendicular A C produced. </s> <s>I ſay, that C E is the Space acquired; <lb></lb>ſo that the Perpendicular being extended above A, and the part A X <lb></lb>equal to C E being taken, a Moveable out of X will paſſe both the<emph.end type="italics"></emph.end><pb xlink:href="040/01/888.jpg" pagenum="195"></pb><emph type="italics"></emph>Spaces X A B in the ſame Time as it would the ſole Space A B out of A. <lb></lb></s> <s>Draw the Horizontal Line X R Parallel to B C, with which let B A <lb></lb>being prolonged meet in R, and then A B being continued out unto D <lb></lb>draw E D Parallel to C B, and upon A D deſcribe a Semicircle, and <lb></lb>from B, and Perpendicular to D A, erect B F till it meet with the Cir<lb></lb>cumference. </s> <s>It is manifeſt that F B is a Mean-proportional betwixt <lb></lb>A B and B D, and that the Line drawn from F to A is a Mean-propor<lb></lb>tional betwixt D A and A B. </s> <s>Suppoſe B S equal to B I, and F H equal <lb></lb>to F B: And becauſe, as A B is to B D, ſo is A C to C E, and becauſe <lb></lb>B F is a Mean-proportional betwixt A B and B D, and becauſe B I is a <lb></lb>Mean-proportional betwixt A C and C E; therefore as B A is to A C, <lb></lb>ſo is F B to B S. </s> <s>And becauſe as B A is to A C, or A N, ſo is F B to <lb></lb>B S, therefore, by Converſion of the proportion, B F is to F S, as A B is <lb></lb>to B N, that is, A L to L C; therefore the Rectangle under F B and <lb></lb>C L, is equal to the Rectangle under A L, and S F: But this Rectangle <lb></lb>A L, and S F, is the exceſſe of the Rectangle under A L and F B, or A I <lb></lb>and B F, over and above the Triangle A I and B S, or A I B; and the <lb></lb>Rectangle F B and L C is the exceſſe of the Rectangle A C and B F <lb></lb>over and above the Rectangle A L and B F: But the Rectangle A C and <lb></lb>B F is equal to the Rectangle A B I; (for as B A is to A C, ſo is F B to <lb></lb>B I:) The exceſſe, therefore, of the Rectangle A B I above the Rectan<lb></lb>gle A I and B F, or A I and F H, is equal to the exceſſe of the Rectangle <lb></lb>A I and F H above the Rectangle A I B: Therefore twice the Rectan<lb></lb>gle A I and F H is equal to the two Rectangles A B I and A I B; that <lb></lb>is twice A I B with the Square of B I. </s> <s>Let the Square A I be common <lb></lb>to both, and twice the Rectangle A I B with the two Squares A I, and <lb></lb>I B, (that is, the Square A B) ſhall be equal to twice the Rectangle <lb></lb>A I and F H, with the Square A I: Again, taking in commonly the <lb></lb>Square B F; the two Squares A B and B F, that is the ſole Square A F <lb></lb>ſhall be equal to twice the Rectangle A I and F H, with the two Squares <lb></lb>A I and F B, that is A I and F H: But the ſame Square A F is equal <lb></lb>to twice the Rectangle A H F, with the two Squares A H and H F: <lb></lb>Therefore twice the Rectangle A I and F H, with the Squares A I and <lb></lb>F H, are equal to twice the Rectangle A H F, with the Squares A H <lb></lb>and H F: And, the Common Square H F being taken away, twice the <lb></lb>Rectangle A I and F H, with the Square A I, ſhall be equal to twice the <lb></lb>Rectangle A H F, with the Square A H. </s> <s>And becauſe that in all the <lb></lb>Rectangles F H is the Common Side, the Line A H ſhall be equal to A I: <lb></lb>For if it ſhould be greater or leſſer, then the Rectangles F H A and the <lb></lb>Square H A would alſo be greater or leſſer than the Rectangles F H and <lb></lb>I A, and the Square I A: Contrary to what hath been demonſtrated.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Now if we ſuppoſe the Time of the Deſcent along A B to be as A B, <lb></lb>the Time along A C ſhall be as A C, and I B the Mean-proportional be<lb></lb>twixt A C and C E ſhall be the Time along C E, or along X A from <lb></lb>Reſt in X: And becauſe betwixt D A and A B, or R B and B A the<emph.end type="italics"></emph.end><pb xlink:href="040/01/889.jpg" pagenum="196"></pb><emph type="italics"></emph>Mean-proportional is A F, and between A B and B D, that is, R A and <lb></lb>A B the Mean is B F, to which F H is equal; Therefore,<emph.end type="italics"></emph.end> exprædemon<lb></lb>ſtratis, <emph type="italics"></emph>the exceſſe A H ſhall be the Time along A B<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in R, or <lb></lb>after the Fall out of X; ſince the Time along the ſaid A B<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in <lb></lb>A, ſhall be A B. </s> <s>Therefore the Time along X A is I B; and along A B <lb></lb>after R A, or after X A, is A I: Therefore the Time along X A B ſhall <lb></lb>be as A B, namely the ſelf-ſame with the Time along the ſole A B<emph.end type="italics"></emph.end> ex qui<lb></lb>ete <emph type="italics"></emph>in A. </s> <s>Which was the Propoſition.<emph.end type="italics"></emph.end></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"></emph>P<emph.end type="italics"></emph.end>erpendicular be<lb></lb>ing aſſigned, to take part in the Inflected Line, <lb></lb>along which alone <emph type="italics"></emph>ex quiete<emph.end type="italics"></emph.end> a Motion may be <lb></lb>made in the ſame Time, as it would be along <lb></lb>the ſame together with the Perpendicular.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Perpendicular be A B, and a Line inflected to it B C. </s> <s>It is <lb></lb>required in B C to take a part, along which alone out of Reſt a <lb></lb>Motion may be made in the ſame Time as it would along the ſame <lb></lb>together with the Perpendicular A B. </s> <s>Draw the Horizon A D, with <lb></lb>which let the Inclined Line C B prolonged meet in E; and ſuppoſe B F <lb></lb>equal to B A, and on the Center E at the diſtance E F deſcribe the Circle <lb></lb>F I G; and continue out F E unto the Circumference in G; and as G B <lb></lb>is to B F, ſo let B H be to H F; and let H I touch the Circle in I. </s> <s>Then <lb></lb>out of B erect B K<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.889.1.jpg" xlink:href="040/01/889/1.jpg"></figure><lb></lb><emph type="italics"></emph>Perpendicular to <lb></lb>F C, with which <lb></lb>let the Line E I L <lb></lb>meet in L; and laſt <lb></lb>of all let fall L M <lb></lb>Perpendicular to E <lb></lb>L, meeting B C in <lb></lb>M. </s> <s>I ſay, that along <lb></lb>the Line B M from <lb></lb>Rest in B a Motion <lb></lb>may be made in the <lb></lb>ſame Time, as it <lb></lb>would be<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in A along both A B and B M. </s> <s>Let E N be made <lb></lb>equal to E L. </s> <s>And becauſe as G B is to B F, ſo is B H to H F; there<lb></lb>fore, by Permutation as G B is to B H, ſo will B F be to F H; and, by <lb></lb>Diviſion, G H ſhall be to H B, as B H is to H F: Wherefore the Rect<lb></lb>angle G H F ſhall be equal to the Square H B: But the ſaid Rectangle <lb></lb>is alſo equal to the Square H I: Therefore B H is equal to the ſame H I.<emph.end type="italics"></emph.end><pb xlink:href="040/01/890.jpg" pagenum="197"></pb><emph type="italics"></emph>And becauſe in the Quadrilateral Figure I L B H the Sides H B and <lb></lb>H I are equal, and the Angles B and I Right Angles, the Side B L ſhall <lb></lb>likewiſe be equal to the Side L I: But E I is equal to E F: Therefore the <lb></lb>whole Line L E, or N E is equal to the two Lines L B and E F: Let <lb></lb>the Common Line E F be taken away, and the remainder F N ſhall be <lb></lb>equal to L B: And F B was ſuppoſed equal to B A: Therefore L B ſhall <lb></lb>be equal to the two Lines A B and B N. Again, if we ſuppoſe the <lb></lb>Time along A B to be the ſaid A B, the Time along E B ſhall be equal to <lb></lb>E B; and the Time along the whole E M ſhall be E N, namely, the <lb></lb>Mean-proportional betwixt M E and E B: I berefore the Time of the <lb></lb>Deſcent of the remaining part B M after E B, or after A B, ſhall be the <lb></lb>ſaid B N: But it hath been ſuppoſed, that the Time along A B is A B: <lb></lb>Therefore the Time of the Fall along both A B and B M is A B N: <lb></lb>And becauſe the Time along E B<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in E is E B, the Time along <lb></lb>B M<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in B ſhall be the Mean-proportional between B E and <lb></lb>B M; and this is B L: The Time, therefore, along both A B M<emph.end type="italics"></emph.end> ex quiete <lb></lb><emph type="italics"></emph>in A is A B N: And the Time along B M only<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in B is B L: <lb></lb>But it was proved that B L is equal to the two A B and B N: Therefore <lb></lb>the Propoſition is manifeſt.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Otherwiſe with more expedition.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Let B C be the Inclined Plane, and B A the Perpendicular. </s> <s>Continue <lb></lb>out C B to E, and unto E C erect a Perpendicular at B, which being <lb></lb>prolonged ſuppoſe B H equal to the exceſſe of B E above B A; and to the <lb></lb>Angle B H E let the Angle H E L be equal; and let E L continued out <lb></lb>meet with B K in L; and from L erect the Perpendicular L M unto E L <lb></lb>meeting B C in M. </s> <s>I ſay, that<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.890.1.jpg" xlink:href="040/01/890/1.jpg"></figure><lb></lb><emph type="italics"></emph>B M is the Space acquired in <lb></lb>the Plane B C. </s> <s>For becauſe <lb></lb>the Angle M L E is a Right<lb></lb>Angle, therefore B L ſhall be <lb></lb>a Mean-proportional betwixt <lb></lb>M B and B E; and L E a <lb></lb>Mean proportional betwixt M <lb></lb>E and E B; to which E L let <lb></lb>E N be cut equal: And the <lb></lb>three Lines N E, E L, and <lb></lb>L H ſhall be equal; and H B ſhall be the exceſſe of N E above B L: But <lb></lb>the ſaid H B is alſo the exceſſe of N E above N B and B A: Therefore <lb></lb>the two Lines N B and B A are equal to B L. </s> <s>And if we ſuppoſe E B <lb></lb>to be the Time along E B, B L ſhall be the Time along B M<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in <lb></lb>B; and B N ſhall be the Time of the ſame B M after E B or after A B; <lb></lb>and A B ſhall be the Time along A B: Therefore the Times along A B M, <lb></lb>namely, A B N, are equal to the Times along the ſole Line B M<emph.end type="italics"></emph.end> ex quiete <lb></lb><emph type="italics"></emph>in B: Which was intended.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/891.jpg" pagenum="198"></pb><p type="head"> <s>LEMMAI.</s></p><p type="main"> <s><emph type="italics"></emph>Let D C be Perpendicular to the Diameter B A; and from the Term <lb></lb>B continue forth B E D at pleaſure, and draw a Line from F to B. </s> <s>I <lb></lb>ſay, that F B is a Mean-proportional be-<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.891.1.jpg" xlink:href="040/01/891/1.jpg"></figure><lb></lb><emph type="italics"></emph>twixt D B and B E. </s> <s>Draw a Line from E <lb></lb>to F, and by B draw the Tangent B G; <lb></lb>which ſhall be Parallel to the former C D: <lb></lb>Wherefore the Angle D B G ſhall be equal <lb></lb>to the Angle F D B, like as the ſame G B D <lb></lb>is equal alſo to the Angle E F B in the al<lb></lb>tern Portion or Segment: Therefore the <lb></lb>Triangles F B D and F E B are alike: And, <lb></lb>as B D is to B F, ſo is F B to B E.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>LEMMA II.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Line A C be greater than D F; and let A B have greater <lb></lb>proportion to B C, than D E hath to E F. </s> <s>I ſay, that A B is greater <lb></lb>than D E. </s> <s>For becauſe A B hath to B C<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.891.2.jpg" xlink:href="040/01/891/2.jpg"></figure><lb></lb><emph type="italics"></emph>greater proportion than D E hath to D F, <lb></lb>therefore look what proportion A B hath to <lb></lb>B C, the ſame ſhall D E have to a Line leſ<lb></lb>ſer than E F; let it have it to E G: And <lb></lb>becauſe A B to B C, is as D E, to E G, there<lb></lb>fore, by Compoſition, and by converting the Proportion, as C A is to A B, <lb></lb>ſo is G D to D E: But C A is greater than G D: Therefore B A ſhall <lb></lb>be greater than D E.<emph.end type="italics"></emph.end></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"></figure><p type="main"> <s><emph type="italics"></emph>Let A C I B be the Quadrant of a Circle: <lb></lb>and to A C let B E be drawn from B Pa<lb></lb>rallel: And out of any Center taken in the <lb></lb>ſame deſcribe the Circle B O E S, touching <lb></lb>A B in B, and cutting the Circumference of <lb></lb>the Quadrant in I; and draw a Line from <lb></lb>C to B, and another from C to I continued <lb></lb>out to S. </s> <s>I ſay, that the Line C I is alwaies <lb></lb>leſſe than C O. </s> <s>Draw a Line from A to I; <lb></lb>which toucheth the Circle B O E. </s> <s>And if <lb></lb>D I be drawn it ſhall be equal to D B: And <lb></lb>becauſé D B toucheth the Quadrant, the ſaid <lb></lb>D I ſhall likewiſe touch it; and ſhall be Per-<emph.end type="italics"></emph.end><pb xlink:href="040/01/892.jpg" pagenum="199"></pb><emph type="italics"></emph>pendicular to the Diameter A I: Wherefore alſo A I toucheth the Cir<lb></lb>cle B O E in I. And, becauſe the Angle A I C is greater than the An<lb></lb>gle A B C, as inſiſting on a larger Periphery: Therefore the Angle <lb></lb>S I N ſhall be alſo greater than the ſame A B C: Therefore the Portion <lb></lb>I E S is greater than the Portion B O; and the Line C S, nearer to the <lb></lb>Center, greater than C B: Therefore alſo C O is greater than C I; <lb></lb>for that S C is to C B, as O C is to C I.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>And the ſame alſo would happen to be greater, if (as in the other <lb></lb>Figure) the Quadrant B I C were<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.892.1.jpg" xlink:href="040/01/892/1.jpg"></figure><lb></lb><emph type="italics"></emph>leſſer: For the Perpendicular D B <lb></lb>will cut the Circle C I B: Wherefore <lb></lb>D I alſo is equal to the ſaid D B; and <lb></lb>the Angle D I A ſhall be Obtuſe, and <lb></lb>therefore A I N will alſo cut B I N: <lb></lb>And becauſe the Angle A B C is leſſe <lb></lb>than the Angle A I C, which is equal <lb></lb>to S I N; and this now is leſſe than that <lb></lb>which would be made at the Contact in <lb></lb>I by the Line S I: Therefore the Porti<lb></lb>on S E I is much greater than the Por<lb></lb>tion B O: Wherefore,<emph.end type="italics"></emph.end> &c. <emph type="italics"></emph>Which was <lb></lb>to be demonſtrated.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>THEOR. <emph type="italics"></emph>XXII.<emph.end type="italics"></emph.end> PROP. <emph type="italics"></emph>XXXVI.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>If from the loweſt point of a Circle erect unto <lb></lb>the Horizon a Plane ſhould be elevated ſub<lb></lb>tending a Circumference not greater than a <lb></lb>Quadrant, from whoſe Terms two other <lb></lb>Planes are Inflected to any point of the Cir<lb></lb>cumference, the Deſcent along both the Infle<lb></lb>cted Planes would be performed in a ſhorter <lb></lb>Time than along the former elevated Plane <lb></lb>alone, or than along but one of the other two, <lb></lb>namely, along the lower.</s></p><p type="main"> <s><emph type="italics"></emph>Let C B D be the Circumference not greater than a Quadrant of a <lb></lb>Circle erect unto the Horizon on the lower point C, in which let <lb></lb>C D be an elevated Plane; and let two Planes be inflected from the <lb></lb>Terms D and C to any point in the Circumference taken at pleaſure, <lb></lb>as B. </s> <s>I ſay, that the Time of the Deſcent along both thoſe Planes D B C <lb></lb>is ſhorter than the Time of the Deſcent along the ſole Plane D C, or <lb></lb>along the other only B C<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in B. </s> <s>Let the Horizontal Line M D A<emph.end type="italics"></emph.end><pb xlink:href="040/01/893.jpg" pagenum="200"></pb><emph type="italics"></emph>be drawn by D, with which let C B prolonged meet in A; and let fall <lb></lb>the Perpendiculars D N and M C to M D, and B N to B D; and about <lb></lb>the Right-angled Triangle D B N deſcribe the Semicircle D F B N, <lb></lb>cutting D C in F; and let D O be a Mean-proportional betwixt C D <lb></lb>and D F; and A V a Mean-proportional betwixt C A and A B: And <lb></lb>let P S be the time in which the whole D C, or B C, ſhall be paſſed; <lb></lb>(for it is manifeſt that they ſhall be both paſt in the ſame Time;) And <lb></lb>look what proportion C D hath to D O, the ſame ſhall the Time S P <lb></lb>have to the Time P R: the Time P R ſhall be that in which a Movea<lb></lb>ble out of D will paſſe D F; and R S that in which it ſhall paſſe the re<lb></lb>mainder F C. </s> <s>And becauſe P S is alſo the Time in which the Movea<lb></lb>ble out of B ſhall paſſe B C; if it be ſuppoſed that as B C is to C D, ſo is <lb></lb>S P to P T, P T ſhall be the Time of the Deſcent out of A to C: by <lb></lb>reaſon D C is a Mean-proportional betwixt A C and C B, by what was <lb></lb>before demonſtrated: Laſt of all, as C A is to A V, ſo let T P be to<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.893.1.jpg" xlink:href="040/01/893/1.jpg"></figure><lb></lb><emph type="italics"></emph>P G: P G ſhall be the Time, <lb></lb>in which thé Moveable out <lb></lb>of A deſcendeth to B. </s> <s>And <lb></lb>becauſe of the Circle D F N <lb></lb>the Diameter erect to the <lb></lb>Horizon is D N, the Lines <lb></lb>D F and D B ſhall be paſ<lb></lb>ſed in equal Times. </s> <s>So that <lb></lb>if it ſhould be demonſtra<lb></lb>ted that the Moveable would <lb></lb>ſooner paſſe B C after the <lb></lb>Deſcent D B, than F C after the Lation D F; we ſhould have our in<lb></lb>tent. </s> <s>But the Moveable will with the ſame Celerity of Time paſſe B C <lb></lb>coming out of D along D B, as if it came out of A along A B: for that <lb></lb>in both the Deſcents D B and A B it acquireth equal Moments of Velo<lb></lb>city: Therefore it ſhall reſt to be demonſtrated that the Time is ſhorter <lb></lb>in which B C is paſſed after A B, than that in which F C is paſt after <lb></lb>D F. </s> <s>But it hath been demonſtrated, that the Time in which B C is <lb></lb>paſſed after A B is G T; and the Time of F C after D F is R S. </s> <s>It is <lb></lb>to be proved therefore, that R S is greater than G T: Which is thus <lb></lb>done. </s> <s>Becauſe as S P is to P R, ſo is C D to D O, therefore, by Conver<lb></lb>ſion of proportion, and by Inverſion, as R S is to S P, ſo is O C to C D: <lb></lb>and as S P is to P T, ſo is D C to C A: And, becauſe as T P is to PG, <lb></lb>ſo is C A to A V: Therefore alſo, by Converſion of the proportion, as <lb></lb>P T is to T G, ſo is A C to C V: therefore, ex equali, as R S is to G T, <lb></lb>ſo is O C to C V. </s> <s>But O C is greater than C V, as ſhall anon be de<lb></lb>monſtrated: Therefore the Time R S is greater than the Time G T: <lb></lb>Which it was required to demonſtrate. </s> <s>And becauſe C F is greater than <lb></lb>C B, and F D leſſe than B A, therefore C D ſhall have greater propor<lb></lb>tion to D F than C A to A B: And as C D is to D F, ſo is the Square<emph.end type="italics"></emph.end><pb xlink:href="040/01/894.jpg" pagenum="201"></pb><emph type="italics"></emph>C O to the Square O F; foraſmuch as C D, D O, and O F are Propor<lb></lb>tionals: And as C A is to A B, ſo is the Square C V to the Square <lb></lb>V B: Therefore C O hath greater proportion to O F, than C V to V B: <lb></lb>Therefore, by the foregoing Lemma, C O is greater than C V. </s> <s>It is <lb></lb>manifeſt moreover, that the Time along D C is to the Time along <lb></lb>D B C, as D O C is to D O together with C V.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>SCHOLIUM.</s></p><p type="main"> <s>From theſe things that have been demonſtrated may evidently <lb></lb>be gathered, that the ſwifteſt of all Motions betwixt Term <lb></lb>and Term is not made along the ſhorteſt Line, that is by the <lb></lb>Right, but along a portion of a Circle.</s></p><p type="main"> <s><emph type="italics"></emph>For in the Quadrat B A E C, whoſe Side B C is erect to the Hori<lb></lb>zon, let the Arch A C be divided into any number of equal parts, <lb></lb>A D, D E, E F, F G, G C; and let Right-lines be drawn from C to <lb></lb>the Points A, D, E, F, G, H; and alſo by Lines joyn A D, D E, E F, <lb></lb>F G. and G C. </s> <s>It is manifest, that the Motion along the two Lines <lb></lb>A D C is ſooner performed than along the<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.894.1.jpg" xlink:href="040/01/894/1.jpg"></figure><lb></lb><emph type="italics"></emph>ſole Line A C, or D C out of Reſt in D: <lb></lb>But out of Reſt in A, D C is ſooner paſt <lb></lb>than the two A D C: But along the two <lb></lb>D E C out of Reſt in A the Deſcent is <lb></lb>likewiſe ſooner made than along the ſole <lb></lb>C D: Therefore the Deſcent along the <lb></lb>three Lines A D E C ſhall be performed <lb></lb>ſooner than along the two A D C. </s> <s>And <lb></lb>in like manner the Deſcent along A D E <lb></lb>preceding, the Motion is more ſpeedily con<lb></lb>ſummated along the two EFC than along the ſole FC: Therfore along the <lb></lb>four A D E F C the Motion is quicklier accompliſhed than along the <lb></lb>three A D E C: And ſo, in the laſt place, along the two F G C after the <lb></lb>precedent Deſcent along A D E F the Motion will be ſooner conſumma<lb></lb>ted than along the ſole F C: Therefore along the five A D E F G C <lb></lb>the Deſcent ſhall be effected in a yet ſhorter Time than along the four <lb></lb>A D E F C: Whereupon the nearer by inſcribed Poligons we approach <lb></lb>the Circumference, the ſooner will the Motion be performed between the <lb></lb>two aſſigned points A C.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>And that which is explained in a Quadrant, holdeth true likewiſe <lb></lb>in a Circumference leſſe than the Quadrant: and the Ratiocination is <lb></lb>the ſame.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/895.jpg" pagenum="202"></pb><p type="head"> <s>PROBL.XV. PROP. XXXVII.</s></p><p type="main"> <s>A Perpendicular and Inclined Plane of the ſame <lb></lb>Elevation being given, to find a part in the In<lb></lb>clined Plane that is equal to the Perpendicu<lb></lb>lar, and paſſed in the ſame Time as the ſaid <lb></lb>Perpendicular.</s></p><p type="main"> <s><emph type="italics"></emph>LET A B be the Perpendicular, and A C the Inclined Plane. </s> <s>It is <lb></lb>required in the Inclined to find a part equal to the Perpendicular <lb></lb>A B, that after Reſt in A may be paſſed in a Time equal to the <lb></lb>Time in which the Perpendicular is paſſed. </s> <s>Let A D be equal to A B, <lb></lb>and cut the Remainder B C in two equal parts in I; and as A C is to<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.895.1.jpg" xlink:href="040/01/895/1.jpg"></figure><lb></lb><emph type="italics"></emph>C I, ſo let C I be to another Line <lb></lb>A E; to which let D G be equal: It <lb></lb>is manifeſt that E G is equal to A D <lb></lb>and to A B. </s> <s>I ſay moreover, that <lb></lb>this ſame E G is the ſame that is <lb></lb>paſſed by the Moveable coming out <lb></lb>of Reſt in A in a Time equal to the <lb></lb>Time in which the Moveable fall eth along A B. </s> <s>For becauſe that as <lb></lb>A C is to C I, ſo is C I to A E, or I D to D G; Therefore by Converſion <lb></lb>of the proportion, as C A is to A I, ſo is D I to I G. </s> <s>And becauſe as the <lb></lb>whole C A is to the whole A I, ſo is the part taken away C I to the part <lb></lb>I G; therefore the Remaining part I A ſhall be to the Remainder A G, <lb></lb>as the whole C A is to the whole A I: Therefore A I is a Mean-propor<lb></lb>tional betwixt C A and A G; and C I a Mean-proportional betwixt <lb></lb>C A and A E: If therefore we ſuppoſe the Time along A B to be as A B; <lb></lb>A C ſhall be the Time along A C, and C I or I D the Time along A E: <lb></lb>And becauſe A I is a Mean-proportional betwixt C A and A G; and <lb></lb>C A is the Time along the whole A C: Therefore A I ſhall be the Time <lb></lb>along. </s> <s>A G; and the Remainder I C that along the Remainder G C: But <lb></lb>D I was the Time along A E: Therefore D I and I C are the Times <lb></lb>along both the Spaces A E and C G: Therefore the Remainder D A ſhall <lb></lb>be the Time along E G, to wit, equal to the Time along A B. </s> <s>Which was <lb></lb>to be done.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>COROLLARIE.</s></p><p type="main"> <s>Hence it is manifeſt, that the Space required is an intermedial be<lb></lb>tween the upper and lower parts that are paſt in equal <lb></lb>Times.</s></p><pb xlink:href="040/01/896.jpg" pagenum="203"></pb><p type="head"> <s><emph type="italics"></emph>P<emph.end type="italics"></emph.end>ROBL. XVI. <emph type="italics"></emph>P<emph.end type="italics"></emph.end>RO<emph type="italics"></emph>P.<emph.end type="italics"></emph.end> XXXVIII.</s></p><p type="main"> <s>Two Horizontal Planes cut by the Perpendicular <lb></lb>being given, to find a ſublime point in the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>er<lb></lb>pendicular, out of which Moveables falling <lb></lb>and being reflected along the Horizontal <lb></lb><emph type="italics"></emph>P<emph.end type="italics"></emph.end>lanes may in Times equal to the Times of <lb></lb>the Deſcents along the ſaid Horizontal <emph type="italics"></emph>P<emph.end type="italics"></emph.end>lanes, <lb></lb>namely, along the upper and along the lower, <lb></lb>paſſe Spaces that have to each other any given <lb></lb>proportion of the leſſer to the greater.</s></p><p type="main"> <s><emph type="italics"></emph>LET the Planes C D and B E be interſected by the Perpendicular <lb></lb>A C B, and let the given proportion of the leſſe to the greater be <lb></lb>N to F G. </s> <s>It is required in the Perpendicular A B to find a point <lb></lb>on high, out of which a Moveable falling, and reflected along C D may <lb></lb>in a Time equal to the Time of its Fall, paſſe a Space, that ſhall have <lb></lb>unto the Space paſſed by the other Moveable coming out of the ſame ſub<lb></lb>lime point in a Time equal to the Time of its Fall with a Reflex Motion <lb></lb>along the Plane B E the ſame proportion as the given Line N batb to<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.896.1.jpg" xlink:href="040/01/896/1.jpg"></figure><lb></lb><emph type="italics"></emph>F G. </s> <s>Let G H be <lb></lb>made equal to the <lb></lb>ſaid N; and as F H <lb></lb>is to H G, ſo let <lb></lb>B C be to C L. </s> <s>I ſay, <lb></lb>L is the ſublime <lb></lb>point required. </s> <s>For <lb></lb>taking C M double <lb></lb>to C L, draw L M <lb></lb>meeting the Plane <lb></lb>B E in O; B O <lb></lb>ſhall be double to <lb></lb>B L: And becauſe, <lb></lb>as F H is to H G, ſo is B C to C L; therefore, by Compoſition and In<lb></lb>verſion, as H G, that is, N is to G F, ſo is C L to L B, that is, C M to <lb></lb>B O: But becauſe C M is double to L C; let the Space C M be that <lb></lb>which by the Moveable coming from L after the Fall L C is paſſed along <lb></lb>the Plane C D; and by the ſame reaſon B O is that which is paſſed after <lb></lb>the Fall L B in a Time equal to the Time of the Fall along L B; foraſ<lb></lb>much as B O is double to B L: Therefore the Propoſition is manifeſt.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/897.jpg" pagenum="204"></pb><p type="main"> <s>SAGR. </s> <s>Really me thinks that we may juſtly grant our <emph type="italics"></emph>Acade<lb></lb>mian<emph.end type="italics"></emph.end> what he without arrogance aſſumed to himſelf in the begining <lb></lb>of this his Treatiſe of ſhewing us a <emph type="italics"></emph>New Science<emph.end type="italics"></emph.end> about <emph type="italics"></emph>a very old <lb></lb>Subject.<emph.end type="italics"></emph.end> And to ſee with what Facility and Perſpicuity he deduceth <lb></lb>from one ſole Principle the Demonſtrations of ſo many Propoſiti<lb></lb>ons, maketh me not a little to wonder how this buſineſs eſcaped <lb></lb>unhandled by <emph type="italics"></emph>Archimedes, Apollonius, Euclid,<emph.end type="italics"></emph.end> and ſo many other <lb></lb><emph type="italics"></emph>I<emph.end type="italics"></emph.end>lluſtrious Mathematicians and Phyloſophers: eſpecially ſince <lb></lb>there are found many great Volumns of <emph type="italics"></emph>Motion.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>There is extant a ſmall Fragment of <emph type="italics"></emph>Euclid<emph.end type="italics"></emph.end> touching <lb></lb><emph type="italics"></emph>Motion,<emph.end type="italics"></emph.end> but there are no marks to be ſeen therein of any ſteps that he <lb></lb>took towards the diſcovery of the Proportion of <emph type="italics"></emph>Acceleration,<emph.end type="italics"></emph.end> and <lb></lb>of its Varieties along different <emph type="italics"></emph>I<emph.end type="italics"></emph.end>nclinations. </s> <s>So that indeed one <lb></lb>may ſay, that never till now was the door opened to a new Con<lb></lb>templation fraught with infinite and admirable Concluſions, which <lb></lb>in times to come may buſie other Wits.</s></p><p type="main"> <s>SAGR. <emph type="italics"></emph>I<emph.end type="italics"></emph.end> verily believe, that as thoſe few Paſſions (<emph type="italics"></emph>I<emph.end type="italics"></emph.end> will ſay <lb></lb>for example) of the Circle demonſtrated by <emph type="italics"></emph>Euclid<emph.end type="italics"></emph.end> in the third of <lb></lb>his <emph type="italics"></emph>Elements<emph.end type="italics"></emph.end> are an introduction to innumerable others more ab<lb></lb>ſtruce, ſo thoſe produced and demonſtrated in this ſhort Tractate, <lb></lb>when they ſhall come to the hands of other Speculative Wits, ſhall <lb></lb>be a manuduction unto infinite others mote admirable: and it is to <lb></lb>be believed that thus it will happen by reaſon of the Nobility of <lb></lb>the Argument above all others Phyſical.</s></p><p type="main"> <s>This daies Conference hath been very long and laborious; in <lb></lb>which <emph type="italics"></emph>I<emph.end type="italics"></emph.end> have taſted more of the ſimple Propoſitions than of their <lb></lb>Demonſtrations; many of which, <emph type="italics"></emph>I<emph.end type="italics"></emph.end> believe, will coſt me more than <lb></lb>an hour a piece well to comprehend them: a task that <emph type="italics"></emph>I<emph.end type="italics"></emph.end> reſerve to <lb></lb>my ſelf to perform at leaſure, you leaving the Book in my hands ſo <lb></lb>ſoon as we ſhall have heard this part that remains about the Moti<lb></lb>on of Projects: which ſhall, if you ſo pleaſe, be to morrow.</s></p><p type="main"> <s>SALV. <emph type="italics"></emph>I<emph.end type="italics"></emph.end> ſhall not fail to be with you.</s></p><p type="head"> <s><emph type="italics"></emph>The End of the Third Dialogue.<emph.end type="italics"></emph.end></s></p></chap><chap><pb xlink:href="040/01/898.jpg" pagenum="205"></pb><p type="head"> <s>GALILEUS, <lb></lb>HIS <lb></lb>DIALOGUES <lb></lb>OF <lb></lb>MOTION.</s></p><p type="head"> <s>The Fourth Dialogue.</s></p><p type="head"> <s><emph type="italics"></emph>INTERLOCUTORS,<emph.end type="italics"></emph.end></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"></emph>Simplicius<emph.end type="italics"></emph.end> likewiſe cometh in the nick of time, therefore <lb></lb>without interpoſing any <emph type="italics"></emph>Reſt<emph.end type="italics"></emph.end> let us proceed to <emph type="italics"></emph>Motion<emph.end type="italics"></emph.end>; <lb></lb>and ſee here the <emph type="italics"></emph>Text<emph.end type="italics"></emph.end> of our <emph type="italics"></emph>Author.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>OF THE MOTION OF <lb></lb>PROJECTS.</s></p><p type="main"> <s><emph type="italics"></emph>What accidents belong to<emph.end type="italics"></emph.end> Equable Motion, <emph type="italics"></emph>as alſo to the<emph.end type="italics"></emph.end> Na<lb></lb>turally Accelerate <emph type="italics"></emph>along all whatever Inclinations of Planes, <lb></lb>we have conſidered above. </s> <s>In this Contemplation which we are now <lb></lb>entering upon, I will attempt to declare, and with ſolid Demonſtrations<emph.end type="italics"></emph.end><pb xlink:href="040/01/899.jpg" pagenum="206"></pb><emph type="italics"></emph>to eſtabliſh ſome of the principal Symptomes, and thoſe worthy of know<lb></lb>ledge, which befall a Moveable whilſt it is moved with a Motion com<lb></lb>pounded of a twofold Lation, to wit, of the Equable and Naturally<lb></lb>Accelerate: and this is that Motion, which we call the Motion of Pro<lb></lb>jects: whoſe Generation I constitute to be in this manner.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>I fancy in my mind a certain Moveable projected or thrown along <lb></lb>an Horizontal Plane, all impediment ſecluded: Now it is manifeſt by <lb></lb>what we have elſewhere ſpoken at large, that that Motion will be Equa<lb></lb>ble and Perpetual along the ſaid Plane, if the Plane be extended<emph.end type="italics"></emph.end> in in<lb></lb>finitum<emph type="italics"></emph>: but if we ſuppoſe it terminate, and placed on high, the Move<lb></lb>able, which I conceive to be endued with Gravity, being come to the end <lb></lb>of the Plane, proceeding forward, it addeth to the Equable and Indeli<lb></lb>ble firſt Lation that propenſion downwards which it receiveth from its <lb></lb>Gravity, and from thence a certain Motion doth reſult compounded of <lb></lb>the Equable Horizontal, and of the Deſcending naturally. </s> <s>Accellerate <lb></lb>Lations: which I call<emph.end type="italics"></emph.end> Projection. <emph type="italics"></emph>Some of whoſe Accidents we will de<lb></lb>monſtrate; the firſt of which ſhall be this.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>THEOR.I. PROP.I.</s></p><p type="main"> <s><emph type="italics"></emph>A Project, when it is moved with a Motion compounded <lb></lb>of the Horizontal Equable, and of the Naturally<lb></lb>Accelerate downwards, ſhall deſcribe a Semipara<lb></lb>bolical Line in its Lation.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>It is requiſite, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> in favour of my ſelf, and, as I <lb></lb>believe, alſo of <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> here to make a pauſe; for I <lb></lb>am not ſo far gone in Geometry as to have ſtudied <emph type="italics"></emph>Apol<lb></lb>lonius,<emph.end type="italics"></emph.end> ſave only ſo far as to know that he treateth of theſe Para<lb></lb>bola's, and of the other Conick Sections, without the knowledge <lb></lb>of which, and of their Paſſions, I do not think that one can under<lb></lb>ſtand the Demonſtrations of other Propoſitions depending on <lb></lb>them. </s> <s>And becauſe already in the very firſt Propoſition it is pro<lb></lb>poſed by the Author to prove the Line deſcribed by the Project to <lb></lb>be Parabolical, I imagine to my ſelf, that being to treat of none <lb></lb>but ſuch Lines, it is abſolutely neceſſary to have a perfect know<lb></lb>ledge, if not of all the Paſſions of thoſe Figures that are demon<lb></lb>ſtrated by <emph type="italics"></emph>Apollonius,<emph.end type="italics"></emph.end> at leaſt of thoſe that are neceſſary for the Sci<lb></lb>ence in hand.</s></p><p type="main"> <s>SALV. </s> <s>You undervalue your ſelf very much, to make ſtrange <lb></lb>of thoſe Notions, which but even now you admitted as very well <lb></lb>underſtood: I told you heretofore, that in the Treatiſe of Reſi<lb></lb>ſtances we had need of the knowledge of certain Propoſitions of <pb xlink:href="040/01/900.jpg" pagenum="207"></pb><emph type="italics"></emph>Apollonius,<emph.end type="italics"></emph.end> at which you made no ſeruple.</s></p><p type="main"> <s>SAGR. </s> <s>It may be either that I knew them by chance, or that I <lb></lb>might for once gueſſe at, and take for granted ſo much as ſerved my <lb></lb>turn in that Tractate: but here where I imagine that we are to <lb></lb>hear all the Demonſtrations that concern thoſe Lines, it is not con<lb></lb>venient, as we ſay, to ſwallow things whole, loſing our time and <lb></lb>pains.</s></p><p type="main"> <s>SIMP. </s> <s>But as to what concerns me, although <emph type="italics"></emph>Sagredus<emph.end type="italics"></emph.end> were, <lb></lb>as I believe he is, well provided for his occaſions, the very firſt <lb></lb>Terms already are new to me: for though our Philoſophers have <lb></lb>handled this Argument of the Motion of Projects, I do not remem<lb></lb>ber that they have confined themſelves to deſine what the Lines <lb></lb>are which they deſcribe, ſave only in general that they are alwaies <lb></lb>Curved Lines, except it be in Projections Perpendicularly upwards. <lb></lb></s> <s>Therefore in caſe that little Geometry that I have learnt from <emph type="italics"></emph>Eu<lb></lb>clid<emph.end type="italics"></emph.end> ſince the Time that we have had other Conferences, be not ſuf<lb></lb>ficient to render me capable of the Notions requiſite for the under<lb></lb>ſtanding of the following Demonſtrations, I muſt content my ſelf <lb></lb>with bare Propoſitions believed, but not underſtood.</s></p><p type="main"> <s>SALV. </s> <s>But I will have you to know them by help of the Au<lb></lb>thor of this Book himſelf, who when he heretofore granted me a <lb></lb>ſight of this his Work, becauſe I alſo at that time was not perfect <lb></lb>in the Books of <emph type="italics"></emph>Apollonius,<emph.end type="italics"></emph.end> took the pains to demonſtrate to me <lb></lb>two moſt principal Paſſions of the Parabola without any other Pre<lb></lb>cognition, of which two, and no more, we ſhall ſtand in need in <lb></lb>the preſent Treatiſe; which are both likewiſe proved by <emph type="italics"></emph>Apollonius,<emph.end type="italics"></emph.end><lb></lb>but after many others, which it would take up a long time to look <lb></lb>over, and I am deſirous that we may much ſhorten the Journey, ta<lb></lb>king the firſt immediately from the pure and ſimple generation of <lb></lb>the ſaid Parabola, and from this alſo immediately ſhall be deduced <lb></lb>the Demonſtration of the ſecond. </s> <s>Coming therefore to the firſt;</s></p><p type="main"> <s>Deſcribe the Right Cone, whoſe Baſe let be the Circle I B K C, <lb></lb>and Vertex the point L, in which, cut by a Plane parallel to the <lb></lb><figure id="id.040.01.900.1.jpg" xlink:href="040/01/900/1.jpg"></figure><lb></lb>Side L K, ariſeth the Section B A C <lb></lb>called a Parabola; and let its Baſe <lb></lb>B C cut the Diameter I K of the <lb></lb>Circle I B K C at Right-Angles; <lb></lb>and let the Axis of the Parabola <lb></lb>A D be Parallel to the ſide L K; <lb></lb>and taking any point F in the Line <lb></lb>B F A, draw the Right-Line F E <lb></lb>parallel to B D. </s> <s>I ſay, that the Square <lb></lb>of B D hath to the Square of F E <lb></lb>the ſame proportion that the Axis <lb></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"></pb>be ſuppoſed to paſſe by the Point E, which ſhall make in the Cone <lb></lb>a Circular Section, whoſe Diameter is G E H. </s> <s>And becauſe upon <lb></lb>the Diameter I K of the Circle I B K, B D is a Perpendicular, the <lb></lb>Square of B D ſhall be equal to the Rectangle made by the parts <lb></lb>I D and D K: And likewiſe in the upper Circle which is underſtood <lb></lb>to paſſe by the points G F H, the Square of the Line F E is equal <lb></lb>to the Rectangle of the parts G E H: Therefore the Square of B D <lb></lb>hath the ſame proportion to the Square of F E, that the Rectangle <lb></lb>I D K hath to the Rectangle G E H. </s> <s>And becauſe the Line E D is <lb></lb>Parallel to H K, E H ſhall be equal to D K, which alſo are Parallels: <lb></lb>And therefore the Rectangle I D K ſhall have the ſame proportion <lb></lb>to the Rectangle G E H, as I D hath to G E; that is, that D A hath <lb></lb>to A E: Therefore the Rectangle I D K to the Rectangle G E H, <lb></lb>that is, the Square B D to the Square F E, hath the ſame proportion <lb></lb>that the Axis D A hath to the part A E: Which was to be de<lb></lb>monſtrated.</s></p><p type="main"> <s>The other Propoſition, likewiſe neceſſary to the preſent Tract, <lb></lb>we will thus make out. </s> <s>Let us deſcribe the Parabola, of which let the <lb></lb>Axis C A be prolonged out unto D; and taking any point B, let the <lb></lb>Line B C be ſuppoſed to be continued out by the ſame Parallel un<lb></lb><figure id="id.040.01.901.1.jpg" xlink:href="040/01/901/1.jpg"></figure><lb></lb>to the Baſe of the ſaid Parabola; <lb></lb>and let D A be ſuppoſed equal <lb></lb>to the part of the Axis C A. </s> <s>I ſay, <lb></lb>that the Right-Line drawn by <lb></lb>the points D and B, falleth not <lb></lb>within the Parabola, but without, <lb></lb>ſo as that it only toucheth the <lb></lb>ſame in the ſaid point B: For, if <lb></lb>it be poſſible for it to fall within, <lb></lb>it cutteth it above, or being pro<lb></lb>longed, it cutteth it below. </s> <s>And <lb></lb>in that Line let any point G be <lb></lb>taken, by which paſſeth the Right <lb></lb>Line F G E. </s> <s>And becauſe the <lb></lb>Square F E is greater than the <lb></lb>Square G E, the ſaid Square F E <lb></lb>ſhall have greater proportion to <lb></lb>the Square B C, than the ſaid Square G E hath to the ſaid B C. </s> <s>And <lb></lb>becauſe, by the precedent, the Square F E is to the Square B C as <lb></lb>E A is to A C; therefore E A hath greater proportion to A C, than <lb></lb>the Square G E hath to the Square B C; that is, than the Square <lb></lb>E D hath to the Square D C: (becauſe in the Triangle D G E as <lb></lb>G E is to the Parallel B C, ſo is E <emph type="italics"></emph>D<emph.end type="italics"></emph.end> to <emph type="italics"></emph>D<emph.end type="italics"></emph.end> C:) But the Line E A to <lb></lb>A C, that is, to A <emph type="italics"></emph>D<emph.end type="italics"></emph.end> hath the ſame proportion that four Rectangles <lb></lb>E A <emph type="italics"></emph>D<emph.end type="italics"></emph.end> hath to four Squares of A <emph type="italics"></emph>D,<emph.end type="italics"></emph.end> that is, to the Square C <emph type="italics"></emph>D,<emph.end type="italics"></emph.end><pb xlink:href="040/01/902.jpg" pagenum="209"></pb>(which is equal to four Squares of A D:) Therefore four Rectan<lb></lb>gles E A D ſhall have greater proportion to the Square C D, than <lb></lb>the Square E D hath to the Square D C: Therefore four Rectan<lb></lb>gles E A D ſhall be greater than the Square E D: which is falſe, <lb></lb>for they are leſſe; becauſe the parts E A and A D of the Line E D <lb></lb>are not equal: Therefore the Line D B toucheth the Parabola in B, <lb></lb>and doth not cut it: Which was to be demonſtrated.</s></p><p type="main"> <s>SIMP. </s> <s>You proceed in your Demonſtrations too ſublimely, <lb></lb>and ſtill, as far as I can perceive, ſuppoſe that the Propoſitions of <lb></lb><emph type="italics"></emph>Euclid<emph.end type="italics"></emph.end> are as familiar and ready with me, as the firſt Axioms them<lb></lb>ſelves, which is not ſo. </s> <s>And the impoſing upon me, juſt now, that <lb></lb>four Rectangles E A <emph type="italics"></emph>D<emph.end type="italics"></emph.end> are leſs than the Square <emph type="italics"></emph>D<emph.end type="italics"></emph.end> E becauſe the <lb></lb>parts E A and A <emph type="italics"></emph>D<emph.end type="italics"></emph.end> of the Line E <emph type="italics"></emph>D<emph.end type="italics"></emph.end> are not equal, doth not ſatisſie <lb></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></lb>ſuppoſe that the Reader hath ready by heart the Elements of <lb></lb><emph type="italics"></emph>Euclid<emph.end type="italics"></emph.end>: And here to ſupply your want, it ſhall ſuſfice to remember <lb></lb>you of a Propoſition in the ſecond Book, in which it is demonſtrated <lb></lb>that when a Line is cut into equal parts, and into unequal, the <lb></lb>Rectangle of the unequal parts is leſs than the Rectangle of the <lb></lb>equal, (that is, than the Square of the half) by ſo much as is the <lb></lb>Square of the Line comprized between the Sections. </s> <s>Whence it is <lb></lb>manifeſt, that the Square of the whole, which continueth four <lb></lb>Squares of the Half, is greater than four Rectangles of the unequal <lb></lb>parts. </s> <s>Now it is neceſſary that we bear in mind theſe two Propoſi<lb></lb>tions which have been demonſtrated, taken from the Conick Ele<lb></lb>ments, for the better underſtanding the things that follow in the <lb></lb>preſent Treatiſe: for of theſe two, and no more, the Author <lb></lb>makes uſe. </s> <s>Now we may reaſſume the Text to ſee in what manner <lb></lb>he doth demonſtrate his firſt Propoſition, in which he intendeth to <lb></lb>prove unto us, That the Line deſcribed by the Grave Moveable, <lb></lb>when it deſcends with a Motion compounded of the Equable <lb></lb>Horizontal, and of the Natural <emph type="italics"></emph>D<emph.end type="italics"></emph.end>eſcending is a Semiparabola.</s></p><p type="main"> <s><emph type="italics"></emph>Suppoſe the Horizontal Line or Plane A B placed on high; upon<emph.end type="italics"></emph.end><lb></lb>[or along] <emph type="italics"></emph>which let the Moveable paſſe with an Equable Motion out <lb></lb>of A unto B: and the ſupport of the Plane failing in B let there be <lb></lb>derived upon the Moveable from its own Gravity a Motion naturally <lb></lb>downwards according to the Perpendicular B N. </s> <s>Let the Line B E be <lb></lb>ſuppoſed applyed unto the Plane A B right out, as if it were the Efflux <lb></lb>or meaſure of the Time, on which at pleaſure note any equal parts of <lb></lb>Time, B C, C D, D E: And out of the points B C D E ſuppoſe Per<lb></lb>pendicular Lines to be let fall equidiſtant or parallel to B N: In the firſt <lb></lb>of which take any part C I, whoſe quadruple take in the following one <lb></lb>D F, nonuple E H, and ſo in the reſt that follow according to the propor-<emph.end type="italics"></emph.end><pb xlink:href="040/01/903.jpg" pagenum="210"></pb><emph type="italics"></emph>tion of the Squares of C B, D B, E B, or, if you will, in the doubled <lb></lb>proportion of the Lines. </s> <s>And if unto the Moveable moved beyond B <lb></lb>towards C with the Equable Lation we ſuppoſe the Perpendicular <lb></lb>Deſcent to be ſuperadded according to the quantity C I, in the Time <lb></lb>B C it ſhall be found conſtituted in the Term I. </s> <s>And proceeding farther,<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.903.1.jpg" xlink:href="040/01/903/1.jpg"></figure><lb></lb><emph type="italics"></emph>in the Time D B, namely, <lb></lb>in the double of B C, the <lb></lb>Space of the Deſcent down<lb></lb>wards ſhall be quadruple to <lb></lb>the firſt Space C I: For <lb></lb>it hath beendemonſtrated in <lb></lb>the firſt Trastate, that the <lb></lb>Spaces paſſed by GraveBo<lb></lb>dies with a Motion Natu<lb></lb>rally Accelerate are in du<lb></lb>plicate proportion of their Times. </s> <s>And it likewiſe followeth, that the <lb></lb>Space E H paſſed in the Time B E, ſhall be as G. </s> <s>So that it is manifeſtly <lb></lb>proved, that the Spaces E H, D F, C I, are to one another as the Squares <lb></lb>of the Lines E B, D B, C B. </s> <s>Now from the points I, F, and H draw <lb></lb>the Right Lines I O, F G, H L, Parallel to the ſaid E B; and each of <lb></lb>the Lines H L, F G, and I O ſhall be equal to each of the other Lines <lb></lb>E B, D B, and C B; as alſo each of thoſe B O, B G, and B L, ſhall be <lb></lb>equal to each of thoſe C I, D F, and E H: And the Square H L ſhall <lb></lb>be to the Square F G, as the Line L B to B G: And the Square F G <lb></lb>ſhall be to the Square I O, as G B to B O: Therefore the Points I, F, <lb></lb>and H are in one and the ſame Parabolical Line. </s> <s>And in like manner <lb></lb>it ſhall be demonſtrated, any equalparticles of Time of whatſoever Mag<lb></lb>nitude being taken, that the place of the Moveable whoſe Motion is <lb></lb>compounded of the like Lations, is in the ſame Times to be found in the <lb></lb>ſame Parabolick Line: Therefore the Propoſition is manifeſt.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>This Concluſion is gathered from the Converſion of the <lb></lb>firſt of thoſe two Propoſitions that went before, for the Parabola <lb></lb>being, for example, deſcribed by the points B H, if either of the <lb></lb>two F or I were not in the deſcribed Parabolick Line, it would be <lb></lb>within, or without; and by conſequence the Line F G would be <lb></lb>either greater or leſſer than that which ſhould determine in the Pa<lb></lb>rabolick Line; Wherefore the Square of HL would have, not to <lb></lb>the Square of F G, but to another greater or leſſer, the ſame pro<lb></lb>portion that the Line L B hath to BG, but it hath the ſame propor<lb></lb>tion to the Square of F G: Therefore the point F is in the Parabo<lb></lb>lick Line: And ſo all the reſt, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>It cannot be denied but that the Diſcourſe is new, in<lb></lb>genious and concludent, arguing <emph type="italics"></emph>ex ſuppoſitione,<emph.end type="italics"></emph.end> that is, ſuppoſing <lb></lb>that the Tranſverſe Motion doth continue alwaies Equable, and <pb xlink:href="040/01/904.jpg" pagenum="211"></pb>that the Natural <emph type="italics"></emph>Dcorſum<emph.end type="italics"></emph.end> do likewiſe keep its tenour of continu<lb></lb>ally Accelerating according to a proportion double to the Times; <lb></lb>and that thoſe Motions and their Velocities in mingling be not al<lb></lb>tered, diſturbed, and impeded, ſo that finally the Line of the Pro<lb></lb>ject do not in the continuation of the Motion degenerate into an<lb></lb>other kind; a thing which ſeemeth to me to be impoſſible. </s> <s>For, in <lb></lb>regard that the Axis of our Parabola, according to which we ſup<lb></lb>poſe the Natural Motion of Graves to be made, being Perpendicu<lb></lb>lar to the Horizon, doth terminate in the Center of the Earth; and <lb></lb>in regard that the Parabolical Line doth ſucceſſively enlarge from <lb></lb>its Axis, no Project would ever come to terminate in the Center, or <lb></lb>if it ſhould come thitherwards, as it ſeemeth neceſſary that it muſt, <lb></lb>the Line of the Project ſhould deſcribe another moſt different from <lb></lb>that of the Parabola.</s></p><p type="main"> <s>SIMP. </s> <s>I add to theſe difficulties ſeveral others; one of which is <lb></lb>that we ſuppoſe, that the Horizontal Plane which hath neither accli<lb></lb>vity or declivity is a Right Line; as if that ſuch a Line were in all <lb></lb>its parts equidiſtant from the Center, which is not true: for depart<lb></lb>ing from its middle it goeth towards the extreams, alwaies more and <lb></lb>more receding from the Center, and therefore alwaies aſcending: <lb></lb>which of conſequence rendereth it Impoſſible that its Motion <lb></lb>ſhould be perpetual, or that it ſhould for any time continue Equa<lb></lb>ble, and neceſſitates it to grow continually more and more weak. <lb></lb></s> <s>Moreover, it is, in my Opinion, impoſſible to avoid the Impedi<lb></lb>ment of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> but that it will take away the Equability of <lb></lb>the Tranſverſe Motion, and the Rule of the Acceleration in falling <lb></lb>Grave Bodies. </s> <s>By all which difficulties it is rendred very improba<lb></lb>ble that the things demonſtrated with ſuch inconſtant Suppoſi<lb></lb>tions ſhould afterwards hold true in the practical Experiments.</s></p><p type="main"> <s>SALV. </s> <s>All the Objections and Difficulties alledged are ſo <lb></lb>well grounded, that I eſteem it impoſſible to remove them; and <lb></lb>for my own part I admit them all, as alſo I believe the Author <lb></lb>himſelf would do. </s> <s>And I grant that the Concluſions thus demon<lb></lb>ſtrated in Abſtract, do alter and prove falſe, and that ſo egregiouſ<lb></lb>ly, in Concrete, that neither is the Tranſverſe Motion Equable, <lb></lb>nor is the Acceleration of the Natural in the proportion ſuppoſe, <lb></lb>nor is the Line of the Project Parabolical, <emph type="italics"></emph>&c. </s> <s>B<emph.end type="italics"></emph.end>ut yet on the <lb></lb>contrary, I deſire that you would not ſcruple to grant to this our <lb></lb>Author that which other famous Men have ſuppoſed, although <lb></lb>falſe. </s> <s>And the ſingle Authority of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> may ſatisfie every <lb></lb>one: who in his Mechanicks, and in the firſt Quadrature of the <lb></lb>Parabola, taketh it as a true Principle, that the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>eam of the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>allance <lb></lb>or Stilliard is a Right Line in all its points equidiſtant from the <lb></lb>Common Center of Grave <emph type="italics"></emph>B<emph.end type="italics"></emph.end>odies, and that the Scale-ropes, to <lb></lb>which the Weights are hanged, are parallel to one another. </s> <s>Which <pb xlink:href="040/01/905.jpg" pagenum="212"></pb>Liberty of his hath been excuſed by ſome, for that in our practices <lb></lb>the Inſtruments we uſe, and the Diſtances which we take are ſo <lb></lb>ſmall in compariſon of our great remoteneſs from the Center of <lb></lb>the Terreſtrial Globe, that we may very well take a Minute of a <lb></lb>degree of the great Circle as if it were a Right Line, and two Per<lb></lb>pendiculars that ſhould hang at its extreams as if they were Paral<lb></lb>lels. </s> <s>For if we were in practical Operations to keep account of <lb></lb>ſuch like Minutes, we ſhould begin to reprove the Architects, who <lb></lb>with the Plumb Line ſuppoſe that they raiſe very high Towers <lb></lb>between Lines equidiſtant. </s> <s>And I here add, that we may ſay that <lb></lb><emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> and others ſuppoſe in their Contemplations that they <lb></lb>were conſtituted remote at an infinite diſtance from the Center; <lb></lb>in which caſe their Aſſumptions were not falſe: And that therefore <lb></lb>they did conclude by Abſolute Demonſtration. </s> <s>Again, if we will <lb></lb>practice the demonſtrated Concluſions in terminate Diſtances, by <lb></lb>ſuppoſing an immenſe Diſtance, we ought to defalk from the <lb></lb>truth demonſtrated that which our Diſtance from the Center doth <lb></lb>import, not being really infinite, but yet ſuch as that it may be <lb></lb>termed Immenſe in compariſon of the Artifices that we make uſe <lb></lb>of, the greateſt of which will be the Ranges of Projects, and amongſt <lb></lb>theſe that only of Canon ſhot; which though it be great, yet ſhall <lb></lb>it not exceed four of thoſe Miles of which we are remote from the <lb></lb>Center well-nigh ſo many thouſands: and theſe coming to deter<lb></lb>mine in the Surface of the Terreſtrial Globe may very well only in<lb></lb>ſenſibly alter that Parabolick Figure, which we grant would be <lb></lb>extreamly transformed in going to determine in the Center. </s> <s>In <lb></lb>the next place as to the perturbation proceeding from the Impedi<lb></lb>ment of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> this is more conſiderable, and, by reaſon of <lb></lb>its ſo great multiplicity of Varieties, incapable of being brought <lb></lb>under any certain Rules, and reduced to a Science: for if we <lb></lb>ſhould propoſe to conſideration no more but the Impediment which <lb></lb>the Air procureth to the Motions conſidered by us, this alone ſhall <lb></lb>be found to diſturb all, and that infinite waies, according as we <lb></lb>infinite waies vary the Figures, Gravities, and Velocities of the <lb></lb>Moveables. </s> <s>For as to the Velocity, according as this ſhall be grea<lb></lb>ter, the greater ſhall the oppoſition be that the Air makes againſt <lb></lb>them, which ſhall yet more impede the ſaid Moveable according as <lb></lb>they are leſs Grave: ſo that although the deſcending Grave Body <lb></lb>ought to go Accelerating in a duplicate proportion to the Duration <lb></lb>of its Motion, yet nevertheleſs, albeit the Moveable were very <lb></lb>Grave, in coming from very great heights, the Impediment of the <lb></lb>Air ſhall be ſo great, as that it will take from it all power of far<lb></lb>ther encreaſing its Velocity, and will reduce it to an Uniform and <lb></lb>Equable Motion: And this Adequation ſhall be ſo much the ſooner <lb></lb>obtained, and in ſo much leſſer heights, by how much the Moveable <pb xlink:href="040/01/906.jpg" pagenum="213"></pb>ſhall be leſs Grave. </s> <s>That Motion alſo which along the Horizontal <lb></lb>Plane, all other Obſtacles being removed, ought to be Equable <lb></lb>and perpetual, ſhall come to be altered, and in the end arreſted by <lb></lb>the Impediment of the Air: and here likewiſe ſo much the ſooner, <lb></lb>by how much the Moveable ſhall be Lighter. </s> <s>Of which Accidents <lb></lb>of Gravity, of Velocity, and alſo of Figure, as being varied ſeve<lb></lb>ral waies, there can no fixed Science be given. </s> <s>And therefore that <lb></lb>we may be able Scientifically to treat of this Matter it is requiſite <lb></lb>that we abſtract from them; and, having found and demonſtrated <lb></lb>the Concluſions abſtracted from the Impediments, that we make <lb></lb>uſe of them in practice with thoſe Limitations that Experience ſhall <lb></lb>from time to time ſhew us. </s> <s>And yet nevertheleſs the benefit ſhall <lb></lb>not be ſmall, becauſe ſuch Matters, and their Figures ſhall be made <lb></lb>choice of as are leſs ſubject to the Impediments of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end>; <lb></lb>ſuch are the very Grave, the Rotund: and the Spaces, and the <lb></lb>Velocities for the moſt part will not be ſo great, but that their ex<lb></lb>orbitances may with eaſie ^{*} Allowance be reduced to a certainty. <lb></lb><arrow.to.target n="marg1095"></arrow.to.target><lb></lb>Yea more, in Projects practicable by us, that are of Grave Matters, <lb></lb>and of Round Figure, and alſo that are of Matters leſſe Grave, <lb></lb>and of Cylindrical Figure, as Arrows, ſhot from Slings or Bows, <lb></lb>the variation of their Motion from the exact Parabolical Figure <lb></lb>ſhall be altogether inſenſible. </s> <s>Nay, (and I will aſſume to my ſelf <lb></lb>a little more freedom) that in ^{*} Inſtruments that are practicable by <lb></lb><arrow.to.target n="marg1096"></arrow.to.target><lb></lb>us, their ſmalneſs rendreth the extern and accidental Impediments, <lb></lb>of which that of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> is moſt conſiderable, to be but of <lb></lb>very ſmall note, I am able by two experiments to make manifeſt. <lb></lb></s> <s>I will conſider the Motions made thorow the Air, for ſuch are thoſe <lb></lb>chiefly of which we ſpeak: againſt which the ſaid Air in two man<lb></lb>ners exerciſeth its power. </s> <s>The one is by more impeding the Movea<lb></lb>bles leſs Grave, than thoſe very Grave. </s> <s>The other is in more oppo<lb></lb>ſing the greater than the leſs Velocity of the ſame Moveable. </s> <s>As <lb></lb>to the firſt; Experience ſhewing us that two Balls of equal <lb></lb>bigneſs, but in weight one ten or twelve times more Grave than the <lb></lb>other, as, for example, one of Lead and another of Oak would <lb></lb>be, deſcending from an height of 150, or 200 Yards, arrive to the <lb></lb>Earth with Velocity very little different, it aſſureth us that the Im<lb></lb>pediment or Retardment of the Air in both is very ſmall: for if <lb></lb>the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>all of Lead departing from on high in the ſame Moment with <lb></lb>that of Wood, were but little retarded, and this much, the Lead at <lb></lb>its coming to the ground ſhould leave the Wood a very conſidera<lb></lb>ble Space behind, ſince it is ten times more Grave; which never<lb></lb>theleſs doth not happen: nay, its Anticipation ſhall not be ſo <lb></lb>much as the hundredth part of the whole height. </s> <s>And between a <lb></lb><emph type="italics"></emph>B<emph.end type="italics"></emph.end>all of Lead, and another of Stone which weighs a third part, or <lb></lb>half ſo much as it, the difference of the Times of their coming to <pb xlink:href="040/01/907.jpg" pagenum="214"></pb>the ground would be hardly obſervable. </s> <s>Now becauſe the <emph type="italics"></emph>Impe<lb></lb>tus<emph.end type="italics"></emph.end> that a <emph type="italics"></emph>B<emph.end type="italics"></emph.end>all of Lead acquireth in falling from an height of 200 <lb></lb>Yards (which is ſo much that continuing it in an Equable Moti<lb></lb>on it would in a like Time run 400 Yards) is very conſiderable in <lb></lb>compariſon of the Velocity that we confer with <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ows or other Ma<lb></lb>chines, upon our Projects (excepting the <emph type="italics"></emph>Impetus's<emph.end type="italics"></emph.end> that depend <lb></lb>on the Fire) we may without any notable Errour conclude and <lb></lb>account the Propoſitions to be abſolutely true that are demonſtra<lb></lb>ted without any regard had to the alteration of the <emph type="italics"></emph>Medium.<emph.end type="italics"></emph.end> In <lb></lb>the next place as touching the other part, that is to ſhew, that the <lb></lb>Impediment that the ſaid Moveable receiveth from the Air whilſt <lb></lb>it moveth with great Velocity is not much greater than that which <lb></lb>oppoſeth it in moving ſlowly, the enſuing Experiment giveth us <lb></lb>full aſſurance of it. </s> <s>Suſpend by two threads both of the ſame <lb></lb>length, <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> four or five Yards, two equal <emph type="italics"></emph>B<emph.end type="italics"></emph.end>alls of Lead: and <lb></lb>having faſtned the ſaid threads on high, let both the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>alls be re<lb></lb>moved from the ſtate of Perpendicularity; but let the one be re<lb></lb>moved 80. or more degrees, and the other not above 4 or 5: ſo <lb></lb>that one of them being left at liberty deſcendeth, and paſſing be<lb></lb>yond the Perpendicular, deſcribeth very great Arches of 160, 150, <lb></lb>140, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> degrees, diminiſhing them by little and little: but the <lb></lb>other ſwinging freely paſſeth little Arches of 10, 8, 6, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> this <lb></lb>alſo diminiſhing them in like manner by little and little. </s> <s>Here I <lb></lb>ſay, in the firſt place, that the firſt <emph type="italics"></emph>B<emph.end type="italics"></emph.end>all ſhall paſs its 180, 160, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end><lb></lb>degrees in as much Time as the other doth its 10, 8, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> From <lb></lb>whence it is manifeſt, that the Velocity of the firſt <emph type="italics"></emph>B<emph.end type="italics"></emph.end>all ſhall be 16 <lb></lb>and 18 times greater than the Velocity of the ſecond: ſo that in <lb></lb>caſe the greater Velocity were to be more impeded by the Air than <lb></lb><arrow.to.target n="marg1097"></arrow.to.target><lb></lb>the leſſer, the Vibrations ſhould be more ^{*} rare in the greateſt <lb></lb>Arches of 180, or 160 degrees, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> than in the leaſt of 10, 8, 4, <lb></lb>and alſo of 2, and of 1; but this is contradicted by Experience: <lb></lb>for if two Aſſiſtants ſhall ſet themſelves to count the Vibrations, <lb></lb>one the greateſt, the other the leaſt, they will find that they ſhall <lb></lb>number not only tens, but hundreds alſo, without diſagreeing one <lb></lb>ſingle Vibration, yea, or one ſole point. </s> <s>And this obſervati<lb></lb>on joyntly aſſureth us of the two Propoſitions, namely, that the <lb></lb>greateſt and leaſt Vibrations are all made one after another under <lb></lb>equal Times, and that the Impediment and Retardment of the Air <lb></lb>operates no more in the ſwifteſt Motion, than in the ſloweſt: <lb></lb>contrary to that which before it ſeemed that we our ſelves alſo <lb></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 ſewer.</s></p><p type="main"> <s>SAGR. Rather, becauſe it cannot be denied but that the Air <lb></lb>impedeth both thoſe and theſe, ſince they both continually grow <lb></lb>more languid, and at laſt ceaſe, it is requiſite to ſay that thoſe Re<lb></lb>tardations are made with the ſame proportion in the one and in the <pb xlink:href="040/01/908.jpg" pagenum="215"></pb>other Operation. </s> <s>And then, the being to make greater Reſiſtance <lb></lb>at one time than at another, from what other doth it proceed, but <lb></lb>only from its being aſſailed at one time with a greater <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> and <lb></lb>Velocity, and at another time with leſſer? </s> <s>And if this be ſo then the <lb></lb>ſame quantity of the Velocity of the Moveable is at once the Cauſe <lb></lb>and the Mealure of the quantity of the Reſiſtance. </s> <s>Therefore all <lb></lb>Motions, whether they be ſlow or ſwift, are retarded and impe<lb></lb>ded in the ſame proportion: a Notion in my judgment not con<lb></lb>temptible.</s></p><p type="main"> <s>SALV. </s> <s>We may alſo in this ſecond caſe conclude, That the <lb></lb>Fallacies in the Concluſions, which are demonſtrated, abſtracting <lb></lb>from the extern Accidents, are in our Inſtruments of very ſmall <lb></lb>conſideration, in reſpect of the Motions of great Velocities of <lb></lb>which for the moſt part we ſpeak, and of the Diſtances which are <lb></lb>but very ſmall in relation to the Semidiameter and great Circles of <lb></lb>the Terreſtrial Globe.</s></p><p type="main"> <s>SIMP. </s> <s>I would gladly hear the reaſon why you ſequeſtrate <lb></lb>the Projects from the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the Fire, that is, as I conceive from <lb></lb>the force of the Powder, from the other Projects made by Slings, <lb></lb>Bows, or Croſs-bows, touching their not being in the ſame manner <lb></lb>ſubject to the Acceleration and Impediment of the Air.</s></p><p type="main"> <s>SALV. </s> <s>I am induced thereto by the exceſſive, and, as I may ſay, <lb></lb>Supernatural Fury or Impetuouſneſs with which thoſe Projects are <lb></lb>driven out: For indeed I think that the Velocity with which a <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ul<lb></lb>let is ſhot out of a Musket or Piece of Ordinance may without any <lb></lb>Hyperbole be called Supernatural. </s> <s>For one of thoſe <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ullets de<lb></lb>ſcending naturally thorow the Air from ſome immenſe height, its <lb></lb>Velocity, by reaſon of the Reſiſtance of the Air will not go in<lb></lb>creaſing perpetually: but that which in Cadent <emph type="italics"></emph>B<emph.end type="italics"></emph.end>odies of ſmall <lb></lb>Gravity is ſeen to happen in no very great ^{*} Space, I mean their <lb></lb><arrow.to.target n="marg1098"></arrow.to.target><lb></lb>being reduced in the end to an Equable Motion, ſhall alſo happen <lb></lb>after a Deſcent of thouſands of yards, in a <emph type="italics"></emph>B<emph.end type="italics"></emph.end>all of Iron or Lead: <lb></lb>and this determinate and ultimate Velocity may be ſaid to be the <lb></lb>greateſt that ſuch a <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ody can obtain or acquire thorow the Air: <lb></lb>which Velocity I account to be much leſſer than that which cometh <lb></lb>to be impreſſed on the ſame <emph type="italics"></emph>B<emph.end type="italics"></emph.end>all by the fired Powder. </s> <s>And of this <lb></lb>a very appoſite Experiment may advertiſe us. </s> <s>At an height of an <lb></lb>hundred or more yards let off a Musket charged with a Leaden <lb></lb><emph type="italics"></emph>B<emph.end type="italics"></emph.end>ullet perpendicularly downwards upon a Pavement of Stone; and <lb></lb>with the ſame Musket ſhoot againſt ſuch another Stone at the Di<lb></lb>ſtance of a yard or two, and then ſee which of the two <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ullets is <lb></lb>more flatted: for if that coming from on high be leſs ^{*} dented than <lb></lb><arrow.to.target n="marg1099"></arrow.to.target><lb></lb>the other, it ſhall be a ſign that the Air hath impeded it, and dimi<lb></lb>niſhed the Velocity conferred upon it by the Fire in the beginning <lb></lb>of the Motion: and that, conſequently, ſo great a Velocity the Air <pb xlink:href="040/01/909.jpg" pagenum="216"></pb>would not ſuffer it to gain coming from never ſo great an height: <lb></lb>for in caſe the Velocity impreſſed upon it by the Fire ſhould not <lb></lb>exceed that which it might acquire of its ſelf deſcending naturally, <lb></lb>the battery downwards ought rather to be more valid than leſs. <lb></lb></s> <s>I have not made ſuch an Experiment, but incline to think that a <lb></lb>Musket or Cannon Bullet falling from never ſo great an height, <lb></lb>will not make that percuſſion which it maketh in a Wall at a Di<lb></lb>ſtance of a few yards, that is of ſo few that the ſhort perforation, <lb></lb>or, if you will, Sciſſure to be made in the Air ſufficeth not to ob<lb></lb>viate the exceſs of the ſupernatural impetuoſity impreſſed on it by <lb></lb>the Fire. </s> <s>This exceſſive <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of ſuch like forced ſhots may <lb></lb>cauſe ſome deformity in the Line of the Projection; making <lb></lb>the beginning of the Parabola leſs inclined or curved than the end. <lb></lb><emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut this can be but of little or no prejudice to our Author in <lb></lb>practical Operations: amongſt the which the principal is the com<lb></lb>poſition of a Table for the Ranges, or Flights, which containeth <lb></lb>the diſtances of the Falls of <emph type="italics"></emph>B<emph.end type="italics"></emph.end>alls ſhot according to all Elevations. <lb></lb></s> <s>And becauſe theſe kinds of Projections are made with Mortar<lb></lb>Pieces, and with no great charge; in theſe the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> not being <lb></lb>ſupernatural, the Ranges deſcribe 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"></emph>B<emph.end type="italics"></emph.end>ut for the preſent let us proceed forwards in the Treatiſe, <lb></lb>where the Author deſireth to lead us to the Contemplation and <lb></lb>Inveſtigation of the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the Moveable whilſt it moveth <lb></lb>with a Motion compounded of two. </s> <s>And firſt of that compoun<lb></lb>ded of two Equable Motions; the one Horizontal, and the other <lb></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></lb>ble Motion, that is, Horizontal and Perpen<lb></lb>dicular, the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> or Moment of the Lation <lb></lb>compounded of both the Motions ſhall be <emph type="italics"></emph>po<lb></lb>tentia<emph.end type="italics"></emph.end> equal to both the Moments of the firſt <lb></lb>Motions.</s></p><p type="main"> <s><emph type="italics"></emph>For let any Moveable be moved Equably with a double Lation, <lb></lb>and let the Mutations of the Perpendicular anſwer to the Space <lb></lb>A B, and let B C anſwer to the Horizontal Lation paſſed in <lb></lb>the ſame Time. </s> <s>Foraſmuch therefore as the Spa-<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.909.1.jpg" xlink:href="040/01/909/1.jpg"></figure><lb></lb><emph type="italics"></emph>ces A B, and B C are paſſed by the Equable Mo<lb></lb>tion in the ſame Time, their Moments ſhall be to <lb></lb>cach other as the ſaid A B and B C. </s> <s>But the <lb></lb>Moveable which is moved according to theſe two Mutations ſhall de-<emph.end type="italics"></emph.end><pb xlink:href="040/01/910.jpg" pagenum="217"></pb><emph type="italics"></emph>ſcribe the Diagonal A C, and its Moment ſhall be as A C. </s> <s>But A C is<emph.end type="italics"></emph.end><lb></lb>potentia <emph type="italics"></emph>equal to the ſaid A B and B C: therefore the Moment com<lb></lb>pounded of both the Moments A B and B C, is<emph.end type="italics"></emph.end> potentia <emph type="italics"></emph>equal to them <lb></lb>both taken together: Which was to be demonſtrated.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SIMP. </s> <s>It is neceſſary that you eaſe me of one Scruple that <lb></lb>cometh into my mind, it ſeemeth to me that this which is now con<lb></lb>cluded oppugneth another Propoſition of the former Tractate: in <lb></lb>which it is affirmed, That the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the Moveable coming <lb></lb>from A into B is equal to that coming from A into C; and now it is <lb></lb>concluded, that the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> in C is greater than that in B.</s></p><p type="main"> <s>SALV. </s> <s>The Propoſitions, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> are both true, but very <lb></lb>different from one another. </s> <s>Here the Author ſpeaks of one ſole <lb></lb>Moveable moved with one ſole Motion, but compounded of two, <lb></lb>both Equable; and there he ſpeaks of two Moveables moved <lb></lb>with Motions Naturally Accelerated, one along the Perpendicular <lb></lb>A B, and the other along the Inclined Plane A C: and moreover, <lb></lb>the Times there are not ſuppoſed equal, but the Time along <lb></lb>the Inclined Plane A C is greater than the Time along the Perpen<lb></lb>dicular A B: but in the Motion ſpoken of at preſent, the Motions <lb></lb>along A B, B C and A C are underſtood to be Equable, and made <lb></lb>in the ſame Time.</s></p><p type="main"> <s>SIMP. </s> <s>Excuſe me, and go on, for I am ſatisfied.</s></p><p type="main"> <s>SALV. </s> <s>The Author proceeds to ſhew us that which hapneth <lb></lb>concerning the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of a Moveable moved in like manner with <lb></lb>one Motion compounded of two, that is to ſay, the one Horizon<lb></lb>tal and Equable, and the other Perpendicular but Naturally-Acce<lb></lb>lerate, of which in fine the Motion of the Project is compounded, <lb></lb>and by which the Parabolick Line is deſcribed; in each point of <lb></lb>which the Author endeavours to determine what the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the <lb></lb>Project is; for underſtanding of which he ſheweth us the manner, <lb></lb>or, if you will, Method of regulating and meaſuring that ſame <emph type="italics"></emph>Im<lb></lb>petus<emph.end type="italics"></emph.end> upon the ſaid Line, along which the Motion of the Grave <lb></lb>Moveable deſcending with a Natural-Accelerate Motion departing <lb></lb>from Reſt is made, ſaying:</s></p><p type="head"> <s>THEOR. III. PROP. III.</s></p><p type="main"> <s><emph type="italics"></emph>Let a Motion be made along the Line A B out of Reſt in A, and <lb></lb>take in ſome point C; and ſuppoſe the ſaid A C to be the Time or <lb></lb>Meaſure of the Time of the ſaid Fall along the Space A C, as alſo <lb></lb>the Meaſure of the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>or Moment in the Point C acquired by <lb></lb>the Deſcent along A C. </s> <s>Now let there be taken in the ſaid Line <lb></lb>A B any other Point, as ſuppoſe B, in which we are to determine of the<emph.end type="italics"></emph.end><lb></lb>Impetus <emph type="italics"></emph>acquired by the Moveable along the Fall A B, in proportion to<emph.end type="italics"></emph.end><pb xlink:href="040/01/911.jpg" pagenum="218"></pb><emph type="italics"></emph>the<emph.end type="italics"></emph.end> Impetus, <emph type="italics"></emph>which it obtaineth in C, whoſe Meaſure is ſuppoſed to be <lb></lb>A C, Let A S be a Mean-proportional betwixt B A and A C. </s> <s>We will <lb></lb>demonſtrate that the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>in B is to the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>in C, as S A is to <lb></lb>A C. </s> <s>Let the Horizontal Line C D be double to the ſaid A C; and B E <lb></lb>double to B A. </s> <s>It appeareth by what hath been demonſtrated, That the <lb></lb>Cadent along A C being turned along the Horizon C D, and according <lb></lb>to the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>acquired in C, with an Equable Motion, ſhall paſs the <lb></lb>Space C D in a Time equal to that <lb></lb>in which the ſaid A C is paſſed<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.911.1.jpg" xlink:href="040/01/911/1.jpg"></figure><lb></lb><emph type="italics"></emph>with an Accelerate Motion; and <lb></lb>likewiſe that B E is paſſed in the <lb></lb>ſame time as A B: But the Time of <lb></lb>the Deſcent along A B is A S: There<lb></lb>fore the Horizontal Line B E is <lb></lb>paſſed in A S. </s> <s>As the Time S A is <lb></lb>to the Time A C, ſo let E B be to <lb></lb>B L. </s> <s>And becauſe the Motion by <lb></lb>B E is Equable, the Space B L ſhall be paſſed in the Time A C ac<lb></lb>cording to the Moment of Celerity in B: But in the ſame Time A C <lb></lb>the Space C D is paſſed, according to the Moment of Velocity in C: <lb></lb>the Moments of Velocity therefore are to one another as the Spaces <lb></lb>which according to the ſame Moments are paſſed in the ſame Time: <lb></lb>Therefore the Moment of Velocity in C is to the Moment of Celerity in <lb></lb>B, as D C is to B L. </s> <s>And becauſe as D C is to B E, ſo are their halfs, <lb></lb>to wit, C A to A B: but as E B is to B L, ſo is B A to A S: Therefore,<emph.end type="italics"></emph.end><lb></lb>exæquali, <emph type="italics"></emph>as D C is to B L, ſo is C A to A S: that is, as the Moment <lb></lb>of Velocity in C is to the Moment of Velocity in B, ſo is C A to A S; that <lb></lb>is, the Time along C A to the Time along A B. </s> <s>I he manner of Meaſu<lb></lb>ring the<emph.end type="italics"></emph.end> Impetus, <emph type="italics"></emph>or the Moment of Velocity upon a Line along which it <lb></lb>makes a Motion of Deſcent is therefore manifeſt; which<emph.end type="italics"></emph.end> Impetus <lb></lb><emph type="italics"></emph>is indeed ſuppoſed to encreaſe according to the Proportion of the <lb></lb>Time.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>But this, before we proceed any farther, is to be premoniſhed, that in <lb></lb>regard we are to ſpeak for the future of the Motion compounded of the <lb></lb>Equable Horizontal, and of the Naturally Accelerate downwards, (for <lb></lb>from this Mixtion reſults, and by it is deſigned the Line of the Project, <lb></lb>that is a Parabola;) it is neceſſary that we define ſome common meaſure <lb></lb>according to which we may meaſure the Velocity,<emph.end type="italics"></emph.end> Impetus, <emph type="italics"></emph>or Moment <lb></lb>of both the Motions. </s> <s>And ſeeing that of the Equable Motion the de<lb></lb>grees of Velocity are innumerable, of which you may not take any <lb></lb>promiſcuouſly, but one certain one which may be be compared and con<lb></lb>joyned with the Degree of Velocity naturally Accelerate. </s> <s>I can think of <lb></lb>no more eaſie way for the electing and determining of that, than by aſ<lb></lb>ſuming another of the ſame kind. </s> <s>And that I may the better expreſs <lb></lb>my meaning; Let A C be Perpendicular to the Horizon C B; and A C<emph.end type="italics"></emph.end><pb xlink:href="040/01/912.jpg" pagenum="219"></pb><emph type="italics"></emph>to be the Altitude, and C B the Amplitude of the Semiparabola A B; <lb></lb>which is deſcribed by the Compoſition of two Lations; of which one is <lb></lb>that of the Moveable deſcending along A C with a Motion Naturally <lb></lb>Acceler ate<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in A; the other is the Equable Tranſverſal Moti<lb></lb>on according to the Horizontal Line A D. The<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>acquired in C <lb></lb>along the Deſcent A C is determined by the quantity of the ſaid height <lb></lb>A C; for the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>of a Moveable<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.912.1.jpg" xlink:href="040/01/912/1.jpg"></figure><lb></lb><emph type="italics"></emph>falling from the ſame height is alwaies <lb></lb>one and the ſame: but in the Horizontal <lb></lb>Line one may aſſign not one, but innume<lb></lb>rable Degrees of Velocities of Equable <lb></lb>Motions: out of which multitude that I <lb></lb>may ſingle out, and as it were point with <lb></lb>the finger to that which I make choice of, <lb></lb>I extend or prolong the Altitude C A<emph.end type="italics"></emph.end> in <lb></lb>ſublimi, <emph type="italics"></emph>in which, as was done before, I <lb></lb>will pitch upon A E; from which if I <lb></lb>conceive in my mind a Moveable to fall<emph.end type="italics"></emph.end><lb></lb>ex quiete <emph type="italics"></emph>in E, it appeareth that its<emph.end type="italics"></emph.end> Im<lb></lb>petus <emph type="italics"></emph>acquired in the Time A, is one with which I conceive the ſame <lb></lb>Moveable being turned along A D to be moved; and its degree of <lb></lb>Vclocity to be that, which in the Time of the Deſcent along E A paſſeth <lb></lb>a Space in the Horizon double to the ſaid E A. </s> <s>This Præmonition I <lb></lb>judged neceſſary.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>It is moreover to be advertized that the Amplitude of the Semi<lb></lb>parabola A B ſhall be called by me the Horizontal Line<emph.end type="italics"></emph.end> [or Plane] <lb></lb><emph type="italics"></emph>C B.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>The Altitude, to with A C, the Axis of the ſaid Parabola.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>And the Line E A, by whoſe Deſcent the Horizontal<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>is de<lb></lb>termined, I call the Sublimity, or height.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Theſe things being declared and defined, I proceed to Demonſtra<lb></lb>tion.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. Stay, I pray you, for here me thinks it is convenient to <lb></lb>adorn this Opinion of our Author with the conformity of it to <lb></lb>the Conceit of <emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> about the determining the different Veloci<lb></lb>ties of the Equable Motions of the Revolutions of the Cœleſtial <lb></lb>Bodies; who, having perhaps had a conjecture that no Moveable <lb></lb>could paſſe from Reſt into any determinate degree of Velocity in <lb></lb>which it ought afterwards to be perpetuated, unleſs by paſſing <lb></lb>thorow all the other leſſer degrees of Velocity, or, if you will, <lb></lb>greater degrees of Tardity, which interpoſe between the aſſigned <lb></lb>degree, and the higheſt degree of Tardity, that is of Reſt, ſaid that <lb></lb>God after he had created the Moveable Cœleſtial <emph type="italics"></emph>B<emph.end type="italics"></emph.end>odies that he <lb></lb>might aſſign them thoſe Velocities wherewith they were afterwards <pb xlink:href="040/01/913.jpg" pagenum="220"></pb>to be perpetually moved with an Equable Circular Motion, made <lb></lb>them, they departing from Reſt, to move along determinate Spaces <lb></lb>with that Natural Motion in a Right Line, according to which we <lb></lb>ſenſibly ſee our Moveables to move from the ſtate of Reſt ſucceſ<lb></lb>ſively Accelerating. </s> <s>And he addeth, that having made them to <lb></lb>acquire that degree in which it pleaſed him that they ſhould after<lb></lb>wards be perpetually conſerved, he converted their Right or direct <lb></lb>Motion into Circular; which only is apt to conſerve it ſelf Equa<lb></lb>ble, alwaies revolving without receding from, or approaching to <lb></lb>any prefixed term by them deſired. </s> <s>The Conceit is truly worthy <lb></lb>of <emph type="italics"></emph>Plato<emph.end type="italics"></emph.end>; and is the more to be eſteemed in that the grounds there<lb></lb>of paſſed over in ſilence by him, and diſcovered by our Author by <lb></lb>taking off the Mask or Poetick Repreſentation, do ſhew it to be <lb></lb>in its native aſpect a true Hiſtory. </s> <s>And I think it very credible that <lb></lb>we having by the Doctrine of Aſtronomy ſufficiently competent <lb></lb>Knowledge of the Magnitudes of the Orbes of the Planets, and of <lb></lb>their Diſtances from the Center about which they move, as alſo <lb></lb>of their Velocities, our Author (to whom <emph type="italics"></emph>Plato's<emph.end type="italics"></emph.end> Conjecture was <lb></lb>not unknown) may ſometime for his curioſity have had ſome <lb></lb>thought of attempting to inveſtigate whether one might aſſign a <lb></lb>determinate Sublimity from which the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>odies of the Planets depar<lb></lb>ting, as from a ſtate of Reſt, and moved for certain Spaces with a <lb></lb>Right and Naturally Accelerate Motion, afterwards converting <lb></lb>the Acquired Velocity into Equable Motions, they might be found <lb></lb>to correſpond with the greatneſs of their Orbes, and with the Times <lb></lb>of their Revolutions.</s></p><p type="main"> <s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>ALV. </s> <s>I think I do remember that he hath heretofore told me, <lb></lb>that he had once made the Computation, and alſo that he found <lb></lb>it exactly to anſwer the Obſervations; but that he had no mind to <lb></lb>ſpeak of them, doubting leſt the two many Novelties by him diſ<lb></lb>covered, which had provoked the diſpleaſure of many againſt him, <lb></lb>might blow up new ſparks. <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut if any one ſhall have the like de<lb></lb>ſire he may of himſelf by the Doctrine of the preſent Tract give <lb></lb>himſelf content. <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut let us purſue our buſineſs, which is to <lb></lb>ſhew;</s></p><p type="head"> <s>PROBL. I. PROP. IV.</s></p><p type="main"> <s>How in a Parabola given, deſcribed by the Pro<lb></lb>ject, the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of each ſeveral point may be <lb></lb>determined.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Semiparabola be B E C, whoſe Amplitude is C D and Al<lb></lb>titude D B, with which continued out on high the Tangent of the <lb></lb>Parabola C A meeteth in A; and along the<emph.end type="italics"></emph.end> Vertex <emph type="italics"></emph>B let B I be<emph.end type="italics"></emph.end><pb xlink:href="040/01/914.jpg" pagenum="221"></pb><emph type="italics"></emph>an Horizontal Line, and parallel to C D. </s> <s>And if the Amplitude C D <lb></lb>be equal to the whole Altitude D A, B I ſhall be equal to B A and B D. <lb></lb></s> <s>And if the Time of the Fall along A B, and the Moment of Velocity <lb></lb>acquired in B along the Deſcent A B<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in A be ſuppoſed to be <lb></lb>meaſured by the ſaid A B, then D C (that is twice B I) ſhall be the <lb></lb>Space which ſhall be paſſed by the<emph.end type="italics"></emph.end> Impetus A <emph type="italics"></emph>B turned along the Hori<lb></lb>zontal Line in the ſame Time: But in the ſame Time falling along B D <lb></lb>out of Reſt in B, it ſhall paſs the Altitude B D: Therefore the Movea<lb></lb>ble falling out of Reſt in A along A B, <lb></lb>being converted with the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>A B<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.914.1.jpg" xlink:href="040/01/914/1.jpg"></figure><lb></lb><emph type="italics"></emph>along the Horizontal Parallel ſhall <lb></lb>paſs a Space equal to D C. </s> <s>And the <lb></lb>Fall along B D ſupervening, it paſſeth <lb></lb>the Altitude B D, and deſcribes the <lb></lb>Parabola B C; whoſe<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>in the <lb></lb>Term C is compounded of the Equable <lb></lb>Tranſverſal whoſe Moment is as A B, <lb></lb>and of another Moment acquired in the <lb></lb>Fall B D in the Term D or C; which <lb></lb>Moments are Equal. </s> <s>If therefore we <lb></lb>ſuppoſe A B to be the Meaſure of one of them, as ſuppoſe of the Equa<lb></lb>ble Tranſverſal; and B I, which is equal to B D, to be the Meaſure of <lb></lb>the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>acquired in D or C; then the Subtenſe I A ſhall be the <lb></lb>quantity of the Moment compound of them both: Therefore it ſhall be <lb></lb>the quantity or Meaſure of the whole Moment which the Project deſcend<lb></lb>ing along the Parabola B C ſhall acquire of<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>in C. </s> <s>This pre<lb></lb>miſed, take in the Parabola any point E, in which we are to determine <lb></lb>of the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>of the Project. </s> <s>Draw the Horizontal Parallel E F, <lb></lb>and let B G be a Mean-proportional between B D and B F. </s> <s>And foraſ<lb></lb>much as A B or B D is ſuppoſed to be the Meaſure of the Time, and of <lb></lb>the Moment of the Velocity in the Fall B D<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in B: B G ſhall <lb></lb>be the Time, or the Meaſure of the Time, and of the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>in F, coming <lb></lb>out of B. </s> <s>If therefore B O be ſuppoſed equal to B G, the Diagonal <lb></lb>drawn from A to O ſhall be the quantity of the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>in E; for <lb></lb>A B hath been ſuppoſed the determinator of the Time, and of the<emph.end type="italics"></emph.end> Impe<lb></lb>tus <emph type="italics"></emph>in B, which turned along the Horizontal Parallel doth alwaies <lb></lb>continue the ſame: And B O determineth the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>in F or in E <lb></lb>along the Deſcent<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in B in the Altitude B F: But theſe two <lb></lb>A B and B O are<emph.end type="italics"></emph.end> potentia <emph type="italics"></emph>equal to the Power A O. </s> <s>Therefore that is <lb></lb>manifeſt which was ſought.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>The Contemplation of the Compoſition of theſe diffe<lb></lb>rent <emph type="italics"></emph>Impetus's,<emph.end type="italics"></emph.end> and of the quantity of that <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> which reſults <lb></lb>from this mixture, is ſo new to me, that it leaveth my mind in no <lb></lb>ſmall confuſion. </s> <s>I do not ſpeak of the mixtion of two Motions <pb xlink:href="040/01/915.jpg" pagenum="222"></pb>Equable, though unequal to one another, made the one along the <lb></lb>Horizontal Line, and the other along the Perpendicular, for I very <lb></lb>well comprehend that there is made a Motion of theſe two <emph type="italics"></emph>poten<lb></lb>tia<emph.end type="italics"></emph.end> equal to both the Compounding Motions, but my confuſion <lb></lb>ariſeth upon the mixing of the Equable-Horizontal and Perpendi<lb></lb>cular-Naturally-Accelerate Motion. </s> <s>Therefore I could wiſh we <lb></lb>might toge ther a little better conſider this buſineſs.</s></p><p type="main"> <s>SIMP. </s> <s>And I ſtand the more in need thereof in that I am not <lb></lb>yet ſo well ſatisfied in Mind as I ſhould be, in the Propoſitions that <lb></lb>are the firſt foundations of the others that follow upon them. </s> <s>I <lb></lb>will add, that alſo in the Mixtion of the two Motions Equable <lb></lb>Horizontal, and Perpendicular, I would better underſtand that <lb></lb><emph type="italics"></emph>Potentia<emph.end type="italics"></emph.end> of their Compound. </s> <s>Now, <emph type="italics"></emph>Salviatus,<emph.end type="italics"></emph.end> you ſee what we <lb></lb>want and deſire.</s></p><p type="main"> <s>SALV. </s> <s>Your deſire is very reaſonable: and I will eſſay whe<lb></lb>ther my having had a longer time to think thereon may facilitate <lb></lb>your ſatisfaction. </s> <s>But you muſt bear with and excuſe me if in diſ<lb></lb>courſing I ſhall repeat a great part of the things hitherto delivered <lb></lb>by our Author.</s></p><p type="main"> <s>It is not poſſible for us to ſpeak poſitively touching Motions and <lb></lb>their Velocities or <emph type="italics"></emph>Impetus's,<emph.end type="italics"></emph.end> be they Equable, or be they Naturally <lb></lb>Accelerate, unleſs we firſt agree upon the Meaſure that we are to <lb></lb>uſe in the commenſuration of thoſe Velocities, as alſo of the Time. <lb></lb></s> <s>As to the Meaſure of the Time, we have already that which is <lb></lb>commonly received by all of Hours, Prime-Minutes, and Se<lb></lb>conds, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> and as for the meaſuring of Time we have that com<lb></lb>mon Meaſure received by all, ſo it is requiſite to aſſign another <lb></lb>Meaſure for the Velocities that is commonly underſtood and re<lb></lb>ceived by every one; that is, which every where is the ſame. </s> <s>The <lb></lb>Author, as hath been declared, adjudged the Velocity of Naturally <lb></lb>deſcending Grave-Bodies to be fit for this purpoſe; the encreaſing <lb></lb>Velocities of which are the ſame in all parts of the World. </s> <s>So that <lb></lb>that ſame degree of Velocity which (for example) a Ball of Lead of <lb></lb>a pound acquireth in having, departing from Reſt, deſcended Per<lb></lb>pendicularly as much as the height of a Pike, is alwaies, and in all <lb></lb>places the ſame, and therefore moſt commodious for explicating <lb></lb>the quantity of the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> that is derived from the Natural De<lb></lb>ſcent. </s> <s>Now it remains to find a way to determine likewiſe the <lb></lb>Quantity of the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> in an Equable Motion in ſuch a manner, <lb></lb>that all thoſe which diſcourſe about it may form the ſame conceit <lb></lb>of its greatneſs and Velocity; ſo that one may not imagine it more <lb></lb>ſwift, and another leſs; whereupon afterwards in conjoyning and <lb></lb>mingling this Equable Motion imagined by them with the eſtabli<lb></lb>ſhed Accelerate Motion ſeveral men may form ſeveral Conceits of <lb></lb>ſeveral greatneſſes of <emph type="italics"></emph>Impetus's.<emph.end type="italics"></emph.end> To determine and repreſent this <pb xlink:href="040/01/916.jpg" pagenum="223"></pb><emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> and particular Velocity our Author hath not found any <lb></lb>way more commodious, than the making uſe of the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> which <lb></lb>the Moveable from time to time acquires in the Naturally-Accele<lb></lb>rate Motion, any acquired Moment of which being reduced into <lb></lb>an Equable Motion retaineth its Velocity preciſely limited, and <lb></lb>ſuch, that in ſuch another Time as that wherein it did Deſcend, it <lb></lb>paſſeth double the Space of the Height from whence it fell. </s> <s>But <lb></lb>becauſe this is the principal point in the buſineſs that we are upon, <lb></lb>it is good to make it to be perfectly underſtood by ſome particular <lb></lb>Example. </s> <s>Reaſſuming therefore the Velocity and <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> acqui<lb></lb>red by the Cadent Moveable, as we ſaid before, from the height <lb></lb>of a Pike, of which Velocity we will make uſe for a Meaſure of <lb></lb>other Velocities and <emph type="italics"></emph>Impetuſſes<emph.end type="italics"></emph.end> upon other occaſions, and ſuppo<lb></lb>ſing, for example, that the Time of that Fall be four ſecond Mi<lb></lb>nutes of an hour, to find by this ſame Meaſure how great the <emph type="italics"></emph>Im<lb></lb>petus<emph.end type="italics"></emph.end> of the Moveable would be falling from any other height <lb></lb>greater, or leſſer, we ought not from the proportion that this other <lb></lb>height hath to the height of a Pike to argue and conclude the quan<lb></lb>tity of the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> acquired in this ſecond height, thinking, for <lb></lb>example, that the Moveable falling from quadruple the height <lb></lb>hath acquired quadruple Velocity, for that it is falſe: for that the <lb></lb>Velocity of the Naturally-Accelerate Motion doth not increaſe or <lb></lb>decreaſe according to the proportion of the Spaces, but according <lb></lb>to that of the Times, than which that of the Spaces is greater in a <lb></lb>duplicate proportion, as was heretofore demonſtrated. </s> <s>Therefore <lb></lb>when in a Right Line we have aſſigned a part for the Meaſure of <lb></lb>the Velocity, and alſo of the Time, and of the Space in that Time <lb></lb>paſſed (for that for brevity ſake all theſe three Magnitudes are <lb></lb>often repreſented by one ſole Line,) to find the quantity of the <lb></lb>Time, and the degree of Velocity that the ſame Moveable would <lb></lb>have acquired in another Diſtance we ſhall obtain the ſame, not <lb></lb>immediataly by this ſecond Diſtance, but by the Line which ſhall <lb></lb>be a Mean-proportional betwixt the two Diſtances. </s> <s>But I will <lb></lb>better declare my ſelf by an Example. </s> <s>In the Line A C Perpendi<lb></lb>cular to the Horizon let the part A B be underſtood to <lb></lb>be a Space paſſed by a Moveable naturally deſcending <lb></lb><figure id="id.040.01.916.1.jpg" xlink:href="040/01/916/1.jpg"></figure><lb></lb>with an Accelerate Motion: the Time of which paſ<lb></lb>ſage, in regard I may repreſent it by any Line, I will, for <lb></lb>brevity, imagine it to be as much as the ſame Line A B <lb></lb>and likewiſe for a Meaſure of the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> and Velocity <lb></lb>acquired by that Motion, I again take the ſame Line <lb></lb>A B; ſo that of all the Spaces that are in the progreſs of <lb></lb>the Diſcourſe to be conſidered the part A B may be the <lb></lb>Meaſure. </s> <s>Having all our pleaſure eſtabliſhed under one <lb></lb>ſole Magnitude A B theſe three Meaſures of different kinds of <pb xlink:href="040/01/917.jpg" pagenum="224"></pb>Quantities, that is to ſay, of Spaces, of Times, and of <emph type="italics"></emph>Impetus's,<emph.end type="italics"></emph.end> let <lb></lb>it be required to determine in the aſſigned Space, and at the height <lb></lb>A C, how much the Time of the Fall of the Moveable from A to <lb></lb>C is to be, and what the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> is that ſhall be found to have been <lb></lb>acquired in the ſaid Term C, in relation to the Time and to the <lb></lb><emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> meaſured by A B. </s> <s>Both theſe queſtions ſhall be reſolved <lb></lb>taking A D the Mean-proportional betwixt the two Lines A C <lb></lb>and A B; affirming the Time of the Fall along the whole Space <lb></lb>A C to be as the Time A D is in relation to A B, aſſigned in the <lb></lb>beginning for the Quantity of the Time in the Fall A B. </s> <s>And like<lb></lb>wiſe we will ſay that the <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> or degree of Velocity that the <lb></lb>Cadent Moveable ſhall obtain in the Term C, in relation to the <lb></lb><emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> that it had in B, is as the ſame Line A D is in relation to <lb></lb>A B, being that the Velocity encreaſeth with the ſame proportion <lb></lb>as the Time doth: Which Concluſion although it was aſſumed as <lb></lb>a <emph type="italics"></emph>Poſtulatum,<emph.end type="italics"></emph.end> yet the Author was pleaſed to explain the Applicati<lb></lb>on thereof above in the third Propoſition.</s></p><p type="main"> <s>This point being well underſtood and proved, we come to the <lb></lb>Conſideration of the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> derived from two compound Moti<lb></lb>ons: whereof let one be compounded of the Horizontal and alwaies <lb></lb>Equable, and of the Perpendicular unto the Horizon, and it alſo <lb></lb>Equable: but let the other be compounded of the Horizontal like<lb></lb>wiſe alwaies Equable, and of the Perpendicular Naturally-Accele<lb></lb>rate. </s> <s>If both ſhall be Equable, it hath been ſeen already that the <lb></lb><emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> emerging from the compoſition of both is <emph type="italics"></emph>potentia<emph.end type="italics"></emph.end> equal to <lb></lb>both, as for more plainneſs we will thus Exemplifie. </s> <s>Let the Move<lb></lb>able deſcending along the Perpendicular A B be ſuppoſed to have, <lb></lb>for example, three degrees of Equable <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> but being tranſ<lb></lb>ported along A B towards C, let the ſaid Velocity and <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> be <lb></lb>ſuppoſed four degrees, ſo that in the ſame Time that falling it would <lb></lb>paſs along the Perpendicular, <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> three yards, <lb></lb><figure id="id.040.01.917.1.jpg" xlink:href="040/01/917/1.jpg"></figure><lb></lb>it would in the Horizontal paſs four, but in <lb></lb>that compounded of both the Velocities it <lb></lb>cometh in the ſame Timefrom the point A un<lb></lb>to the Term C, deſcending all the way along the Diagonal Line <lb></lb>A C, which is not ſeven yards long, as that ſhould be which is com<lb></lb>pounded of the two Lines A B, 3, and B C, 4, but is 5; which 5 is <lb></lb><emph type="italics"></emph>potentia<emph.end type="italics"></emph.end> equal to the two others, 3 and 4: For having found the <lb></lb>Squares of 3 and 4, which are 9 and 16, and joyning theſe together, <lb></lb>they make 25 for the Square of A C, which is equal to the two <lb></lb>Squares of A B and B C: whereupon A C ſhall be as much as is the <lb></lb>Side, or, if you will, Root of the Square 25, which is 5. For a conſtant <lb></lb>and certain Rule therefore, when it is required to aſſign the <lb></lb>Quantity of the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> reſulting from two <emph type="italics"></emph>Impetus's<emph.end type="italics"></emph.end> given, the <lb></lb>one Horizontal, and the other Perpendicular, and both Equable, <pb xlink:href="040/01/918.jpg" pagenum="225"></pb>they are each of them to be ſquared, and their Squares being put <lb></lb>together the Root of the Aggregate is to be extracted, which ſhall <lb></lb>give us the quantity of the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> compounded of them both. <lb></lb></s> <s>And thus in the foregoing example, that Moveable that by vertue <lb></lb>of the Perpendicular Motion would have percuſſed upon the Hori<lb></lb>zon with three degrees of Force, and with only the Horizontal Mo<lb></lb>tion would have percuſſed in C with four degrees, percuſſing with <lb></lb>both the <emph type="italics"></emph>Impetus's<emph.end type="italics"></emph.end> conjoyned, the blow ſhall be like to that of the <lb></lb>Percutient moved with five degrees of Velocity and Force. </s> <s>And <lb></lb>this ſame Percuſſion would be of the ſame Impetuoſity in all the <lb></lb>points of the Diagonal A C, for that the compounded <emph type="italics"></emph>Impetus's<emph.end type="italics"></emph.end><lb></lb>are alwaies the ſame, never encreaſing or diminiſhing.</s></p><p type="main"> <s>Let us now ſee what befalls in compounding the Equable Hori<lb></lb>zontal Motion with another Perpendicular to the Horizon which <lb></lb>beginning from Reſt goeth Naturally Accelerating. </s> <s>It is already <lb></lb>manifeſt, that the Diagonal, which is the Line of the Motion com<lb></lb>pounded of theſe two, is not a Right Line, but Semiparabolical, <lb></lb>as hath been demonſtrated; ^{*} in which the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> doth go con<lb></lb><arrow.to.target n="marg1100"></arrow.to.target><lb></lb>tinually encreaſing by means of the continual encreaſe of the Ve<lb></lb>locity of the Perpendicular Motion: Wherefore, to determine what <lb></lb>the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> is in an aſſigned point of that Parabolical Diagonal, it <lb></lb>is requiſite firſt to aſſign the Quantity of the Uniform Horizontal <lb></lb><emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> and then to find what is the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the falling Movea<lb></lb>ble in the point aſſigned: the which cannot be determined without <lb></lb>the conſideration of the Time ſpent from the beginning of the <lb></lb>Compoſition of the two Motions: which Conſideration of the <lb></lb>Time is not required in the Compoſition of Equable Motions, the <lb></lb>Velocities and <emph type="italics"></emph>Impetus's<emph.end type="italics"></emph.end> of which are alwaies the ſame: but here <lb></lb>where there is inſerted into the mixture a Motion which beginning <lb></lb>from extream Tardity goeth encreaſing in Velocity according to <lb></lb>the continuation of the Time, it is neceſſary that the quantity of <lb></lb>the Time do ſhew us the quantity of the degree of Velocity in the <lb></lb>aſſigned point: for, as to the reſt, the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> compounded of theſe <lb></lb>two (as in Uniform Motions) is <emph type="italics"></emph>potentia<emph.end type="italics"></emph.end> equal to both the others <lb></lb>compounding. </s> <s>But here again I will better explain my meaning by <lb></lb>an example. </s> <s>In A C the Perpendicular to the Horizon let any part <lb></lb>be taken A B; the which I will ſuppoſe to ſtand for the Meaſure <lb></lb>of the Space of the Natural Motion made along the ſaid Perpen<lb></lb>dicular, and likewiſe let it be the Meaſure of the Time, and alſo of <lb></lb>the degree of Velocity, or, if you will, of the <emph type="italics"></emph>Impetus's.<emph.end type="italics"></emph.end> It is ma<lb></lb>nifeſt in the firſt place, that if the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the Moveable in B <lb></lb><emph type="italics"></emph>ex quiete<emph.end type="italics"></emph.end> in A ſhall be turned along B D parallel to the Horizon in <lb></lb>an Equable Motion, the quantity of its Velocity ſhall be ſuch that <lb></lb>in the Time A B it ſhall paſs a Space double to the Space A B, which <lb></lb>let be the Line B D. </s> <s>Then let B C be ſuppoſed equal to B A, and <pb xlink:href="040/01/919.jpg" pagenum="226"></pb>let C E be drawn parallel and equal to B D, and thus by the Points <lb></lb>B and E we ſhall deſcribe the Parabolick Line B E I. </s> <s>And becauſe <lb></lb>that in the Time A B with the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> A B the Horizontal Line B D <lb></lb>or C E is paſſed, double to A B, and in ſuch another Time the Per<lb></lb>pendicular B C is paſſed with an acquiſt of <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> in C equal to <lb></lb>the ſaid Horizontal Line; therefore the Moveable in ſuch another <lb></lb>Time as A B ſhall be found to have paſſed from B to E along the <lb></lb>Parabola B E with an <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> compounded of two, each equal to <lb></lb>the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> A B. </s> <s>And becauſe one of them is Horizontal, and the <lb></lb>other Perpendicular, the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> compound of them ſhall be equal <lb></lb>in Power to them both, that is <lb></lb><figure id="id.040.01.919.1.jpg" xlink:href="040/01/919/1.jpg"></figure><lb></lb>double to one of them. </s> <s>So that <lb></lb>ſuppoſing B F equal to B A, and <lb></lb>drawing the Diagonal A F, the <lb></lb><emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> or the Percuſſion in E <lb></lb>ſhall be greater than the Percuſ<lb></lb>ſion in B of the Moveable fal<lb></lb>ling from the Height A, or than <lb></lb>the Percuſſion of the Horizon<lb></lb>tal <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> along B D, according <lb></lb>to the proportion of A F to <lb></lb>A B. </s> <s>But in caſe, ſtill retaining <lb></lb>B A for the Meaſure of the <lb></lb>Space of the Fall from Reſt in <lb></lb>A unto B, and for the Meaſure of the Time and of the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of <lb></lb>the falling Moveable acquired in B, the Altitude B O ſhould not be <lb></lb>equal to, but greater than A B, taking B G to be a Mean-propor<lb></lb>tional betwixt the ſaid A B and B O, the ſaid B G would be the <lb></lb>Meaſure of the Time and of the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> in O, acquired in O by the <lb></lb>Fall from the height B O; and the Space along the Horizontal <lb></lb>Line, which being paſſed with the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> A B in the Time A B <lb></lb>would be double to A B, ſhall, in the whole duration of the Time <lb></lb>B G, be ſo much the greater, by how much in proportion B G is <lb></lb>greater than B A. </s> <s>Suppoſing therefore L B equal to B G, and draw<lb></lb>ing the Diagonal A L, it ſhall give us the quantity compounded of <lb></lb>the two <emph type="italics"></emph>Impetus's<emph.end type="italics"></emph.end> Horizontal and Perpendicular, by which the <lb></lb>Parabola is deſcribed; and of which the Horizontal and Equable is <lb></lb>that acquired in B by the fall of A B, and the other is that acquired <lb></lb>in O, or, if you will, in I by the Deſcent B O, whoſe Time, as alſo <lb></lb>the quantity of its Moment was B G. </s> <s>And in this Method we ſhall <lb></lb>inveſtigate the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> in the extream term of the Parabola, in caſe <lb></lb>its Altitude were leſſer than the Sublimity A B, taking the Mean<lb></lb>proportional betwixt them both: which being ſet off upon the Ho<lb></lb>rizontal Line in the place of B F, and the Diagonal drawn, as A F, <lb></lb>we ſhall hereby have the quantity of the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> in the extream <lb></lb>term of the Parabola.</s></p><pb xlink:href="040/01/920.jpg" pagenum="227"></pb><p type="margin"> <s><margin.target id="marg1100"></margin.target>* Or along <lb></lb>which.</s></p><p type="main"> <s>And to what hath hitherto been propoſed touching <emph type="italics"></emph>Impetus's,<emph.end type="italics"></emph.end><lb></lb>Blows, or if you pleaſe, Percuſſions of ſuch like Projects, it is ne<lb></lb>ceſſary to add another very neceſſary Conſideration; and this it is: <lb></lb>That it doth not ſuffice to have regard to the Velocity only of the <lb></lb>Project for the determining rightly of the Force and Violence of the <lb></lb>Percuſſion, but it is requiſite likewiſe to examine apart the State <lb></lb>and Condition of that which receiveth the Percuſſion, in the effica<lb></lb>cy of which it hath for many reſpects a great ſhare and intereſt. <lb></lb></s> <s>And firſt there is no man but knows that the thing ſmitten doth ſo <lb></lb>much ſuffer violence from the Velocity of the Percutient by how <lb></lb>much it oppoſeth it, and either totally or partially checketh its <lb></lb>Motion: For if the Blow ſhall light upon ſuch an one as yieldeth to <lb></lb>the Velocity of the Percutient without any Reſiſtance, that Blow <lb></lb>ſhall be nullified: And he that runneth to hit his Enemy with his <lb></lb>Launce, if at the overtaking of him it ſhall fall out that he moveth, <lb></lb>giving back with the like Velocity, he ſhall make no thruſt, and the <lb></lb>Action ſhall be a meer touch without doing any harm.</s></p><p type="main"> <s>But if the Percuſſion ſhall happen to be received upon an Object <lb></lb>which doth not wholly yield to the Percutient, but only partially, <lb></lb>the Percuſſion ſhall do hurt, though not with its whole <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> but <lb></lb>only with the exceſs of the Velocity of the ſaid Percutient above <lb></lb>the Velocity of the recoile and receſſion of the Object percuſſed: <lb></lb>ſo that, if <emph type="italics"></emph>v. </s> <s>g.<emph.end type="italics"></emph.end> the Percutient ſhall come with 10 degrees of Velo<lb></lb>city upon the Percuſſed Body, which giving back in part retireth <lb></lb>with 4 degrees, the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> and Percuſſion ſhall be as if it were of <lb></lb>6 degrees. </s> <s>And laſtly, the Percuſſion ſhall be entire and perfect on <lb></lb>the part of the Percutient when the thing percuſſed yieldeth not, <lb></lb>but wholly oppoſeth and ſtoppeth the whole Motion of the Percu<lb></lb>tient; if haply there can be ſuch a caſe. </s> <s>And I ſay on the part of <lb></lb>the Percutient, for when the Body percuſſed moveth with a contra<lb></lb>ry Motion towards the Percutient, the Blow and Shock ſhall be <lb></lb>ſo much the more Impetuous by how much the two Velocities uni<lb></lb>ted are greater than the ſole Velocity of the Percutient. </s> <s>More<lb></lb>over, you are likewiſe to take notice, that the more or leſs yielding <lb></lb>may proceed not only from the quality of the Matter more or leſs <lb></lb>hard, as if it be of Iron, of Lead, or of Wooll, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> but alſo from <lb></lb>the Poſition of the Body that receiveth the Percuſſion. </s> <s>Which Po<lb></lb>ſition if it ſhall be ſuch as that the Motion of the Percutient hap<lb></lb>neth to hit it at Right-Angles, the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the Percuſſion ſhall <lb></lb>be the greateſt: but if the Motion ſhall proceed obliquely, and, as <lb></lb>we ſay, aſlant, the Percuſſion ſhall be weaker; and that more, and <lb></lb>more according to its greater and greater Obliquity: for an Ob<lb></lb>ject in that manner ſcituate, albeit of very ſolid matter, doth not <lb></lb>damp or arreſt the whole <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> and Motion of the Percutient, <lb></lb>which ſlanting paſſeth farther, continuing at leaſt in ſome part to <pb xlink:href="040/01/921.jpg" pagenum="228"></pb>move along the Surface of the oppoſed Body Reſiſting. </s> <s>When <lb></lb>therefore we have even now determined of the greatneſs of the <lb></lb><emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the Project in the end of the Parabolicall Line, it ought <lb></lb>to be underſtood to be meant of the Percuſſion received upon a <lb></lb>Line at Right Angles with the ſame Parabolick Line, or with the <lb></lb>Line that is Tangent to the Parabola in the foreſaid point: for <lb></lb>although that ſame Motion be compounded of an Horizontal and <lb></lb>a Perpendicular Motion, the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> is not at the greateſt either <lb></lb>upon the Horizontal Plane, or upon that erect to the Horizon, be<lb></lb>ing received upon them both obliquely.</s></p><p type="main"> <s>SAGR. </s> <s>Your ſpeaking of theſe Blows, and theſe Percuſſions <lb></lb>hath brought into my mind a Problem, or, if you will, Queſtion <lb></lb>in the Mechanicks, the ſolution whereof I could never find in any <lb></lb>Author, nor any thing that doth diminiſh my admiration, or ſo <lb></lb>much as in the leaſt afford my judgment ſatisfaction. </s> <s>And my <lb></lb>doubt and wonder lyeth in my not being able to comprehend <lb></lb>whence that Immenſe Force and Violence ſhould proceed, and on <lb></lb>what Principle it ſhould depend, which we ſee to conſiſt in Per<lb></lb>cuſſion, in that with the ſimple ſtroke of an Hammer, that doth <lb></lb>not weigh above eight or ten pounds, we ſee ſuch Reſiſtances to be <lb></lb>overcome as would not yield to the weight of a Grave Body that <lb></lb>without Percuſſion hath an <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> only by preſſing and bearing <lb></lb>upon it, albeit the weight of this be many hundreds of pounds <lb></lb>more. </s> <s>I would likewiſe find out a way to meaſure the Force of this <lb></lb>Percuſſion, which I do not think to be infinite, but rather hold <lb></lb>that it hath its Term in which it may be compared, and in the end <lb></lb>Regulated with other Forces of preſſing Gravities, either of Lea<lb></lb>vers, or of Screws, or of other Mechanick Inſtruments, of whoſe <lb></lb>multiplication of Force I am thorowly ſatisfied.</s></p><p type="main"> <s>SALV. </s> <s>You are not alone in the admirableneſs of the effect, <lb></lb>and the obſcurity of the cauſe of ſo ſtupendious an Accident. </s> <s>I <lb></lb>ruminated a long time upon it in vain, my ſtupifaction ſtill encrea<lb></lb>ſing; till in the end meeting with our <emph type="italics"></emph>Academian,<emph.end type="italics"></emph.end> I received from <lb></lb>him a double ſatisfaction: firſt in hearing that he alſo had been a <lb></lb>long time at the ſame loſs; and next in underſtanding that after he <lb></lb>had at times ſpent many thouſands of hours in ſtudying and con<lb></lb>templating thereon, he had light upon certain Notions far from <lb></lb>our firſt conceptions, and therefore new, and for their Novelty to <lb></lb>be admired. </s> <s>And becauſe that I already ſee that your Curioſity <lb></lb>would gladly hear thoſe Conceits which are Remote from common <lb></lb>Conjecture, I ſhall not ſtay for your entreaty, but I give you my <lb></lb>word that ſo ſoon as we ſhall have finiſhed the Reading of this <lb></lb>Treatiſe of Projects, I will ſet before you all thoſe Fancies, or, I <lb></lb>might ſay, Extravagancies that are yet left in my memory of the <lb></lb>Diſcourſes of the Academick. </s> <s>In the mean time let us proſecute <lb></lb>the Propoſitions of our Author.</s></p><pb xlink:href="040/01/922.jpg" pagenum="229"></pb><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></lb>a ſublime point out of which the Moveable <lb></lb>falling ſhall deſcribe the ſaid Parabola.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Parabola be A B, its Amplitude H B, and its prolonged <lb></lb>Axis H E; in which a Sublimity is to be found, out of which the <lb></lb>Moveable falling, and converting the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>conceived in A <lb></lb>along the Horizontal Line, deſcribeth the Parabola A B. </s> <s>Draw the <lb></lb>Horizontal Line A G, which ſhall be Parallel to B H, and ſuppoſing A F <lb></lb>equal to A H draw the Right Line F B, which toucheth the Parabola in <lb></lb>B, and cutteth the Horizontal Line A G in G; and unto F A and A G <lb></lb>let A E be a third Proportional. </s> <s>I ſay, that E is the ſublime Point re<lb></lb>quired, out of which the Moveable falling<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in E, and the<emph.end type="italics"></emph.end> Im<lb></lb>petus <emph type="italics"></emph>conceived in A being converted along the Horizontal Line over<lb></lb>taking the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>of the Deſcent<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.922.1.jpg" xlink:href="040/01/922/1.jpg"></figure><lb></lb><emph type="italics"></emph>in H<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in A, deſcribeth the <lb></lb>Parabola A B. </s> <s>For if we ſuppoſe <lb></lb>E A to be the Meaſure of the Time <lb></lb>of the Fall from E to A, and of <lb></lb>the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>acquired in A, A G <lb></lb>(that is a Mean-proportional be<lb></lb>tween E A and A F) ſhall be the <lb></lb>Time and the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>coming <lb></lb>from F to A, or from A to H. </s> <s>And <lb></lb>becauſe the Moveable coming out of <lb></lb>E in the Time E A with the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>acquired in A paſſeth in the Ho<lb></lb>rizontal Lation with an Equable Motion the double of E A; There<lb></lb>fore likewiſe moving with the ſame<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>it ſhall in the Time A G <lb></lb>paſs the double of G A, to wit, the Mean-proportional B H (for the <lb></lb>Spaces paſſed with the ſame Equable Motion are to one another as the <lb></lb>Times of the ſaid Motions:) And along the Perpendicular A H ſhall <lb></lb>be paſſed with a Motion<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in the ſame Time G A: Therefore <lb></lb>the Amplitude H B, and Altitude A H are paſſed by the Moveable in the <lb></lb>ſame Time: Therefore the Parabola A B ſhall be deſcribed by the <lb></lb>Deſcent of the Project coming from the Sublimity E: Which was re<lb></lb>quired.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>COROLLARY.</s></p><p type="main"> <s>Hence it appeareth that the half of the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>aſe or Amplitude of the <lb></lb>Semiparabola (which is the fourth part of the Amplitude of <lb></lb>the whole Parabola) is a Mean-proportional betwixt its Al<lb></lb>titude and the Sublimity out of which the Moveable falling <lb></lb>deſcribeth it.</s></p><pb xlink:href="040/01/923.jpg" pagenum="230"></pb><p type="head"> <s>PROBL. III. <emph type="italics"></emph>P<emph.end type="italics"></emph.end>RO<emph type="italics"></emph>P.<emph.end type="italics"></emph.end> VI.</s></p><p type="main"> <s>The Sublimity and Altitude of a Semiparabola <lb></lb>being given to find its Amplitude.</s></p><p type="main"> <s><emph type="italics"></emph>Let A C be perpendicular to the<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.923.1.jpg" xlink:href="040/01/923/1.jpg"></figure><lb></lb><emph type="italics"></emph>Horizontal Line D C, in <lb></lb>which let the Altitude C B and <lb></lb>the Sublimity B A be given: It is <lb></lb>required in the Horizontal Line <lb></lb>D C to find the Amplitude of the <lb></lb>Semiparabola that is deſcribed out of <lb></lb>the Sublimity B A with the Alti<lb></lb>tude B C. </s> <s>Take a Mean proportional <lb></lb>between C B and B A, to which let <lb></lb>C D be double, I ſay, that C D is <lb></lb>the Amplitude required. </s> <s>The which <lb></lb>is manifeſt by the precedent Propoſition.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>THEOR. IV. PROP. VII.</s></p><p type="main"> <s>In Projects which deſcribe Semiparabola's of the <lb></lb>ſame Amplitude, there is leſs <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> required <lb></lb>in that which deſcribeth that whoſe Ampli<lb></lb>tude is double to its Altitude, than in any <lb></lb>other.</s></p><p type="main"> <s><emph type="italics"></emph>For let the Semiparabola be B D, whoſe Amplitude C D is dou<lb></lb>ble to its Altitude C B; and in its Axis extended on high let B A <lb></lb>be ſuppoſed equal to the Altitude B C; and draw a Line from <lb></lb>A to D which toucheth the Semiparabola in D, and ſhall cut the Hori<lb></lb>zontal Line B E in E; and B E ſhall be equal to B C or to B A: It is <lb></lb>manifeſt that it is deſcribed by the Project whoſe Equable Horizontal<emph.end type="italics"></emph.end><lb></lb>Impetus <emph type="italics"></emph>is ſuch as is that gained in B of a thing falling from Reſt in A, <lb></lb>and the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>of the Natural Motion downwards, ſuch as is that of <lb></lb>a thing coming to C<emph.end type="italics"></emph.end> ex quiete <emph type="italics"></emph>in B. </s> <s>Whence it is manifeſt, that the<emph.end type="italics"></emph.end><lb></lb>Impetus <emph type="italics"></emph>compounded of them, and that ſtriketh in the Term D is as the <lb></lb>Diagonal A E, that is<emph.end type="italics"></emph.end> potentia <emph type="italics"></emph>equal to them both. </s> <s>Now let there be <lb></lb>another Semiparabola G D, whoſe Amplitude is the ſame C D, and the <lb></lb>Altitude C G leſs, or greater than the Altitude B C, and let H D touch <lb></lb>the ſame, cutting the Horizontal Line drawn by G in the point K; and <lb></lb>as H G is to G K, ſo let K G be to G L: by what hath been demonſtrated <lb></lb>G L ſhall be the Altitude from which the Project falling deſcribeth the<emph.end type="italics"></emph.end><pb xlink:href="040/01/924.jpg" pagenum="231"></pb><emph type="italics"></emph>Parabola G D. </s> <s>Let G M be a Mean-proportional betwixt A B and <lb></lb>G L; G M ſhall be the Time, and the Moment or<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>in G of the <lb></lb>Project falling from L, (for it hath been ſuppoſed that A B is the Mea<lb></lb>ſure of the Time and<emph.end type="italics"></emph.end> Impetus.) <emph type="italics"></emph>Again, let G N be a Mean-propor<lb></lb>tional betwixt B C and C G: this G N ſhall be the Meaſure of the <lb></lb>Time and the<emph.end type="italics"></emph.end><lb></lb>Impetus <emph type="italics"></emph>of the<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.924.1.jpg" xlink:href="040/01/924/1.jpg"></figure><lb></lb><emph type="italics"></emph>Project falling <lb></lb>from G to C. <lb></lb></s> <s>If therefore a <lb></lb>Line be drawn <lb></lb>from M to N <lb></lb>it ſhall be the <lb></lb>the Meaſure of <lb></lb>the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>of <lb></lb>the Project a<lb></lb>long the Para<lb></lb>bola B D, ſcri<lb></lb>king in the <lb></lb>term D. Which<emph.end type="italics"></emph.end><lb></lb>Impetus, <emph type="italics"></emph>I ſay, <lb></lb>is greater than the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>of the Project along the Parabola B D, <lb></lb>whoſe quantity was A E. </s> <s>For becauſe G N is ſuppoſed the Mean-pro<lb></lb>portional betwixt B C and C G, and B C is equal to B E, that is to H G; <lb></lb>(for they are each of them ſubduple to D C:) Therefore as C G is to <lb></lb>G N, ſo ſhall N G be to G K: and, as C G or H G is to G K, ſo ſhall the <lb></lb>Square N G be to the Square of G K: But as H G is to G K, ſo was <lb></lb>K G ſuppoſed to be to G L: Therefore as N G is to the Square G K, ſo <lb></lb>is K G to G L: But as K G is to G L, ſo is the Square K G unto the <lb></lb>Square G M, (for G M is the Mean between K G and G L:) Therefore <lb></lb>the three Squares N G, K G, and G M are continual proportionals: And <lb></lb>the two extream ones N G and G M taken together, that is the Square <lb></lb>M N is greater than double the Square K G, to which the Square A E <lb></lb>is double: Therefore the Square M N is greater than the Square A E: <lb></lb>and the Line M N greater than the Line A E: Which was to be de<lb></lb>monſtrated.<emph.end type="italics"></emph.end></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></lb>along the Semiparabola D B, leſs <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> is required than <lb></lb>along any other according to the greater or leſſer Elevation <lb></lb>of the Semiparabola B D, which is according to the Tan<lb></lb>gent A D, containing half a Right-Angle upon the Hori<lb></lb>zon.</s></p><pb xlink:href="040/01/925.jpg" pagenum="232"></pb><p type="head"> <s>COROLLARRY II.</s></p><p type="main"> <s>And that being ſo, it followeth, that if Projections be made with <lb></lb>the ſame <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> out of the Term D, according to ſeveral <lb></lb>Elevations, that ſhall be the greateſt Projection or Amplitude <lb></lb>of the Semiparabola or whole Parabola which followeth at <lb></lb>the Elevation of a ^{*} Semi-Right-Angle; and the reſt, made <lb></lb><arrow.to.target n="marg1101"></arrow.to.target><lb></lb>according to greater or leſſer Angles, ſhall be greater or <lb></lb>leſſer.</s></p><p type="margin"> <s><margin.target id="marg1101"></margin.target>* Or, at the Ele<lb></lb>vation of 45 de<lb></lb>grees.</s></p><p type="main"> <s>SAGR. </s> <s>The ſtrength of Neceſſary Demonſtrations are full of <lb></lb>pleaſure and wonder; and ſuch are only the Mathematical. </s> <s>I un<lb></lb>derſtood before upon truſt from the Relations of ſundry Gunners, <lb></lb>that of all the Ranges of a Cannon, or of a Mortar-piece, the grea<lb></lb>teſt, <emph type="italics"></emph>ſcilicet<emph.end type="italics"></emph.end> that which carryeth the Ball fartheſt was that made at <lb></lb>the Elevation of a Semi-Right-Angle, which they call, of the Sixth <lb></lb>point of the Square: but the knowledge of the Cauſe whence it <lb></lb>hapneth infinitely ſurpaſſeth the bare Notion that I received upon <lb></lb>their atteſtation, and alſo from many repeated Experiments.</s></p><p type="main"> <s>SALV. </s> <s>You ſay very right: and the knowledge of one ſingle <lb></lb>Effect acquired by its Cauſes openeth the Intellect to underſtand <lb></lb>and aſcertain our ſelves of other effects, without need of repairing <lb></lb>unto Experiments, juſt as it hapneth in the preſent Caſe; in which <lb></lb>having found by demonſtrative Diſcourſe the certainty of this, <lb></lb>That the greateſt of all Ranges is that of the Elevation of a Semi<lb></lb>Right-Angle, the Author demonſtrates unto us that which poſſibly <lb></lb>hath not been obſerved by Experience: and that is, that of the <lb></lb>other Ranges thoſe are equal to one another whoſe Elevations ex<lb></lb>ceed or fall ſhort by equal Angles of the Semi-right: ſo that the <lb></lb>Balls ſhot from the Horizon, one according to the Elevation of ſe<lb></lb>ven Points, and the other of 5, ſhall light upon the Horizon at <lb></lb>equal Diſtances: and ſo the Ranges of 8 and of 4 points, of 9 and <lb></lb>of 3, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> ſhall be equal. </s> <s>Now hear the Demonſtration of it.</s></p><p type="head"> <s>THEOR. V. PROP. VIII.</s></p><p type="main"> <s>The Amplitudes of Parabola's deſcribed by Pro<lb></lb>jects expulſed with the ſame <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> according <lb></lb>to the Elevations by Angles equidiſtant above, <lb></lb><arrow.to.target n="marg1102"></arrow.to.target><lb></lb>and beneath from the ^{*} Semi-right, are equal to <lb></lb>each other.</s></p><pb xlink:href="040/01/926.jpg" pagenum="233"></pb><p type="margin"> <s><margin.target id="marg1102"></margin.target>* Or Angle of <lb></lb>45.</s></p><p type="main"> <s><emph type="italics"></emph>Of the Triangle M C B, about the Right-Angle C, let the Ho<lb></lb>rizontal Line B C and the Perpendicular C M be equal; for <lb></lb>ſo the Angle M B C ſhall be Semi-right; and prolonging C M <lb></lb>to D, let there be conſtituted in B two equal Angles above and below <lb></lb>the Diagonal M B,<emph.end type="italics"></emph.end> viz. <emph type="italics"></emph>M B E, and M B D. </s> <s>It is to be demonſtrated <lb></lb>that the Amplitudes of the Parabola's deſcribed by the Projects be<lb></lb>ing emitted<emph.end type="italics"></emph.end> [or ſhot off] <emph type="italics"></emph>with the ſame<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>out of the Term B, <lb></lb>according to the Elevations of the Angles E B C and D B C, are equal. <lb></lb></s> <s>For in regard that the extern Angle B M C, is equal to the two intern <lb></lb>M D B and M B D, the Angle M B C ſhall alſo be equal to them. </s> <s>And if <lb></lb>we ſuppoſe M B E inſtead of the Angle M B D, <lb></lb>the ſaid Angle M B C ſhall be equal to the two<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.926.1.jpg" xlink:href="040/01/926/1.jpg"></figure><lb></lb><emph type="italics"></emph>Angles M B E and B D C: And taking away <lb></lb>the common Angle M B E, the remaining An<lb></lb>gle B D C ſhall be equal to the remaining An<lb></lb>gle E B C: Therefore the Triangles D C B <lb></lb>and B C E are alike. </s> <s>Let the Right Lines <lb></lb>D C and E C be divided in the midſt in H and <lb></lb>F; and draw H I and F G parallel to the Ho<lb></lb>rizontal Line C B; and as D H is to H I, ſo <lb></lb>let I H be to H L: the Triangle I H L ſhall be <lb></lb>like to the Triangle I H D, like to which alſo is E G F. </s> <s>And ſeeing <lb></lb>that I H and G F are equal (to wit, halves of the ſame B C:) There<lb></lb>fore F E, that is F C, ſhall be equal to H L: And, adding the common <lb></lb>Line F H, C H ſhall be equal to F L. </s> <s>If therefore we underſtand the Se<lb></lb>miparabola to be deſcribed along by H and B, whoſe Altitude ſhall be <lb></lb>H C, and Sublimity H L, its Amplitude ſhall be C B, which is double <lb></lb>to HI, that is, the Mean betwixt D H, or C H, and HL: And D B <lb></lb>ſhall be a Tangent to it, the Lines C H and H D being equal. </s> <s>And if, <lb></lb>again, we conceive the Parabola to be deſcribed along by F and B from <lb></lb>the Sublimity FL, with the Altitude F C, betwixt which the Mean<lb></lb>proportional is F G, whoſe double is the Horizontal Line C B: C B, as <lb></lb>before, ſhall be its Amplitude; and E B a Tangent to it, ſince E F and <lb></lb>F C are equal: But the Angles D B C and E B C<emph.end type="italics"></emph.end> (ſcilicet, <emph type="italics"></emph>their Eleva<lb></lb>tions) ſhall be equidiſtant from the Semi-Right Angle: Therefore the <lb></lb>Propoſition is demonſtrated.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>THEOR. VI. <emph type="italics"></emph>P<emph.end type="italics"></emph.end>RO<emph type="italics"></emph>P.<emph.end type="italics"></emph.end> IX.</s></p><p type="main"> <s>The Amplitudes of Parabola's, whoſe Altitudes <lb></lb>and Sublimities anſwer to each other <emph type="italics"></emph>è contra<lb></lb>rio,<emph.end type="italics"></emph.end> are equall.</s></p><pb xlink:href="040/01/927.jpg" pagenum="234"></pb><p type="main"> <s><emph type="italics"></emph>Let the Altitude G F of the Parabola F H have the ſame proporti<lb></lb>on to the Altitude C B of the Parabola B D, as the Sublimity B A <lb></lb>hath to the Sublimity F E. </s> <s>I ſay, that the Amplitude H G is equal <lb></lb>to the Amplitude D C. </s> <s>For ſince the firſt G F hath the ſame propor<lb></lb>tion to the ſecond C B, as the third B A hath to the fourth F E; There<lb></lb>fore, the Rectangle<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.927.1.jpg" xlink:href="040/01/927/1.jpg"></figure><lb></lb><emph type="italics"></emph>G F E of the firſt and <lb></lb>fourth, ſhall be equal to <lb></lb>the Rectangle C B A <lb></lb>of the ſecond and <lb></lb>third: Therefore the <lb></lb>Squares that are equal <lb></lb>to theſe Rectangles ſhall <lb></lb>be equal to one another: <lb></lb>But the Square of half of G H is equal to the Rectangle G F E; and <lb></lb>the Square of half of C D is equal to the Rectangle C B A: There<lb></lb>fore theſe Squares, and their Sides, and the doubles of their Sides ſhall <lb></lb>be equal: But theſe are the Amplitudes G H and C D: Therefore the <lb></lb>Propoſition is manifeſt.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>LEMMA <emph type="italics"></emph>pro ſequenti.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>If a Right Line be cut according to any proportion, the Squares <lb></lb>of the Mean-proportionals between the whole and the two <lb></lb>parts are equal to the Square of the whole.</s></p><p type="main"> <s><emph type="italics"></emph>Let A B be cut according to any proportion in C. </s> <s>I ſay, that the <lb></lb>Squares of the Mean-proportional Lines between the whole A B and <lb></lb>the parts A C and C B, being taken together are equal to the Square of <lb></lb>the whole A B. </s> <s>And this appeareth, a Semi-<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.927.2.jpg" xlink:href="040/01/927/2.jpg"></figure><lb></lb><emph type="italics"></emph>circle being deſcribed upon the whole Line <lb></lb>B A, and from C a Perpendicular being ere<lb></lb>cted C D, and Lines being drawn from D to <lb></lb>A, and from D to B. </s> <s>For D A is the Mean<lb></lb>proportional betwixt A B and A C; and D B is the Mean-proporti<lb></lb>onal between A B and B C: And the Squares of the Lines D A and <lb></lb>D B taken together are equal to the Square of the whole Line A B, <lb></lb>the Angle A D B in the Semicircle being a Right-Angle: Therefore <lb></lb>the Propoſition is manifest.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/928.jpg" pagenum="235"></pb><p type="head"> <s>THEOR. VII. PROP. X.</s></p><p type="main"> <s>The <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> or Moment of any Semiparabola is <lb></lb>equal to the Moment of any Moveable falling <lb></lb>naturally along the Perpendicular to the Ho<lb></lb>rizon that is equal to the Line compounded of <lb></lb>the Sublimity and of the Altitude of the Se<lb></lb>miparabola.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Semiparabola be A B, its Sublimity D A, and Altitude <lb></lb>A C, of which the Perpendicular D C is compounded. </s> <s>I ſay, that <lb></lb>the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>of the Semiparabola in B is equal to the Moment of <lb></lb>the Moveable Naturally falling from D to C. </s> <s>Suppoſe D C it ſelf to be <lb></lb>the Meaſure of the Time and of the<emph.end type="italics"></emph.end> Impetus; <emph type="italics"></emph>and take a Mean-pro<lb></lb>portional betwixt C D and D A, to which let<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.928.1.jpg" xlink:href="040/01/928/1.jpg"></figure><lb></lb><emph type="italics"></emph>C F be equal; and withal let C E be a Mean<lb></lb>proportional between D C and C A: Now C F <lb></lb>ſhall be the Meaſure of the Time and of the Mo<lb></lb>ment of the Moveable ſalling along D A out of <lb></lb>Reſt in D; and C E ſhall be the Time and Mo<lb></lb>ment of the Moveable falling along A C, out of <lb></lb>Reſt in A, and the Moment of the Diagonal E F <lb></lb>ſhall be that compounded of both the others,<emph.end type="italics"></emph.end> ſcil. <lb></lb><emph type="italics"></emph>that of the Semiparabola in B. </s> <s>And becauſe <lb></lb>D C is cut according to any proportion in A, and becauſe C F and C E <lb></lb>are Mean-Proportionals between C D and the parts D A and A C; the <lb></lb>Squares of them taken together ſhall be equal to the Square of the <lb></lb>whole; by the Lemma aforegoing: But the Squares of them are alſo <lb></lb>equal to the Square of E F: Therefore D F is equal alſo to the Line D C: <lb></lb>Whence it is manifeſt that the Moments along D C, and along the Se<lb></lb>miparabola A B, are equal in C and B: Which was required.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>COROLLARY.</s></p><p type="main"> <s>Hence it is manifeſt, that of all Parabola's whoſe Altitudes and <lb></lb>Sublimities being joyned together are equal, the <emph type="italics"></emph>Impetus's<emph.end type="italics"></emph.end> are <lb></lb>alſo equal.</s></p><pb xlink:href="040/01/929.jpg" pagenum="236"></pb><p type="head"> <s>PROBL. IV. PROP. XI.</s></p><p type="main"> <s>The <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> and Amplitude of a Semiparabola be<lb></lb>ing given, to find its Altitude, and conſequently <lb></lb>its Sublimity.</s></p><p type="main"> <s><emph type="italics"></emph>Let the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>given be defined by the Perpendicular to the Ho<lb></lb>rizon A B; and let the Amplitude along the Horizontal Line be <lb></lb>B C. </s> <s>It is required to find the Altitude and Sublimity of the <lb></lb>Parabola whoſe<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>is A B, and Amplitude B C. </s> <s>It is manifeſt, <lb></lb>from what hath been already demonſtrated, that half the Amplitude B C <lb></lb>will be a Mean-proportional betwixt the Altitude and the Sublimity of <lb></lb>the ſaid Semiparabola, whoſe<emph.end type="italics"></emph.end> Impetus, <emph type="italics"></emph>by the precedent Propoſition, is <lb></lb>the ſame with the<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>of the Moveable falling from Reſt in A along <lb></lb>the whole Perpendicular A B: Wherefore B A is ſo to be cut that the <lb></lb>Rectangle contained by its parts may be equal to the Square of half of <lb></lb>B C, which let be B D. </s> <s>Hence it appeareth <lb></lb>to be neceſſary that D B do not exceed the<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.929.1.jpg" xlink:href="040/01/929/1.jpg"></figure><lb></lb><emph type="italics"></emph>half of B A; for of Rectangles contained by <lb></lb>the parts the greateſt is when the whole <lb></lb>Line is cut into two equal parts. </s> <s>Therefore <lb></lb>let B A be divided into two equal parts in E. <lb></lb></s> <s>And if B D be equal to B E the work is <lb></lb>done; and the Altitude of the Semipara<lb></lb>bola ſhall be B E, and its Sublimity E A: <lb></lb>(and ſee here by the way that the Amplitude <lb></lb>of the Parabola of a Semi-right Elevation, <lb></lb>as was demonſtrated above, is the greateſt of <lb></lb>all thoſe deſcribed with the ſame<emph.end type="italics"></emph.end> Impetus.) <lb></lb><emph type="italics"></emph>But let B D be leſs than the half of B A, <lb></lb>which is ſo to be cut that the Rectangle under the parts may be equal to <lb></lb>the Square B D. </s> <s>Upon E A deſcribe a Semicircle, upon which out of A <lb></lb>ſet off A F equal to B D, and draw a Line from F to E, to which cut <lb></lb>a part equal E G. </s> <s>Now the Rectangle B G A, together with the Square <lb></lb>E G, ſhall be equal to the Square E A; to which the two Squares A F <lb></lb>and F E are alſo equal: Therefore the equal Squares G E and F E be<lb></lb>ing ſubſtracted, there remaineth the Rectangle B G A equal to the <lb></lb>Square A F,<emph.end type="italics"></emph.end> ſcilicet, <emph type="italics"></emph>to B D; and the Line B D is a Mean-proportional <lb></lb>betwixt B G and G A. </s> <s>Whence it appeareth, that of the Semipa<lb></lb>rabola whoſe Amplitude is B C, and<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>A B, the Altitude is <lb></lb>B G, and the Sublimity G A. </s> <s>And if we ſet off B I below equal to G A, <lb></lb>this ſhall be the Altitude, and I A the Sublimity of the Semiparabola <lb></lb>I C. </s> <s>From what hath been already demonſtrated we are able,<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/930.jpg" pagenum="237"></pb><p type="head"> <s>PROBL. V. PROP. XII.</s></p><p type="main"> <s>To collect by Calculation of the Amplitudes of all <lb></lb>Semiparabola's that are deſcribed by Projects <lb></lb>expulſed with the ſame <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> and to make <lb></lb>Tables thereof.</s></p><p type="main"> <s><emph type="italics"></emph>It is obvious, from the things demonſtrated, that Parabola's are de<lb></lb>ſcribed by Projects of the ſame<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>then, when their Subli<lb></lb>mities together with their Altitudes do make up equal Perpendicu<lb></lb>lars upon the Horizon. </s> <s>Theſe Perpendiculars therefore are to be com<lb></lb>prehended between the ſame Horizontal Parallels. </s> <s>Therefore let the <lb></lb>Horizontal Line C B be ſuppoſed equal to the Perpendicular B A, and <lb></lb>draw the Diagonal from A to C. </s> <s>The Angle A C B ſhall be Semi<lb></lb>right, or 45 Degrees. </s> <s>And the Perpendicular B A being divided into <lb></lb>two equal parts in D, the Semiparabola D C ſhall be that which is de<lb></lb>ſcribed from the Sublimity A D together with the Altitude D B: and <lb></lb>its<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>in C ſhall be as great as that of the Moveable coming out of <lb></lb>Reſt in A along the Perpendicular A B is in B. </s> <s>And if A G be drawn <lb></lb>parallel to B C, the united Altitudes and Sublimities of all other re<lb></lb>maining Semiparabola's whoſe future<emph.end type="italics"></emph.end> Impetus's <emph type="italics"></emph>are the ſame with thoſe <lb></lb>now mentioned muſt be bounded by the Space between the Parallels<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.930.1.jpg" xlink:href="040/01/930/1.jpg"></figure><lb></lb><emph type="italics"></emph>A G and B C. Farthermore, it having <lb></lb>been but now demonſtrated, that the Am<lb></lb>plitudes of the Semiparabola's whoſe <lb></lb>Tangents are equidiſtant either above or <lb></lb>below from the Semi right Elevation are <lb></lb>equal, the Calculations that we frame <lb></lb>for the greater Elevations will likewiſe <lb></lb>ſerve for the leſſer. </s> <s>We chooſe moreover <lb></lb>a number of ten thouſand parts for the <lb></lb>greateſt Amplitude of the Projection of <lb></lb>the Semiparabola made at the Elevation <lb></lb>of 45 degrees: ſo much therefore the Line <lb></lb>B A, and the Amplitude of the Semipa<lb></lb>rabola B C, are to be ſuppoſed. </s> <s>And we <lb></lb>make choice of the number 10000, becauſe we in our Calculation uſe <lb></lb>the Table of Tangents, in which this number agreeth with the Tangent <lb></lb>of 45 degrees. </s> <s>Now, to come to the buſineſs, let C E be drawn, contain<lb></lb>ing the Angle E C B greater (Acute nevertheleſs,) than the Angle <lb></lb>A C B; and let the Semiparabola be deſcribed which is touched by the <lb></lb>Line E C, and whoſe Sublimity united with its Altitude is equal to <lb></lb>B A. </s> <s>In the Table of Tangents take the ſaid B E for the Tangent at the<emph.end type="italics"></emph.end><pb xlink:href="040/01/931.jpg" pagenum="238"></pb><emph type="italics"></emph>given Angle B C E, which divide into two equal parts at F. </s> <s>Then <lb></lb>find a third Proportional to B F and B C, (or to the half of B C,) <lb></lb>which ſhall of neceſſity be greater than F A; therefore let it be F O: <lb></lb>Of the Semiparabola, therefore, inſcribed in the Triangle E C B, ac<lb></lb>cording to the Tangent C E, whoſe Amplitude is C B, the Altitude B F, <lb></lb>and the Sublimity F O is found: But the whole Line B O riſeth above <lb></lb>the Parallels A G and C B, whereas our work was to bound it between <lb></lb>them: For ſo both it and the Semiparabola D C ſhall be deſcribed by <lb></lb>the Projects out of C expelled with the ſame<emph.end type="italics"></emph.end> Impetus. <emph type="italics"></emph>Therefore we <lb></lb>are to ſeek another like to this, (for innumerable greater and ſmaller, <lb></lb>like to one another, may be deſcribed within the Angle B C E) to whoſe <lb></lb>united Sublimity and Altitude B A ſhall be equal. </s> <s>Therefore as O B is <lb></lb>to B A, ſo let the Amplitude B C be to C R: and C R ſhall be found,<emph.end type="italics"></emph.end><lb></lb>ſcilicet <emph type="italics"></emph>the Amplitude of the Semiparabola according to the Elevation <lb></lb>of the Angle B C E, whoſe conjoyned Sublimity and Altitude is equal <lb></lb>to the Space contained between the Parallels G A and C B: Which <lb></lb>was required. </s> <s>The work, therefore, ſhall be after this manner.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Take the Tangent of the given Angle B C E, to the half of which <lb></lb>add the third Proportional of it, and half of B C, which let be F O: <lb></lb>Then as O B is to B A, ſo let B C be to another, which let be C R, to wit, <lb></lb>the Amplitude ſought. </s> <s>Let us give an Example.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Let the Angle E C B be 50 degrees, its Tangent ſhall be 11918, <lb></lb>whoſe half, to wit, B F, is 5959, and the half of B C is 5000, the third <lb></lb>proportional of theſe halves is 4195, which added to the ſaid B F <lb></lb>maketh 10154: for the ſaid B O. Again, as O B is to B A, that is as <lb></lb>10154 is to 10000, ſo is B E, that is 10000 (for each of them is the <lb></lb>Tangent of 45 degrees) to another: and that ſhall give us the required <lb></lb>Altitude R C 9848, of ſuch as B C (the greateſt Amplitude) is <lb></lb>10000. To theſe the Amplitudes of the whole Parabola's are double,<emph.end type="italics"></emph.end><lb></lb>ſcilicet <emph type="italics"></emph>19696 and 20000. And ſo much likewiſe is the Amplitude of <lb></lb>the Parabola according to the Elevation of 40 degrees, ſince it is equal<lb></lb>ly diſtant from 45 degrees.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>For the perfect underſtanding of this Demonſtration I <lb></lb>muſt be informed how true it is, that the Third Proportional to <lb></lb>B F and B I, is (as the Author ſaith) neceſſarily greater than <lb></lb>F A.</s></p><p type="main"> <s>SALV. </s> <s>That inference, as I conceive, may be deduced thus. <lb></lb></s> <s>The Square of the Mean of three proportional Lines is equal to <lb></lb>the Rectangle of the other two: whence the Square of B I, or of <lb></lb>B D equal to it, ought to be equal to the Rectangle of the firſt F B <lb></lb>multiplied into the third to be found: which third is of neceſſity to <lb></lb>be greater than F A, becauſe the Rectangle of B F multiplied into <lb></lb>F A is leſs than the Square B D: and the Defect is as much as the <lb></lb>Square of D F, as <emph type="italics"></emph>Euclid<emph.end type="italics"></emph.end> demonſtrates in a Propoſition of his <pb xlink:href="040/01/932.jpg" pagenum="239"></pb>Second Book. </s> <s>You muſt alſo know, that the point F which divi<lb></lb>deth the Tangent E B in the middle, will many other times fall <lb></lb>above the point A, and once alſo in the ſaid A: In which caſes it is <lb></lb>evident of it ſelf, that the third proportional to the half of the Tan<lb></lb>gent, and to B I (which giveth the Sublimity) is all above A. </s> <s>But <lb></lb>the Author hath taken a Caſe in which it was not manifeſt that the <lb></lb>ſaid third Proportional is alwaies greater than F A: and which <lb></lb>therefore being ſet off above the point F paſſeth beyond the Paral<lb></lb>lel A G. </s> <s>Now let us proceed.</s></p><p type="main"> <s><emph type="italics"></emph>It will not be unprofitable if by help of this Table we compoſe ano<lb></lb>ther, ſhewing the Altitudes of the ſame Semiparabola's of Projects of <lb></lb>the ſame<emph.end type="italics"></emph.end> Impetus. <emph type="italics"></emph>And the Conſtruction of it is in this manner.<emph.end type="italics"></emph.end></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></lb>the following Table ſet down, keeping the <lb></lb>common <emph type="italics"></emph>Impeius<emph.end type="italics"></emph.end> with which every one of <lb></lb>them is deſcribed, to compute the Altitudes of <lb></lb>each ſeveral Semiparabola.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Amplitude given be B C, and of the<emph.end type="italics"></emph.end> Impetus, <emph type="italics"></emph>which is <lb></lb>ſuppoſed to be alwaies the ſame, let the Meaſure be O B, to wit, <lb></lb>the Aggregate of the Altitude and Sublimity. </s> <s>The ſaid Altitude <lb></lb>is required to be found and diſtinguiſhed. </s> <s>Which ſhall then be done when <lb></lb>B O is ſo divided as that the Rectangle contained under its parts is <lb></lb>equal to the Square of half the Amplitude B C. </s> <s>Let that ſame divi<lb></lb>ſion fall in F; and let both O B and B C be cut in the midſt at D and I.<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.932.1.jpg" xlink:href="040/01/932/1.jpg"></figure><lb></lb><emph type="italics"></emph>The Square I B, therefore, is equal to the <lb></lb>Rectangle B F O: And the Square D O is <lb></lb>equal to the ſame Rectangle together with the <lb></lb>Square F D. </s> <s>If therefore from the Square <lb></lb>D O we deduct the Square B I, which is equal <lb></lb>to the Rectangle B F O, there ſhall remain <lb></lb>the Square F D; to whoſe Side D F, B D be<lb></lb>ing added it ſhall give the deſired Altitude <lb></lb>Altitude B F. </s> <s>And it is thus compounded<emph.end type="italics"></emph.end><lb></lb>ex datis. <emph type="italics"></emph>From half of the Square B O known <lb></lb>ſubſtract the Square B I alſo known, of the remainder take the Square <lb></lb>Root, to which add D B known; and you ſhall have the Altitude ſought <lb></lb>B F. </s> <s>For example. </s> <s>The Altitude of the Parabola deſcribed at the <lb></lb>Elevation of 55 degrees is to be found. </s> <s>The Amplitude, by the follow<lb></lb>ing Table is 9396, its half is 4698, the Square of that is 22071204,<emph.end type="italics"></emph.end><pb xlink:href="040/01/933.jpg" pagenum="240"></pb><emph type="italics"></emph>this ſubſtracted from the Square of the half B O, which is alwaies <lb></lb>the ſame, to wit, 2500000, the remainder is 2928796, whoſe Square <lb></lb>Root is 1710 very near, this added to the half of B O, to wit, 5000, <lb></lb>gives 67101, and ſo much is the Altitude B F. </s> <s>It will not be unprofi<lb></lb>table, to give the Third Table, containing the Altitudes and Sublimi<lb></lb>ties of Semiparabola's, whoſe Amplitude ſhall be alwaies the ſame.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>This I would very gladly ſee ſince by it I may come to <lb></lb>know the Difference of the <emph type="italics"></emph>Impetus's,<emph.end type="italics"></emph.end> and of the Forces that are <lb></lb>required for carrying the Project to the ſame Diſtance with Ranges <lb></lb>which are called at Random: which Difference I believe is very <lb></lb>great according to the different Elevations [<emph type="italics"></emph>or Mountures:<emph.end type="italics"></emph.end>] ſo that <lb></lb>if, for example, one would at the Elevation of 3 or 4 degrees, or of <lb></lb>87 or 88 make the Ball to fall where it did, being ſhot at the Ele<lb></lb>vation of <emph type="italics"></emph>gr.<emph.end type="italics"></emph.end> 45. (where, as hath been ſhewn, the leaſt <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> is <lb></lb>required) I believe that it would require a very much greater <lb></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></lb>full execution in all the Elevations it is requiſite to make great Pro<lb></lb>greſſions towards an infinite <emph type="italics"></emph>Impetus.<emph.end type="italics"></emph.end> Now let us ſee the Conſtru<lb></lb>ction of the Table.<pb xlink:href="040/01/934.jpg" pagenum="241"></pb><arrow.to.target n="table75"></arrow.to.target><lb></lb><arrow.to.target n="table76"></arrow.to.target><lb></lb><arrow.to.target n="table77"></arrow.to.target></s></p><pb xlink:href="040/01/935.jpg" pagenum="242"></pb><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, deſcribed with the ſame <emph type="italics"></emph>Impetus.<emph.end type="italics"></emph.end></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, whoſe <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> is the ſame.</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, whoſe Am-plitudes are the ſame, that is to ſay, 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></lb>rabola's whoſe Amplitudes ſhall be equal for <lb></lb>each degree of Elevation.</s></p><p type="main"> <s><emph type="italics"></emph>This we ſhall eaſily do. </s> <s>For ſuppoſing the Amplitude of the Semi<lb></lb>par abola to be of 10000 parts, the half of the Tangent of each <lb></lb>degree of Elevation ſhews the Altitude. </s> <s>As for example, of the <lb></lb>Semiparabola whoſe Elevation is 30 degrees, and Amplitude, as is <lb></lb>ſuppoſed, 10000 parts, the Altitude ſhall be 2887, for ſo much, very <lb></lb>near, is the half of the Tangent. </s> <s>And having found the Altitude the <lb></lb>Sublimity is to be known in this manner. </s> <s>For aſmuch as it hath been <lb></lb>demonſtrated that the half of the Amplitude of a Semiparabola is the <lb></lb>Mean proportional betwixt the Altitude and Sublimity, and the Alti<lb></lb>tude being already found, and the half of the Amplitude being alwaies <lb></lb>the ſame, to wit, 5000 parts, if we ſhall divide the Square thereof by <lb></lb>the Altitude found, the deſired Sublimity ſhall come forth. </s> <s>As in the <lb></lb>Example: The Altitude found was 2887; The Square of the 5000 <lb></lb>parts is 25000000; which being divided by 2887, giveth 8659, ve<lb></lb>ry near, for the Sublimity ſought.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SALV. </s> <s>Now here we ſee, in the ſirſt place, that the Conje<lb></lb>cture is very true which was mentioned afore, that in different <lb></lb>Elevations the farther one goeth from the middlemoſt, whether it <lb></lb>be in the Higher, or in the Lower, ſo much greater <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> and Vio<lb></lb>lence is required to carry the Project to the ſame Diſtance. </s> <s>For the <lb></lb><emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> lying in the mixture of the two Motions, Equable, Hori<lb></lb>zontal, and Perpendicular Naturally-Accelerate, of which <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end><lb></lb>the Aggregate of the Altitude and Sublimity is the Meaſure, we do <lb></lb>ſee in the propounded Table that that ſame Aggregate is leaſt in <lb></lb>the Elevation of <emph type="italics"></emph>gr.<emph.end type="italics"></emph.end> 45, in which the Altitude and Sublimity are <lb></lb>equal, <emph type="italics"></emph>ſcilicet<emph.end type="italics"></emph.end> each 5000, and their Aggregate 10000. But if we <lb></lb>ſhould look on any greater Elevation, as, for example, of <emph type="italics"></emph>gr.<emph.end type="italics"></emph.end> 50, we <lb></lb>ſhould ſind the Altitude to be 5959, and the Sublimity 4196, which <lb></lb>added together make 10155. And ſo much alſo we ſhould find the <lb></lb><emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of <emph type="italics"></emph>gr.<emph.end type="italics"></emph.end> 40 to be, this and that Elevation being equally re<lb></lb>mote from the middlemoſt. </s> <s>Where we are to note, in the ſecond <lb></lb>place, that it is true, That equal <emph type="italics"></emph>Impetus's<emph.end type="italics"></emph.end> are ſought by two, and <lb></lb>two in the Elevations equidiſtant from the middlemoſt, with this <lb></lb>pretty variation over and above that the Altitudes and the Subli<lb></lb>mities of the ^{*} ſuperiour Elevations anſwer alternally to the Sub<lb></lb><arrow.to.target n="marg1103"></arrow.to.target><lb></lb>limities and Altitudes of the Inferiour: ſo that whereas in the <pb xlink:href="040/01/936.jpg" pagenum="243"></pb>example propoſed, in the Elevation of <emph type="italics"></emph>gr.<emph.end type="italics"></emph.end> 50. the Altitude is 5959 <lb></lb>and the Sublimity 4196, in the Elevation of <emph type="italics"></emph>gr.<emph.end type="italics"></emph.end> 40. it falls out on <lb></lb>the contrary that the Altitude is 4196, and the Sublimity 5959: <lb></lb>And the ſame happens in all others without any difference; ſave <lb></lb>only that for the avoyding of tediouſneſs in Calculations we have <lb></lb>kept no account of ſome fractions, which in ſo great ſums are of no <lb></lb>value, but may without any prejudice be omitted.</s></p><p type="margin"> <s><margin.target id="marg1103"></margin.target>* <emph type="italics"></emph>i.e.<emph.end type="italics"></emph.end> Thoſe above <lb></lb>45 deg.</s></p><p type="main"> <s>SAGR. </s> <s>I am obſerving that of the two <emph type="italics"></emph>Impetus's<emph.end type="italics"></emph.end> Horizontal and <lb></lb>Perpendicular in Projections, the more Sublime they are, they need <lb></lb>ſo much the leſs of the Horizontal, and the more of the Perpendi<lb></lb>cular. </s> <s>Moreover in thoſe of ſmall Elevation, great muſt be the <lb></lb>Force of the Horizontal <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> which is to carry the Project in a <lb></lb>little Altitude. </s> <s>But although I comprehend very well that in the <lb></lb>Total Elevation of <emph type="italics"></emph>gr.<emph.end type="italics"></emph.end> 90, all the force in the world ſufficeth not <lb></lb>to drive the Project one ſingle Inch from the Perpendicular, but <lb></lb>that it muſt of neceſſity fall in the ſame place whence it was expel<lb></lb>led; yet dare I not with the like certainty affirm that likewiſe in the <lb></lb>nullity of Elevation, that is in the Horizontal Line, the Project <lb></lb>cannot by any Force leſs than infinite, be driven to any di<lb></lb>ſtance: So, as that, for example, a Culverin it ſelf ſhould not be <lb></lb>able to carry a Ball of Iron Horizontally, or, as they ſay, at Point <lb></lb>blank, that is at no point, which is when it hath no Elevation. </s> <s>I <lb></lb>ſay, in this caſe I ſtand in ſome doubt; and that I do not reſolute<lb></lb>ly deny the thing, the reaſon depends on another Accident which <lb></lb>ſeems no leſs ſtrange, and yet I have a very neceſſary Demonſtrati<lb></lb>on for it. </s> <s>And the Accident is this, the Impoſſibility of diſtending <lb></lb>a Rope, ſo, as that it may be ſtretched right out, and parallel to the <lb></lb>Horizon, but that it alwaies ſwayes and bendeth, nor is there any <lb></lb>Force that can ſtretch it otherwiſe.</s></p><p type="main"> <s>SALV. </s> <s>So then, <emph type="italics"></emph>Sagredus,<emph.end type="italics"></emph.end> your wonder ceaſeth in this caſe of <lb></lb>the Rope becauſe you have the Demonſtration of it. </s> <s>But if we <lb></lb>ſhall well conſider the matter, it may be we ſhall find ſome corre<lb></lb>ſpondence between the Accident of the Project and this of the <lb></lb>Rope. </s> <s>The Curvity of the Line of the Horizontal Projection ſeem<lb></lb>eth to be derived from two Forces, of which one, (which is that of <lb></lb>the Projicient) driveth it Horizontally, and the other, (which <lb></lb>is the Gravity of the Project) draweth it downwards Perpendicu<lb></lb>larly. </s> <s>Now ſo in the ſtretching of the Rope, there are the Forces <lb></lb>of thoſe that pull it Horizontally, and there is alſo the weight of <lb></lb>the Rope it ſelf, which naturally inclineth it downwards. </s> <s>Theſe <lb></lb>two effects are very much alike in the generation of them. </s> <s>And if <lb></lb>you allow the weight of the Rope ſo much ſtrength and power as to <lb></lb>be able to oppoſe and overcome any whatever Immenſe Force, that <lb></lb>would diſtend it right out, why will you deny the like to the weight <lb></lb>of the Bullet? </s> <s>But beſides, I ſhall tell you, and at once procure your <pb xlink:href="040/01/937.jpg" pagenum="244"></pb>wonder, and delight, that the Rope thus tentered, and ſtretcht little <lb></lb>or much, doth ſhape it ſelf into Lines that come very near to Para<lb></lb>bolical, and the reſemblance is ſo great, that if you draw a Para<lb></lb>bolical Line upon a plain Superficies that is erect unto the Horizon, <lb></lb>and holding it reverſed, that is with the Vertex downwards and <lb></lb>with the Baſe Parallel to the Horizon, you cauſe a Chain to be held <lb></lb>pendent, and ſuſtained at the extreams of the Baſe of the Deſcribed <lb></lb>Parabola, you ſhall ſee the ſaid Chain, as you ſlaken it more or leſs, <lb></lb>to incurvate and apply it ſelf to the ſame Parabola, and this ſame <lb></lb>Application ſhall be ſo much the more exact, when the deſcribed <lb></lb>Parabola is leſs curved, that is more diſtended: So that in Parabola's <lb></lb>deſcribed with Elevations under <emph type="italics"></emph>gr.<emph.end type="italics"></emph.end> 45, the Chain anſwereth the <lb></lb>Parabola almoſt to an hair.</s></p><p type="main"> <s>SAGR. </s> <s>It ſeems then that with ſuch a Chain wrought into ſmall <lb></lb>Links one might in an inſtant trace out many Parabolick Lines up<lb></lb>on a plain Superficies.</s></p><p type="main"> <s>SALV. </s> <s>One might, and that alſo with no ſmall commodity, as I <lb></lb>ſhall tell you anon.</s></p><p type="main"> <s>SIMP. </s> <s>But before you paſs any farther, I alſo would gladly be <lb></lb>aſcertained at leaſt in that Propoſition of which you ſay there is a <lb></lb>very neceſſary Demonſtration, I mean that of the Impoſſibility of <lb></lb>diſtending a Rope, by any whatever immenſe Force, right out and <lb></lb>equidiſtant from the Horizon.</s></p><p type="main"> <s>SAGR. </s> <s>I will ſee if I remember the Demonſtration, for under<lb></lb>ſtanding of which it is neceſſary, <emph type="italics"></emph>Simplicius,<emph.end type="italics"></emph.end> that you ſuppoſe for <lb></lb>true, that which in all Mechanick Inſtruments is confirmed, not on<lb></lb>ly by Experience, but alſo by Demonſtration: and this it is, That <lb></lb>the Velocity of the Mover, though its Force be very ſmall, may <lb></lb>overcome the Reſiſtance, though very great, of a Reſiſter, which <lb></lb>muſt be moved ſlowly when ever the Velocity of the Mover hath <lb></lb>greater proportion to the Tardity of the Reſiſter, than the Reſi<lb></lb>ſtance of that which is to be moved hath to the Force of the Mo<lb></lb>ver.</s></p><p type="main"> <s>SIMP. </s> <s>This I know very well, and it is demonſtrated by <emph type="italics"></emph>Ari<lb></lb>ſtotle<emph.end type="italics"></emph.end> in his Mechanical Queſtions, and is manifeſtly ſeen in the Lea<lb></lb>ver and in the Stiliard, in which the Roman which weigheth not <lb></lb>above 4 pounds, will lift up a weight of 400 in caſe the diſtance of <lb></lb>the ſaid Roman from the Center on which the Beam turneth be <lb></lb>more than an hundred times greater than the diſtance of that point <lb></lb>at which the great weight hangeth from the ſame Center: and this <lb></lb>cometh to paſs becauſe in the deſcent which the Roman maketh <lb></lb>paſſeth a Space above an hundred times greater than the Space <lb></lb>which the great weight mounteth in the ſame Time: Which is all <lb></lb>one as to ſay, that the little Roman moveth with a Velocity above <lb></lb>an hundred times greater than the Velocity of the great Weight.</s></p><pb xlink:href="040/01/938.jpg" pagenum="245"></pb><p type="main"> <s>SAGR. </s> <s>You argue very well, and make no ſeruple at all of <lb></lb>granting, that be the Force of the Mover never ſo ſmall it ſhall ſu<lb></lb>perate any what ever great Reſiſtance at all times when that ſhall <lb></lb>more exceed in Velocity than this doth in Force and Gravity. <lb></lb></s> <s>Now come we to the caſe of the Rope. </s> <s>And drawing a ſmall <lb></lb>Scheme be pleaſed to underſtand for once that this Line A B, reſt<lb></lb>ing upon the two fixed and ſtanding points A and B, to have hang<lb></lb>ing at its ends, as you ſee, two immenſe Weights C and D, which <lb></lb>drawing it with great Force make it to ſtand directly diſtended, it <lb></lb>being a ſimple Line without any gravity. </s> <s>And here I proceed, and <lb></lb>tell you, that if at the midſt of that which is the point E, you ſhould <lb></lb>hang any never ſo little a Weight, as is this H, the Line A B would <lb></lb>yield, and inclining towards the point F, and by conſequence <lb></lb>lengthening, will conſtrain the two great Weights C and D to <lb></lb>aſcend upwards: which I demonſtrate to you in this manner: <lb></lb>About the two points A and B as Centers I deſcribe two Quadrants <lb></lb>E F G, and E L M, and in regard that the two Semidiameters AI <lb></lb>and B L are equal to the two Semidiameters A E and E B, the exceſ<lb></lb>ſes F I and F L ſhall be the quantity of the prolongations of the <lb></lb>parts A F and F B, above A E and E B; and of conſequence ſhall <lb></lb><figure id="id.040.01.938.1.jpg" xlink:href="040/01/938/1.jpg"></figure><lb></lb>determine the Aſcents <lb></lb>of the Weights C and <lb></lb>D, in caſe that the <lb></lb>Weight H had had a <lb></lb>power to deſcend to F: <lb></lb>which might then be <lb></lb>in caſe the Line E F, <lb></lb>which is the quantity <lb></lb>of the Deſcent of the <lb></lb>ſaid Weight H, had <lb></lb>greater proportion to <lb></lb>the Line F I which de<lb></lb>termineth the Aſcent of <lb></lb>the two Weights C & <lb></lb>D, than the pondero<lb></lb>ſity of both thoſe Weights hath to the ponderoſity of the Weight <lb></lb>H. </s> <s>But this will neceſſarily happen, be the ponderoſity of the <lb></lb>Weights C and D never ſo great, and that of H never ſo ſmall; for <lb></lb>the exceſs of the Weights C and D above the Weight His not ſo <lb></lb>great, but that the exceſs of the Tangent E F above the part of the <lb></lb>Secant F I may bear a greater proportion. </s> <s>Which we will prove <lb></lb>thus: Let there be a Circle whoſe Diameter is G A I; and look <lb></lb>what proportion the ponderoſity of the Weights C and D have to <lb></lb>the ponderoſity of H, let the Line B O have the ſame proportion to <lb></lb>another, which let be C, than which let D be leſſer: So that B O <pb xlink:href="040/01/939.jpg" pagenum="246"></pb>ſhall have greater proportion to D, than to C. </s> <s>Unto O B and D <lb></lb>take a third proportional B E; and as O E is to E B, ſo let the Dia<lb></lb>meter G I (prolonging it) be to I F: and from the Term F <lb></lb>draw the Tangent F N. </s> <s>And becauſe it hath been preſuppoſed, <lb></lb>that as O E is to E B, ſo is G I to I F: therefore, by Compoſition, as <lb></lb>O B is to B E, ſo is G F to F I: But betwixt O B and B E the Mean<lb></lb>proportional is D; and betwixt G F and F I the Mean-proporti<lb></lb>onal is N F: Therefore N F hath the ſame proportion to F I that <lb></lb>O B hath to D: which proportion is greater than that of the <lb></lb>Weights C and D to the Weight H. Therefore, the Deſcent or <lb></lb>Velocity of the Weight H having greater proportion to the Aſcent <lb></lb>or Velocity of the Weights C and D, than the ponderoſity of the <lb></lb>ſaid Weights C and D hath to the ponderoſity of the Weight H: <lb></lb>It is manifeſt, that the Weight H ſhall deſcend, that is, that the <lb></lb>Line A B ſhall depart from Horizontal Rectitude. </s> <s>And that which <lb></lb>befalleth the right Line A B deprived of Gravity in caſe any ſmall <lb></lb>Weight H cometh to be hanged at the ſame in E, happens alſo to <lb></lb>the ſaid Rope A B, ſuppoſed to be of ponderous Matter, without <lb></lb>the addition of any other Grave Body; for that the Weight of <lb></lb>the Matter it ſelf compounding the ſaid Rope AB is ſuſpended <lb></lb>thereat.</s></p><p type="main"> <s>SIMP. </s> <s>You have fully ſatisfied me; therefore <emph type="italics"></emph>Salviatus<emph.end type="italics"></emph.end> may ac<lb></lb>cording to his promiſe declare unto us, what the Commodity is that <lb></lb>may be drawn from ſuch like Chains, and after that relate unto us <lb></lb>thoſe Speculations which have been made by our <emph type="italics"></emph>Accademian<emph.end type="italics"></emph.end><lb></lb>touching the Force of Percuſſion.</s></p><p type="main"> <s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>ALV. </s> <s>We are for this day ſufficiently employed in the Con<lb></lb>templations already delivered, and the Time, which is pretty late, <lb></lb>would not be enough to carry us through the matters you mention; <lb></lb>therefore we ſhall defer our Conference till ſome more convenient <lb></lb>time.</s></p><p type="main"> <s>SAGR. </s> <s>I concur with you in opinion, for that by ſundry diſ<lb></lb>courſes that I have had with the Friends of our <emph type="italics"></emph>Academick<emph.end type="italics"></emph.end> I have <lb></lb>learnt that this Argument of the Force of Percuſſion is very ob<lb></lb>ſcure, nor hath hitherto any one that hath treated thereof penetra<lb></lb>ted its intricacies, full of darkneſs, and altogether remote from <lb></lb>mans firſt imaginations: and amongſt the Concluſions that I have <lb></lb>heard of, one runs in my mind that is very extravagant and odde, <lb></lb>namely, That the Force of Percuſſion is Interminate, if not Infi<lb></lb>nite. </s> <s>We will therefore attend the leaſure of <emph type="italics"></emph>Salviatus.<emph.end type="italics"></emph.end> But for <lb></lb>the preſent, tell me what things are thoſe which are written at the <lb></lb>end of the Treatiſe of Projects?</s></p><p type="main"> <s>SALV. </s> <s>Theſe are certain Propoſitions touching the Center of <lb></lb>Gravity of Solids, which our <emph type="italics"></emph>Academick<emph.end type="italics"></emph.end> found out in his youth, <lb></lb><arrow.to.target n="marg1104"></arrow.to.target><lb></lb>conceiving that what ^{*} <emph type="italics"></emph>Frederico Comandino<emph.end type="italics"></emph.end> had writ touching the <pb xlink:href="040/01/940.jpg" pagenum="247"></pb>ſame was not altogether without Imperſection. </s> <s>He therefore <lb></lb>thought that with theſe Propoſitions, which here you ſee written, <lb></lb>he might ſupply that which is wanting in the Book of <emph type="italics"></emph>Comandine<emph.end type="italics"></emph.end>; <lb></lb>and he applyed himſelf to the ſame at the Inſtance of the moſt <lb></lb>Illuſtrious Lord Marqueſs <emph type="italics"></emph>Guid' Vbaldo dal Monte,<emph.end type="italics"></emph.end> the moſt ex<lb></lb>cellent Mathematician of his Time, as his ſeveral Printed Works <lb></lb>do ſpeak him; and gave a Copy thereof to that Noble Lord with <lb></lb>thoughts to have purſued the ſame Argument in other Solids not <lb></lb>mentioned by <emph type="italics"></emph>Comandine:<emph.end type="italics"></emph.end> But he chanced after ſome Time to <lb></lb>meet with the ^{*} Book of <emph type="italics"></emph>Signore Luca Valerio,<emph.end type="italics"></emph.end> a moſt famous <lb></lb><arrow.to.target n="marg1105"></arrow.to.target><lb></lb>Geometrician, and ſaw that he reſolveth all theſe matters with<lb></lb>out omiſſion of any thing, he proceeded no farther, although his <lb></lb>Agreſſions were by methods very different from theſe of <emph type="italics"></emph>Signore <lb></lb>Valerio.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1104"></margin.target>* <emph type="italics"></emph>Fredericus Co<lb></lb>mandinus.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1105"></margin.target>* <emph type="italics"></emph>De.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>SAGR. </s> <s>It would be a favour, therefore, if, for this time, which <lb></lb>interpoſeth between this and our next Meeting, you would pleaſe <lb></lb>to leave the Book in my hands: for I ſhall all the while be read<lb></lb>ing and ſtudying the Propoſitions that are conſequently therein <lb></lb>writ.</s></p><p type="main"> <s>SALV. </s> <s>I ſhall very willingly obey your Command; and hope <lb></lb>that you will take pleaſure in theſe Propoſitions.</s></p></chap><chap><pb xlink:href="040/01/941.jpg" pagenum="248"></pb><p type="head"> <s>AN <lb></lb>APPENDIX, <lb></lb>In which is contained certain <lb></lb>THE OREMS and their DEMONSTRATIONS: <lb></lb>Formerly written by the ſame Author, touching the <lb></lb><emph type="italics"></emph>CENTER<emph.end type="italics"></emph.end> of <emph type="italics"></emph>GRAVITY,<emph.end type="italics"></emph.end> of <lb></lb>SOLIDS.</s></p><p type="head"> <s>POSTVLATVM.</s></p><p type="main"> <s><emph type="italics"></emph>We preſuppoſe equall Weights to be alike diſpo<lb></lb>ſed in ſever all Ballances, if the Center of Gra<lb></lb>vity of ſome of thoſe Compounds ſhall divide the Ballance <lb></lb>according to ſome proportion, and the Ballance ſhall <lb></lb>alſo divide their Center of Gravity according to the <lb></lb>ſame proportion.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>LEMMA.</s></p><p type="main"> <s><emph type="italics"></emph>Let the line A B be cut in two equall parts in C, <lb></lb>whoſe half A C let be divided in E, ſo that as B E is to <lb></lb>E A, ſo may A E be to E C. </s> <s>I ſay that B E is double<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.941.1.jpg" xlink:href="040/01/941/1.jpg"></figure><lb></lb><emph type="italics"></emph>to E A. </s> <s>For as B E is to E <lb></lb>A, ſo is E A to E C: there<lb></lb>fore by Compoſition and by Permutation of Proportion, as <lb></lb>B A is to A C, ſo is A E to E C: But as A E is to E C, <lb></lb>that is, B A to A C, ſo is B E to E A: Wherefore B <lb></lb>E is double to E A.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>This ſuppoſed, we will Demonſtrate, That,<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/942.jpg" pagenum="249"></pb><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>If certain Magnitudes at any Rate equally exceed<lb></lb>ing one another, and whoſe exceſs is equal to <lb></lb>the leaſt of them, be ſo diſpoſed in the Balance, <lb></lb>as that they hang at equal diſtances, to divide <lb></lb>the Center of Gravity of the whole Balance <lb></lb>ſo, that the part towards the leſſer Magnitudes <lb></lb>be double to the remainder.</s></p><p type="main"> <s><emph type="italics"></emph>In the ^{*} Ballance A B, therefore, let there be ſuſpended at equal di-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1106"></arrow.to.target><lb></lb><emph type="italics"></emph>ſtances any number of Magnitudes, as hath been ſaid, F, G, H, K, <lb></lb>N; of which let the leaſt be N, and let the points of the Suſpenſions <lb></lb>be A, C, D, E, B, and let the Center of Gravity of all the Magnitudes <lb></lb>ſo diſpoſed be X. </s> <s>It is to be proved that the part of the Ballance B X <lb></lb>towards the leſſer Magnitudes is double to the remaining part X A.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1106"></margin.target>* Or Beam.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Ballance be divided in two equal parts in D, for it muſt ei<lb></lb>ther fall in ſome point of the Suſpenſions, or elſe in the middle point be<lb></lb>tween two of the points of the Suſpenſions: and let the remaining di<lb></lb>ſtances of the Suſpenſions which fall between A and D, be all divided <lb></lb>into halves by the Points M and I; and let all the Magnitudes be divi-<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.942.1.jpg" xlink:href="040/01/942/1.jpg"></figure><lb></lb><emph type="italics"></emph>ded into parts equal to <lb></lb>N: Now the parts of F <lb></lb>ſhall be ſo many in num<lb></lb>ber, as thoſe Magnitudes <lb></lb>be which are ſuſpended <lb></lb>at the Ballance, and the <lb></lb>parts of G one fewer, <lb></lb>and ſo of the reſt. </s> <s>Let <lb></lb>the parts of F therefore be N, O, R, S, T, and let thoſe of G be N, O, <lb></lb>R, S, thoſe of H alſo N, O, R, then let thoſe of K be N, O: and all the <lb></lb>Magnitudes in which are N ſhall be equal to F; and all the Magnitudes <lb></lb>in which are O ſhall be equal to G; and all the Magnitudes in which <lb></lb>are R ſhall be equal to H; and thoſe in which S ſhall be equal to K; and <lb></lb>the Magnitude T is equal to N. </s> <s>Becauſe therefore all the Magnitudes <lb></lb>in which are N are equal to one another, they ſhall equiponderate in <lb></lb>the point D, which divideth the Ballance into two equal parts; and for <lb></lb>the ſame cauſe all the Magnitudes in which are O do equiponderate in <lb></lb>I; and thoſe in which are R in C; and in which are S in M do equi<lb></lb>ponderate; and T is ſuſpended in A. </s> <s>Therefore in the Ballance A D at <lb></lb>the equal diſtances D, I, C, M, A, there are Magnitudes ſuſpended ex<lb></lb>ceeding one another equally, and whoſe exceſs is equal to the leaſt: and <lb></lb>the greateſt, which is compounded of all the N N hangeth at D, the<emph.end type="italics"></emph.end><pb xlink:href="040/01/943.jpg" pagenum="250"></pb><emph type="italics"></emph>leaſt which is T hangeth at A; and the reſt are ordinately diſpoſed. <lb></lb></s> <s>And again there is another Ballance A B in which other Magnitudes <lb></lb>equal in number and Magnitude to the former are diſpoſed in the ſame <lb></lb>order. </s> <s>Wherefore the Ballances A B and A D are divided by the Cen<lb></lb>ter of all the Magnitudes according to the ſame proportion: But the <lb></lb>Center of Gravity of the aforeſaid Magnitudes is X: Wherefore X <lb></lb>divideth the Ballances B A and A D according to the ſame proportion; <lb></lb>ſo that as B X is to X A, ſo is X A to X D: Wherefore B X is double <lb></lb>to X A, by the Lemma aforegoing: Which was to be proved.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>If in a Parabolical Conoid Figure be deſcribed, <lb></lb>and another circumſcribed by Cylinders of <lb></lb>equal Altitude; and the Axis of the ſaid Co<lb></lb>noid be divided in ſuch proportion that the <lb></lb>part towards the Vertex be double to that to<lb></lb>wards the Baſe; the Center of Gravity of the <lb></lb>inſcribed Figure of the Baſe portion ſhall be <lb></lb>neareſt to the ſaid point of diviſion; and the <lb></lb>Center of Gravity of the circumſcribed from <lb></lb>the Baſe of the Conoid ſhall be more remote: <lb></lb>and the diſtance of either of thoſe Centers <lb></lb>from that ſame point ſhall be equal to the Line <lb></lb>that is the ſixth part of the Altitude of one of <lb></lb>the Cylinders of which the Figures are com<lb></lb>poſed.</s></p><p type="main"> <s><emph type="italics"></emph>Take therefore a Parabolical Conoid, and the Figures that have <lb></lb>been mentioned: let one of them be inſcribed, the other circum<lb></lb>ſcribed; and let the Axis of the Conoid, which let be A E, be di<lb></lb>vided in N, in ſuch proportion as that A N be double to N E. </s> <s>It is to <lb></lb>be proved that the Center of Gravity of the inſcribed Figure is in the <lb></lb>Line N E, but the Center of the circumſcribed in the Line A N. </s> <s>Let <lb></lb>the Plane of the Figures ſo diſpoſed be cut through the Axis, and let <lb></lb>the Section be that of the Parabola B A C: and let the Section of the <lb></lb>cutting Plane, and of the Baſe of the Conoid be the Line B C; and <lb></lb>let the Sections of the Cylinders be the Rectangular Figures; as ap<lb></lb>peareth in the deſcription. </s> <s>Firſt, therefore, the Cylinder of the inſcri<lb></lb>bed whoſe Axis is D E, hath the ſame proportion to the Cylinder whoſe <lb></lb>Axis is D Y, as the Quadrate I D hath to the Quadrate S Y; that is, <lb></lb>as D A hath to A Y: and the Cylinder whoſe Axis is D Y is<emph.end type="italics"></emph.end> potentia <pb xlink:href="040/01/944.jpg" pagenum="251"></pb><emph type="italics"></emph>to the Cylinder Y Z as S Y to R Z, that is, as Y A to A Z: and, by the <lb></lb>ſame reaſon, the Cylinder whoſe Axis is Z Y is to that whoſe Axis is <lb></lb>Z V, as Z A is to A V. </s> <s>The ſaid Cylinders, therefore, are to one ano<lb></lb>ther as the Lines D A, A Y; Z A, A V: But theſe are equally exceed<lb></lb>ing to one another, and the exceſs is equal to the leaſt, ſo that A Z is <lb></lb>double to A V; and A Y is triple the<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.944.1.jpg" xlink:href="040/01/944/1.jpg"></figure><lb></lb><emph type="italics"></emph>ſame; and D A Quadruple. </s> <s>Thoſe <lb></lb>Cylinders, therefore, are certain Mag<lb></lb>nitudes in order equally exceeding one <lb></lb>another, whoſe exceſs is equal to the <lb></lb>leaſt of them, and is the Line X M, <lb></lb>in which they are ſuſpended at equal <lb></lb>diſtances (for that each of the Cy<lb></lb>linders hath its Center of Gravity in <lb></lb>the miaſt of the Axis.) Wherefore, <lb></lb>by what hath been above demonſtra<lb></lb>ted, the Center of Gravity of the Mag<lb></lb>nitude compounded of them all divi<lb></lb>deth the Line X M ſo, that the part <lb></lb>towards X is double to the reſt. </s> <s>Divide it, therefore, and, let X<emph.end type="italics"></emph.end> <foreign lang="grc">α</foreign> <emph type="italics"></emph>be <lb></lb>double<emph.end type="italics"></emph.end> <foreign lang="grc">α</foreign> <emph type="italics"></emph>M: therefore is<emph.end type="italics"></emph.end> <foreign lang="grc">α</foreign> <emph type="italics"></emph>the Center of Gravity of the inſcribed Fi<lb></lb>gure. </s> <s>Divide A V in two equal parts in<emph.end type="italics"></emph.end> <foreign lang="grc">ε</foreign>: <foreign lang="grc">ε</foreign> <emph type="italics"></emph>X ſhall be double to <lb></lb>M E: But X<emph.end type="italics"></emph.end> <foreign lang="grc">α</foreign> <emph type="italics"></emph>is double to<emph.end type="italics"></emph.end> <foreign lang="grc">α</foreign> <emph type="italics"></emph>M: Wherefore<emph.end type="italics"></emph.end> <foreign lang="grc">ε</foreign> <emph type="italics"></emph>E ſhall be triple E<emph.end type="italics"></emph.end> <foreign lang="grc">α.</foreign> <emph type="italics"></emph>But<emph.end type="italics"></emph.end><lb></lb><foreign lang="grc">α</foreign> <emph type="italics"></emph>E is triple E N: It is manifeſt, therefore, that E N is greater than <lb></lb>E X; and for that cauſe<emph.end type="italics"></emph.end> <foreign lang="grc">α,</foreign> <emph type="italics"></emph>which is the Center of Gravity of the in<lb></lb>ſcribed Figure, cometh nearer to the Baſe of the Conoid than N. </s> <s>And <lb></lb>becauſe that as A E is to E N, ſo is the part taken away<emph.end type="italics"></emph.end> <foreign lang="grc">ε</foreign> <emph type="italics"></emph>E to the part <lb></lb>taken away E<emph.end type="italics"></emph.end> <foreign lang="grc">α</foreign>: <emph type="italics"></emph>and the remaining part ſhall be to the remaming part, <lb></lb>that is, A<emph.end type="italics"></emph.end> <foreign lang="grc">ε</foreign> <emph type="italics"></emph>to N<emph.end type="italics"></emph.end> <foreign lang="grc">α,</foreign> <emph type="italics"></emph>as A E to E N. Therefore<emph.end type="italics"></emph.end> <foreign lang="grc">α</foreign> <emph type="italics"></emph>N is the third part of <lb></lb>A<emph.end type="italics"></emph.end> <foreign lang="grc">ε,</foreign> <emph type="italics"></emph>and the ſixt part of A V. </s> <s>And in the ſame manner the Cylinders of <lb></lb>the circumſcribed Figure may be demonſtrated to be equally exceeding <lb></lb>one another, and the exceſs to me equal to the least; and that they have <lb></lb>their Centers of Gravity at equal diſtances in the Line<emph.end type="italics"></emph.end> <foreign lang="grc">ε</foreign> <emph type="italics"></emph>M. </s> <s>If therefore<emph.end type="italics"></emph.end><lb></lb><foreign lang="grc">ε</foreign> <emph type="italics"></emph>M be divided in<emph.end type="italics"></emph.end> <foreign lang="grc">π,</foreign> <emph type="italics"></emph>ſo as that<emph.end type="italics"></emph.end> <foreign lang="grc">ε π</foreign> <emph type="italics"></emph>be double to the remaining part<emph.end type="italics"></emph.end> <foreign lang="grc">π</foreign> <emph type="italics"></emph>M;<emph.end type="italics"></emph.end><lb></lb><foreign lang="grc">π</foreign> <emph type="italics"></emph>ſhall be the Center of Gravity of the whole circumſcribed Magnitude. <lb></lb></s> <s>And ſince<emph.end type="italics"></emph.end> <foreign lang="grc">ε π</foreign> <emph type="italics"></emph>is double to<emph.end type="italics"></emph.end> <foreign lang="grc">π</foreign> <emph type="italics"></emph>M; and A<emph.end type="italics"></emph.end> <foreign lang="grc">ε</foreign> <emph type="italics"></emph>leſs than double EM: (for <lb></lb>that they are equal:) the whole A E ſhall be leſs than triple E<emph.end type="italics"></emph.end> <foreign lang="grc">π</foreign><emph type="italics"></emph>: Where<lb></lb>fore E<emph.end type="italics"></emph.end> <foreign lang="grc">π</foreign> <emph type="italics"></emph>ſhall be greater than E N. And, ſince<emph.end type="italics"></emph.end> <foreign lang="grc">ε</foreign> <emph type="italics"></emph>M is triple to M<emph.end type="italics"></emph.end> <foreign lang="grc">π,</foreign><lb></lb><emph type="italics"></emph>and M E with twice<emph.end type="italics"></emph.end> <foreign lang="grc">ε</foreign> <emph type="italics"></emph>A is likewiſe triple to M E: the whole A E with <lb></lb>A<emph.end type="italics"></emph.end> <foreign lang="grc">ε</foreign> <emph type="italics"></emph>ſhall be triple to E<emph.end type="italics"></emph.end> <foreign lang="grc">π</foreign><emph type="italics"></emph>: But A E is triple to E N: Wherefore the <lb></lb>remaining part A<emph.end type="italics"></emph.end> <foreign lang="grc">ε</foreign> <emph type="italics"></emph>ſhall be triple to the remaining part<emph.end type="italics"></emph.end> <foreign lang="grc">π</foreign> <emph type="italics"></emph>N. </s> <s>Therefore <lb></lb>N<emph.end type="italics"></emph.end> <foreign lang="grc">π</foreign> <emph type="italics"></emph>is the ſixth part of A V. </s> <s>And theſe are the things that were to be <lb></lb>demonſtrated.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/945.jpg" pagenum="252"></pb><p type="head"> <s>COROLLARY.</s></p><p type="main"> <s>Hence it is manifeſt, that a Conoid may be inſcribed in a Para<lb></lb>bolical Figure, and another circumſcribed, ſo, as that the <lb></lb>Centers of their Gravities may be diſtant from the point N <lb></lb>leſs than any Line given.</s></p><p type="main"> <s><emph type="italics"></emph>For if we aſſume a Line ſexcuple of the propoſed Line, and make the <lb></lb>Axis of the Cylinders, of which the Figures are compounded given <lb></lb>leſſer than this aſſumed Line, there ſhall fall Lines between the Centers <lb></lb>of Gravities of theſe Figures and the mark N that are leſs than the <lb></lb>Line propoſed.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The former Propoſition another way.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Axis of the Conoid (which let be C D) be divided in <lb></lb>O, ſo, as that C O be double to O D. </s> <s>It is to be proved that the <lb></lb>Center of Gravity of the inſcribed Figure is in the Line O D; <lb></lb>and the Center of the circumſcribed in C O. </s> <s>Let the Plane of the Fi<lb></lb>gures be cut through the Axis and C, as hath been ſaid. </s> <s>Becauſe there<lb></lb>fore the Cylinders S N, T M, V I,<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.945.1.jpg" xlink:href="040/01/945/1.jpg"></figure><lb></lb><emph type="italics"></emph>X E are to one another as the Squares <lb></lb>of the Lines S D, T N, V M, X I; <lb></lb>and theſe are to one another as the <lb></lb>Lines N C, C M, C I, C E: but <lb></lb>theſe do exceed one another equally; <lb></lb>and the exceſs is equal to the leaſt, to <lb></lb>wit, C E: And the Cylinder T M is <lb></lb>equal to the Cylinder Q N; and the <lb></lb>Cylinder V I equal to P N; and X E <lb></lb>is equal to L N: Therefore the Cylin<lb></lb>ders S N, Q N, P N, and L N do <lb></lb>equally exceed one another, and the <lb></lb>exceſs is equal to the leaſt of them, <lb></lb>namely, to the Cylinder L N. </s> <s>But <lb></lb>the exceſs of the Cylinder S N, above <lb></lb>the Cylinder Q N is a Ring whoſe <lb></lb>height is Q T; that is, N D; and <lb></lb>its breadth S <expan abbr="q.">que</expan> And the exceſs of the Cylinder Q N above P N, is a <lb></lb>Ring, whoſe breadth is Q P. </s> <s>And the exceſs of the Cylinder P N above <lb></lb>L N is a Ring, whoſe breadth is P L. </s> <s>Wherefore the ſaid Rings S Q, <lb></lb>Q P, P L, are equal to another, and to the Cylinder L N. </s> <s>Therefore the <lb></lb>Ring S T equalleth the Cylinder X E: the Ring Q V, which is double <lb></lb>to S T, equalleth the Cylinder V I; which likewiſe is double to the<emph.end type="italics"></emph.end><pb xlink:href="040/01/946.jpg" pagenum="253"></pb><emph type="italics"></emph>Cylinder X E: and for the ſame cauſe the Ring P X is equal to the <lb></lb>Cylinder T M; and the Cylinder L E ſhall be equal to the Cylinder S N. <lb></lb></s> <s>In the Beam or Ballance, therefore, K F connecting the middle points of <lb></lb>the Right-lines E I and D N, and cut into equal parts in the points H <lb></lb>and G, are certain Magnitudes ſuſpended, to wit the Cylinders S N, <lb></lb>T M, V I, X E; and the Center of Gravity of the firſt Cylinder is K; <lb></lb>and of the ſecond H; of the third G; of the fourth F. </s> <s>And we have <lb></lb>another Ballance M K, which is the half of the ſaid F K, and a like <lb></lb>number of points diſtributed into equal parts, to wit, M H, H N, N K, <lb></lb>and on it other Magnitudes, equal in number and bigneſs to thoſe which <lb></lb>are on the Beam F K, and having the Centers of Gravity in the points <lb></lb>M, H, N, and K, and diſpoſed in the ſame order. </s> <s>For the Cylinder L E <lb></lb>hath its Center of Gravity in M; and is equal to the Cylinder S N that <lb></lb>hath its Center in K: And the Ring P X hath the Center H; and is <lb></lb>equal to the Cylinder T M, whoſe Center is H: And the Ring Q V ha<lb></lb>ving the Center N is equal to the V I whoſe Center is G: And laſtly, <lb></lb>the Ring S T having the Center K, is equal to the Cylinder X E whoſe <lb></lb>Center is F. </s> <s>Therefore the Center of Gravity of the ſaid Magnitudes <lb></lb>divideth the Beam in the ſame proportion: But the Center of them is <lb></lb>one, and therefore ſome point common to both the Beams or Ballance, <lb></lb>which let be Y. </s> <s>Therefore F Y and Y K ſhall be as K Y and Y M. </s> <s>F Y <lb></lb>therefore is double to Y K: and C E being divided into two equal parts <lb></lb>in Z, Z F, ſhall be double to K D: and for that cauſe Z D triple to D Y: <lb></lb>But to the Right Line D O C D is triple: Therefore the Right Line <lb></lb>D O is greater than D Y: And for the like cauſe Y the Center of the <lb></lb>inſcribed Figure approacheth nearer the Baſe than the point O. </s> <s>And <lb></lb>becauſe as C D is to D O, ſo is the part taken away Z D to the part ta<lb></lb>ken away D Y; the remaining part C Z ſhall be to the remaining part <lb></lb>Y O, as C D is to D O; that is Y O ſhall be the third part of C Z; <lb></lb>that is, the ſixth part of C E. </s> <s>Again we will, by the ſame reaſon, de<lb></lb>monſtrate the Cylinders of the circumſcribed Figure to exceed one ano<lb></lb>ther equally, and that the exceſs is equal to the leaſt, and that their <lb></lb>Centers of Gravity are conſtituted in equal diſtances upon the Beam <lb></lb>K Z: and likewiſe that the Rings equal to thoſe ſame Cylinders are in <lb></lb>like manner diſpoſed on another Beam K G, the half of the ſaid K Z, <lb></lb>and that therefore the Center of Gravity of the circumſcribed Figure, <lb></lb>which let be R, ſo divideth the Beam, as that Z R is to R K, as K R is to <lb></lb>R G. </s> <s>Therefore Z R ſhall be double to R K: But C Z is equal to the <lb></lb>Right Line K D, and not double to it. </s> <s>The whole C D ſhall be leſſer <lb></lb>than triple to D R: Wherefore the Right Line D R is greater than D O; <lb></lb>that is to ſay, the Center of the circumſcribed Figure recedeth from the <lb></lb>Baſe more than the point O. </s> <s>And becauſe Z K is triple to K R; and <lb></lb>K D with twice Z C is triple to K D; the whole C D with C Z ſhall be <lb></lb>triple to D R: But C D is triple to D O: Wherefore the remaining <lb></lb>part C Z ſhall be triple to the remaining part R O; that is, O R<emph.end type="italics"></emph.end><pb xlink:href="040/01/947.jpg" pagenum="254"></pb><emph type="italics"></emph>is the ſixth part of E C: Which was the Propoſition.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>This being pre-demonſtrated, we will prove that<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>The Center of Gravity of the Parabolick <lb></lb>Conoid doth ſo divide the Axis, as that the <lb></lb>part towards the Vertex is double to the re<lb></lb>maining part towards the Baſe.</s></p><p type="main"> <s><emph type="italics"></emph>Let there be a Parabolick Conoid whoſe Axis let be A B divided in <lb></lb>N ſo as that A N be double to N B. </s> <s>It is to be proved that the Cen<lb></lb>ter of Gravity of the Conoid is the point N. </s> <s>For if it be not N, it <lb></lb>ſhall be either above or below it. </s> <s>Firſt let it be below; and let it be X: <lb></lb>And ſet off upon ſome place by it ſelf the Line L O equal to N X; and let <lb></lb>L O be divided at pleaſure in S: and look what proportion B X and <lb></lb>O S both together have to O S, and the ſame ſhall the Conoid have to <lb></lb>the Solid R. </s> <s>And in the Conoid let Figures be deſcribed by Cylinders <lb></lb>having equal Altitudes, ſo, as that that which lyeth between the Center <lb></lb>of Gravity and the point N be leſs than L S: and let the exceſs of the <lb></lb>Conoid above it be leſs than the Solid R: and that this may be done is <lb></lb>clear. </s> <s>Take therefore the inſcribed, whoſe Center of Gravity let be I: <lb></lb>now I X ſhall be greater than S O: And becauſe that as X B with S O <lb></lb>is to S O, ſo is the Conoid to the Solid R: (and R is greater than the <lb></lb>exceſs by which the Conoid exceeds the inſcribed Figure:) the proporti<lb></lb>on of the Conoid to the ſaid exceſs ſhall be greater than both B X and <lb></lb>O S unto S O: And, by Diviſion, the inſcribed Figure ſhall have grea<lb></lb>ter proportion to the ſaid exceſs than B X to S O: But B X hath to <lb></lb>X I a proportion yet leſs than to S O: Therefore the inſcribed Figure <lb></lb>ſhall have much greater proportion to the reſt of the proportions than <lb></lb>B X to X I: Therefore what proportion the inſcribed Figure hath to <lb></lb>thereſt of the portions, the ſame ſhall a certain other Line have to X I: <lb></lb>which ſhall neceſſarily be greater than B X: Let it, therefore, be M X. <lb></lb></s> <s>We have therefore the Center of Gravity of the Conoid X: But the <lb></lb>Center of Gravity of the Figure inſcribed in it is I: of the reſt of the <lb></lb>portions by which the Conoid exceeds the inſcribed Figure the Center of <lb></lb>Gravity ſhall be in the Line X M, and in it that point in which it ſhall <lb></lb>be ſo terminated, that look what proportion the inſcribed Figure hath <lb></lb>to the exceſs by which the Conoid exceeds it, the ſame it ſhall have to <lb></lb>X I: But it hath been proved, that this proportion is that which M X <lb></lb>hath to X I: Therefore M ſhall be the Center of Gravity of thoſe pro<lb></lb>portions by which the Conoid exceeds the inſcribed Figure: Which <lb></lb>certainly cannot be. </s> <s>For if along by M a Plane be drawn equidiſtant to <lb></lb>the Baſe of the Conoid, all thoſe proportions ſhall be towards one and<emph.end type="italics"></emph.end><pb xlink:href="040/01/948.jpg" pagenum="255"></pb><emph type="italics"></emph>the ſame part, and not by it divided. </s> <s>Therefore the Center of Gravity <lb></lb>of the ſaid Conoid is not below the point N: Neither is it above. </s> <s>For, <lb></lb>if it may, let it be H: and again, as before, ſet the Line L O by it ſelf <lb></lb>equalto the ſaid H N, and divided at pleaſure in S: and the ſame pro<lb></lb>portion that B N and S O both together have to S L, let the Conoid <lb></lb>have to R: and about the Conoid let a Figure be circumſcribed conſi<lb></lb>ſting of Cylinders, as hath been ſaid: by which let it be exceeded a leſs <lb></lb>quantity than that of the Solid R: and let the Line betwixt the Center <lb></lb>of Gravity of the circumſcribed Figure and the point N be leſſer than <lb></lb>S O: the remainder V H ſhall be greater than S L. </s> <s>And becauſe that as <lb></lb>both B N and O S is to SL, ſo is the<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.948.1.jpg" xlink:href="040/01/948/1.jpg"></figure><lb></lb><emph type="italics"></emph>Conoid to R: (and R is greater <lb></lb>than the exceſs by which the circum<lb></lb>ſcribed Figure exceeds the Conoid:) <lb></lb>Therefore B N and S O hath leſs pro<lb></lb>portion to S L than the Conoid to the <lb></lb>ſaid exceſs. </s> <s>And B V is leſſer than <lb></lb>both B N and S O; and V H is grea<lb></lb>ter than S L: much greater proporti<lb></lb>on, therefore, hath the Conoid to the <lb></lb>ſaid proportions, than B V hath to <lb></lb>V H. </s> <s>Therefore whatever proporti<lb></lb>on the Conoid hath to the ſaid pro<lb></lb>portions, the ſame ſhall a Line greater <lb></lb>than B V have to V H. </s> <s>Let the ſame be M V: And becauſe the Center <lb></lb>of Gravity of the circumſcribed Figure is V, and the Center of the <lb></lb>Conoid is H. and ſince that as the Conoid to the reſt of the proportions, <lb></lb>ſois M V to V H, M ſhall be the Center of Gravity of the remaining <lb></lb>proportions: which likewiſe is impoſſible: Therefore the Center of <lb></lb>Gravity of the Conoid is not above the point N: But it hath been de<lb></lb>monſtrated that neither is it beneath: It remains, therefore, that it ne<lb></lb>ceſſarily be in the point N it ſelf. </s> <s>And the ſame might be demonſtrated <lb></lb>of Conoidal Plane cut upon an Axis not erect. </s> <s>The ſame in other terms, <lb></lb>as appears by what followeth:<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>The Center of Gravity of the Parabolick Co<lb></lb>noid falleth betwixt the Center of the cir<lb></lb>cumſcribed Figure and the Center of the in<lb></lb>ſcribed.</s></p><pb xlink:href="040/01/949.jpg" pagenum="256"></pb><p type="main"> <s><emph type="italics"></emph>Let there be a Conoid whoſe Axis is A B, and the Center of the <lb></lb>circumſcribed Figure C, and the Center of the inſcribed O. </s> <s>I ſay <lb></lb>the Center of the Conoid is betwixt the points C and O. </s> <s>For if <lb></lb>not, it ſhall be either above them, or below them, or in one of them. </s> <s>Let <lb></lb>it be below, as in R. </s> <s>And becauſe R is the Center of Gravity of the <lb></lb>whole Conoid; and the Center of Gravity of the inſcribed Figure is O: <lb></lb>Therefore of the remaining proportions by which the Conoid exceeds <lb></lb>the inſcribed Figure the Center of Gravity ſhall be in the Line O R ex<lb></lb>tended towards R, and in that point in which it is ſo determined, that, <lb></lb>what proportion the ſaid proportions have to the inſcribed Figure, the <lb></lb>ſame ſhall O R have to the Line falling betwixt R and that falling point. <lb></lb></s> <s>Let this proportion be that of O R to R X. </s> <s>Therefore X falleth either <lb></lb>without the Conoid or within, or in its<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.949.1.jpg" xlink:href="040/01/949/1.jpg"></figure><lb></lb><emph type="italics"></emph>Baſe. </s> <s>That it falleth without, or in its <lb></lb>Baſe it is already manifeſt to be an abſur<lb></lb>dity. </s> <s>Let it fall within: and becauſe X R <lb></lb>is to R O, as the inſcribed Figure is to <lb></lb>the exceſs by which the Conoid exceeds <lb></lb>it; the ſame proportion that B R hath to <lb></lb>R O, the ſame let the inſcribed Figure <lb></lb>have to the Solid K: Which neceſſarily <lb></lb>ſhall be leſſer than the ſaid exceſs. </s> <s>And let <lb></lb>another Figure be inſcribed which may be <lb></lb>exceeded by the Conoid a leſs quantity <lb></lb>than is K, whoſe Center of Gravity falleth betwixt O and C. </s> <s>Let it <lb></lb>be V. And, becauſe the firſt Figure is to K as B R to R O, and the ſe<lb></lb>cond Figure, whoſe Center V is greater than the firſt, and exceeded <lb></lb>by the Conoid a leſs quantity than is K; what proportion the ſecond <lb></lb>Figure hath to the exceſs by which the Conoid exceeds it, the ſame <lb></lb>ſhall a Line greater than B R have to R V. </s> <s>But R is the Center of Gra<lb></lb>vity of the Conoid; and the Center of the ſecond inſcribed Figure V: <lb></lb>The Center therefore of the remaining proportions ſhall be without <lb></lb>the Conoid beneath B: Which is impoſſible. </s> <s>And by the ſame means <lb></lb>we might demonſtrate the Center of Gravity of the ſaid Conoid not to <lb></lb>be in the Line C A. </s> <s>And that it is none of the points betwixt C and <lb></lb>O is manifeſt. </s> <s>For ſay, that there other Figures deſcribed, greater <lb></lb>ſomething than the inſcribed Figure whoſe Center is O, and leſs than <lb></lb>that circumſcribed Figure whoſe Center is C, the Center of the Conoid <lb></lb>would fall without the Center of theſe Figures: Which but now was <lb></lb>concluded to be impoſſible: It reſts therefore that it be betwixt the Cen<lb></lb>ter of the circumſcribed and inſcribed Figure. </s> <s>And if ſo, it ſhall ne<lb></lb>ceſſarily be in that point which divideth the Axis, ſo as that the part <lb></lb>towards the Vertex is double to the remainder; ſince N may circum<lb></lb>ſcribe and inſcribe Figures, ſo, that thoſe Lines which fall between<emph.end type="italics"></emph.end><pb xlink:href="040/01/950.jpg" pagenum="257"></pb><emph type="italics"></emph>their Centers and the ſaid points, may be leſſer than any other Lines. <lb></lb></s> <s>To expreſs the ſame in other terms, we have reduced it to an impoſſibi<lb></lb>lity, that the Center of the Conoid ſhould not fall betwixt the Centers of <lb></lb>the inſcribed and circumſcribed Figures.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>Suppoſing three proportional Lines, and that <lb></lb>what proportion the leaſt hath to the exceſs <lb></lb>by which the greateſt exceeds the leaſt, the <lb></lb>ſame ſhould a Line given have to two thirds of <lb></lb>the exceſs by which the greateſt exceeds the <lb></lb>middlemoſt: and moreover, that what pro<lb></lb>portion that compounded of the greateſt, and <lb></lb>of double the middlemoſt, hath unto that com<lb></lb>pounded of the triple of the greateſt and mid<lb></lb>dlemoſt, the ſame hath another Line given, to <lb></lb>the exceſs by which the greateſt exceeds the <lb></lb>middle one; both the given Lines taken toge<lb></lb>ther ſhall be a third part of the greateſt of the <lb></lb>proportional Lines.</s></p><p type="main"> <s><emph type="italics"></emph>Let A B, B C, and B F, be three proportional Lines; and what <lb></lb>proportion B F hath to F A, the ſame let M S have to two thirds <lb></lb>of C A. </s> <s>And what proportion that compounded of A B and the <lb></lb>double of B C hath to that compounded of the triple of both A B and <lb></lb>B C, the ſame let another, to wit S N, have to A C. </s> <s>Becauſe therefore <lb></lb>that A B, B C, and C F,<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.950.1.jpg" xlink:href="040/01/950/1.jpg"></figure><lb></lb><emph type="italics"></emph>are proportionals, A G <lb></lb>and C F ſhall, for the ſame <lb></lb>reaſon, be likewiſe ſo. <lb></lb></s> <s>Therefore, as A B is to <lb></lb>B C, ſo is A C to C F: <lb></lb>and as the triple of A B is to the triple of B C, ſo is A C to C F: <lb></lb>Therefore, what proportion the triple of A B with the triple of B C <lb></lb>hath to the triple of C B, the ſame ſhall A C have to a Line leſs than <lb></lb>C F. </s> <s>Let it be C O. </s> <s>Wherefore by Compoſition and by Converſion of <lb></lb>proportion, O A ſhall have to A C, the ſame proportion, as triple A B <lb></lb>with Sextuple B C, hath to triple A B with triple B C. </s> <s>But A C hath <lb></lb>to S N the ſame proportion, that triple A B with triple B C hath to A B <lb></lb>with double B C: Therefore,<emph.end type="italics"></emph.end> ex equali, <emph type="italics"></emph>O A to NS ſhall have the <lb></lb>ſame proportion, as triple A B with Sexcuple B C hath to A B with<emph.end type="italics"></emph.end><pb xlink:href="040/01/951.jpg" pagenum="258"></pb><emph type="italics"></emph>double B C: But triple A B with ſexcuple B C, are triple to A B with <lb></lb>double B C. </s> <s>Therefore A O is triple to S N.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Again, becauſe O C is to C A as triple C B is to triple A B with tri<lb></lb>ple C B: and becauſe as C A is to A F, ſo is triple A B to triple B C: <lb></lb>Therefore,<emph.end type="italics"></emph.end> ex equali, <emph type="italics"></emph>by perturbed proportion, as O C is to C F, ſo ſhall <lb></lb>triple A B be to triple A B with treble B C: And, by Converſion of <lb></lb>proportion, as O F is to F C, ſo is triple B C to triple A B with triple <lb></lb>B C: And as C F is to F B, ſo is A C to C B, and triple A C to triple <lb></lb>C B: Therefore,<emph.end type="italics"></emph.end> ex equali, <emph type="italics"></emph>by Perturbation of proportion, as O F is <lb></lb>to F B, ſo is triple A C to the triple of both A B and A C together. <lb></lb></s> <s>And becauſe F C and C A are in the ſame proportion as C B and B A; <lb></lb>it ſhall be that as F C is to C A, ſo ſhall B C be to B A. And, by Com<lb></lb>poſition, as F A is to A C, ſo are both B A and B C to B A: and ſo the <lb></lb>triple to the triple: Therefore as F A is to A C, ſo the compound of tri<lb></lb>ple B A and triple B C is to triple A B. Wherefore, as F A is to two <lb></lb>thirds of A C, ſo is the compound of triple B A and triple B C to two <lb></lb>thirds of triple B A; that is, to double B A: But as F A is to two thirds <lb></lb>of A C, ſo is F B to M S: Therefore, as F B is to M S, ſo is the compound <lb></lb>of triple B A and triple B C to double B A: But as O B is to F B, ſo <lb></lb>was Sexcuple A B to triple of both A B and B C: Therefore,<emph.end type="italics"></emph.end> ex equa<lb></lb>li, <emph type="italics"></emph>O B ſhall have to M S the ſame proportion as Sexcuple A B hath to <lb></lb>double B A. </s> <s>Wherefore M S ſhall be the third part of O B: And it <lb></lb>hath been demonſtrated, that S N is the third part of A O: It is mani<lb></lb>feſt therefore, that MN is a third part likewiſe of A B: And this is <lb></lb>that which was to be demonſtrated.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>Of any <emph type="italics"></emph>Fruſtum<emph.end type="italics"></emph.end> or Segment cut off from a Para<lb></lb>bolick Conoid the Center of Gravity is in the <lb></lb>Right Line that is Axis of the <emph type="italics"></emph>Fruſtum<emph.end type="italics"></emph.end>; which <lb></lb>being divided into three equal parts the Cen<lb></lb>ter of Gravity is in the middlemoſt and ſo di<lb></lb>vides it, as that the part towards the leſſer Baſe <lb></lb>hath to the part towards the greater Baſe, the <lb></lb>ſame proportion that the greater Baſe hath to <lb></lb>the leſſer.</s></p><p type="main"> <s><emph type="italics"></emph>From the Conoid whoſe Axis is R B let there be cut off the Solid <lb></lb>whoſe Axis is B E; and let the cutting Plane be equidiſtaut to <lb></lb>the Baſe: and let it be cut in another Plane along the Axis erect <lb></lb>upon the Baſe, and let it be the Section of the Parabola V R C: R B <lb></lb>ſhall be the Diameter of the proportion, or the equidiſtant Diameter<emph.end type="italics"></emph.end><pb xlink:href="040/01/952.jpg" pagenum="259"></pb><emph type="italics"></emph>L M, V C: they ſhall be ordinately applyed. </s> <s>Divide therefore E B in<lb></lb>to three equal parts, of which let the middlemoſt be Q Y: and divide <lb></lb>this ſo in the point I that Q I may have the ſame proportion to I Y, as <lb></lb>the Baſe whoſe Diameter is V C hath to the Baſe whoſe Diameter is <lb></lb>L M; that is, that the Square V C hath to Square L M. </s> <s>It is to be de<lb></lb>monſtrated that I is the Center of Gravity of the Fruſtrum L M C. <lb></lb></s> <s>Draw the Line N S, by the by, equall to B R: and let S X be equal to <lb></lb>E R: and unto N S and S X aſſume a third proportional S G: and as <lb></lb>N G is to G S, ſo let B Q be to I O. </s> <s>And it nothing matters whether <lb></lb>the point O fall above or below L M. </s> <s>And becauſe in the Section V R C <lb></lb>the Lines L M and V C are ordinately<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.952.1.jpg" xlink:href="040/01/952/1.jpg"></figure><lb></lb><emph type="italics"></emph>applyed, it ſhall be that as the Square <lb></lb>V C is to the Square L M, ſo is the Line <lb></lb>B R to R E: And as the Square V C is <lb></lb>to the Square L M, ſo is Q I to I Y: and <lb></lb>as B R is to R E, ſo is N S to S X: There<lb></lb>fore Q I is to I Y, as R S is to S X. </s> <s>Where<lb></lb>fore as G Y is to Y I, ſo ſhall both N S and <lb></lb>S X be to S X: and as E B is to Y I, ſo <lb></lb>ſhall the compound of triple N S and tri<lb></lb>ple S X be to S X: But as E B is to B Y, <lb></lb>ſo is the compound of triple N S and S X <lb></lb>both together to the compound of N S and S X: Therefore, as E B is to <lb></lb>B I, ſo is the compound of triple N S and triple S X to the compound of <lb></lb>N S and double S X. </s> <s>Therefore N S, S X, and S G are three proporti<lb></lb>onal Lines: And as S G is to G N, ſo is the aſſumed O I to two thirds <lb></lb>of E B; that is, to N X: And as the compound of N S and double <lb></lb>S X is to the compound of triple N S and triple S X, ſo is another aſſu<lb></lb>med Line I B to B E; that is, to N X. </s> <s>By what therefore hath been <lb></lb>above demonſtrated, thoſe Lines taken together are a third part of N S; <lb></lb>that is, of R B: Therefore R B is triple to B O: Wherefore O ſhall <lb></lb>be the Center of Gravity of the Conoid v R C. </s> <s>And let it be the Cen<lb></lb>ter of Gravity of the<emph.end type="italics"></emph.end> Fruſtrum <emph type="italics"></emph>L R M of the Conoid: Therefore the <lb></lb>Center of Gravity of V L M C is in the Line O B, and in that point <lb></lb>which ſo terminates it, that as V L M C of the<emph.end type="italics"></emph.end> Fruſtrum <emph type="italics"></emph>is to the <lb></lb>proportion L R M, ſo is the Line A O to that which intervenes betwixt <lb></lb>O and the ſaid point. </s> <s>And becauſe R O is two thirds of R B; and <lb></lb>R A two thirds of R E; the remaining part A O ſhall be two thirds <lb></lb>of the remaining part E B. </s> <s>And becauſe that as the<emph.end type="italics"></emph.end> Fruſtum <emph type="italics"></emph>V L M C <lb></lb>is to the proportion L R M, ſo is N G to G S: and as N G to G S, ſo is <lb></lb>two thirds of E B to O I: and two thirds of E B is equal to the Line <lb></lb>A O: it ſhall be that as the<emph.end type="italics"></emph.end> Fruſtum <emph type="italics"></emph>V L M O is to the proportion <lb></lb>L R M, ſo is A O to O I. </s> <s>It is manifeſt therefore that of the<emph.end type="italics"></emph.end> Fruſtum <lb></lb><emph type="italics"></emph>V L M C the Center of Gravity is the point I, and ſo divideth the Axis, <lb></lb>[as?] that the part towards the leſſer Baſe is to the part towards the grea-<emph.end type="italics"></emph.end><pb xlink:href="040/01/953.jpg" pagenum="260"></pb><emph type="italics"></emph>ter, as the double of the greater Baſe together with the Leſſer is to the <lb></lb>double of the leſſer together with the greater. </s> <s>Which is the Propoſition <lb></lb>more elegantly expreſſed.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>If any number of Magnitudes ſo diſpoſed to one <lb></lb>another, as that the ſecond addeth unto the firſt <lb></lb>the double of the firſt, the third addeth unto <lb></lb>the ſecond the triple of the firſt, the fourth <lb></lb>addeth unto the third the quadruple of the <lb></lb>firſt, and ſo every one of the following ones <lb></lb>addeth unto the next unto it the magnitude of <lb></lb>the firſt multiplyed according to the number <lb></lb>which it ſhall hold in order; if, I ſay, theſe <lb></lb>Magnitudes be ſuſpended ordinarily on the <lb></lb>Ballance at equal diſtances; the Center of the <lb></lb><emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> of all the compounding Magni<lb></lb>tudes ſhall ſo divide the Beam, as that the part <lb></lb>towards the leſſer Magnitudes is triple to the <lb></lb>remainder.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Beam be L T, and let ſuch Magnitudes as were ſpoken of <lb></lb>hang upon it; and let them be A, F, G, H, K; of which A is in <lb></lb>the firſt place ſuſpended at T. </s> <s>I ſay, that the Center of the<emph.end type="italics"></emph.end> Equi<lb></lb>librium <emph type="italics"></emph>ſo cuts the Beam T L as that the part towards T is triple to the <lb></lb>reſt. </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"></emph.end><lb></lb><figure id="id.040.01.953.1.jpg" xlink:href="040/01/953/1.jpg"></figure><lb></lb><emph type="italics"></emph>and L P to L O: I P, <lb></lb>P N, N O, and O L <lb></lb>ſhall be equal. </s> <s>And <lb></lb>in F let a Magnitude <lb></lb>be placed double to A; <lb></lb>in G another trebble to <lb></lb>the ſame; in H ano<lb></lb>ther Quadruple; and <lb></lb>ſo of the reſt: and let <lb></lb>thoſe Magnitudes be <lb></lb>taken in which there <lb></lb>is A; and let the ſame <lb></lb>be done in the Magni<lb></lb>tudes F, G, H, K. </s> <s>And <lb></lb>becauſe in F the remaining Magnitude, to wit B, is equal to A; take it<emph.end type="italics"></emph.end><pb xlink:href="040/01/954.jpg" pagenum="261"></pb><emph type="italics"></emph>double in G, triple in H, &c. </s> <s>and let thoſe Magnitudes be taken in <lb></lb>which there is B: and in the ſame manner let thoſe be taken in which is <lb></lb>C, D, and E: now all thoſe in which there is A ſhall be equal to K: and <lb></lb>the compound of all the B B ſhall equal H; and the compound of C C <lb></lb>ſhall equal G; and the compound of all the D D ſhall equal F; and <lb></lb>E ſhall equal A. </s> <s>And becauſe T I is double to I L, I ſhall be the point <lb></lb>of the<emph.end type="italics"></emph.end> Equilibrium <emph type="italics"></emph>of the Magnitudes compoſed of all the A A: and <lb></lb>likewiſe ſince S P is double to P L, P ſhall be the point of the<emph.end type="italics"></emph.end> Equilibri<lb></lb>um <emph type="italics"></emph>of the compost of B B: and for the ſame cauſe N ſhall be the point <lb></lb>of the<emph.end type="italics"></emph.end> Equilibrium <emph type="italics"></emph>of the compoſt of C C: and O of the compound <lb></lb>of D D: and L that of E. </s> <s>Therefore T L is a Beam on which at <lb></lb>equal diſtances certain Magnitudes K, H, G, F, A do hang. </s> <s>And again <lb></lb>L I is another Ballance, on which, at diſtances in like manner equal, do <lb></lb>hang ſuch a number of Magnitudes, and in the ſame order equal to the <lb></lb>former. </s> <s>For the compound of all the A A, which hang on I, is equal to <lb></lb>K hanging at L; and the compoſt of all B B, which is ſuſpended at P, is <lb></lb>equal to H hanging at P; and likewiſe the compound of C C, which <lb></lb>hangeth at N do equal G; and the compoſt of D, which hang on O, <lb></lb>are equal to F; and E, hanging on L, is equal to A. </s> <s>Wherefore the <lb></lb>Ballances are divided in the ſame proportion by the Center of the com<lb></lb>pounds of the Magnitudes And the Center of the compound of, the ſaid <lb></lb>Magnitudes is one. </s> <s>Therefore the common point of the Right Line T L, <lb></lb>and of the Right Line L I ſhall be the Center, which let be X. </s> <s>Therefore <lb></lb>as T X is to X L, ſo ſhall L X be to X I; and the whole T L to the whole <lb></lb>L I. </s> <s>But T L is triple to L I: Wherefore T X ſhall alſo be triple to X L.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>If any number of Magnitudes be ſo taken, that the <lb></lb>ſecond addeth unto the firſt the triple of the <lb></lb>firſt, and the third addeth unto the ſecond the <lb></lb>quintuple of the firſt, and the fourth addeth <lb></lb>unto the third the ſeptuple of the firſt, and ſo <lb></lb>the reſt, every one encreaſing above the next to <lb></lb>it, and proceedeth ſtill to a new multiplex of <lb></lb>the firſt Magnitude according to the conſe<lb></lb>quent odd numbers, like as the Squares of <lb></lb>Lines equally exceeding one another do pro<lb></lb>ceed, whereof the exceſs is equal to the leaſt, <lb></lb>and if they be ſuſpended on a Ballance at equal <lb></lb>Diſtances, the Center of <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> of all the <lb></lb>compound Magnitudes ſo divideth the Beam <pb xlink:href="040/01/955.jpg" pagenum="262"></pb>that the part towards the leſſer Magnitudes is <lb></lb>more than triple the remaining part; and alſo <lb></lb>one may take a diſtance that is to the ſame leſs <lb></lb>than triple.</s></p><p type="main"> <s><emph type="italics"></emph>In the Ballance B E let there be Magnitudes, ſuch as were ſpoken off, <lb></lb>from which let there be other Magnitudes taken away that were to <lb></lb>one another as they were diſpoſed in the precedent, and let it be of <lb></lb>the compound of all <lb></lb>the A A: the reſt<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.955.1.jpg" xlink:href="040/01/955/1.jpg"></figure><lb></lb><emph type="italics"></emph>in which are C <lb></lb>ſhall be diſtributed <lb></lb>in the ſame order, <lb></lb>but the greateſt de<lb></lb>ficient. </s> <s>Let E D be <lb></lb>triple to D B; and <lb></lb>G F triple to F B. <lb></lb></s> <s>D ſhall be the Center <lb></lb>of the<emph.end type="italics"></emph.end> Equilibrium <lb></lb><emph type="italics"></emph>of the compound con<lb></lb>ſiſting of all the A A; <lb></lb>and F that of the <lb></lb>compound of all the <lb></lb>C C. </s> <s>Wherefore the <lb></lb>Center of the com<lb></lb>pound of both A A <lb></lb>and C C falleth be<lb></lb>tween D and F. </s> <s>Let <lb></lb>it be O. </s> <s>It is there<lb></lb>fore manifeſt that <lb></lb>E O is more than triple to O B; but G O leſs thantriple to the <lb></lb>ſame O B: Which was to be demonſtrated.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/956.jpg" pagenum="263"></pb><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>If to any Cone or portion of a Cone a Eigure con<lb></lb>ſiſting of Cylinders of equal heights be inſcri<lb></lb>bed and another circumſcribed; and if its Axis <lb></lb>be ſo divided as that the part which lyeth be<lb></lb>twixt the point of diviſion and the Vertex be <lb></lb>triple to the reſt; the Center of Gravity of <lb></lb>the inſcribed Figure ſhall be nearer to the Baſe <lb></lb>of the Cone than that point of diviſion: and <lb></lb>the Center of Gravity of the circumſcribed <lb></lb>ſhall be nearer to the Vertex than that ſame <lb></lb>point.</s></p><p type="main"> <s><emph type="italics"></emph>Take therefore a Cone, whoſe Axis is N M. </s> <s>Let it be divided <lb></lb>in S ſo, as that N S be triple to the remainder S M. </s> <s>I ſay, that <lb></lb>the Center of Gravity of any Figure inſcribed, as was ſaid, in <lb></lb>a Cone doth conſiſt in the Axis N M, and approacheth nearer to the Baſe <lb></lb>of the Cone than the point S: and that the Center of Gravity of the <lb></lb>Circumſcribed is likewiſe in the Axis N M, and nearer to the Vertex <lb></lb>than is S. </s> <s>Let a Figure therefore be ſuppoſed to be inſcribed by the Cy<lb></lb>linders whoſe Axis M C, C B, B E, E A are equal. </s> <s>Firſt therefore <lb></lb>the Cylinder whoſe Axis is M C hath<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.956.1.jpg" xlink:href="040/01/956/1.jpg"></figure><lb></lb><emph type="italics"></emph>to the Cylinder whoſe Axis is C B the <lb></lb>ſame proportion as its Baſe hath to <lb></lb>the Baſe of the other (for their Alti<lb></lb>tudes are equal.) But this propor<lb></lb>tion is the ſame with that which the <lb></lb>Square C N hath to the Square N B. <lb></lb></s> <s>And ſo we might prove, that the Cy<lb></lb>linder whoſe Axis is C B hath to the <lb></lb>Cylinder whoſe Axis is B E the ſame <lb></lb>proportion, as the Square B N hath to <lb></lb>the Square N E: and the Cylinder <lb></lb>whoſe Axis is B E hath to the Cylin<lb></lb>der whoſe Axis is E A the ſame pro<lb></lb>portion that the Square E N hath to <lb></lb>the Square N A. </s> <s>But the Lines N C, <lb></lb>N B, E N, and N A equally exceed one <lb></lb>another, and their exceſs equalleth the <lb></lb>leaſt, that is N A. </s> <s>Therefore they are certain Magnitudes, to wit, in<lb></lb>ſcribed Cylinders having conſequently to one another the ſame proporti<lb></lb>on as the Squares of Lines that equally exceed one another, and the ex-<emph.end type="italics"></emph.end><pb xlink:href="040/01/957.jpg" pagenum="264"></pb><emph type="italics"></emph>ceſs of which is equal to the leaſt: and they are ſo diſpoſed on the Beam <lb></lb>T I that their ſeveral Centers of Gravity conſiſt in it, and that at equal <lb></lb>diſtances. </s> <s>Therefore by the things above demonſtrated it appeareth that <lb></lb>the Center of Gravity of all ſo compoſed Magnitudes do ſo divide the <lb></lb>Balance T I, that the part to wards T is more than triple to the remain<lb></lb>der. </s> <s>Let this Center be O. </s> <s>T O therefore is more than triple to O I. <lb></lb></s> <s>But T N is triple to I M. </s> <s>Therefore the whole M O will be leſs than a <lb></lb>fourth part of the whole M N, whoſe fourth part was ſuppoſed to be <lb></lb>M S. </s> <s>It is manifeſt, therefore, that the point O doth nearer approach <lb></lb>the Baſe of the Cone than S. </s> <s>And let the circumſcribed Figure be com<lb></lb>poſed of the Cylinders whoſe Axis M C, C B, B E, E A and A N are <lb></lb>equal to each other, and, like as in thoſe inſcribed, let them be to one <lb></lb>another as the Squares of the Lines M N, N C, B N, N E, A N, <lb></lb>which equally exceed one another, and the exceſs is equal to the leaſt <lb></lb>A N. Wherefore, by the premiſes, the Center of Gravity of all the Cy<lb></lb>linders ſo diſpoſed, which let be V, doth ſo divide the Beam R I, that the <lb></lb>part towards R, to wit R V, is more than triple to the remaining part <lb></lb>V I: but T V ſhall be leſs than triple to the ſame. </s> <s>But N T is triple to <lb></lb>all I M: Therefore all V M is more than the fourth part of all M N, <lb></lb>whoſe fourth part was ſuppoſed to be M S. </s> <s>Therefore the point V is <lb></lb>nearer to the Vertex than the Point S. </s> <s>Which was to be demonſtra<lb></lb>ted.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>About a given Cone a Figure may be circumſcri<lb></lb>bed and another inſcribed conſiſting of Cylin<lb></lb>ders of equal height, ſo, as that the Line which <lb></lb>lyeth betwixt the Center of Gravity of the <lb></lb>circumſcribed, and the Center of Gravity of <lb></lb>the inſcribed, may be leſſer than any Line <lb></lb>given.</s></p><p type="main"> <s><emph type="italics"></emph>Let a Cone be given, whoſe Axis is A B; and let the Right Line <lb></lb>given be K. </s> <s>I ſay; Let there be placed by the Cylinder L <lb></lb>equal to that inſcribed in the Cone, having for its Altitude half <lb></lb>of the Axis A B: and let A B be divided in C, ſo as that A C be tri<lb></lb>ple to C B: And as A C is to K, ſo let the Cylinder L be to the Solid X. <lb></lb></s> <s>And about the Cone let there be a Figure circumſcribed of Cylin<lb></lb>ders that have equal Altitude, and let another be inſcribed, ſo as that <lb></lb>the circumſcribed exceed the inſcribed a leſs quantity than the Solid X. <lb></lb></s> <s>And let the Center of Gravity of the circumſcribed be E; which falls <lb></lb>above C: and let the Center of the inſcribed be S, falling beneath C.<emph.end type="italics"></emph.end><pb xlink:href="040/01/958.jpg" pagenum="265"></pb><emph type="italics"></emph>I ſay now, that the Line E S is leſſer than K. </s> <s>For if not, then let C A <lb></lb>be ſuppoſed equal to E O. </s> <s>Becauſe therefore O E hath to K the ſame <lb></lb>proportion that L hath to X; and the inſcribed Figure is not leſs than <lb></lb>the Cylinder L; and the exceſs with which the ſaid Figure is exceeded <lb></lb>by the circumſcribed is leſs than the Solid X: therefore the inſcribed <lb></lb>Figure ſhall have to the ſaid exceſs<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.958.1.jpg" xlink:href="040/01/958/1.jpg"></figure><lb></lb><emph type="italics"></emph>greater proportion than O E hath to <lb></lb>K: But the proportion of O E to K is <lb></lb>not leſs than that which O E hath to <lb></lb>E S with E S. </s> <s>Let it not be leſs than <lb></lb>K. </s> <s>Therefore the inſcribed Figure <lb></lb>hath to the exceſs of the circumſcri<lb></lb>bed Figure above it greater propor<lb></lb>tion than O E hath to E S. </s> <s>Therefore <lb></lb>as the inſcribed is to the ſaid exceſs, <lb></lb>ſo ſhall it be to the Line E S. </s> <s>Let E R <lb></lb>be a Line greater than E O; and the <lb></lb>Center of Gravity of the inſcribed <lb></lb>Figure is S; and the Center of the cir<lb></lb>cumſcribed is E. </s> <s>It is manifeſt there<lb></lb>fore, that the Center of Gravity of <lb></lb>the remaining proportions by which <lb></lb>the circumſcribed exceedeth the in <lb></lb>ſcribed is in the Line R E, and in that point by which it is ſo termina<lb></lb>ted, that as the inſcribed Figure is to the ſaid proportions, ſo is the Line <lb></lb>included betwixt E and that point to the Line E S. </s> <s>And this propor<lb></lb>tion hath R E to E S. </s> <s>Therefore the Center of Gravity of the remain<lb></lb>ing proportions with which the circumſcribed Figure exceeds the in<lb></lb>ſcribed ſhall be R, which is impoſſible. </s> <s>For the Plane drawn thorow <lb></lb>R equidiſtant to the Baſe of the Cone doth not cut thoſe proportions. </s> <s>It <lb></lb>is therefore falſe that the Line E S is not leſſer than K. </s> <s>It ſhall therefore <lb></lb>be leſs. </s> <s>The ſame alſo may be done in a manner not unlike this in Pyra<lb></lb>mides, as ne could demonſtrate.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>COROLLARY.</s></p><p type="main"> <s>Hence it is manifeſt, that a given Cone may circumſcribe one <lb></lb>Figure and inſcribe another conſiſting of Cylinders of equal <lb></lb>Altitudes ſo, as that the Lines which are intercepted betwixt <lb></lb>their Centers of Gravity and the point which ſo divides the <lb></lb>Axis of the Cone, as that the part towards the Vertex is tri<lb></lb>ple to the leſt, are leſs than any given Line.</s></p><p type="main"> <s><emph type="italics"></emph>For, ſince it hath been demonſtrated, that the ſaid point dividing the <lb></lb>Axis, as was ſaid, is alwaies found betwixt the Centers of Gravity<emph.end type="italics"></emph.end><pb xlink:href="040/01/959.jpg" pagenum="266"></pb><emph type="italics"></emph>of the Circumſcribed and inſcribed Figures: and that it's poſſible, that <lb></lb>there be a Line in the middle betwixt thoſe Centers that is leſs than any <lb></lb>Line aſſigned; it followeth that the ſame given Line be much leſs that <lb></lb>lyeth betwixt one of the ſaid Centers and the ſaid point that divides <lb></lb>the Axis.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>The Center of Gravity divideth the Axis of any <lb></lb>Cone or Pyramid ſo, that the part next the <lb></lb>Vertex is triple to the remainder.</s></p><p type="main"> <s><emph type="italics"></emph>Let there be a Cone whoſe Axis is A B. </s> <s>And in C let it be divided, <lb></lb>ſo that A C be triple to the remaining part C B. </s> <s>It is to be proved, <lb></lb>that C is the Center of Gravity of the Cone. </s> <s>For if it be not, the <lb></lb>Cone's Center ſhall be either above or below the point C. </s> <s>Let it be firſt <lb></lb>beneath, and let it be E. </s> <s>And draw the Line L P, by it ſelf, equal to <lb></lb>C E; which divided at pleaſure in N. </s> <s>And as both B E and P N to<lb></lb>gether are to P N, ſo let the Cone be to the Solid X: and inſcribe in the <lb></lb>Cone a Solid Figure of Cylinders that have equal Baſes, whoſe Center <lb></lb>of Gravity is leſs diſtant from the point C than is the Line L N, and <lb></lb>the exceſs of the Cone above it leſs than the Solid X. </s> <s>And that this <lb></lb>may be done is manifeſt from what hath been already demonſtrated. <lb></lb></s> <s>Now let the inſcribed Figure be ſuch as<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.959.1.jpg" xlink:href="040/01/959/1.jpg"></figure><lb></lb><emph type="italics"></emph>was required, whoſe Center of Gravity <lb></lb>let be I. </s> <s>The Line I E therefore ſhall be <lb></lb>greater than N P together with L P. </s> <s>Let <lb></lb>C E and I C leſs L N be equal: And be<lb></lb>cauſe both together B E and N P is to N P <lb></lb>as the Cone to X: and the exceſs by which <lb></lb>the Cone exceeds the inſcribed Figure is <lb></lb>leſs than the Solid X: Therefore the Cone <lb></lb>ſhall have greater proportion to the ſaid <lb></lb>X S than both B E and N P to N P: and, by <lb></lb>Diviſion, the inſcribed Figure ſhall have <lb></lb>greater proportion to the exceſs by which <lb></lb>the Cone exceeds it, than B E to N P: But B E hath leſs proportion to <lb></lb>E I than to N P with I E. </s> <s>Let N P be greater. </s> <s>Then the inſcribed Fi<lb></lb>gure hath to the exceſs of the Cone above it much greater proportion <lb></lb>than B E to E I. </s> <s>Therefore as the inſcribed Figure is to the ſaid exceſs, <lb></lb>ſo ſhall a Line bigger than B E be to E I. </s> <s>Let that Line be M E. Becauſe, <lb></lb>therefore, M E is to E I as the inſcribed Figure is to the exceſs of the <lb></lb>Cone above the ſaid Figure, and D is the Center of Gravity of the <lb></lb>Cone, and I the Center of Gravity of the inſcribed Figure: Therefore<emph.end type="italics"></emph.end><pb xlink:href="040/01/960.jpg" pagenum="267"></pb><emph type="italics"></emph>M ſhall be the Center of Gravity of the remaining proportions by which <lb></lb>the Cone exceeds the inſcribed Figure. </s> <s>Which is impoſſible. </s> <s>Therefore <lb></lb>the Center of Gravity of the Cone is not below the point C. </s> <s>Nor is it <lb></lb>above it. </s> <s>For if it may be, let it be R. </s> <s>And again aſſume L P cut at <lb></lb>pleaſure in N: And as both B C and N P together are to N L, ſo let the <lb></lb>Cone be to X. </s> <s>And let a Figure be, in like manner, circumſcribed about <lb></lb>the Cone, which exceeds the ſaid Cone a leſs quantity than the Solid X. <lb></lb></s> <s>And let the Line which intercepts bet wixt its Center of Gravity and C, <lb></lb>be leſſer than N P. </s> <s>Now take the circumſcribed Figure, whoſe Center <lb></lb>let be O; the remainder O R ſhall be greater than the ſaid N L. </s> <s>And <lb></lb>becauſe, as both together B C and P N is to N L, ſo is the Cone to X: <lb></lb>And the exceſs by which the circumſcribed exceeds the Cone is leſſer <lb></lb>than X: And B O is leſſer than B C and P N together: And O R grea<lb></lb>ter than L N: The Cone therefore ſhall have much greater proportion to <lb></lb>the remaining proportions by which it was exceeded by the circumſcribed <lb></lb>Figure, than B O to O R. </s> <s>Let it be as M O is to O R. </s> <s>M O ſhall <lb></lb>be greater than B C; and M ſhall be the Center of Gravity of the pro<lb></lb>portions by which the Cone is exceeded by the circumſcribed Figure. <lb></lb></s> <s>Which is inconvenient. </s> <s>Therefore the Center of Gravity of the Cone is <lb></lb>not above the point C. </s> <s>But neither is it below it; as hath been proved. <lb></lb></s> <s>Therefore it ſhall be C it ſelf. </s> <s>And ſo in like manner may it be demon<lb></lb>ſtrated in any Pyramid.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>If there were four Lines continual proportionals; <lb></lb>and as the leaſt of them were to the exceſs by <lb></lb>which the greateſt exceeds the leaſt, ſo a Line <lb></lb>taken at pleaſure ſhould be to 3/4 the exceſs by <lb></lb>which the greateſt exceeds the ſecond; and as <lb></lb>the Line equal to theſe (<emph type="italics"></emph>viz.<emph.end type="italics"></emph.end> to the greateſt, <lb></lb>double of the ſecond, and triple of the third) <lb></lb>is to the Line equal to the quadruple of the <lb></lb>fourth, the quadruple of the ſecond, and the <lb></lb>quadruple of the third, ſo ſhould another Line <lb></lb>taken be to the exceſs of the greateſt above the <lb></lb>ſecond: theſe two Lines taken together ſhall <lb></lb>be a fourth part of the greateſt of the propor<lb></lb>tionals.</s></p><pb xlink:href="040/01/961.jpg" pagenum="268"></pb><p type="main"> <s><emph type="italics"></emph>For let A B, B C, B D, and B E be four proportional Lines. </s> <s>And <lb></lb>as B E is to E A, ſo let F G be to 3/4 of A C. </s> <s>And as the Line equal <lb></lb>to A B and to double B C and to triple B D is to the Line equal <lb></lb>to the quadruples of A B, B C, and B D, ſo let H G be to A C. </s> <s>It is <lb></lb>to be proved, that H F is a fourth part of A B. </s> <s>Foraſmuch therefore <lb></lb>as A B, B C, B D, and B E<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.961.1.jpg" xlink:href="040/01/961/1.jpg"></figure><lb></lb><emph type="italics"></emph>are proportionals, A C, <lb></lb>C D, and D E ſhall be in <lb></lb>the ſame proportion: And <lb></lb>as the quadruple of the ſaid <lb></lb>A B, B C, and B D is to <lb></lb>A B with the double of B C and triple of B D, ſo is the quadruple of <lb></lb>A C, C D, and D E; that is, the quadruple of A E; to A C with the <lb></lb>double of C D, and triple of D E. </s> <s>And ſo is A C to H G. </s> <s>Therefore <lb></lb>as the triple of A E is to A C, with the double of C D and triple of <lb></lb>D E, ſo is 3/4 of A C to H G. </s> <s>And as the triple of A E is to the triple of <lb></lb>E B, ſo is 3/4 A C to G F: Therefore, by the Converſe of the twenty <lb></lb>fourth of the fifth, As triple A E is to A C with double C D and tri<lb></lb>ple D B, ſo is 3/4 of A C to H F: And as the quadruple of A E is to A C <lb></lb>with the double of C D and triple of D B; that is, to A B with C B and <lb></lb>B D, ſo is A C to H F. And, by Permutation, as the quadruple of A E <lb></lb>is to A C, ſo is A B with C B and B D to H F. </s> <s>And as A C is to A E, ſo <lb></lb>is A B to A B with C B and B D. Therefore,<emph.end type="italics"></emph.end> ex æquali, <emph type="italics"></emph>by Perturbed <lb></lb>proportion, as quadruple A E is to A E, ſo is A B to H F. </s> <s>Wherefore it <lb></lb>is manifeſt that H F is the fourth part of A B.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROPOSITION.</s></p><p type="main"> <s>The Center of Gravity of the <emph type="italics"></emph>Fruſtum<emph.end type="italics"></emph.end> of any Py<lb></lb>ramid or Cone, cut equidiſtant to the Plane <lb></lb>of the Baſe, is in the Axis, and doth ſo divide <lb></lb>the ſame, that the part towards the leſſer Baſe <lb></lb>is to the remainder, as the triple of the greater <lb></lb>Baſe, with the double of the mean Space be<lb></lb>twixt the greater and leſſer Baſe, together <lb></lb>with the leſſer Baſe is to the triple of the leſſer <lb></lb>Baſe, together with the ſame double of the <lb></lb>mean Space, as alſo of the greater Baſe.</s></p><pb xlink:href="040/01/962.jpg" pagenum="269"></pb><p type="main"> <s><emph type="italics"></emph>From a Cone or Pyramid whoſe Axis is A D, and equidiſtant to <lb></lb>the Plane of the Baſe, let a<emph.end type="italics"></emph.end> Fruſtum <emph type="italics"></emph>be cut whoſe Axis is V D. <lb></lb></s> <s>And as the triple of the greateſt Baſe with the double of the <lb></lb>mean and leaſt is to the triple of the leaſt and double of the mean and <lb></lb>greateſt, ſo is \ O to O D. </s> <s>It is to be proved that the Center of Gra<lb></lb>vity of the<emph.end type="italics"></emph.end> Fruſtum <emph type="italics"></emph>is in O. </s> <s>Let V M be the fourth part of V D. <lb></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></lb>and unto H X K let X L be a third proportional, and X S a fourth. <lb></lb></s> <s>And as H S is to S X, ſo let M D be to the Line taken from O towards <lb></lb>A: which let be O N. </s> <s>And becauſe the greater Baſe is in proportion <lb></lb>to that which is mean betwixt the <lb></lb>greater and leſſer as D A to A V; that<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.962.1.jpg" xlink:href="040/01/962/1.jpg"></figure><lb></lb><emph type="italics"></emph>is, as H X, to X K, but the ſaid <lb></lb>mean is to the leaſt as K X to X L; <lb></lb>the greater, mean, and leſſer Baſes <lb></lb>ſhall be in the ſame proportion as <lb></lb>H X, X K, and X L. </s> <s>Wherefore as <lb></lb>triple the greater Baſe, with double <lb></lb>the mean and leſſer, is to triple the <lb></lb>leaſt with double the mean and grea<lb></lb>teſt; that is, as V O is to O D; ſo is <lb></lb>triple H X with double X K and X L <lb></lb>to triple X L, with double X K and <lb></lb>X H: And by Compoſition and Converting the proportion, O D ſhall <lb></lb>be to V D, as H X, with double X K and triple X L, to quadruple H X, <lb></lb>X K, and X L. </s> <s>There are, therefore, four proportional Lines, H X, <lb></lb>X K, X L, and X S: And as X S is to S H, ſo is the Line taken N O <lb></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></lb>with double X K and triple X L is to quadruple H X, X K and X L; <lb></lb>ſo is another Line taken O D to D V; that is, to H K. Therefore, by <lb></lb>the things demonſtrated, D N ſhall be the fourth part of H X; that <lb></lb>is, of A D. </s> <s>Wherefore the point N ſhall be the Center of Gravity <lb></lb>of the Cone or Pyramid whoſe Axis is A D. </s> <s>Let the Center of Gra<lb></lb>vity of the Pyramid or Cone whoſe Axis is A V be I. </s> <s>It is therefore <lb></lb>manifeſt that the Center of Gravity of the<emph.end type="italics"></emph.end> Fruſtum <emph type="italics"></emph>is in the Line <lb></lb>I N inclining towards the part N, and in that point of it which with <lb></lb>the point N include a Line to which I M hath the ſame proportion that <lb></lb>the<emph.end type="italics"></emph.end> Fruſtum <emph type="italics"></emph>cut hath to the Pyramid or Cone whoſe Axis is A V. <lb></lb></s> <s>It remaineth therefore to prove that I N hath the ſame proportion <lb></lb>to N O, that the<emph.end type="italics"></emph.end> Fruſtum <emph type="italics"></emph>hath to the Cone whoſe Axis is A V. </s> <s>But <lb></lb>as the Cone whoſe Axis is D A is to the Cone whoſe Axis is A V, ſo <lb></lb>is the Cube D A to the Cube D V; that is, the Cube H X to the <lb></lb>Cube X K: But this is the ſame proportion that H X hath to X S. <lb></lb>Wherefore, by Diviſion, as H S is to S X, ſo ſhall the<emph.end type="italics"></emph.end> Fruſtum <emph type="italics"></emph>whoſe<emph.end type="italics"></emph.end><pb xlink:href="040/01/963.jpg" pagenum="270"></pb><emph type="italics"></emph>Axis is D V be to the Cone or Pyramid whoſe Axis is V A. </s> <s>And as <lb></lb>H S is to S X, ſo alſo is M D to O N. </s> <s>Wherefore the<emph.end type="italics"></emph.end> Fruſtum <emph type="italics"></emph>is to the <lb></lb>Pyramid whoſe Axis is A V, as M D to N O. </s> <s>And becauſe A N <lb></lb>is 3/4 of A D; and A I is 3/4 of A V; the remainder I N ſhall be 3/4 of the <lb></lb>remainder V D. </s> <s>Wherefore I N ſhall be equal to M D. <lb></lb></s> <s>And it hath been demonſtrated that M D is to N O, <lb></lb>as the<emph.end type="italics"></emph.end> Fruſtum <emph type="italics"></emph>to the Cone A V. </s> <s>It is mani<lb></lb>feſt, therefore, that I N hath likewiſe <lb></lb>the ſame proportion to N O: <lb></lb>Wherefore the Propo<lb></lb>ſition is manifeſt.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>FINIS.<emph.end type="italics"></emph.end><lb></lb></s></p> </chap> <pb xlink:href="040/01/964.jpg"></pb><chap> <pb xlink:href="040/01/965.jpg" pagenum="271"></pb><p type="head"> <s>GALILEUS, <lb></lb>HIS <lb></lb>MECHANICKS: <lb></lb>OF THE BENEFIT DERIVED <lb></lb>FROM THE SCIENCE OF MECHANICKS, <lb></lb>AND FROM ITS INSTRUMENTS.</s></p> </chap> <chap> <p type="main"> <s>I judged it extreamly neceſſary, before our <lb></lb>deſcending to the Speculation of Mecha<lb></lb>nick Inſtruments, to conſider how I might, <lb></lb>as it were, ſet before your eyes in a gene<lb></lb>ral Diſcourſe, the many benefits that are <lb></lb>derived from the ſaid Inſtruments: and <lb></lb>this I have thought my ſelf the more ob<lb></lb>liged to do, for that (if I am not miſtaken) <lb></lb>I have ſeen the generality of <emph type="italics"></emph>M<emph.end type="italics"></emph.end>echaniti<lb></lb>ans deceive themſelves in going about to apply Machines to many <lb></lb>operations of their own nature impoſſible; by the ſucceſſe where<lb></lb>of they have been diſappointed, and others likewiſe fruſtrate of <lb></lb>the hope which they had conceived upon the promiſe of thoſe pre<lb></lb>ſumptuous undertakers: of which miſtakes I think I have found <lb></lb>the principall cauſe to be the belief and conſtant opinion theſe <pb xlink:href="040/01/966.jpg" pagenum="272"></pb>Artificers had, and ſtill have, that they are able with a ſmall force <lb></lb>to move and raiſe great weights; (in a certain manner with their <lb></lb>Machines cozening nature, whoſe Inſtinct, yea moſt poſitive con<lb></lb>ſtitution it is, that no Reſiſtance can be overcome, but by a Force <lb></lb>more potent then it:) which conjecture how falſe it is, I hope by <lb></lb>the enſuing true and neceſſary Demonſtrations to evince.</s></p><p type="main"> <s>In the mean time, ſince I have hinted, that the benefit and help <lb></lb>derived from Machines is not, to be able with leſſe Force, by help <lb></lb>of the Machine to move thoſe weights, which, without it, could <lb></lb>not be moved by the ſame Force: it would not be beſides the <lb></lb>purpoſe to declare what the Commodities be which are derived to <lb></lb>us from ſuch like faculties, for if no profit were to be hoped for, <lb></lb>all endeavours employed in the acquiſt thereof will be but loſt <lb></lb>labour.</s></p><p type="main"> <s>Proceeding therefore according to the nature of theſe Studies, <lb></lb>let us firſt propoſe four things to be conſidered. </s> <s>Firſt, the weight <lb></lb>to be transferred from place to place; and ſecondly, the Force <lb></lb>and Power which ſhould move it; thirdly, the Diſtance between <lb></lb>the one and the other Term of the Motion; Fourthly, the Time <lb></lb>in which that mutation is to be made: which Time becometh the <lb></lb>ſame thing with the Dexterity, and Velocity of the Motion; we <lb></lb>determining that Motion to be more ſwift then another, which in <lb></lb>leſſe Time paſſeth an equal Diſtance.</s></p><p type="main"> <s>Now, any determinate Reſiſtance and limited Force whatſoever <lb></lb>being aſſigned, and any Diſtance given, there is no doubt to be <lb></lb>made, but that the given Force may carry the given Weight to the <lb></lb>determinate Diſtance; for, although the Force were extream <lb></lb>ſmall, yet, by dividing the Weight into many ſmall parts, none <lb></lb>of which remain ſuperiour to the Force, and by transferring them <lb></lb>one by one, it ſhall at laſt have carried the whole Weight to the <lb></lb>aſſigned Term: and yet one cannot at the end of the Work with <lb></lb>Reaſon ſay, that that great Weight hath been moved, and tranſ<lb></lb>ported by a Force leſſe then it ſelf, howbeit indeed it was done <lb></lb>by a Force, that many times reiterated that Motion, and that <lb></lb>Space, which ſhall have been meaſured but only once by the whole <lb></lb>Weight. </s> <s>From whence it appears, that the Velocity of the Force <lb></lb>hath been as many times Superiour to the Reſiſtance of the weight, <lb></lb>as the ſaid Weight was ſuperiour to the Force; for that in the <lb></lb>ſame Time that the moving Force hath many times meaſured the <lb></lb>intervall between the Terms of the Motion, the ſaid Moveable <lb></lb>happens to have paſt it onely once: nor therefore ought we to <lb></lb>affirm a great Reſiſtance to have been overcome by a ſmall Force, <lb></lb>contrary to the conſtitution of Nature. </s> <s>Then onely may we ſay <lb></lb>the Natural Conſtitution is overcome, when the leſſer Force tranſ<lb></lb>fers the greater Reſiſtance, with a Velocity of Motion like to that <pb xlink:href="040/01/967.jpg" pagenum="273"></pb>wherewith it ſelf doth move; which we affirm abſolutely to be <lb></lb>impoſſible to be done with any Machine imaginable. </s> <s>But becauſe <lb></lb>it may ſometimes come to paſſe, that having but little Force, it is <lb></lb>required to move a great Weight all at once, without dividing it <lb></lb>in pieces, on this occaſion it will be neceiſary to have recourſe to <lb></lb>the Machine, by means whereof the propoſed Weight may be <lb></lb>transferred to the aſſigned Space by the Force given. </s> <s>But yet <lb></lb>this doth not hinder, but that the ſame Force is to move, meaſuring <lb></lb>that ſame Space, or another equall to it, as many ſeverall times as <lb></lb>it is exceeded by the ſaid Weight. </s> <s>So that in the end of the a<lb></lb>ction we ſhall ſind that we have received from the Machine no <lb></lb>other benefit tnen only that of tranſporting the ſaid Weight with <lb></lb>the given Force to the Term given, all at once. </s> <s>Which Weight, <lb></lb>being divided into parts, would without any Machine have been <lb></lb>carried by the ſame Force, in the ſame Time, through the ſame <lb></lb>Intervall. </s> <s>And this ought to paſſe for one of the benefits taken <lb></lb>from the Mechanicks: for indeed it frequently happens, that be<lb></lb>ing ſcanted in Force but not Time, we are put upon moving great <lb></lb>Weights unitedly or in groſſe: but he that ſhould hope, and at<lb></lb>tempt to do the ſame by the help of Machines without increaſe of <lb></lb>Tardity in the Moveable, would certainly be deceived, and would <lb></lb>declare his ignorance of the uſe of Mechanick Inſtruments, and <lb></lb>the reaſon of their effects.</s></p><p type="main"> <s>Another benefit is drawn from the Inſtruments, which depend<lb></lb>eth on the place wherein the operation is to be made: for all In<lb></lb>ſtruments cannot be made uſe of in all places with equall conve<lb></lb>nience. </s> <s>And ſo we ſee (to explain our ſelves by an example) that <lb></lb>for drawing of Water out of a Well, we make uſe of onely a <lb></lb>Rope and a Bucket fitted to receive and hold Water, wherewith <lb></lb>we draw up a determinate quantity of Water, in a certain Time, <lb></lb>with our limited ſtrength: and he that ſhould think he could with <lb></lb>a Machine of whatſoever Force, with the ſame ſtrength, and in <lb></lb>the ſame Time, take up a great quantity of Water, is in a groſſe <lb></lb>Errour. </s> <s>And he ſhall find himſelf ſo much the more deceived, <lb></lb>the more he ſhall vary and multiply his Inventions: Yet never<lb></lb>theleſſe we ſee Water drawn up with other Engines, as with a Pump <lb></lb>that drinks up Water in the Hold of Ships; where you muſt note <lb></lb>that the Pump was not imployed in thoſe Offices, for that it draws <lb></lb>up more Water in the ſame Time, and with the ſame ſtrength <lb></lb>then that which a bare Bucket would do, but becauſe in that place <lb></lb>the uſe of the Bucket or any ſuch like Veſſel could not effect what <lb></lb>is deſired, namely to keep the Hold of the Ship quite dry from e<lb></lb>very little quantity of Water; which the Bucket cannot do, for <lb></lb>that it cannot dimerge and dive, where there is not a conſiderable <lb></lb>depth of Water. </s> <s>And thus we ſee the Holds of Ships by the <pb xlink:href="040/01/968.jpg" pagenum="274"></pb>ſaid Inſtrument kept dry, when Water cannot but onely oblique<lb></lb>ly be drawn up, which the ordinary uſe of the Bucket would not <lb></lb>effect, which riſeth and deſcends with its Rope perpendicu<lb></lb>larly.</s></p><p type="main"> <s>The third is a greater benefit, haply, then all the reſt that are <lb></lb>derived from Mechanick Inſtruments, and reſpects the aſſiſtance <lb></lb>which is borrowed of ſome Force exanimate, as of the ſtream of a <lb></lb>River, or elſe animate, but of leſſe expence by far, then that which <lb></lb>would be neceſſary for maintaining humane ſtrength: as when to <lb></lb>turn Mills, we make uſe of the Current of a River, or the ſtrength <lb></lb>of a Horſe, to effect that, which would require the ſtrength of five <lb></lb>or fix Men. </s> <s>And this we may alſo advantage our ſelves in raiſing <lb></lb>Water, or making other violent Motions, which muſt have been <lb></lb>done by Men, if there were no other helps; becauſe with one ſole <lb></lb>Veſſel we may take Water, and raiſe, and empty it where occaſion <lb></lb>requires; but becauſe the Horſe, or ſuch other Mover wanteth <lb></lb>Reaſon, and thoſe Inſtruments which are requiſite for holding and <lb></lb>emptying the Veſſel in due time, returning again to fill it, and one<lb></lb>ly is endued with Force, therefore it's neceſſary that the Mecha<lb></lb>nitian ſupply the naturall defect of that Mover, furniſhing it with <lb></lb>ſuch devices and inventions, that with the ſole application of it's <lb></lb>Force the defired effect may follow. </s> <s>And therein is very great <lb></lb>advantage, not becauſe that a Wheel or other Machine can enable <lb></lb>one to tranſport the ſame Weight with leſſe Force, and greater <lb></lb>Dexterity, or a greater Space than an equall Force, without thoſe <lb></lb>Inſtruments, but having Judgment and proper Organs, could have <lb></lb>done; but becauſe that the ſtream of a River coſteth little or <lb></lb>nothing, and the charge of keeping of an Horſe or other Beaſt, <lb></lb>whoſe ſtrength is greater then that of eight, or it may be more <lb></lb>Men, is far leſſe then what ſo many Men would be kept <lb></lb>for.</s></p><p type="main"> <s>Theſe then are the benefits that may be derived from Mecha<lb></lb>nick Inſtruments, and not thoſe which ignorant Engineers dream <lb></lb>of, to their own diſgrace, and the abuſe of ſo many Princes, <lb></lb>whilſt they undertake impoſſible enterprizes; of which, both <lb></lb>by the little which hath been hinted, and by the much which <lb></lb>ſhall be demonſtrated in the Progreſſe of this Treatiſe, we ſhall <lb></lb>come to aſſure our ſelves, if we attentively heed that which ſhall <lb></lb>be ſpoken.</s></p><pb xlink:href="040/01/969.jpg" pagenum="275"></pb><p type="head"> <s>DEFINITIONS.</s></p><p type="main"> <s>That which in all Demonſtrative Sciences is neceſſary to be <lb></lb>obſerved, we ought alſo to follow in this Diſcourſe, that is; <lb></lb>to propound the Definitions of the proper Terms of this <lb></lb>Art, and the primary Suppoſitions, from which, as from ſeeds full <lb></lb>of fecundity, may of conſequence ſpring and reſult the cauſes, <lb></lb>and true Demonſtrations, of the Nature of all the Mechanick <lb></lb>Engines which are uſed, for the moſt part about the Motions of <lb></lb>Grave Matters, therefore we will determine, firſt, what is <emph type="italics"></emph>GRA<lb></lb>VITIE.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>We call <emph type="italics"></emph>GRAVITIE<emph.end type="italics"></emph.end> then, That propenſion of moving <lb></lb>naturally downwards, which is found in ſolid Bodies, cauſed by <lb></lb>the greater or leſſe quantity of matter, whereof they are conſti<lb></lb>tuted.</s></p><p type="main"> <s><emph type="italics"></emph>MOMENT<emph.end type="italics"></emph.end> is the propenſion of deſcending, cauſed not ſo <lb></lb>much by the Gravity of the moveable, as by the diſpoſure which <lb></lb>divers Grave Bodies have in relation to one another; by means of <lb></lb>whichMoment, we oft ſee a Body leſs Grave counterpoiſe another <lb></lb>of greater Gravity: as in the Stiliard, a great Weight is raiſed by <lb></lb>a very ſmall counterpoiſe, not through exceſs of Gravity, but <lb></lb>through the remoteneſſe from the point whereby the Beam is up<lb></lb>held, which conjoyned to the Gravity of the leſſer weight adds <lb></lb>thereunto Moment, and <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of deſcending, wherewith the <lb></lb>Moment of the other greater Gravity may be exceeded. <emph type="italics"></emph>MO<lb></lb>MENT<emph.end type="italics"></emph.end> then is that IMPETUS of deſcending, compounded <lb></lb>of Gravity, Poſition, and the like, whereby that propenfion may <lb></lb>be occaſioned</s></p><p type="main"> <s>The <emph type="italics"></emph>CENTER<emph.end type="italics"></emph.end> of <emph type="italics"></emph>GRAVITY<emph.end type="italics"></emph.end> we define to be that point <lb></lb>in every Grave Body, about which conſiſt parts of equall Moment: <lb></lb>ſo that, imagining ſome Grave Body to be ſuſpended and ſuſtain<lb></lb>ed by the ſaid point, the parts on the right hand will Equilibrate <lb></lb>thoſe on the left, the Anteriour, the Poſteriour, and thoſe above <lb></lb>thoſe below; ſo that be it in any whatſoever fite, and poſition, <lb></lb>provided it be ſuſpended by the ſaid <emph type="italics"></emph>CENTER,<emph.end type="italics"></emph.end> it ſhall ſtand <lb></lb>ſtill: and this is that point which would gladly unite with the <lb></lb>univerſall Center of Grave Bodies, namely withthat of the Earth, <lb></lb>if it might thorow ſome free <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> deſcend thither. </s> <s>From <lb></lb>whence we take theſe Suppoſitions.</s></p><pb xlink:href="040/01/970.jpg" pagenum="276"></pb><p type="head"> <s>SUPPOSITIONS.</s></p><p type="main"> <s>Any Grave Body, (as to what belongeth to it's proper ver<lb></lb>tue) moveth downwards, ſo that the Center of it's Gravity <lb></lb>never ſtrayeth out of that Right Line which is produced <lb></lb>from the ſaid Center placed in the firſt Term of the Motion unto <lb></lb>the univerſal Center of Grave Bodies. </s> <s>Which is a Suppoſition <lb></lb>very manifeſt, becauſe that ſingle Center being obliged to endea<lb></lb>vour to unite with the common Center, it's neceſſary, unleſſe ſome <lb></lb>impediment intervene, that it go ſeeking it by the ſhorteſt Line, <lb></lb>which is the Right alone: And from hence may we ſecondarily <lb></lb>ſuppoſe</s></p><p type="main"> <s>Every Grave Body putteth the greateſt ſtreſſe, and weigheth <lb></lb>moſt on the Center of it's Gravity, and to it, as to its proper ſeat, <lb></lb>all <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> all Ponderoſity, and, in ſome, all Moment hath re<lb></lb>courſe.</s></p><p type="main"> <s>We laſtly ſuppoſe the Center of the Gravity of two Bodies e<lb></lb>qually Grave to be in the midſt of that Right Line which conjoyns <lb></lb>the ſaid two Centers; or that two equall weights, ſuſpended in <lb></lb>equall diſtence, ſhall have the point of <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> in the common <lb></lb>Center, or meeting of thoſe equal Diſtances. </s> <s>As for Example, <lb></lb>the Diſtance C E being equall to the Diſtance E D, and there be<lb></lb>ing by them two equall weights ſuſpended, A and B, we ſuppoſe <lb></lb>the point of <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> to be in the point E, there being no <lb></lb>greater reaſon for inclining to <lb></lb>one, then to the other part. </s> <s>But <lb></lb><figure id="id.040.01.970.1.jpg" xlink:href="040/01/970/1.jpg"></figure><lb></lb>here is to be noted, that the Di<lb></lb>ſtances ought to be meaſured <lb></lb>with Perpendicular Lines, which <lb></lb>from the point of Suſpenſion E, <lb></lb>fall on the Right Lines, that from <lb></lb>the Center of the Gravity of the <lb></lb>Weights A and B, are drawn to <lb></lb>the common Center of things <lb></lb>Grave; and therefore if the Diſtance E D were tranſported into <lb></lb>E F, the weight B would not counterpoiſe the weight A, becauſe <lb></lb>drawing from the Centers of Gravity two Right Lines to the Cen<lb></lb>ter of the Earth, we ſhall ſee that which cometh from the Center <lb></lb>of the Weight I, to be nearer to the Center E, then the other <lb></lb>produced from the Center of the weight A. </s> <s>Therefore our ſaying <lb></lb>that equal Weights are ſuſpended by [or at] equal Diſtances, is <lb></lb>to be underſtood to be meant when as the Right Lines that go from <lb></lb>their Centers & to ſeek out the common Center of Gravity, ſhall be <lb></lb>equidiſta nt from that Right Line, which is produced from the ſaid <pb xlink:href="040/01/971.jpg" pagenum="277"></pb>Term of thoſe Diſtances, that is from the point of Suſpenſion, to <lb></lb>the ſame Center of the Earrh.</s></p><p type="main"> <s>Theſe things determined and ſuppoſed, we come to the explica<lb></lb>tion of a Principle, the moſt common and materiall of the greater <lb></lb>part of Mechanick Inſtruments: demonſtrating, that unequall <lb></lb>Weights weigh equally when ſuſpended by [or at] unequal Diſtan<lb></lb>ces, which have contrary proportion to that which thoſe weights <lb></lb>are found to have, See the Demonſtration in the beginning of the <lb></lb>ſecond Dialogue of Local-Motions.</s></p><p type="head"> <s><emph type="italics"></emph>Some Adveriiſements about what hath been ſaid.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Now being that Weights unequall come to acquire equall <lb></lb>Moment, by being alternately ſuſpended at Diſtances that <lb></lb>have the ſame proportion with them; I think it not fit to <lb></lb>over paſſe with ſilence another congruicy and probability, which <lb></lb>may confirm the ſame truth; for let the Ballance A B, be conſide<lb></lb>red, as it is divided into unequal parts in the point C, and let the <lb></lb>Weights be of the ſame propor<lb></lb><figure id="id.040.01.971.1.jpg" xlink:href="040/01/971/1.jpg"></figure><lb></lb>tion that is between the Diſtan<lb></lb>ces B C, and C A, alternately <lb></lb>ſuſpended by the points A, and <lb></lb>B: It is already manifeſt, that <lb></lb>the one will counterpoiſe the <lb></lb>other, and conſequently, that <lb></lb>were there added to one of them <lb></lb>a very ſmall Moment of Gravity, it would preponderate, raiſing <lb></lb>the other, ſo that an inſenſible Weight put to the Grave B, the <lb></lb>Ballance would move and deſcend from the point B towards E, <lb></lb>and the other extream A would aſcend into D, and in regard that <lb></lb>to weigh down B, every ſmall Gravity is ſufficient, therefore not <lb></lb>keeping any accompt of this inſenſible Moment, we will put no <lb></lb>difference between one Weights <emph type="italics"></emph>ſuſtaining,<emph.end type="italics"></emph.end> and one Weights <lb></lb><emph type="italics"></emph>moving<emph.end type="italics"></emph.end> another. </s> <s>Now, let us conſider the Motion which the <lb></lb>Weight B makes, deſcending into E, and that which the other <lb></lb>A makes in aſcending into D, we ſhall without doubt find the <lb></lb>Space B E to be ſo much greater than the Space A D, as the Di<lb></lb>ſtance B C is greater than C A, forming in the Center C two an<lb></lb>gles D C A, and E C B, equall as being at the Cock, and conſe<lb></lb>quently two Circumferences A D and B E alike; and to have the <lb></lb>ſame proportion to one another, as have the Semidiameters B C, <lb></lb>and C A, by which they are deſcribed: ſo that then the Velocity <lb></lb>of the Motion of the deſcending Grave B cometh to be ſo much <lb></lb>Superiour to the Velocity of the other aſcending Moveable A, as <lb></lb>the Gravity of this exceeds the Gravity of that; and it not being <pb xlink:href="040/01/972.jpg" pagenum="278"></pb>poſſible that the Weight A ſhould be raiſed to D, although ſlow<lb></lb>ly, unleſſe the other Weight B do move to E ſwiftly, it will not <lb></lb>be ſtrange, or inconſiſtent with the Order of Nature, that the <lb></lb>Velocity of the Motion of the Grave B, do compenſate the greater <lb></lb>Reſiſtance of the Weight A, ſo long as it moveth ſlowly to D, <lb></lb>and the other deſcendeth ſwiftly to E, and ſo on the contrary, <lb></lb>the Weight A being placed in the point D, and the other B in <lb></lb>the point E, it will not be unreaſonable that that falling leaſurely <lb></lb>to A, ſhould be able to raiſe the other haſtily to B, recovering by <lb></lb>its Gravity what it had loſt by it's Tardity of Motion. </s> <s>And by <lb></lb>this Diſcourſe we may come to know how the Velocity of the <lb></lb>Motion is able to encreaſe Moment in the Moveable, according to <lb></lb>that ſame proportion by which the ſaid Velocity of the Motion is <lb></lb>augmented.</s></p><p type="main"> <s>There is alſo another thing, before we proceed any farther, to <lb></lb>be confidered; and this is touching the Diſtances, whereat, or <lb></lb>wherein Weights do hang: for it much imports how we are to <lb></lb>underſtand Diſtances equall, and unequall; and, in ſum, in what <lb></lb>manner they ought to be mea<lb></lb><figure id="id.040.01.972.1.jpg" xlink:href="040/01/972/1.jpg"></figure><lb></lb>ſured: for that A B being the <lb></lb>Right Line, and two equall <lb></lb>Weights being ſuſpended at <lb></lb>the very ends thereof, the point <lb></lb>C being taken in the midſt of <lb></lb>the ſaid Line, there ſhall be an <lb></lb><emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> upon the ſame: <lb></lb>And the reaſon is for that the <lb></lb>Diſtance C B is equal to C A. <lb></lb></s> <s>But if elevating the Line C B, moving it about the point C, it <lb></lb>ſhall be transferred into CD, ſo that the Ballance ſtand according <lb></lb>to the two Lines A C, and C D, the two equall Weights hanging <lb></lb>at the Terms A and D, ſhall no longer weigh equally on that <lb></lb>point C, becauſe the diſtance of the Weight placed in D, is made <lb></lb>leſſe then it was when it hanged in B. </s> <s>For if we confider the Lines, <lb></lb>along [or by] which the ſaid Graves make their Impulſe, and <lb></lb>would deſcend, in caſe they were freely moved, there is no doubt <lb></lb>but that they would make or deſcribe the Lines A G, D F, B H: <lb></lb>Therefore the Weight hanging on the point D, maketh it's Moment <lb></lb>and <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> according to the Line D F: but when it hanged in <lb></lb>B, it made <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> in the Line B H: and becauſe the Line D F is <lb></lb>nearer to the Fulciment C, then is the Line B H Therefore we <lb></lb>are to underſtand that the Weights hanging on the points A and D, <lb></lb>are not equi-diſtant from the point C, as they be when they are <lb></lb>conſtituted according to their Right Line A C B: And laſtly, <lb></lb>we are to take notice, that the Diſtance is to be meaſured by <pb xlink:href="040/01/973.jpg" pagenum="279"></pb>Lines, which fall at Right Angles on thoſe whereon the Weights <lb></lb>hang, and would move, if ſo be they were permitted to deſcend <lb></lb>freely.</s></p><p type="head"> <s>Of the BALLANCE and LEAVER.</s></p><p type="main"> <s>Having underſtood by certain Demonſtration, one of the <lb></lb>firſt Principles, from which, as from a plentiſul Fountain, <lb></lb>many of the Mechanical Inſtruments are derived, we may <lb></lb>take occaſion without any difficulty to come to the knowledge of <lb></lb>the nature of them: and firſt ſpeaking of the Stiliard, an Inſtru<lb></lb>ment of moſt ordinary uſe, with which divers Merchandizes are <lb></lb>weighed, ſuſtaining them, though very heavy, with a very ſmall <lb></lb>counterpoiſe, which is com<lb></lb>monly called the Roman or <lb></lb><figure id="id.040.01.973.1.jpg" xlink:href="040/01/973/1.jpg"></figure><lb></lb>Plummet, we ſhall prove that <lb></lb>there is no more to be done in <lb></lb>ſuch an operation, but to re<lb></lb>duce into act and practice <lb></lb>what hath been above contemplated. </s> <s>For if we propoſe the Bal<lb></lb>lance A B, whoſe Fulciment or Lanquet is in the point C, by <lb></lb>which, at the ſmall Diſtance C A, hangeth the heavy Weight D, <lb></lb>and if along the other greater C B, (which we call the Needle of <lb></lb>the Stiliard) we ſhould ſuppoſe the Roman F, though of but little <lb></lb>weight in compariſon of the Grave Body D to be ſlipped to and <lb></lb>fro, it ſhall be pofſible to place it ſo remotely from the Lanquet C, <lb></lb>that the ſame proportion may be found between the two Weights <lb></lb>D and F, as is between the Diſtances F C, and C A: and then ſhall <lb></lb>an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> ſucceed; unequall Weights hanging at Diſtances <lb></lb>alternately proportional to them.</s></p><p type="main"> <s>Nor is this Inſtrument different from that other called <emph type="italics"></emph>Vectis,<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1107"></arrow.to.target><lb></lb>and vulgarly the ^{*} Leaver, wherewith great Weights are moved <lb></lb>by ſmall Force; the application of which is according to the Fi<lb></lb>gure prefixed; wherein the Leaver <lb></lb>is repreſented by the Bar of wood <lb></lb>or other ſolid matter, <emph type="italics"></emph>B<emph.end type="italics"></emph.end> C D, let <lb></lb><figure id="id.040.01.973.2.jpg" xlink:href="040/01/973/2.jpg"></figure><lb></lb>the heavy Weight to be raiſed be <lb></lb>A, and let the ſteadfaſt ſupport <lb></lb>or Fulciment on which the Leaver <lb></lb>reſts and moves be ſuppoſed to be <lb></lb>E, and putting one end of the <lb></lb>Leaver under the Weight A, as <lb></lb>may be ſeen in the point C, en<lb></lb>creaſing the Weight or Force at the other end D, it will be able <lb></lb>to lift up the Weight A, though not much, whenever the Force in <pb xlink:href="040/01/974.jpg" pagenum="280"></pb>D hath the ſame proportion to the Reſiſtance made by the Weight <lb></lb>A, in the point C: as the Diſtance <emph type="italics"></emph>B<emph.end type="italics"></emph.end> C hath to the Diſtance C D, <lb></lb>whereby it's clear, that the nearer the Fulciment E ſhall approach <lb></lb>to the Term B, encreaſing the proportion of the Diſtance D C to <lb></lb>the Diſtance C <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> the more may one diminiſh the Force in D which <lb></lb>is to raiſe the Weight A. </s> <s>And here it is to be noted, which I ſhall <lb></lb>alſo in its place remember you of, that the benefit drawn from all <lb></lb>Mechanical Inſtruments, is not that which the vulgar Mechanitians <lb></lb>do perſwade us, to wit, ſuch, that there by Nature is overcome, and <lb></lb>in a certain manner deluded, a ſmall Force over-powring a very <lb></lb>great Reſiſtance with help of the Leaver; for we ſhall demonſtrate, <lb></lb>that without the help of the length of the Leaver, the ſame Force, <lb></lb>in the ſame Time, ſhall work the ſame effect. </s> <s>For taking the ſame <lb></lb>Leaver B C D, whoſe reſt or Fulci<lb></lb>ment is in C, let the Diſtance C D <lb></lb><figure id="id.040.01.974.1.jpg" xlink:href="040/01/974/1.jpg"></figure><lb></lb>be ſuppoſed, for example, to be <lb></lb>in quintuple proportion to the <lb></lb>Diſtance C <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> & the ſaid Leaver to <lb></lb>be moved till it come to I C G: In <lb></lb>the Time that the Force ſhall have <lb></lb>paſſed the Space D I, the Weight <lb></lb>ſhall have been moved from B <lb></lb>to G: and becauſe the Diſtance <lb></lb>D C, was ſuppoſed quintuple to the other C B, it is manifeſt from <lb></lb>the things demonſtrated, that the Weight placed in B may be five <lb></lb>times greater then the moving Force ſuppoſed to be in D: but now, <lb></lb><arrow.to.target n="marg1108"></arrow.to.target><lb></lb>if on the contrary, we take notice of the ^{*} Way paſſed by <lb></lb>the Force from D unto I, whilſt the Weight is moved from B unto <lb></lb>G, we ſhall find likewiſe the Way D I, to be quintuple to the Space <lb></lb>B G. </s> <s>Moreover if we take the Diſtance C L, equal to the Diſtance <lb></lb>C B, and place the ſame Force that was in D, in the point L, and <lb></lb>in the point B the fifth part onely of the Weight that was put there <lb></lb>at firſt, there is no queſtion, but that the Force in L being now <lb></lb>equal to this Weight in B, and the Diſtances L C and C B being <lb></lb>equall, the ſaid Force ſhall be able, being moved along the Space LM <lb></lb>to transfer the Weight equall to it ſelf, thorow the other equall <lb></lb>Space B G: which five times reiterating this ſame action, ſhall tranſ<lb></lb>port all the parts of the ſaid Weight to the ſame Term G: But <lb></lb>the repeating of the Space L M, is certainly nothing more nor leſſe <lb></lb>then the onely once meaſuring the Space D I, quintuple to the <lb></lb>ſaid L M. </s> <s>Therefore the transferring of the Weight from B to G, <lb></lb>requireth no leſſe Force, nor leſſe Time, nor a ſhorter Way if it <lb></lb>wee placed in D, than it would need if the ſame were applied <lb></lb>in L: And, in ſhort, the benefit that is derived from the length of <lb></lb>the Leaver C D, is no other, ſave the enabling us to move that <pb xlink:href="040/01/975.jpg" pagenum="281"></pb>Body all at once, which would not have been moved by the ſame <lb></lb>Force, in the ſame Time, with an equall Motion, ſave onely in <lb></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></lb>called a Crow, <lb></lb>if of wood, a Bar <lb></lb>or Hand-ſpike.</s></p><p type="margin"> <s><margin.target id="marg1108"></margin.target>Or Space.</s></p><p type="head"> <s><emph type="italics"></emph>Of the<emph.end type="italics"></emph.end> CAPSTEN <emph type="italics"></emph>and of the<emph.end type="italics"></emph.end> CRANE.</s></p><p type="main"> <s>The Inſtruments which we are now about to declare, have <lb></lb>immediate dependence upon the Leaver, nay, are no other <lb></lb>but a perpetual Vectis or Leaver. </s> <s>For if we ſhall ſuppoſe the <lb></lb>Leaver B A C to be ſuſtained in <lb></lb>the point A, and the Weight G to <lb></lb><figure id="id.040.01.975.1.jpg" xlink:href="040/01/975/1.jpg"></figure><lb></lb>hang at the point B, the Force be<lb></lb>ing placed in C; It is manifeſt, <lb></lb>that transferring the Leaver unto <lb></lb>the points D A E, the Weight G <lb></lb>doth alter according to the Di<lb></lb>ſtance B D, but cannot much far<lb></lb>ther continue to raiſe it, ſo that <lb></lb>if it were required to elevate it yet <lb></lb>higher, it would be neceſſary to <lb></lb>ſtay it by ſome other Fulciment <lb></lb>in this Poſition, and to remit or return the Leaver to its former Po<lb></lb>ſition B A C, and ſuſpending the Weight anew thereat, to raiſe it <lb></lb>once again to the like height B D; and in this manner repeating <lb></lb>the work, many times one ſhall come with an interrupted Motion <lb></lb>to effect the drawing up of the Weight, which for many reſpects <lb></lb>will not prove very beneficial: whereupon this difficulty hath bin <lb></lb>thought on, and remedied, by finding out a way how to unite to<lb></lb>gether almoſt infinite Leavers, perpetuating the operation without <lb></lb>any interruption; and this hath been done by framing a Wheel <lb></lb>about the Center A, according to the Semidiameter A C, and an <lb></lb>Axis or Nave, about the ſame Center, of which let the Line A B <lb></lb>be the Semidiameter; and all this of very tough wood, or of other <lb></lb>ſtrong and ſolid matter, afterwards ſuſtaining the whole Machine <lb></lb>upon a Gudgeon or Pin of Iron planted in the point A, which <lb></lb>paſſeth quite thorow, where it is held faſt by two fixed Fulciments, <lb></lb>and the Rope D B G, at which the weight G hangeth, being be-laid <lb></lb>or wound about the Axis or Barrell, and applying another Rope <lb></lb>about the greater Wheel, at which let the other Grave I be hang<lb></lb>ed: It is manifeſt, that the length C A having to the other A B <lb></lb>the ſelf-ſame proportion that the Weight G hath to the Weight I, <lb></lb>it may ſuſtain the Grave G, and with any little Moment more ſhall <lb></lb>move it: and becauſe the Axis turning round together with the <lb></lb>Wheel, the Ropes that ſuſtain the Weights are alwaies pendent and <lb></lb>contingent with the extream Circumferences of that Wheel and <pb xlink:href="040/01/976.jpg" pagenum="282"></pb>Axis, ſo that they ſhall conſtantly maintain alike Site and Poſition <lb></lb>in reſpect of the Diſtances B A and A C, the Motion ſhall be <lb></lb>perpetuated, the Weight I deſcending, and forcing the other G <lb></lb>to aſcend. </s> <s>Where we are to obſerve the neceſſity of be-laying <lb></lb>or winding the Rope about the Wheel, that ſo the Weight I may <lb></lb>hang according to the Line that is tangent to the ſaid Wheel: for <lb></lb>if one ſhould ſuſpend the ſaid Weight, ſo as that it did hang by the <lb></lb>point F, cutting the ſaid Wheel, as is ſeen along the Line F N M, <lb></lb>the Motion would ceaſe, the Moment of the Weight M being di<lb></lb>miniſhed; which would weigh no more then if it did hang by the <lb></lb>point N: becauſe the Diſtance of its Suſpenſion from the Center <lb></lb>A, cometh to be determined by the Line A N, which falleth per<lb></lb>pendicularly upon the Rope F M, and is no longer terminated by <lb></lb>the Semidiameter of the Wheel A F, which falleth at unequall <lb></lb>Angles upon the ſaid Line F M. </s> <s>A violence therefore being offered <lb></lb>in the Circumference of the Wheel by a Grave and Exanimate <lb></lb>Body that hath no other <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> then that of Deſcending, it is <lb></lb>neceſſary that it be ſuſtained by a Line that is contingent with <lb></lb>the Wheel, and not by one that cutteth it. </s> <s>But if in the ſame <lb></lb>Circumference an Animate Force were employed, that had a Mo<lb></lb>ment or Faculty of making an <emph type="italics"></emph>Impulſe<emph.end type="italics"></emph.end> on all ſides, the work might <lb></lb>be effected in any whatever place of the ſaid Circumference. </s> <s>And <lb></lb>thus being placed in F, it would draw up the Weight by turning <lb></lb>the Wheel about, pulling not according to the Line F M down<lb></lb>wards, but ſide-waies according to the Contingent Line F L, which <lb></lb>maketh a Right Angle, with that which is drawn from the Center <lb></lb>A unto the point of Contact F: ſo, that if in this manner one do <lb></lb>meaſure the Diſtance from the Center A to the Force placed in <lb></lb>F, according to the Line A F perpendicular to F L, along which <lb></lb>the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> is made, a man ſhall not in any part have altered the <lb></lb>uſe of the ordinary Leaver. </s> <s>And we muſt note, that the ſame <lb></lb>would be poſſible to be done likewiſe with an Exanimate Force, <lb></lb>in caſe that a way were found out to cauſe that its Moment might <lb></lb>make Impulſe in the point F, drawing according to the Contingent <lb></lb>Line F L: which would be done by adjoyning beneath the Line F L <lb></lb>a turning Pulley, making the Rope wound about the Wheel to <lb></lb>paſſe along upon it, as it is ſeen to do by the Line F L X, ſuſpending <lb></lb>at the end thereof the Weight X equall to the other I, which ex<lb></lb>erciſing its Force according to the Line F L, ſhall alwaies keep a <lb></lb>Diſtance from the Center A equall unto the Semidiameter of the <lb></lb>Wheel. </s> <s>And from what hath been declared we will gather for a <lb></lb>Concluſion, That in this Inſtrument the Force hath alwaies the <lb></lb>ſame proportion to the Weight, as the Semidiameter of the Axis <lb></lb>or Barrell hath to the Semidiameter of the Wheel.</s></p><pb xlink:href="040/01/977.jpg" pagenum="283"></pb><p type="main"> <s>From the Inſtrument laſt deſcribed, the other Inſtrument which <lb></lb>we call the Crane is not much different, as to form, nay, differeth <lb></lb>nothing, ſave in the way of applying or employing it: For that the <lb></lb>Capſten moveth and is conſtituted perpendicular to the Horizon, <lb></lb>and the Crane worketh with its Moment parallel to the ſame Ho<lb></lb><figure id="id.040.01.977.1.jpg" xlink:href="040/01/977/1.jpg"></figure><lb></lb>rizon. </s> <s>For if upon the Circle D A E we ſuppoſe an Axis to be <lb></lb>placed Column-wiſe, turning about the Center B, and about which <lb></lb>the Rope D H, faſtened to the Weight that is to be drawn, is be<lb></lb>laid, and if the Bar F E B D be let into the ſaid Axis [<emph type="italics"></emph>by the Mor<lb></lb>tace B<emph.end type="italics"></emph.end>] and the Force of a Man, of an Horſe, or of ſome other <lb></lb>Animal apt to draw, be applyed at its end F, which moving round, <lb></lb>paſſeth along the Circumference F G C, the Crane ſhall be framed <lb></lb>and finiſhed, ſo that by carrying round the Bar F B D, the Barrell <lb></lb>or Axis E A D ſhall turn about, and the Rope which is twined a<lb></lb>bout it, ſhall conſtrain the Weight H to go forward: And becauſe <lb></lb>the point of the Fulciment about which the Motion is made, is the <lb></lb>point B, and the Moment keeps at a Diſtance from it according to <lb></lb>the Line B F, and the Reſiſtor at the Diſtance B D, the Leaver <lb></lb>F B D is formed, by vertue of which the Force acquireth Moment <lb></lb>equall to the Reſiſtance, if ſo be, that it be in proportion to it, as <lb></lb>the Line B D is to B F, that is, as the Semidiameter of the Axis to <lb></lb>the Semidiameter of the Circle, along whoſe Circumference the <lb></lb>Force moveth. </s> <s>And both in this, and in the other Inſtrument we <lb></lb>are to obſerve that which hath been frequently mentioned, that is, <lb></lb>That the benefit which is derived from theſe Machines, is not that <lb></lb>which the generality of the Vulgar promiſe themſelves from the <lb></lb>Mechanicks; namely, that being too hard for Nature, its poſſible <pb xlink:href="040/01/978.jpg" pagenum="284"></pb>with a Machine to overcome a Reſiſtance, though great, with a <lb></lb>ſmall Force, in regard, that we ſhall manifeſtly prove that the ſame <lb></lb>Force placed in F, might in the ſame Time conveigh the ſame <lb></lb>Weight, with the ſame Motion, unto the ſame Diſtance, without <lb></lb>any Machine at all: For ſuppoſing, for example, that the Reſiſtance <lb></lb>of the Grave H be ten times greater than the Force placed in F, it <lb></lb><figure id="id.040.01.978.1.jpg" xlink:href="040/01/978/1.jpg"></figure><lb></lb>will be requiſite for the mo<lb></lb>ving of the ſaid Reſiſtance, <lb></lb>that the Line F B be decuple <lb></lb>to B D; and conſequently, <lb></lb>that the Circumference of the <lb></lb>Circle F G C be alſo decuple <lb></lb>to the Circumference E A D: <lb></lb>and becauſe when the Force <lb></lb>ſhall be moved once along the <lb></lb>whole Circumference of the <lb></lb>Circle F G C, the Barrel EAD, <lb></lb>about which the Rope is be-laid which draweth the Weight, ſhall <lb></lb>likewiſe have given one onely turn; it is manifeſt, that the Weight <lb></lb>H ſhall not have been moved more than the tenth part of that way <lb></lb>which the Mover ſhall have gone. </s> <s>If therefore the Force that is to <lb></lb>move a Reſiſtance that is greater than it ſelf, for ſuch an aſſigned <lb></lb>Space by help of this Machine, muſt of neceſſity move ten times as <lb></lb>far, there is no doubt, but that dividing that Weight into ten parts, <lb></lb>each of them ſhall be equall to the Force, and conſequently, might <lb></lb>have been tranſported one at a Time, as great a Space as that <lb></lb>which it ſelf did move, ſo that making ten journeys, each equal to <lb></lb>the Circumference E A D, it ſhall not have gone any farther than <lb></lb>if it did move but once alone about the Circumference F G C; <lb></lb>and ſhall have conveighed the ſame Weight H to the ſame Di<lb></lb>ſtance. </s> <s>The benefit therefore that is to be derived from theſe <lb></lb>Machines is, that they carry all the Weight together, but not with <lb></lb>leſſe Labour, or with greater Expedition, or a greater Way than <lb></lb>the ſame Force might have done conveying it by parcels.</s></p><p type="head"> <s>Of PULLIES.</s></p><p type="main"> <s>The Inſtruments, whoſe Natures are reducible unto the Bal<lb></lb>lance, as to their Principle and Foundation, and others little <lb></lb>differing from them, have been already deſcribed; now for <lb></lb>the underſtanding of that which we have to ſay touching Pullies, <lb></lb>it is requiſite, that we conſider in the firſt place another way to uſe <lb></lb>the Leaver, which will conduce much towards the inveſtigation of <lb></lb>the Force of Pullies, and towards the underſtanding of other Me<lb></lb>chanical Effects. </s> <s>The uſe of the Leaver above declared ſuppoſed <pb xlink:href="040/01/979.jpg" pagenum="285"></pb>the Weight to be at one extream, and the Force at the other, and <lb></lb>the Fulciment placed in ſome point between the extreams: but we <lb></lb>may make uſe of the Leaver another way, yet, placing, as we ſee, <lb></lb>the Fulciment in the extream A, the Force in the other extream C, <lb></lb>and ſuppoſing the Weight D to hang by ſome point in the midſt, <lb></lb><figure id="id.040.01.979.1.jpg" xlink:href="040/01/979/1.jpg"></figure><lb></lb>as here we ſee by the point B, in <lb></lb>this example it's manifeſt, that if <lb></lb>the Weight did hang at a point <lb></lb>Equi-diſtant from the two ex<lb></lb>treams A and C, as at the point F, <lb></lb>the labour of ſuſtaining it would <lb></lb>be equally divided betwixt the <lb></lb>two points A and C, ſo that half <lb></lb>the Weight would be felt by the <lb></lb>Force C, the other half being ſu<lb></lb>ſtained by the Fulciment A: but if the Grave Body ſhall be hanged <lb></lb>at another place, as at B, we ſhall ſhew that the Force in C is ſuffi<lb></lb>cient to ſuſtain the Weight in B, as it hath the ſame proportion <lb></lb>to it, that the Diſtance, A B hath to the Diſtance A C. </s> <s>For De<lb></lb>monſtration of which, let us imagine the Line B A to be continued <lb></lb>right out unto G, and let the Diſtance B A be equall to A G, and <lb></lb>let the Weight hanging at G, be ſuppoſed equall to D: It is ma<lb></lb>nifeſt, that by reaſon of the equality of the Weights D and E, and <lb></lb>of the Diſtances G A and A B, the Moment of the Weight E <lb></lb>ſhall equalize the Moment of the Weight D, and is ſufficient to <lb></lb>ſuſtain it: Therefore whatever Force ſhall have Moment equall to <lb></lb>that of the Weight E, and that ſhall be able to ſuſtain it, ſhall be <lb></lb>ſufficient likewiſe to ſuſtain the Weight D: But for ſuſtaining the <lb></lb>Weight E, let there be placed in the point C ſuch a Force, whoſe <lb></lb>Moment hath that proportion to the Weight E, that the Diſtance <lb></lb>G A hath to the Diſtance A C, it ſhall be ſufficient to ſuſtain it: <lb></lb>Therefore the ſame Force ſhall likewiſe be able to ſuſtain the <lb></lb>Weight D, whoſe Moment is equall to the of E: But look what <lb></lb>Proportion the Line G A hath to the Line A C; and A B alſo hath <lb></lb>the ſame to the ſaid A C, G A having been ſuppoſed equall to A B: <lb></lb>And becauſe the Weights E and D are equall, each of them ſhall <lb></lb>have the ſame proportion to the Force placed in C: Therefore the <lb></lb>Force in C is concluded to equall the Moment of the Weight D, <lb></lb>as often as it hath unto it the ſame proportion that the Diſtance B A <lb></lb>hath to the Diſtance C A. </s> <s>And by moving the Weight, with the <lb></lb>Leaver uſed in this manner, it is gathered in this alſo, as well as in <lb></lb>the other Inſtruments, that what is gained in Force is loſt in Velo<lb></lb>city: for the Force C raiſing the Leaver, and transferring it to A I, <lb></lb>the Weight is moved the Space B H, which is as much leſſer than <lb></lb>the Space C I paſſed by the Force, as the Diſtance A B is leſſer <pb xlink:href="040/01/980.jpg" pagenum="286"></pb>than the Diſtance A C; that is, as the Force is leſſe than the <lb></lb>Weight.</s></p><p type="main"> <s>Theſe Principles being declared, we will paſſe to the Contem<lb></lb>plation of Pullies, the compoſition and ſtructure of which, together <lb></lb>with their uſe, ſhall be deſcribed by us. </s> <s>And firſt let us ſuppoſe the <lb></lb><arrow.to.target n="marg1109"></arrow.to.target><lb></lb>^{*} Little Pulley A B C, made of Mettall or hard Wood, voluble a<lb></lb>bout it's Axis which paſſeth thorow it's Center D, and about this <lb></lb><figure id="id.040.01.980.1.jpg" xlink:href="040/01/980/1.jpg"></figure><lb></lb>Pulley let the Rope E A B C be put, <lb></lb>at one end of whichlet the Weight E <lb></lb>hang, and at the other let us ſuppoſe <lb></lb>the Force F. </s> <s>I ſay, that the Weight <lb></lb>being ſuſtained by a Force equall to <lb></lb>it ſelf in the upper Nut or Pulley <lb></lb>A B C, bringeth ſome benefit, as the <lb></lb>moving or ſuſtaining of the ſaid <lb></lb>Weight with the Force placed in F: <lb></lb>For if we ſhall underſtand, that from <lb></lb>the Center D, which is the place of the Fulciment, two Lines be <lb></lb>drawn out as far as the Circumference of the Pulley in the points <lb></lb>A and C, in which the pendent Cords touch the Circumference, we <lb></lb>ſhall have a Ballance of equal Arms which determine the Diſtance <lb></lb>of the two Suſpenſions from the Center and Fulciment D: Where<lb></lb>upon it is manifeſt, that the Weight hanging at A cannot be ſuſtain<lb></lb>ed by a leſſer Weight hanging at G, but by one equal to it; ſuch <lb></lb>is the nature of equal Weights hanging at equal Diſtances. </s> <s>And <lb></lb>although in moving downwards, the Force F cometh to turn about <lb></lb>the Pulley A B C, yet there followeth no alteration of the Alti<lb></lb>tude or Reſpect, that the Weight and Force have unto the two <lb></lb>Diſtances A D and D C, nay, the Pulley encompaſſed becometh a <lb></lb>Ballance equal to A C, but perpetuall. </s> <s>Whence we may learn, <lb></lb>how childiſhly <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> deceiveth himſelf, who holds, that by making <lb></lb>the ſmall Pulley A B C bigger, one might draw up the Weight with <lb></lb>a leſſer Force; he conſidering that upon the enlargement of the <lb></lb>ſaid Pulley, the Diſtance D C encreaſed, but not conſidering that <lb></lb>there was as great an encreaſe of the other Diſtance of the Weight, <lb></lb>that is, the other Semidiameter D A. </s> <s>The benefit therefore that may <lb></lb>be drawn from the Inſtrument above ſaid, is nothing at all as to the <lb></lb>diminution of the labour: and if any one ſhould ask how it hap<lb></lb>pens, that on many occaſions of raiſing Weights, this means is made <lb></lb>uſe of to help the Axis, as we ſee, for example, in drawing up the <lb></lb>Water of Wells; it is anſwered, that that is done, becauſe that <lb></lb>by this means the manner of employing the Force is found more <lb></lb>commodious: for being to pull downwards, the proper Gravity of <lb></lb>our Arms and other parts help us, whereas if we were to draw <lb></lb>the fame Weight upwards with a meer Rope, by the ſole ſtrength <pb xlink:href="040/01/981.jpg" pagenum="287"></pb>of the Members and Muſcles, and as we uſe to ſay, by Force of <lb></lb>Armes, beſides the extern Weight, we are to lift up the Weight of <lb></lb>our own Armes, in which greater pains is required. </s> <s>Conclude we, <lb></lb>therefore, that this upper Pulley doth not bring any Facility to the <lb></lb>Force ſimply conſidered, but onely to the manner of applying it: <lb></lb>but if we ſhall make uſe of the like Machine <lb></lb><figure id="id.040.01.981.1.jpg" xlink:href="040/01/981/1.jpg"></figure><lb></lb>in another manner, as we are now about to <lb></lb>declare; we may raiſe the Weight with di<lb></lb>minution of Forces: For let the Pulley <lb></lb>B D C be voluble about the Center E placed <lb></lb>in it's Frame B L C, at which hang the <lb></lb>Grave G; and let the Rope A B D C F <lb></lb>paſſe about the Pulley; of which let the end <lb></lb>A be faſtned to ſome fixed ſtay, and in the <lb></lb>other F let the Force be placed; which <lb></lb>moving to wards H ſhall raiſe the Machine <lb></lb>B L C, and conſequently the Weight G: <lb></lb>and in this operation I ſay, that the Force in <lb></lb>F is the half of the Weight ſuſtained by it. <lb></lb></s> <s>For the ſaid Weight being kept to Rights by the two ^{*} Ropes A B <lb></lb><arrow.to.target n="marg1110"></arrow.to.target><lb></lb>and F C, it is manifeſt, that the Labour is equally ſhared betwixt <lb></lb>the Force F and the Fulciment A: and more ſubtilly examining the <lb></lb>nature of this Inſtrument, if we but continue forth the Diameter <lb></lb>B E C, we ſhall ſee a Leaver to be made, at the midſt of which, that <lb></lb>is at the point E, the Grave doth hang, and the Fulciment cometh <lb></lb>to be at the end B, and the Force in the Term C: whereupon, by <lb></lb>what hath been above demonſtrated, the Force ſhall have the ſame <lb></lb>proportion to the Weight, that the Diſtance E B hath to the Di<lb></lb>ſtance; Therefore it ſhall be the half of the ſaid Weight: And <lb></lb>becauſe the Force riſing towards A, the Pulley turneth round, <lb></lb>therefore that Reſpect or Conſtitution which the Fulciment B and <lb></lb>Center E, on which the Weight and Term C, in which the Force <lb></lb>is employed do depend, ſhall not change all the while; but yet in <lb></lb>the Circuinduction the Terms B and C happen to vary in number, <lb></lb>but not in vertue, others and others continually ſucceeding in their <lb></lb>place, whereby the Leaver B C cometh to be perpetuated. </s> <s>And <lb></lb>here (as hath been done in the other Inſtruments, and ſhall be in <lb></lb>thoſe that follow) we will not paſſe without conſidering how that <lb></lb>the journey that the Force maketh, is double to the Moment of the <lb></lb>Weight. </s> <s>For in caſe the Weight ſhall be moved ſo far, till that <lb></lb>the Line B C come to arrive with it's points B and C, at the points <lb></lb>A and F, it is neceſſary that the two equal Ropes be diſtended in <lb></lb>one ſole Line F H, and conſequently, when the Weight ſhall have <lb></lb>aſcended along the Intervall B A, the Force ſhall have been moved <lb></lb>twice as far, that is, from <emph type="italics"></emph>F<emph.end type="italics"></emph.end> unto H. </s> <s>Then conſidering that the <pb xlink:href="040/01/982.jpg" pagenum="288"></pb>Force in <emph type="italics"></emph>F,<emph.end type="italics"></emph.end> that it may raiſe the Weight, muſt move upwards, which <lb></lb>to exanimate Movers, as being for the moſt part Grave Bodies, is al<lb></lb><figure id="id.040.01.982.1.jpg" xlink:href="040/01/982/1.jpg"></figure><lb></lb>together impoſſible, or at leaſt more laborious, <lb></lb>than the making of the ſame <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce down<lb></lb>wards: Therefore to help this inconvenience, <lb></lb>a Remedy hath been found by adjoyning an<lb></lb>other Nut or Pulley above, as in the adjacent <lb></lb><emph type="italics"></emph>F<emph.end type="italics"></emph.end>igure is ſeen, where the Rope C E <emph type="italics"></emph>F<emph.end type="italics"></emph.end> hath <lb></lb>been made to paſs about the upper Pulley <emph type="italics"></emph>F<emph.end type="italics"></emph.end> G <lb></lb>upheld by the Hook L, ſo that the Rope paſſing <lb></lb>to H, and thither transferring the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce E, it <lb></lb>ſhall be able to move the Weight X by pulling <lb></lb>downwards, but not that it may be leſſer than <lb></lb>it was in E: <emph type="italics"></emph>F<emph.end type="italics"></emph.end>or the Motions of the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce <lb></lb><emph type="italics"></emph>F<emph.end type="italics"></emph.end> H, hanging at the equal Diſtances <emph type="italics"></emph>F<emph.end type="italics"></emph.end> D and <lb></lb>D G of the upper Pulley, do alwaies continue <lb></lb>equal; nor doth that upper Pulley (as hath <lb></lb>been ſhewn above) come to produce any di<lb></lb>minution in the Labour. </s> <s>Moreover it having been neceſſary by <lb></lb>the addition of the upper Pulley to introduce the Appendix B, by <lb></lb>which it is ſuſtained, it will prove of ſome benefit to us to raiſe <lb></lb>the other A, to which one end of the Rope was faſtned, transferring <lb></lb>it to a Ring annexed to the lower part of the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>rame of the upper <lb></lb>Pulley, as we ſee it done in M. </s> <s>Now finally, this Machine com<lb></lb>pounded of upper and lower Pullies, is that which the Greeks call <lb></lb><arrow.to.target n="marg1111"></arrow.to.target><lb></lb><foreign lang="grc">Τποχίλιον.</foreign></s></p><p type="margin"> <s><margin.target id="marg1109"></margin.target>*Called by ſome <lb></lb>a Nut.</s></p><p type="margin"> <s><margin.target id="marg1110"></margin.target>* Or two ends of <lb></lb>the ſame Rope.</s></p><p type="margin"> <s><margin.target id="marg1111"></margin.target>In Latine <emph type="italics"></emph>Tro<lb></lb>chlea.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>We have hitherto explained, how by help of Pullies one may <lb></lb>double the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce, it remaineth that with the greateſt brevity poſ<lb></lb>ſible, we ſhew the way how to encreaſe it according to any Multi<lb></lb>plicity. </s> <s>And firſt we will ſpeak of the Multiplicity according to <lb></lb>the even numbers, and then the odde: To ſhew how we may mul<lb></lb>tiply the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce in a quadruple Proportion, we will propound the <lb></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"></emph>F<emph.end type="italics"></emph.end>ulciments in the ex<lb></lb><figure id="id.040.01.982.2.jpg" xlink:href="040/01/982/2.jpg"></figure><lb></lb>treams A and C; and at the middles <lb></lb>of each of them let the Grave G hang, <lb></lb>ſuſtained by two <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces of equal Mo<lb></lb>ment placed in B and D. </s> <s>I ſay, that <lb></lb>the Moment of each of them will <lb></lb>equal the Moment of the fourth part <lb></lb>of the Weight G. <emph type="italics"></emph>F<emph.end type="italics"></emph.end>or the two <emph type="italics"></emph>F<emph.end type="italics"></emph.end>or<lb></lb>ces B and D bearing equally, it is <lb></lb>manifeſt, that the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce D hath not <lb></lb>contraſted with more then one half of the Weight G: But if the <lb></lb><emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce D do by benefit of the Leaver D C ſuſtain the half of the <pb xlink:href="040/01/983.jpg" pagenum="289"></pb>Weight G hanging at <emph type="italics"></emph>F,<emph.end type="italics"></emph.end> it hath been already demonſtrated, that <lb></lb>the ſaid <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce D hath to the Weight ſo by it ſuſtained, that ſame <lb></lb>proportion which the Diſtance <emph type="italics"></emph>F<emph.end type="italics"></emph.end> C hath to the Diſtance C D: <lb></lb>Which is ſubduple proportion: Therefore the Moment D is ſub<lb></lb>duple to the Moment of half of the Weight G ſuſtained by it: <lb></lb>Wherefore it followeth, that it is the fourth part of the Moment <lb></lb>of the whole Weight. </s> <s>And in the ſame manner the ſame thing is <lb></lb>demonſtrated, of the Moment <emph type="italics"></emph>B<emph.end type="italics"></emph.end>; and it is but reaſonable, that the <lb></lb>Weight G being ſuſtained by the four points, A, <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> C, D, each of <lb></lb>them ſhould feel an equall part of the Labour.</s></p><p type="main"> <s>Let us come now to apply this Conſideration to Pullies, and let <lb></lb>the Weight X be ſuppoſed to hang at the two Pullies A B and D E <lb></lb>entwining about them, and about the uppermoſt Pulley G H, the <lb></lb>Rope, as we ſee, I D E H G A B, ſuſtaining the whole Machine in <lb></lb>the point K. </s> <s>Now I ſay, that placing the Force in L, it ſhall be able <lb></lb>to ſuſtain the Weight X, if ſo be, it be equal to the fourth part of <lb></lb>it. </s> <s>For if we do imagine the two Diameters D E and A B, and the <lb></lb>Weights hanging at the middle points F and C, we ſhall have two <lb></lb>Leavers like to thoſe before deſcribed, the Fulciments of which an<lb></lb>ſwer to the points D and A. </s> <s>Whereupon the Force placed in B, <lb></lb><figure id="id.040.01.983.1.jpg" xlink:href="040/01/983/1.jpg"></figure><lb></lb>or if you will, in L, ſhall be able to ſu<lb></lb>ſtain the Weight X, being the fourth <lb></lb>part of it: And if we adde another Pul<lb></lb>ley above the other two, making the <lb></lb>Rope or Cord to paſs along L M N, trans<lb></lb>ferring the Force L into N, it ſhall be <lb></lb>able to bear the ſame Weight gravitating <lb></lb>downwards, the upper Pulley neither aug<lb></lb>menting or diminiſhing the Force, as hath <lb></lb>been declared. </s> <s>And we will likewiſe <lb></lb>note, that to make the: Weight aſcend the <lb></lb><arrow.to.target n="marg1112"></arrow.to.target><lb></lb>four Ropes B L, E H, D I, and A G <lb></lb>ought to paſs, whereupon the Mover will <lb></lb>be to begin, as much as thoſe Ropes are <lb></lb>long; and yet nevertheleſs the Weight <lb></lb>ſhall move but only as much as the length <lb></lb>of one of them: So that we may ſay by <lb></lb>way of advertiſement, and for confirma<lb></lb>tion of what hatn been many times ſpo<lb></lb>ken, namely, that look with what proportion the Labour of the <lb></lb><arrow.to.target n="marg1113"></arrow.to.target><lb></lb>Mover is diminiſhed, the length of the Way, on the contrary, is <lb></lb>encreaſed with the ſame proportion</s></p><p type="margin"> <s><margin.target id="marg1112"></margin.target>* Or four parts <lb></lb>of the ſame Rope</s></p><p type="margin"> <s><margin.target id="marg1113"></margin.target>* The word <emph type="italics"></emph>Gy<lb></lb>rilla<emph.end type="italics"></emph.end> ſignifieth a <lb></lb>Shiver, Rundle, <lb></lb>or ſmall Wheel <lb></lb>of a Pulley, tran<lb></lb>ſlated by we <lb></lb>ſometimes Pul<lb></lb>ley, ſometimes <lb></lb>Nut or Girill.</s></p><p type="main"> <s>But if we would encreaſe the Force in ſexcuple proportion, it <lb></lb>will be requiſite that we adjoyn another ^{*} ſmall Pulley or Gyrill <lb></lb>to the inferiour Pulley which that you may the better underſtand <pb xlink:href="040/01/984.jpg" pagenum="290"></pb>we will ſet before you the preſent Contemplation. </s> <s>Suppoſe, there<lb></lb>fore, that A B, C D, and E F are three Leavers; and that on the <lb></lb>middle points of them G, H, and I the Weight K doth hang in <lb></lb>common, ſo that every one of them ſhall ſuſtain the third part of <lb></lb><figure id="id.040.01.984.1.jpg" xlink:href="040/01/984/1.jpg"></figure><lb></lb>it: And becauſe the Power in <lb></lb>B, ſuſtaining with the Leaver <lb></lb>B A thependent Weight in G, <lb></lb>hapneth to be the half of the <lb></lb>ſaid Weight, and it hath been <lb></lb>already ſaid, that it ſuſtaineth <lb></lb>the third part of the Weight <lb></lb>K: Therefore the Moment of <lb></lb>the Force B is equal to half of <lb></lb>the third part of the Weight K; that is, to the ſixth part of it: <lb></lb>And the ſame ſhall be demonſtrated of the other Forces D and F: <lb></lb>From whence we may eaſily gather, that putting three Gyrils or <lb></lb>Rundles into the inferiour Pulley, and two or three into the upper<lb></lb><figure id="id.040.01.984.2.jpg" xlink:href="040/01/984/2.jpg"></figure><lb></lb>moſt, we may multiply the Force accor<lb></lb><arrow.to.target n="marg1114"></arrow.to.target><lb></lb>ding to our ^{*} <emph type="italics"></emph>Senarius.<emph.end type="italics"></emph.end> And if we would <lb></lb>encreaſe it according to any other even <lb></lb>Number, the Gyrils of the Pulley below <lb></lb>muſt be multiplyed according to the half <lb></lb>of that Number, according to which the <lb></lb>Force is to be multiplyed, circumpoſing <lb></lb>the Rope about the Pulleys, ſo as that one <lb></lb>of the ends be faſtned to the upper Pul<lb></lb>ley, and let the Force be in the other; as <lb></lb>in this Figure adjoyning may manifeſtly <lb></lb>be gathered.</s></p><p type="margin"> <s><margin.target id="marg1114"></margin.target>* Or in Sexcuple <lb></lb>proportion.</s></p><p type="main"> <s>Now paſſing to the Declaration of the <lb></lb>manner how to multiply the Force ac<lb></lb>cording to the odd Numbers, and begin<lb></lb><figure id="id.040.01.984.3.jpg" xlink:href="040/01/984/3.jpg"></figure><lb></lb>ning at the triple proportion: firſt, let us <lb></lb>propoſe the preſent Contemplation, as <lb></lb>that, on the underſtanding of which the <lb></lb>knowledge of all the Work in hand <lb></lb>doth depend. </s> <s>Let therefore the Leaver <lb></lb>be A B, its Fulciment A, and from the <lb></lb>middle of it, that is, at the point C let <lb></lb>the Grave D be hanged; and let it be ſu<lb></lb>ſtained by two equal Forces; and let one of them be applied to the <lb></lb>point C, and the other to the term B. </s> <s>I ſay, that each of thoſe Powers <lb></lb>have Moment equal to the third part of the Weight D. </s> <s>For the <lb></lb>Force in C ſuſtaineth a Weight equal to it ſelf, being placed in the <lb></lb>ſame Line in which the Weight D doth hang & Gravitate: But the <pb xlink:href="040/01/985.jpg" pagenum="291"></pb>Force in B ſuſtaineth a part of the Weight D double to it ſelf, its <lb></lb>Diſtance from the Fulciment A, that is, the Line B A being dou<lb></lb>ble to the Diſtance A C at which the Grave hangeth: But becauſe <lb></lb>the two Forces in B and C are ſuppoſed to be equal to each other: <lb></lb>Therefore the part of the Weight D, which is ſuſtained by the <lb></lb>Force in B, is double to the part ſuſtained by the Force in C. </s> <s>If <lb></lb>therefore, of the Grave D two parts be made, the one double to <lb></lb>the remainder, the greater is ſuſtained by the Force in B, and the <lb></lb>leſſer by the Force in C: But this leſſer is the third part of the <lb></lb>Weight D: Therefore the Moment of the Force in C is equal to <lb></lb>the Moment of the third part of the Weight D; to which, of <lb></lb>conſequence, the Force B ſhall be equal, we having ſuppoſed it <lb></lb>equal to the other Force C: Wherefore our intention is manifell, <lb></lb>which we were to demonſtrate, how that each of the two Powers <lb></lb>C and B is equal to the third part of the Weight D. </s> <s>Which be<lb></lb>ing demonſtrated, we will paſs forwards to the Pulleys, and will <lb></lb>deſcribe the inferiour Gyrils of A C B, voluble about the Center <lb></lb>G, and the Weight H hanging thereat, we will draw the other up<lb></lb>per one E F, winding about them both the Rope D F E A C B I, <lb></lb>of which let the end D be faſtned to the inferiour Pulley, and to <lb></lb><figure id="id.040.01.985.1.jpg" xlink:href="040/01/985/1.jpg"></figure><lb></lb>the other I let the Force be applyed: <lb></lb>Which, I ſay, ſuſtaining or moving the <lb></lb>Weight H, ſhall feele no more than the <lb></lb>third part of the Gravity of the ſame. </s> <s>For <lb></lb>conſidering the contrivance of this Ma<lb></lb>chine, we ſhall find that the Diameter A B <lb></lb>ſupplieth the place of a Leaver, in whoſe <lb></lb>term B the Force I is applied, and in the <lb></lb>other A the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>uiciment is placed, at the mid<lb></lb>dle G the Grave H is hanged, and another <lb></lb><emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce D applied at the ſame place: ſo that <lb></lb><arrow.to.target n="marg1115"></arrow.to.target><lb></lb>the Weight is faſtned to the ^{*} three Ropes <lb></lb>I B, <emph type="italics"></emph>F<emph.end type="italics"></emph.end> D, and E A, which with equal Labour <lb></lb>ſuſtain the Weight. </s> <s>Now, by what hath <lb></lb>already been contemplated, the two <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces <lb></lb>D and B being applied, one, to the midſt of the Leaver A B, and <lb></lb>the other to the extream term B, it is manifeſt, that each of them <lb></lb>holdeth no more but the third part of the Weight H: Therefore <lb></lb>the Power I, having a Moment equal to the third part of the <lb></lb>Weight H, ſhall be able to ſuſtain and move it: but yet the Way <lb></lb>of the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce in I ſhall be triple to the Way that the Weight ſhall <lb></lb>paſs; the ſaid Force being to diſtend it ſelf according to the <lb></lb>Length of the three Ropes I B, <emph type="italics"></emph>F<emph.end type="italics"></emph.end> D, and E A, of which one alone <lb></lb>meaſureth the Way of the Weight H.</s></p><pb xlink:href="040/01/986.jpg" pagenum="292"></pb><p type="margin"> <s><margin.target id="marg1115"></margin.target>* Or three parts <lb></lb>of one Rope.</s></p><p type="head"> <s><emph type="italics"></emph>Of the<emph.end type="italics"></emph.end> SCREW.</s></p><p type="main"> <s>Amongſt the reſt of Mechanick Inſtruments for ſundry uſes <lb></lb>found out by the Wit of Man, the Screw doth, in my opi<lb></lb>nion, both for Invention and for Utility, hold the firſt <lb></lb>place, as that which is appoſitely accommodated, and ſo contrived <lb></lb>not only to move, but alſo to ſtay and preſs with very great Force, <lb></lb>that taking up but little room, it worketh thoſe effects which other <lb></lb>Inſtruments cannot, unleſs they were reduced to a great Machine. <lb></lb></s> <s>The Screw therefore being of moſt ingenious and commodious <lb></lb>contrivance, we ought deſervedly to be at ſome pains in explaining, <lb></lb>with all the plainneſs that is poſſible, the Original and Nature of <lb></lb>it. </s> <s>The which that we may do, we will begin at a Speculation, <lb></lb>which, though at firſt bluſh it may appear ſomewhat remote from <lb></lb>the conſideration of this Inſtrument, yet is the <emph type="italics"></emph>Baſis<emph.end type="italics"></emph.end> and Founda<lb></lb>tion thereof.</s></p><p type="main"> <s>No doubt, but that Natures operation in the Motions of Grave <lb></lb>Bodies is ſuch, that any whatever Body that hath a Gravity in it <lb></lb>hath a propenſion of moving, being at liberty, towards the Cen<lb></lb><arrow.to.target n="marg1116"></arrow.to.target><lb></lb>ter, and that not only ^{*} by the Right Line perpendicularly, but al<lb></lb>ſo (when it cannot do otherwiſe) by any other Line, which ha<lb></lb>ving ſome inclination towards the Center goeth more and more <lb></lb>abaſing. </s> <s>And thus we ſee the Water not only to fall downwards <lb></lb>along the Perpendicular from ſome eminent place, but alſo to run <lb></lb>about the Surface of the Earth along Lines though very little en<lb></lb>clined; as we ſee in the Courſe of Rivers, the Waters of which, if ſo <lb></lb>be that the Bed have any the leaſt declivity, go freely declining <lb></lb>downwards. </s> <s>Which very effect, like as it is diſcerned in all Fluid <lb></lb>Bodies, would appear alſo in hard Bodies, if ſo be, that their Fi<lb></lb>gure and other Accidental and Extern Impediments did not hinder <lb></lb>it. </s> <s>So that we, having a Superficies very well ſmoothed and poli<lb></lb>ſhed, as for inſtance, that of a Looking-glaſs, and a Ball exactly <lb></lb>rotund and ſleek, either of Marble, or of Glaſs, or of any other <lb></lb>Matter apt to be poliſhed, this being placed upon that Superficies <lb></lb>ſhall trundle along, in caſe that this have any, though very ſmall, <lb></lb>inclination; and ſhall lie ſtill only upon that Superficies which is <lb></lb>exactly levelled and parallel to the Plane of the Horizon: as is <lb></lb>that, for example, of a Lake or ſtanding Water being frozen, up<lb></lb>on which the ſaid Spherical Body would ſtand ſtill, but in a con<lb></lb>dition of being moved by every ſmall Force. </s> <s>For we having ſup<lb></lb>poſed that if that Plane did incline but an hairs breadth only, the <lb></lb>ſaid Ball would move along it ſpontaneouſly towards the part de<lb></lb>clining, and on the oppoſite would have a Reſiſtance, nay, would <lb></lb>not be able without ſome Violence to move towards the part <pb xlink:href="040/01/987.jpg" pagenum="293"></pb>riſing or aſcending: it of neceſſity remaineth manifeſt, that in the <lb></lb>Superficies which is exactly equilibrated, the ſaid Ball remaineth in<lb></lb>different and dubious between Motion and Reſt, ſo that every ſmall <lb></lb>Force is ſufficient to move it, as on the contrary, every ſmall Reſi<lb></lb>ſtance, and no greater than that of the meer Air that environs it, is <lb></lb>able to hold it ſtill.</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 Concluſion for indubitable, That <lb></lb>Crave Bodies, all Extern and Adventitious Impediments being re<lb></lb>moved, may be moved along the Plane of the Horizon by any ne<lb></lb>ver ſo ſmall Force: but when the ſame Grave is to be thrown along <lb></lb>an Aſcending Plane, then, it beginning to ſtrive againſt that aſcent, <lb></lb>having an inclination to the contrary Motion, there ſhall be requi<lb></lb>red greater Violence, and ſtill greater the more Elevation that ſame <lb></lb>Plane ſhall have. </s> <s>As for example, the Moveable G, being poſited <lb></lb>upon the Line A B parallel to the Horizon, it ſhall, as hath been <lb></lb>ſaid, be indifferent on it either to Motion or Reſt, ſo that it may <lb></lb>be moved by a very ſmall Force: But if we ſhall have the Planes <lb></lb>Elevated, they ſhall not be driven along without Violence; which <lb></lb><figure id="id.040.01.987.1.jpg" xlink:href="040/01/987/1.jpg"></figure><lb></lb>Violence will be required to be <lb></lb>greater to move it along the Line <lb></lb>A D, than along A C; and ſtill <lb></lb>greater along A E than along A D: <lb></lb>The which hapneth, becauſe it hath <lb></lb>greater <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of going down<lb></lb>wards along A E than along A D, <lb></lb>and along A D than along A C. </s> <s>So <lb></lb>that we may likewiſe conclude <lb></lb>Grave Bodies to have greater Reſiſtance upon Planes differently <lb></lb>Elevared, to their being moved along the ſame, according as one <lb></lb>ſhall be more or leſs elevated than the other; and, in fine, that the <lb></lb>greateſt Reſiſtance of the ſame Grave to its being raiſed is in the <lb></lb>Perpendicular A F. </s> <s>But it will be neceſſary to declare exactly what <lb></lb>proportion the Force muſt have to the Weight, that it may be able <lb></lb>to carry it along ſeveral elevated Planes, before we proceed any <lb></lb>farther, to the end that we may perfectly underſtand all that which <lb></lb>remains to be ſpoken.</s></p><p type="main"> <s>Letting, therefore, Perpendiculars fall from the points C, D, <lb></lb>and E unto the Horizontal Line A B, which let be C H, D I, and <lb></lb>E K: it ſhall be demonſtrated that the ſame Weight ſhall be mo<lb></lb>ved along the Plane A C with leſſer Force than along the Perpendi<lb></lb>cular A F, (where it is raiſed by a Force equal to it ſelf) accor<lb></lb>ding to the proportion by which the Perpendicular C H is leſs than <lb></lb>A C: and that along the Plane A D, the Force hath the ſame pro<lb></lb>portion to the Weight, that the Perpendicular I D hath to D A: <lb></lb>and, laſtly, that in the Plane A E the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce to the Weight obſer<lb></lb>veth the proportion of E K and E A.</s></p><pb xlink:href="040/01/988.jpg" pagenum="294"></pb><p type="main"> <s>The preſent Speculation hath been attempted by <emph type="italics"></emph>Pappus Alex<lb></lb>andrinus<emph.end type="italics"></emph.end> in <emph type="italics"></emph>Lib.<emph.end type="italics"></emph.end> 8. <emph type="italics"></emph>de Collection. </s> <s>Mathemat.<emph.end type="italics"></emph.end> but, if I be in the <lb></lb>right, he hath not hit the mark, and was overſeen in the Aſſumpti<lb></lb>on that he maketh, where he ſuppoſeth that the Weight ought to <lb></lb>be moved along the Horizontal Line by a <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce given; which is <lb></lb>falſe: there needing no ſenſible <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce (removing the Accidental <lb></lb>Impediments, which in the Theory are not regarded) to move the <lb></lb>given Weight along the Horizon, ſo that he goeth about in vain <lb></lb>afterwards to ſeek with what <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce it is to be moved along the <lb></lb>elevated Plane. </s> <s>It will be therefore better, the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce that moveth <lb></lb>the Weight upwards perpendicularly, (which equalizeth the Gra<lb></lb>vity of that Weight which is to be moved) being given, to <lb></lb>ſeek the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce that moveth it along the Elevated Plane: Which <lb></lb>we will endeavour to do in a Method different from that of <lb></lb><emph type="italics"></emph>Pappus.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let us therefore ſuppoſe the Circle A I C, and in it the Diame<lb></lb>ter A B C, and the Center B, and two Weights of equal Moment <lb></lb>in the extreams B and C; ſo that the Line A C being a Leaver, <lb></lb>or Ballance moveable about the Center B, the Weight C ſhall <lb></lb>come to be ſuſtained by the Weight A. </s> <s>But if we ſhall imagine <lb></lb>the Arm of the Ballance B C to be inclined downwards according <lb></lb>to the Line B F, but yet in ſuch a manner that the two Lines <emph type="italics"></emph>A B<emph.end type="italics"></emph.end><lb></lb>and <emph type="italics"></emph>B F<emph.end type="italics"></emph.end> do continue ſolidly conjoyned in the point <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> in this caſe <lb></lb>the Moment of the Weight C ſhall not be equal to the Moment <lb></lb><figure id="id.040.01.988.1.jpg" xlink:href="040/01/988/1.jpg"></figure><lb></lb>of the Weight <emph type="italics"></emph>A,<emph.end type="italics"></emph.end> for that the Di<lb></lb>ſtance of the point <emph type="italics"></emph>F<emph.end type="italics"></emph.end> from the Line <lb></lb>of Direction, which goeth accord<lb></lb>ing to B I, from the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>ulciment B un<lb></lb>to the Center of the Earth, is dimi<lb></lb>niſhed: But if from the point <emph type="italics"></emph>F<emph.end type="italics"></emph.end> we <lb></lb>erect a Perpendicular unto B C, as is <lb></lb><emph type="italics"></emph>F<emph.end type="italics"></emph.end> K, the Moment of the Weight in <lb></lb><emph type="italics"></emph>F<emph.end type="italics"></emph.end> ſhall be as if it did hang by the <lb></lb>Line K <emph type="italics"></emph>F,<emph.end type="italics"></emph.end> and look how much the <lb></lb>Diſtance K B is diminiſhed by the <lb></lb>Diſtance B <emph type="italics"></emph>A,<emph.end type="italics"></emph.end> ſo much is the Moment of the Weight <emph type="italics"></emph>F<emph.end type="italics"></emph.end> diminiſhed <lb></lb>by the Moment of the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>eight <emph type="italics"></emph>A. A<emph.end type="italics"></emph.end>nd in this faſhion inclining <lb></lb>the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>eight more, as for inſtance, according to B L, its Moment ſhall <lb></lb>ſtill diminiſh and ſhall be as if it did hang at the Diſtance <emph type="italics"></emph>B<emph.end type="italics"></emph.end> M, ac<lb></lb>cording to the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine M <emph type="italics"></emph>L,<emph.end type="italics"></emph.end> in which point <emph type="italics"></emph>L<emph.end type="italics"></emph.end> it ſhall be ſuſtained by <lb></lb>a <emph type="italics"></emph>W<emph.end type="italics"></emph.end>eight placed in <emph type="italics"></emph>A,<emph.end type="italics"></emph.end> ſo much leſs than it ſelf, by how much the <lb></lb>Diſtance B <emph type="italics"></emph>A<emph.end type="italics"></emph.end> is greater than the Diſtance <emph type="italics"></emph>B<emph.end type="italics"></emph.end> M. </s> <s>See therefore that <lb></lb>the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>eight placed in the extream of the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>eaver B C, in inclining <lb></lb>downwards along the Circumference C <emph type="italics"></emph>F L<emph.end type="italics"></emph.end> I, cometh to diminiſh <lb></lb>its Moment and <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of going downwards from time to time, <pb xlink:href="040/01/989.jpg" pagenum="295"></pb>more and leſs, as it is more or leſs ſuſtained by the Lines B F and <lb></lb>B L: But the conſidering that this Grave deſcending, and ſuſtained <lb></lb>by the Semidiameters B F and B L is one while leſs, and another <lb></lb>while more conſtrained to paſs along the Circumference C F L, is <lb></lb>no other, than if we ſhould imagine the ſame Circumference <lb></lb>C F L I to be a Superſicies ſo curved, and put under the ſame <lb></lb>Moveable: ſo that bearing it ſelf thereon it were conſtrained to <lb></lb>deſcend along thereby; for if in the one and other manner the <lb></lb>Moveable deſcribeth the ſame Courſe or Way, it will nothing im<lb></lb>port whether, if ſuſpended at the Center B, it is ſuſtained by the <lb></lb>Semidiameter of the Circle, or elſe, whether that Fulciment being <lb></lb>taken away, it proceed along the Circumference C F L I: So that <lb></lb>we may confidently affirm, that the Grave deſcending downwards <lb></lb>from the point C along the Circumference C F L I, its Moment <lb></lb>of Deſcent in the point C is total and entire, becauſe it is not in <lb></lb>any part ſuſtained by the Circumference: And there is not in that <lb></lb>firſt point C, any indiſpoſition to Motion different from that, which <lb></lb>being at liberty, it would make along the Perpendicular and Con<lb></lb>tingent Line D C E: But if the Moveable ſhall be placed in the <lb></lb>point F, then its Gravity is in part ſuſtained, and its Moment of <lb></lb>Deſcent is diminiſhed by the Circular Path or Way that is placed <lb></lb>under it, in that proportion wherewith the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine <emph type="italics"></emph>B<emph.end type="italics"></emph.end> K is overcome <lb></lb>by <emph type="italics"></emph>B<emph.end type="italics"></emph.end> C: But if when the Moveable is in F, at the firſt inſtant of <lb></lb>ſuch its Motion, it be as if it were in the Plane elevated according <lb></lb>to the Contingent <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine G F H, for that reaſon the inclination of the <lb></lb>Circumference in the point F differeth not from the inclination of <lb></lb>the Contingent <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine F G any more ſave the inſenſible Angle of <lb></lb>the Contact. </s> <s>And in the ſame manner we ſhall find the Moment <lb></lb>of the ſaid Moveable to diminiſh in the point <emph type="italics"></emph>L,<emph.end type="italics"></emph.end> as the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine BM <lb></lb>is diminiſhed by B C; ſo that in the Plane contingent to the Circle <lb></lb>in the point <emph type="italics"></emph>L,<emph.end type="italics"></emph.end> as for inſtance, according to the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine N <emph type="italics"></emph>L<emph.end type="italics"></emph.end> O, the <lb></lb>Moment of Deſcent diminiſheth in the Moveable with the ſame <lb></lb>proportion. </s> <s>If therefore ^{*} upon the Plane HG the Moment of the <lb></lb><arrow.to.target n="marg1117"></arrow.to.target><lb></lb>Moveable be diminiſhed by the total <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> which it hath in its <lb></lb>Perpendicular D C E, according to the proportion of the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine K B <lb></lb>to the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine B C, and B F, being by the Solicitude of the Triangles <lb></lb>K B F and K F H the ſame proportion betwixt the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ines K F and <lb></lb>F H, as betwixt the ſaid K B and <emph type="italics"></emph>B<emph.end type="italics"></emph.end> F, we will conclude that the <lb></lb>proportion of the entire and abſolute Moment, that the Moveable <lb></lb>hath in the Perpendicular to the Horizon to that which it hath up<lb></lb>on the Inclined Plane H F, hath the ſame proportion that the <lb></lb><emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine H F hath to the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine F K; that is, that the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ength of the <lb></lb>Inclined Plane hath to the Perpendicular which ſhall fall from it <lb></lb>unto the Horizon. </s> <s>So that paſſing to a more diſtinct Figure, ſuch <lb></lb>as this here preſent, the Moment of Deſcending which the Move<pb xlink:href="040/01/990.jpg" pagenum="296"></pb>able hath upon the inclined Plane C A hath to its total Moment <lb></lb>wherewith it gravitates in the Perpendicular to the Horizon C P the <lb></lb>ſame proportion that the ſaid Line P C hath to C A. </s> <s>And if thus it <lb></lb>be, it is manifeſt, that like as the Force that ſuſtai<lb></lb>neth the Weight in the Perpendiculation P C ought <lb></lb><figure id="id.040.01.990.1.jpg" xlink:href="040/01/990/1.jpg"></figure><lb></lb>to be equal to the ſame, ſo for ſuſtaining it in the <lb></lb>inclined Plane C A, it will ſuffice that it be ſo much <lb></lb>leſſer, by how much the ſaid Perpendicular C P wan<lb></lb>teth of the Line C A: and becauſe, as ſometimes we <lb></lb>ſce, it ſufficeth, that the Force for moving of the <lb></lb>Weight do inſenſibly ſuperate that which ſuſtaineth it, therefore <lb></lb>we will infer this univerſal Propoſition, [That upon an Elevated <lb></lb>Plane the Force hath to the Weight the ſame proportion, as the <lb></lb>Perpendicular let fall from the Plane unto the Horizon hath to the <lb></lb>Length of the ſaid 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 firſt Intention, which was to inveſtigate <lb></lb>the Nature of the Screw, we will conſider the Triangle A B C, of <lb></lb>which the Line A B is Horizontal, B C perpendicular to the ſaid <lb></lb>Horizon, and A C a Plane elevated; upon which the Moveable D <lb></lb>ſhall be drawn by a Force ſo much leſs than it, by how much the <lb></lb>Line B C is ſhorter than C A: But to elevate or raiſe the ſaid <lb></lb>Weight along the ſaid Plane A C, is as much as if the Triangle <lb></lb>C A B ſtanding ſtill, the Weight <lb></lb><figure id="id.040.01.990.2.jpg" xlink:href="040/01/990/2.jpg"></figure><lb></lb>D be moved towards C, which is <lb></lb>the ſame, as if the ſame Weight <lb></lb>never removing from the Perpen<lb></lb>dicular A E, the Triangle did <lb></lb>preſs forwards towards H. </s> <s>For if <lb></lb>it were in the Site F H G, the <lb></lb>Moveable would be found to <lb></lb>have mounted the height A I. <lb></lb>Now, in fine, the primary Form and Eſſence of the Screw is no<lb></lb>thing elſe but ſuch a Triangle A C B, which being forced for<lb></lb>wards, ſhall work it ſelf under the Grave Body to be raiſed, and <lb></lb>lifteth it up, as we ſay, by the ^{*} head and ſhoulders. </s> <s>And this was <lb></lb><arrow.to.target n="marg1118"></arrow.to.target><lb></lb>its firſt Original: For its firſt Inventor (whoever he was) conſi<lb></lb>dering how that the Triangle A B C going forwards raiſeth the <lb></lb>Weight D, he might have framed an Inſtrument like to the ſaid <lb></lb>Triangle, of a very ſolid Matter, which being thruſt forwards did <lb></lb>raiſe up the propoſed Weight: But afterwards conſidering better, <lb></lb>how that that ſame Machine might be reduced into a much leſſer <lb></lb>and more commodious Form, taking the ſame Triangle he twined <lb></lb>and wound it about the Cylinder A B C D in ſuch a faſhion, that <lb></lb>the height of the ſaid Triangle, that is the Line C B, did make the <lb></lb>Height of the Cylinder, and the Aſcending Plane did beget upon <pb xlink:href="040/01/991.jpg" pagenum="297"></pb>the ſaid Cylinder the Helical Line deſcribed by the Line AEFGH, <lb></lb>which we vulgarly call the Wale of the Screw, which was produ<lb></lb>ced by the Line A C. </s> <s>And in this manner is the Inſtrument made, <lb></lb>which is by the Greeks called <foreign lang="grc">Κόχλος,</foreign> and by us a Screw; which <lb></lb><arrow.to.target n="marg1119"></arrow.to.target><lb></lb>winding about <lb></lb>cometh to work <lb></lb><figure id="id.040.01.991.1.jpg" xlink:href="040/01/991/1.jpg"></figure><lb></lb>and inſinu<lb></lb>ate with its <lb></lb>Wales under <lb></lb>the Weight, and <lb></lb>with facility rai<lb></lb>ſeth it. </s> <s>And we <lb></lb>having demon<lb></lb>ſtrated, That up<lb></lb>on [<emph type="italics"></emph>or along<emph.end type="italics"></emph.end>] <lb></lb>the elevated Plane the Force hath the ſame proportion to the <lb></lb>Weight, that the perpendicular Altitude of the ſaid Plane hath to <lb></lb>its Length; ſo, ſuppoſing that the Force in the Screw A B C D is <lb></lb>multiplied according to the proportion by which the Length of the <lb></lb>whole Wale exceedeth the Altitude C B, from hence we come <lb></lb>to know that making the Screw with its Helix's more thick or cloſe <lb></lb>together, it becometh ſo much the more forceable, as being begot <lb></lb>by a Plane leſs elevated, and whoſe Length regards its own Per<lb></lb>pendicular Altitude with greater proportion. </s> <s>But we will not <lb></lb>omit to advertiſe you, that deſiring to find the Force of a propo<lb></lb>ſed Screw, it will not be needful that we meaſure the Length of <lb></lb>all its Wales, and the Altitude of the whole Cylinder, but it <lb></lb>will be enough if we ſhall but examine how many times the Di<lb></lb>ſtance betwixt two ſingle and Contiguous terms do enter into one <lb></lb>ſole Turn of the ſame Wale, as for example, how many times <lb></lb>the Diſtance AF is contained in the Length of the Turn AEF: <lb></lb>For this is the ſame proportion that the Altitude CB hath to all <lb></lb>the Wale.</s></p><p type="margin"> <s><margin.target id="marg1118"></margin.target><emph type="italics"></emph>Levar in capo<emph.end type="italics"></emph.end><lb></lb> ſignfieth to lift <lb></lb>on high by force</s></p><p type="margin"> <s><margin.target id="marg1119"></margin.target>* <foreign lang="grc">Κόχλος,</foreign> in La<lb></lb>tine <emph type="italics"></emph>Cocblea,<emph.end type="italics"></emph.end> any <lb></lb>Screw winding <lb></lb>like the Shell of <lb></lb>a Snail.</s></p><p type="main"> <s>If all that be underſtood which we have hitherto ſpoken touch<lb></lb>ing the Nature of this Inſtrument, I do not doubt in the leaſt but <lb></lb>that all the other circumſtances may without difficulty be compre<lb></lb>hended: as for inſtance, that inſteed of making the Weight to <lb></lb>mount upon the Screw if one accommodates its Nut with <lb></lb>the Helix incavated or made hollow, into which the Male Screw <lb></lb>that is the Wale entring, & then being turned round it raiſeth and <lb></lb>lifteth up the Nut or Male Screw together with the Weight which <lb></lb>was hanged thereat. </s> <s>Laſtly, we are not to paſs over that Conſidera<lb></lb>tion with ſilence which at the beginning hath been ſaid to be neceſ<lb></lb>ſary for us to have in all Mechanick Inſtruments, to wit, That <lb></lb>what is gained in Force by their aſſiſtance, is loſt again in Time, <pb xlink:href="040/01/992.jpg" pagenum="298"></pb>and in the Velocity: which peradventure, might not have ſeemed <lb></lb>to ſome ſo true and manifeſt in the preſent Contemplation; nay, <lb></lb>rather it ſeems, that in this caſe the Force is multiplied without the <lb></lb>Movers moving a longer way than the Moveable: In regard, that <lb></lb>if we ſhall in the Triangle A B C ſuppoſe the Line A B to be the <lb></lb>Plane of the Horizon, A C the elevated Plane, whoſe Altitude is <lb></lb>meaſured by the Perpendicular C B, a Moveable placed upon the <lb></lb>Plane A C, and the Cord E D <emph type="italics"></emph>F<emph.end type="italics"></emph.end> tyed to it, and a <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce or Weight <lb></lb>applyed in <emph type="italics"></emph>F<emph.end type="italics"></emph.end> that hath to the <lb></lb>Gravity of the Weight E the <lb></lb><figure id="id.040.01.992.1.jpg" xlink:href="040/01/992/1.jpg"></figure><lb></lb>ſame proportion that the Line <lb></lb>B C hath to C A; by what <lb></lb>hath been demonſtrated, the <lb></lb>Weight <emph type="italics"></emph>F<emph.end type="italics"></emph.end> ſhall deſcend <lb></lb>downwards, drawing the <lb></lb>Moveable E along the eleva<lb></lb>ted Plane; nor ſhall the Move<lb></lb>able E meaſure a greater Space <lb></lb>when it ſhall have paſſed the <lb></lb>whole Line A <emph type="italics"></emph>C,<emph.end type="italics"></emph.end> than that which the ſaid Grave <emph type="italics"></emph>F<emph.end type="italics"></emph.end> meaſureth in its <lb></lb>deſcent downwards. </s> <s>But here yet it muſt be advertiſed, that al<lb></lb>though the Moveable E ſhall have paſſed the whole Line A C, in <lb></lb>the ſame Time that the other Grave <emph type="italics"></emph>F<emph.end type="italics"></emph.end> ſhall have been abaſed the <lb></lb>like Space, nevertheleſs the Grave E ſhall not have retired from the <lb></lb>common Center of things Grave more than the Space of the Per<lb></lb>pendicular <emph type="italics"></emph>C<emph.end type="italics"></emph.end> B. but yet the Grave <emph type="italics"></emph>F<emph.end type="italics"></emph.end> deſcending Perpendicularly ſhall <lb></lb>be abaſed a Space equal to the whole Line A <emph type="italics"></emph>C.<emph.end type="italics"></emph.end> And becauſe Grave <lb></lb>Bodies make no Reſiſtance to Tranſverſal Motions, but only ſo <lb></lb>far as they happen to recede from the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>enter of the Earth; There<lb></lb>fore the Moveable E in all the Motion A <emph type="italics"></emph>C<emph.end type="italics"></emph.end> being raiſed no more <lb></lb>than the length of the Line <emph type="italics"></emph>C<emph.end type="italics"></emph.end>B, but the other <emph type="italics"></emph>F<emph.end type="italics"></emph.end> being abaſed per<lb></lb>pendicularly the quantity of all the Line A <emph type="italics"></emph>C<emph.end type="italics"></emph.end>: Therefore we may <lb></lb>deſervedly affirm that Way of the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce E maintaineth the ſame <lb></lb>proportion to the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce <emph type="italics"></emph>F<emph.end type="italics"></emph.end> that the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine A <emph type="italics"></emph>C<emph.end type="italics"></emph.end> hath to <emph type="italics"></emph>C<emph.end type="italics"></emph.end> B; that is, <lb></lb>the Weight E to the Weight <emph type="italics"></emph>F.<emph.end type="italics"></emph.end> It very much importeth, therefore, <lb></lb>to conſider by [<emph type="italics"></emph>or along<emph.end type="italics"></emph.end>] what <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ines the Motions are made, eſpe<lb></lb>cially in exanimate Grave Bodies, the Moments of which have their <lb></lb>total Vigour, and entire Reſiſtance in the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine Perpendicular to <lb></lb>the Horizon; and in the others tranſverſally Elevated and Inclined <lb></lb>they feel the more or leſs Vigour, <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> or Reſiſtance, the more <lb></lb>or leſs thoſe Inclinations approach unto the Perpendicular Inclina<lb></lb>tion.</s></p><pb xlink:href="040/01/993.jpg" pagenum="299"></pb><p type="head"> <s><emph type="italics"></emph>Of the SCREW of<emph.end type="italics"></emph.end> ARCHIMEDES <lb></lb><emph type="italics"></emph>to draw Waier.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>I Do not think it ſit in this place to paſs over with Silence the <lb></lb>Invention of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> to raiſe Wa er with the Screw, which <lb></lb>is not only marvellous, but miraculous: for we ſhall find that <lb></lb>the Water aſcendeth in the Screw continually deſcending; and in <lb></lb>a given Time, with a given Force doth raiſe an unſpeakable quan<lb></lb>tity therof. </s> <s>But before we proceed any farther, let us declare the uſe <lb></lb>of the Screw in making Water to riſe: And in the enſuing Figure, <lb></lb>let us conſider the Line I L O P Q <lb></lb><figure id="id.040.01.993.1.jpg" xlink:href="040/01/993/1.jpg"></figure><lb></lb>R S H being wrapped or twined <lb></lb>about the Collumn M I K H, <lb></lb>which Line you are to ſuppoſe to <lb></lb>be a Chanel thorow which the <lb></lb>Water may run: If we ſhall put <lb></lb>the end I into the Water, making <lb></lb>the Screw to ſtand leaning, ſo as <lb></lb>the point L may be lower than <lb></lb>the firſt I, as the Diagram ſhew<lb></lb>eth, and ſhall turn it round about <lb></lb>on the two Axes, T and V, the Water ſhall run thorow the Cha<lb></lb>nel, till that in the end it ſhall diſcharge ſorth at the mouth H. <lb></lb></s> <s>Now I ſay, that the Water, in its conveyance from the point I to <lb></lb>the point H, doth go all the way deſcending, although the point H <lb></lb>be higher than the point I. </s> <s>Which that it is ſo, we will declare <lb></lb>in this manner. </s> <s>We will deſcribe the Triangle A C B, which is <lb></lb>that of which the Screw H I is generated, in ſuch ſort that the <lb></lb>Chanel of the Screw is repreſented by the Line A C, whoſe <lb></lb>Aſcent and Elevation is determined by the Angle C A B; that is <lb></lb>to ſay, if ſo be, that that Angle ſhall be the third or fourth part of a <lb></lb>Right Angle, then the Elevation of the Chanel A C ſhall be ac<lb></lb>cording to 1/3, or 1/4 of a Right Angle. </s> <s>And it is manifeſt; that the <lb></lb>Riſe of that ſame Chanel A C will be taken away debaſing the <lb></lb>point C as far as to B: for then the Chanel A C ſhall have no <lb></lb>Elevation. </s> <s>And debaſing the point C a little below B, the Water <lb></lb>will naturally run along the Chanel A C downwards from the <lb></lb>point A towards C. </s> <s>Let us therefore conclude, that the Angle A <lb></lb>being 1/3 of a Right Angle, the Chanel A C ſhall no longer have any <lb></lb>Riſe, debaſing it on the part <emph type="italics"></emph>C<emph.end type="italics"></emph.end> for 1/3 of a Right Angle.</s></p><p type="main"> <s>Theſe things underſtood, let us infold the Triangle about the <lb></lb>Column, and let us make the Screw B A E F G, &c. </s> <s>which if it <lb></lb>ſhall be placed at Right Angles with the end B in the Water, turn<lb></lb>ing it about, it ſhall not this way draw up the Water, the Chanel <lb></lb>about the Column being elevated, as may be ſeen by the part B A.</s> <pb xlink:href="040/01/994.jpg" pagenum="300"></pb><s>But although the Column ſtand erect at Right-Angles, yet for all <lb></lb>that, the Riſe along the Screw, folded about the Column, is not of <lb></lb>a greater Elevation than of 1/3 of a Right Angle, it being generated <lb></lb>by the Elevation of the Chanel A C: Therefore if we incline the <lb></lb>Column but 1/3 of the <lb></lb><figure id="id.040.01.994.1.jpg" xlink:href="040/01/994/1.jpg"></figure><lb></lb>ſaid Right Angle, and <lb></lb>a little more, as we ſee <lb></lb>I K H M, there is a <lb></lb>Tranſition and Moti<lb></lb>on along the Chanel <lb></lb>I L: Therefore the <lb></lb>Water from the point <lb></lb>I to the point L ſhall <lb></lb>move deſcending, and <lb></lb>the Screw being turned <lb></lb>about, the other parts <lb></lb>of it ſhall ſucceſſively <lb></lb>diſpoſe or preſent <lb></lb>themſelves to the Wa<lb></lb>ter in the ſame Poſition as the part I L: Whereupon the Water <lb></lb>ſhall go ſucceſſively deſcending, and in the end ſhall be found to <lb></lb>be aſcended from the point I to the point H. </s> <s>Which how admira<lb></lb>ble a thing it is, I leave ſuch to judge who ſhall perfectly have un<lb></lb>derſtood it. </s> <s>And by what hath been ſaid, we come to know, That <lb></lb>the Screw for raiſing of Water ought to be inclined a little more <lb></lb>than the quantity of the Angle of the Triangle by which the ſaid <lb></lb>Screw is deſcribed.</s></p><p type="head"> <s><emph type="italics"></emph>Of the Force of the <lb></lb>HAMMER, MALLET, or BEETLE.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The Inveſtigation of the cauſe of the Force of theſe Percuti<lb></lb>ents is neceſſary for many Reaſons: and firſt, becauſe that <lb></lb>there appeareth in it much more matter of admiration than <lb></lb>is obſerved in any other Mechanick Inſtrument whatſoever. </s> <s>For <lb></lb>ſtriking with the Hammer upon a Nail, which is to be driven into <lb></lb>a very tough Poſt, or with the Beetle upon a Stake that is to pene<lb></lb>trate into very ſtiffe ground, we ſee, that by the ſole vertue of the <lb></lb>blow of the Percutient both the one and the other is thruſt for<lb></lb>wards: ſo that without that, only laying the Beetle upon the <lb></lb>Nail or Stake it will not move then, nay, more, although you <lb></lb>ſhould lay upon them a Weight very much heavier than the ſaid <lb></lb>Beetle. </s> <s>An effect truly admirable, and ſo much the more worthy <lb></lb>of Contemplation, in that, as I conceive, none of thoſe who have <pb xlink:href="040/01/995.jpg" pagenum="301"></pb>hitherto diſcourſed upon it, have ſaid any thing that hits the mark; <lb></lb>which we may take for a certain Sign and Argument of the Obſcu<lb></lb>rity and difficulty of this <emph type="italics"></emph>S<emph.end type="italics"></emph.end>peculation. </s> <s>For <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> or others, <lb></lb>who would reduce the cauſe of this admirable Effect unto the <lb></lb>length of the <emph type="italics"></emph>Manubrium,<emph.end type="italics"></emph.end> or Handle, may, in my judgement, be <lb></lb>made to ſee their miſtake in the effect of thoſe Inſtruments, which <lb></lb>having no Handle, yet percuſs, either in falling from on high <lb></lb>downwards, or by being thrown with Velocity ſidewaies. </s> <s>There<lb></lb>fore it is requiſite, that we have recourſe to ſome other Principle, if <lb></lb>we would find out the truth of this buſineſs; the cauſe of which, <lb></lb>although it be of its own nature ſomewhat obſcure, and of diffi<lb></lb>cult conſideration, yet nevertheleſs we will attempt with the grea<lb></lb>teſt perſpicuity poſſible to render it clear and obvious, ſhewing, for <lb></lb>a cloſe of all, that the Principle and Original of this Effect is deri<lb></lb>ved from no other Fountain than this, from which the reaſons of all <lb></lb>other Mechanick Effects do proceed: and this we will do, by ſetting <lb></lb>before your eyes that very thing which is ſeen to befall in every <lb></lb>other Mechanick Operation, <emph type="italics"></emph>ſcilicet,<emph.end type="italics"></emph.end> That the Force, the Reſiſtance, <lb></lb>and the Space by which the Motion is made, do go alternately <lb></lb>with ſuch proportion operating, and with ſuch a rate anſwering to <lb></lb>each other, that a Reſiſtance, equal to the Force, ſhall be moved by <lb></lb>the ſaid Force along an equal Space, with Velocity equal to that <lb></lb>with which it is moved. </s> <s>Likewiſe, That a Force that is leſs by half <lb></lb>than a Reſiſtance ſhall be able to move it, ſo that it be moved <lb></lb>with double Velocity, or, if you will, for a Diſtance twice as great <lb></lb>as that which the moved Reſiſtance ſhall paſs: and, in a word, it <lb></lb>hath been ſeen in all the other Inſtruments, that any, never ſo great, <lb></lb>Reſiſtance may be moved by every ſmall Force given, provided, <lb></lb>that the Space, along which the Reſiſtance ſhall move, have the <lb></lb>ſame proportion that is found to be betwixt the ſaid great Reſi<lb></lb>ſtance and the Force: and that this is according to the neceſſary <lb></lb>Order and Conſtitution of Nature: So that inverting the Diſcourſe, <lb></lb>and Arguing the contrary way, what wonder ſhall it be, if that <lb></lb>Power that ſhall move a ſmall Reſiſtance a great way, ſhall carry <lb></lb>one an hundred times bigger an hundredth part of that Diſtance? <lb></lb></s> <s>Certainly none at all: nay, it would be abſurd, yea, impoſſible <lb></lb>that it ſhould be otherwiſe. </s> <s>Let us therefore conſider, what the <lb></lb>Reſiſtance of the Beetle unto Motion may be in that point where <lb></lb>it is to ſtrike, and how far, if it do not ſtrike, it would be carryed <lb></lb>by the received Force beyond that point: and again, what Reſi<lb></lb>ſtance to Motion there is in him who ſtriketh, and how much by <lb></lb>that ſame Percuſſion he is moved: and, having found that this <lb></lb>great Reſiſtance goeth forwards by a percuſſion ſo much leſs than <lb></lb>the Beetle driven by the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of him that moveth it would do, <lb></lb>by how much that ſame great Reſiſtance is greater than that of <pb xlink:href="040/01/996.jpg" pagenum="302"></pb>the Beetle; we ſhall ceaſe to wonder at the Effect, which doth not <lb></lb>in the leaſt exceed the terms of Natural Conſtitutions, and of <lb></lb>what hath been ſpoken. </s> <s>Let us, for better underſtanding, give an <lb></lb>example thereof in particular Terms. </s> <s>There is a Beetle, which ha<lb></lb>ving four degrees of Reſiſtance, is moved by ſuch a Force, that <lb></lb>being freed from it in that term where it maketh the Percuſſion, it <lb></lb>would, meeting with no ſtop, go ten Paces beyond it, and in that <lb></lb>term a great poſt being oppoſed to it, whoſe Reſiſtance to Moti<lb></lb>on is as four thouſand, that is, a thouſand times greater than that of <lb></lb>the Beetle, (but yet is not immoveable) ſo that it without mea<lb></lb>ſure or proportion exceeds the Reſiſtance of the Beetle, yet the <lb></lb>Percuſſion being made on it, it ſhall be driven forwards, though in<lb></lb>deed no more but the thouſandth part of the ten Paces which the <lb></lb>Beetle ſhall be moved: and thus in an inverted method, changing <lb></lb>that which hath been ſpoken touching the other Mechanical Effects, <lb></lb>we may inveſtigate the reaſon of the Force of the Percutient. </s> <s>I <lb></lb>know that here ariſe difficulties and objections unto ſome, which <lb></lb>they will not eaſily be removed from, but we will freely remit them <lb></lb><arrow.to.target n="marg1120"></arrow.to.target><lb></lb>to the ^{*} Problems Mechanical, which we ſhall adjoyn in the end of <lb></lb>this Diſcourſe.</s></p><p type="margin"> <s><margin.target id="marg1120"></margin.target>* Theſe Pro<lb></lb>blems he here <lb></lb>promiſeth were <lb></lb>never yet ex<lb></lb>tant.</s></p><pb xlink:href="040/01/997.jpg" pagenum="303"></pb><p type="head"> <s>THE <lb></lb>BALLANCE <lb></lb>OF <lb></lb><emph type="italics"></emph>Signeur GALILEO GALILEI<emph.end type="italics"></emph.end>;</s></p><p type="head"> <s>In which, in immitation of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> in the <lb></lb>Problem of the Crown, he ſheweth how to <lb></lb>find the proportion of the Alloy of <lb></lb>Mixt-Metals; and how to make <lb></lb>the ſaid Inſtrument.</s></p><p type="main"> <s>As it is well known, by ſuch who take the pains to read <lb></lb>old Authors, that <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> detected the Cheat of <lb></lb>the Goldſmith in the Crown of ^{*} <emph type="italics"></emph>Hieron,<emph.end type="italics"></emph.end> ſo I think it <lb></lb><arrow.to.target n="marg1121"></arrow.to.target><lb></lb>hitherto unknown what method this Great Philoſo<lb></lb>pher obſerved in that Diſcovery: for the opinion, that he did per<lb></lb>form it by putting the Crown into the Water, having firſt put in<lb></lb><arrow.to.target n="marg1122"></arrow.to.target><lb></lb>to it ſuch another Maſs of pure Gold, and another of Silver ſeve<lb></lb>rally, and that from the differences in their making the Water <lb></lb>more or leſs riſe and run over, he came to know the Mixture or <lb></lb>Alloy of the Gold with the Silver, of which that Crown was <lb></lb>compounded; ſeems a thing (if I may ſpeak it) very groſs, and <lb></lb>far from exactneſs. </s> <s>And it will ſeem ſo much the more dull to <lb></lb>ſuch who have read and underſtood the exquiſite Inventions of ſo <lb></lb>Divine a Man amongſt the Memorials that are extant of him; by <lb></lb>which it is very manifeſt that all other Wits are inferiour to that <lb></lb>of <emph type="italics"></emph>Archimedes.<emph.end type="italics"></emph.end> Indeed I believe, that Fame divulging it abroad, <lb></lb>that <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> had diſcovered that ſame Fraud by means of the <lb></lb>Water, ſome Writer of thoſe Times committed the memory there<lb></lb>of to Poſterity, and that this perſon, that he might add ſomething <lb></lb>to that little which he had heard by common Fame, did relate that <lb></lb><emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> had made uſe of the Water in that manner, as ſince <lb></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"></emph>Sicily,<emph.end type="italics"></emph.end><lb></lb>and Kinſman to <lb></lb>that Great Ma<lb></lb>thematician.</s></p><p type="margin"> <s><margin.target id="marg1122"></margin.target><emph type="italics"></emph>Plutarch in Vit. <lb></lb></s> <s>Marcel.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>But in regard I know, that that method is altogether fallacious, <lb></lb>and falls ſhort of that exactneſs which is required in Mathematical <lb></lb>Matters, I have often thought in what manner, by help of the <lb></lb>Water, one might exactly find the Mixture of two Metals, and <lb></lb>in the end, after I had diligently peruſed that which <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end><lb></lb>demonſtrateth in his Books <emph type="italics"></emph>De inſidentibus aquæ,<emph.end type="italics"></emph.end> and thoſe others <pb xlink:href="040/01/998.jpg" pagenum="304"></pb><emph type="italics"></emph>De æquiponder antium,<emph.end type="italics"></emph.end> there came into my thoughts a Rule which <lb></lb>exquiſitely reſolveth our Queſtion; which Rule I believe to be <lb></lb>the ſame that <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> made uſe of, ſeeing that beſides the <lb></lb>uſe that is to be made of the Water, the exactneſs of the Work <lb></lb>dependeth alſo upon certain Demonſtrations found by the ſaid <lb></lb><emph type="italics"></emph>Archimedes.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The way is by help of a Ballance, whoſe Conſtruction and Uſe <lb></lb>ſhall be ſhewn by and by, after we ſhall have declared what is <lb></lb>neceſſary for the knowledge thereof. </s> <s>You muſt know there<lb></lb>fore, that the Solid Bodies that ſink in the Water weigh ſo much <lb></lb>leſs in the Water than in the Air, as a Maſs of Water equal to <lb></lb>the ſaid Solid doth weigh in the Air: which hath been demon<lb></lb>ſtrated by <emph type="italics"></emph>Archimedes.<emph.end type="italics"></emph.end> But, in regard his Demonſtration is very <lb></lb>mediate, becauſe I would not be over long, laying it aſide, I ſhall <lb></lb>declare the ſame another way. </s> <s>Let us conſider, therefore, that <lb></lb>putting into the Water <emph type="italics"></emph>v. </s> <s>g.<emph.end type="italics"></emph.end> a Maſs of Gold, if that Maſs were <lb></lb>of Water it would have no weight at all: For the Water moveth <lb></lb>neither upwards, nor downwards in the Water: It remains, <lb></lb>therefore, that the Maſs of Gold weigheth in the Water only ſo <lb></lb>much as the Gravity of the Gold exceeds the Gravity of the Wa<lb></lb>ter. </s> <s>And the like is to be underſtood of other Metals. </s> <s>And be<lb></lb>cauſe the Metals are different from each other in Gravity, their <lb></lb>Gravity in the Water ſhall diminiſh according to ſeveral proporti<lb></lb>ons. </s> <s>As for example: Let us ſuppoſe that Gold weigheth twenty <lb></lb>times more than Water, it is manifeſt by that which hath been <lb></lb>ſpoken, that the Gold will weigh leſs in the Water than in the <lb></lb>Air by a twentieth part of its whole weight. </s> <s>Now, let us ſuppoſe <lb></lb>that Silver, as being leſs Grave than Gold, weigheth 12 times more <lb></lb>than Water: this then, being weighed in the Water, ſhall di<lb></lb>miniſh in Gravity the twelfth part of its whole weight. </s> <s>Therefore <lb></lb>the Gravity of Gold in the Water decreaſeth leſs than that of <lb></lb>Silver; for that diminiſheth a twentieth part, and this a twelfth. <lb></lb></s> <s>If therefore in an exquiſite Ballance we ſhall hang a Metal at the <lb></lb>one Arm, and at the other a Counterpoiſe that weigheth equally <lb></lb>with the ſaid Metal in the Water, leaving the Counterpoiſe in the <lb></lb>Air, to the end that it may equivalate and compenſate the Me<lb></lb>tal, it will be neceſſary to hang it nearer the Perpendicular or <lb></lb>Cook. </s> <s>As for example, Let the Ballance be A B, its Perpendicu<lb></lb><figure id="id.040.01.998.1.jpg" xlink:href="040/01/998/1.jpg"></figure><lb></lb>lar C, and let a <lb></lb>Maſs of ſome <lb></lb>Metal be ſu<lb></lb>ſpended at B, <lb></lb>counterpoiſedby <lb></lb>the Weight D: putting the Weight B into the Water, the <lb></lb>Weight D in A would weigh more: therefore that they may <pb xlink:href="040/01/999.jpg" pagenum="305"></pb>weigh equally it would be neceſſary to hang it nearer to the <lb></lb>Perpendicular C, as <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> in E: and look how many times the Di<lb></lb>ſtance C A ſhall contain A E, ſo many times ſhall the Metal <lb></lb>weigh more than the Water. </s> <s>Let us therefore ſuppoſe that the <lb></lb>Weight in B be Gold, and that weighed in the Water it with<lb></lb>draws the Counterpoiſe D into E; and then doing the ſame with <lb></lb>pure Silver, let us ſuppoſe that its Counterpoiſe, when afterwards <lb></lb>it is weighed in the Water, returneth to F: which point ſhall be <lb></lb>nearer to the point C, as Experience ſheweth, becauſe the Silver <lb></lb>is leſs grave than the Gold: And the Diſtance that is between <lb></lb>A and F ſhall have the ſame Difference with the Diſtance A E, <lb></lb>that the Gravity of the Gold hath with that of the Silver. </s> <s>But if <lb></lb>we have a Mixture of Gold and Silver, it is clear, that by reaſon it <lb></lb>participates of Silver, it ſhall weigh leſs than the pure Gold, and <lb></lb>by reaſon it participates of Gold, it ſhall weigh more than the <lb></lb>pure Silver: and therefore being weighed in the Air, and deſiring <lb></lb>that the ſame Counterpoiſe ſhould counterpoiſe it, when that <lb></lb>Mixture ſhall be put into the Water it will be neceſſary to draw <lb></lb>the ſaid Counterpoiſe more towards the Perpendicular C, than the <lb></lb>point E is, which is the term of the Gold; and more from C <lb></lb>than F is, which is the term of the pure Silver; Therefore it ſhall <lb></lb>fall between the points E and F: And the proportion into which <lb></lb>the Diſtance EF ſhall be divided, ſhall exactly give the proportion <lb></lb>of the two Metals which compound that Mixture. </s> <s>As for exam<lb></lb>ple: Let us ſuppoſe the Mixture of Gold and Silver to be in B, <lb></lb><figure id="id.040.01.999.1.jpg" xlink:href="040/01/999/1.jpg"></figure><lb></lb>counterpoiſed in <lb></lb>the Air by D, <lb></lb>which Counter<lb></lb>poiſe when the <lb></lb>Compound Me<lb></lb>tal is put into the Water returneth into G: I ſay now, that the <lb></lb>Gold and the Silver which compound this Mixture are to one ano<lb></lb>ther in the ſame proportion, as the Diſtance F G is to the Diſtance <lb></lb>G E. </s> <s>But you muſt know that the Diſtance G F terminated in <lb></lb>the mark of the Silver, ſhall denote unto us the quantity of the <lb></lb>Gold, and the Diſtance G E, terminated in the mark of the Gold, <lb></lb>ſhall ſhew us the quantity of the Silver: inſomuch that if F G <lb></lb>ſhall prove double to G E, then that Mixture ſhall be two parts <lb></lb>Gold, and one part Silver: and in the ſame method proceeding in<lb></lb>the examination of other Mixtures, one ſhall exactly find the <lb></lb>quantity of the ſimple Metals.</s></p><p type="main"> <s>To compoſe the Ballance, therefore, take a Rod at leaſt a yard <lb></lb>long, (and the longer it is, the exacter the Inſtrument ſhall be) <lb></lb>and divide it in the midſt, where place the Perpendicular: then <lb></lb>adjuſt the Arms that they may ſtand in <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> by filing or <pb xlink:href="040/01/1000.jpg" pagenum="306"></pb>ſhaving that leſs which weigheth moſt; and upon one of the Arms <lb></lb>note the terms to which the Counterpoiſes of ſimple Metals return <lb></lb>when they ſhall be weighed in the Water: taking care to weigh the <lb></lb>pureſt Metals that can be found. </s> <s>This being done, it remaineth <lb></lb>that we find out a way, how we may with facility diſcover the <lb></lb>proportion, according to which, the Diſtances between the terms <lb></lb>of the ſimple and pure Metals are divided by the Marks of the <lb></lb>Mixt Metals: Which ſhall be effected in this manner.</s></p><p type="main"> <s>We are to have two very ſmall Wires drawn thorow the ſame <lb></lb>drawing-Iron, one of Steel, the other of Braſs, and above the <lb></lb>terms of the ſimple Metals we muſt wind the Steel Wyer; as for <lb></lb>example: above the point E, the term of the pure Gold, we are <lb></lb>to wind the Steel Wyer, and under it the other Braſs Wyre, and <lb></lb>having made ten folds of the Steel Wyer, we muſt make ten <lb></lb>more with that of Braſs, and thus we are to continue to do with <lb></lb>ten of Steel, and ten of Braſs, until that the whole Space be<lb></lb>tween the points E and F, the terms of the pure Metals, be full; <lb></lb>cauſing thoſe two terms to be alwaies viſible and perſpicuous: <lb></lb>and thus the Diſtance E F ſhall be divided into many equal parts, <lb></lb>and numbred by ten and ten. </s> <s>And if at any time we would know <lb></lb>the proportion that is between F G and G E, we muſt count the <lb></lb>Wyers F G, and the Wyers G E: and finding the Wyers F G <lb></lb>to be, for example, 40, and the Wyers G E, 21: we will ſay that <lb></lb>there is in the mixt Metal 40 parts of Gold, and 21 of Silver. </s> <s>But <lb></lb>here you muſt note, that there is ſome difficulty in the counting, <lb></lb>for thoſe Wyers being very ſmall, as it is requiſite for exactneſs <lb></lb>ſake, it is not poſſible with the eye to tell them, becauſe the <lb></lb>ſmalneſs of the Spaces dazleth & confoundeth the Sight. </s> <s>Therefore <lb></lb>to number them with facility, take a Bodkin as ſharp as a Needle <lb></lb>and ſet it into an handle, or a very fine pointed Pen-knife, with <lb></lb>which we may eaſily run over all the ſaid Wyers, and this way <lb></lb>partly by help of hearing, partly by the impediments the hand <lb></lb>ſhall feel at every Wyer, thoſe Wyers ſhall be counted; <lb></lb>the number of which, as I ſaid before, ſhall give us the exact <lb></lb>quantity of the ſunple Metals, of which the Mixt-Metal is com<lb></lb>pounded: taking notice that the Simple anſwer alternately to the <lb></lb>Diſtances. </s> <s>As for example, in a Mixture of Gold and Silver, <lb></lb>the Wyers that ſhall be towards the term of Gold ſhall ſhew us <lb></lb>the quantity of the Silver: And the ſame is to be underſtood of <lb></lb>other Metals.</s></p><pb xlink:href="040/01/1001.jpg" pagenum="307"></pb><p type="head"> <s>Annotations of <emph type="italics"></emph>Dominico Mantovani<emph.end type="italics"></emph.end> upon the Bal<lb></lb>lance of <emph type="italics"></emph>Signore Galileo Galilei.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Firſt, I conceive that the difficulty of Numbring the Wyres <lb></lb>is removed by wrapping about the Ballance ten of Steel, <lb></lb>and then ten of Braſs, which being divided by tens, there <lb></lb>only remains that tenth part to be numbred, in which the term <lb></lb>of the Mixt Metal falleth. </s> <s>For although <emph type="italics"></emph>Signore Galileo,<emph.end type="italics"></emph.end> who is <lb></lb>Author of this Invention, makes mention of two Wyres, one of <lb></lb>Steel, the other of Braſs, yet he doth not ſay, that we are to <lb></lb>take ^{*} ten of the one, and ten of the other: which it may be <lb></lb><arrow.to.target n="marg1123"></arrow.to.target><lb></lb>hapneth by the negligence of him that hath tranſcribed it; al<lb></lb>though I muſt confeſs that the Copy which came to my hands was <lb></lb>of his own writing.</s></p><p type="margin"> <s><margin.target id="marg1123"></margin.target>* <emph type="italics"></emph>Galileus<emph.end type="italics"></emph.end> ſaith it <lb></lb>expreſly in this <lb></lb>Copy which I fol<lb></lb>low, but might <lb></lb>omit it in the Co<lb></lb>py which came to <lb></lb>the hands of <emph type="italics"></emph>Man<lb></lb>tovani.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Secondly, it is ſuppoſed in this Problem that the Compoſition <lb></lb>of two Metals do retain the ſame proportion of Maſs in the <lb></lb>Mixture as the two Simple Metals, of which it is compounded, <lb></lb>had at firſt. </s> <s>I mean, that the Simple Metals retain and keep in <lb></lb>the Compoſition (after that they are incorporated and commix<lb></lb>ed) the ſame proportion in Maſs that the Simple Metals had <lb></lb>when they were ſeparated: Which in the Caſe of <emph type="italics"></emph>Signore Gali<lb></lb>leo,<emph.end type="italics"></emph.end> touching the Commixtion of Gold and Silver, I do neither <lb></lb>deny, nor particularly confeſs. </s> <s>But if one would, for example, <lb></lb>unite 101 pounds of Copper with 21 pounds of Tin, to make <lb></lb>thereof 120 pounds of Bell-Metal, (I abate two pounds, <lb></lb>ſuppoſed to be waſted in the Melting) I do think that 120 <lb></lb>pounds of Compound Metal will have a leſs Bulk than the 100 <lb></lb>pounds of pure Copper, and the 20 pounds of Tin unmixt, that <lb></lb>is, before they were incorporated and melted into one Maſs, and <lb></lb>that the Compoſition is more grave <emph type="italics"></emph>in Specie<emph.end type="italics"></emph.end> than the ſingle Cop<lb></lb>per, and the ſingle Braſs: and in the Caſe of <emph type="italics"></emph>Signore Galileo<emph.end type="italics"></emph.end> the <lb></lb>Compoſition of Gold and Silver is ſuppoſed to be lighter <emph type="italics"></emph>in Specie<emph.end type="italics"></emph.end><lb></lb>than the pure Gold, and heavier <emph type="italics"></emph>in Specie<emph.end type="italics"></emph.end> than the pure Silver. </s> <s>Of <lb></lb>which it would be eaſie to make ſome ſuch like experiment, melt<lb></lb>ing together, <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> 10 pounds of Lead with 5 pounds of Tin, <lb></lb>and obſerving whether thoſe 15 pounds, or whatever the Mixture <lb></lb>maketh, do give the difference betwixt the weight in the Water <lb></lb>to the weight in the Air, in the proportion that the 15 pounds of <lb></lb>the two Metals diſ-united gave before: I do not ſay, the ſame diffe<lb></lb>rence, becauſe I pre ſuppoſe that they will waſte in melting down, <lb></lb>and that the Compound will be leſs than 15 pounds, therefore I <lb></lb>ſay in proportion.</s></p><p type="main"> <s>Thirdly, He doth alſo ſuppoſe, that one ought to take the <pb xlink:href="040/01/1002.jpg" pagenum="308"></pb>Simple Metals, that is, the Gold and the Silver, each of the ſame <lb></lb>weight as the Mixture, although he doth not ſay ſo; which may <lb></lb>be collected in that he marketh the ballance only betwixt the <lb></lb>Terms of the Gold and the Silver, which is the cauſe of the great <lb></lb>facility in reſolving the Problem by only counting the <lb></lb>Wyers.</s></p><p type="main"> <s>One might take the pure Gold, and pure Silver of the ſame <lb></lb>weight, in reſpect of one another, but yet different from the <lb></lb>weight of the Mixture, that is, either more or leſs grave than the <lb></lb>Mixt Metal: and being equal in weight to one another they <lb></lb>might ſhew the proportion of the Maſs of the Gold to that of the <lb></lb>Silver; but yet with this difference, that the more grave will ſhew <lb></lb>the ſaid proportion more exactly than the ſmall and leſs grave. <lb></lb></s> <s>But the Simple and pure Metals not being of the ſame weight as <lb></lb>the Compound, it will be neceſſary, having found the proportion <lb></lb>of the Maſs of the Gold to that of the Silver; to find by numbers <lb></lb>proportionally the exact quantity of each of the two Metals com<lb></lb>pounding the Mixture.</s></p><p type="main"> <s>A man may likewiſe uſe the quantity of the ſimple Metals ac<lb></lb>cording to neceſſity and convenience, although of different <lb></lb>Weights, both as to each other, and to the Mixture, provided that <lb></lb>each of them be pure in its kind: but then we muſt after<lb></lb>wards by numbers find the proportion of the Maſſes of the two <lb></lb>Simple ones of equal weight (which is ſoon done, taking them of <lb></lb>equal weight as was ſaid before) and then according to this pro<lb></lb>portion to find, by means of the Weight, and of the Maſs of the <lb></lb>Compound Metal, the diſtinct quantity of each of the two Sim<lb></lb>ple ones that make the Compoſition: of each of which Caſes <lb></lb>examples might be given. </s> <s>But to conclude, if the pure Gold, <lb></lb>and pure Silver, and the Mixt Metal ſhould be of equal Maſs, <lb></lb>they would be unequal in Weight, and it would not need to <lb></lb>weigh them in the Water, for being of equal Bulk, the differen<lb></lb>ces of their Weights in the Air and in the Water would be alſo <lb></lb>equal: for the difference of the weight of any Body in the Air <lb></lb>to its weight in the Water, is alwaies equal to the Weight of ſo <lb></lb>much Water as equalleth the ſame Body in Maſs, by <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end><lb></lb>his fifth Propoſition, <emph type="italics"></emph>De ijs quæ vehuntur in aqua.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And laſt of all, the Simple and pure Metals may have the ſame <lb></lb>proportion in Gravity, mutually or reciprocally, as their Bodies <lb></lb>have in Bulk: In which caſe, as well the Maſs, found by help of <lb></lb>the weight in Water, or by any other meanes, as their Weight in <lb></lb>the Air ſhall ſhew the proportion of their Specifical Gravities; as <lb></lb>their Weights in the Water do when their Weights in the Air <lb></lb>are equal; but yet alternately weighed: that is to ſay, the Spe<lb></lb>cifical Gravity of the Gold ſhall have ſuch proportion to the <pb xlink:href="040/01/1003.jpg" pagenum="309"></pb>Specifical Gravity of the Silver, as the Maſs of the Silver hath to <lb></lb>the Maſs of the Gold; that is, as the difference betwixt the <lb></lb>Weight in Water and Weight in Air of the Silver, hath to the <lb></lb>difference betwixt the Weight in Water and Weight in Air of <lb></lb>the Gold.</s></p><p type="main"> <s>With this ſame Ballance one may with facility meaſure the <lb></lb>Maſs or Magnitude of any Body, in any manner whatſoever Irre<lb></lb>gular in manner following, namely:</s></p><p type="main"> <s>We will have at hand a Solid Body of a ſubſtance more grave <lb></lb><emph type="italics"></emph>in Specie<emph.end type="italics"></emph.end> than the Water; as for inſtance of Lead; or if it were <lb></lb>of Wood, or other matter more light <emph type="italics"></emph>in Specie<emph.end type="italics"></emph.end> than the Water, <lb></lb>it may be made heavier by faſtning unto it Lead, or ſome other <lb></lb>thing that makes it ſink in the Water, and let us take ſome <lb></lb>known Meaſure, and with it meaſure the Irregular Solid; as for <lb></lb>inſtance, the Roman Palm, the Geometrical Foot, or any other <lb></lb>known meaſure, or part of the ſame, as the half Foot, the quar<lb></lb>ter of a Foot, or any ſuch like part known; then let it be weighed <lb></lb>in the Air, and ſuppoſe that it weigh 10 pounds; let the ſame <lb></lb>Meaſure be weighed in the Air, and ſuppoſe that it weigh 8 <lb></lb>pounds: and ſubſtract 8 pounds, the Weight in the Water, from <lb></lb>10 pounds, the Weight in the Air, and there remaineth 2 pounds <lb></lb>for the Weight of a Body of Water equal in Magnitude to the <lb></lb>Meaſure known. </s> <s>Now, if we would meaſure a Statue of Mar<lb></lb>ble, let it be weighed firſt in the Air, and then in the Water, and <lb></lb>ſubſtract the Weight in the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>ater from the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>eight in the Air, and <lb></lb>the remainder ſhall be the weight of ſo much <emph type="italics"></emph>W<emph.end type="italics"></emph.end>ater as equalleth <lb></lb>the Statue in Maſs; which being divided by the difference betwixt <lb></lb>the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>eight in <emph type="italics"></emph>W<emph.end type="italics"></emph.end>ater and the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>eight in Air of the Meaſure known, <lb></lb>the Quotient will give how many times the Statue containeth the <lb></lb>ſame given Meaſure. </s> <s>As for example; if the Statue in Air weigh <lb></lb>100 pounds, and in the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>ater 80 pounds, 80 pounds being ſub<lb></lb>ſtracted from 100 there reſteth 20 pounds for the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>eight of ſo <lb></lb>much <emph type="italics"></emph>W<emph.end type="italics"></emph.end>ater in Maſs as equalleth the Statue. </s> <s>But becauſe the <lb></lb>difference betwixt the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>eight in <emph type="italics"></emph>W<emph.end type="italics"></emph.end>ater, and the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>eight in Air <lb></lb>equal in Magnitude to the Meaſure known, was ſuppoſed to be <lb></lb>2 pounds; divide 18 pounds by two pounds, and the Quotient <lb></lb>is 9, for the number of times that the propoſed Statue containeth <lb></lb>the given Meaſure. </s> <s>The ſame Method may be obſerved, if it <lb></lb>were required, to meaſure a Statue, or other Maſs of any kind of <lb></lb>Metal: only it muſt be advertiſed, that all the holes muſt be <lb></lb>ſtopt, that the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>ater may not enter into the Body of the Statue: <lb></lb>but he that deſireth only the Solid content of the Metal of the <lb></lb>ſaid Statue muſt open the holes, and with Tunnels fill the whole <lb></lb>cavity of the Statue with <emph type="italics"></emph>W<emph.end type="italics"></emph.end>ater. </s> <s>And if the Statue were of a <lb></lb>Subſtance lighter <emph type="italics"></emph>in Specie<emph.end type="italics"></emph.end> than the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>ater; as, for example, of <pb xlink:href="040/01/1004.jpg" pagenum="310"></pb>Wax, it will be requiſite to add unto the Statue ſome Counter<lb></lb>poiſe, that maketh it ſink in the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>ater, and then to meaſure the <lb></lb>Counterpoiſe, as above, and to ſubſtract its meaſure from the <lb></lb>Compound Body, and there will remain the Meaſure of the <lb></lb>Statue of <emph type="italics"></emph>W<emph.end type="italics"></emph.end>ax. </s> <s>And laſtly, to make uſe of the ſaid Ballance, <lb></lb>inſtead of ſeeking the numbers of the pounds of the Differences <lb></lb>of the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>eights of the Meaſure known, and of the Solid <lb></lb>to be meaſured in <emph type="italics"></emph>W<emph.end type="italics"></emph.end>ater, and in Air, we may count the <lb></lb><emph type="italics"></emph>W<emph.end type="italics"></emph.end>yers of the Arm of the Ballance, which <lb></lb>being very ſmall will give the <lb></lb>Meaſure exactly.</s></p><p type="head"> <s><emph type="italics"></emph>FINIS.<emph.end type="italics"></emph.end></s></p></chap><chap> <pb xlink:href="040/01/1005.jpg" pagenum="311"></pb><p type="head"> <s>DISCOURSES <lb></lb>OF THE <lb></lb>MECHANICKS: <lb></lb>A MANVSCRIPT of <lb></lb>Monſieur Des-Cartes.</s></p><p type="head"> <s>The Explication.</s></p><p type="main"> <s><emph type="italics"></emph>Of Engines, by help of which we may raiſe a very great <lb></lb>weight with ſmall ſtrength.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The Invention of all theſe Engines de<lb></lb>pends upon one ſole Principle, which is, <lb></lb>That the ſame Force that can lift up a <lb></lb>Weight, for example, of 100 pounds to <lb></lb>the height of one foot, can life up one of <lb></lb>200 pounds to the height of half a foot, <lb></lb>or one of 400 pounds to the height of a <lb></lb>fourth part of a foot, and ſo of the reſt, <lb></lb>be there never ſo much applyed to it: and <lb></lb>this Principle cannot be denied if we conſider, that the Effect <lb></lb>ought to be proportioned to the Action that is neceſſary for the <lb></lb>production of it; ſo that, if it be neceſſary to employ an Action by <lb></lb>which we may raiſe a Weight of 100 pounds to the height of two <lb></lb>foot, for to raiſe one ſuch to the height of one foot only this ſame <lb></lb>ought to weigh 200 pounds: for its the ſame thing to raiſe 100 <lb></lb>pounds to the height of one foot, and again yet another 100 <lb></lb>pounds to the height of one foot, as to raiſe one of 200 pounds to <lb></lb>the height of one foot, and the ſame, alſo, as to raiſe 100 pounds <lb></lb>to the height of two feet.</s></p><p type="main"> <s>Now, the Engines which ſerve to make this Application of a <lb></lb>Force which acteth at a great Space upon a <emph type="italics"></emph>W<emph.end type="italics"></emph.end>eight which it cau<pb xlink:href="040/01/1006.jpg" pagenum="312"></pb>ſeth to be raiſed by a leſſer, are the Pulley, the Inclined Plane, the <lb></lb>Wedg, the Capſten, or Wheel, the Screw, the Leaver, and ſome <lb></lb>others, for if we will not apply or compare them one to another, <lb></lb>we cannot well number more, and if we will apply them we need <lb></lb>not inſtance in ſo many.</s></p><p type="head"> <s>The PVLLEY, <emph type="italics"></emph>Trochlea.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let A B C be a Chord put about the Pulley D, to which let <lb></lb>the Weight E be faſtned; and firſt, ſuppoſing that two <lb></lb>men ſuſtain or pull up equally each of them one of the <lb></lb><figure id="id.040.01.1006.1.jpg" xlink:href="040/01/1006/1.jpg"></figure><lb></lb>ends of the ſaid Chord: <lb></lb>it is manifeſt, that if the <lb></lb>Weight weigheth 200 <lb></lb>pounds, each of thoſe <lb></lb>men ſhal employ but the <lb></lb>half thereof, that is to ſay, <lb></lb>the Force that is requiſite <lb></lb>for ſuſtaining or raiſing <lb></lb>of 100 pounds, for each <lb></lb>of them ſhal bear but the <lb></lb>half of it.</s></p><p type="main"> <s>Afterwards, let us ſup<lb></lb>poſe that A, one of the <lb></lb>ends of this Chord, being <lb></lb>made faſt to ſome Nail, <lb></lb>the other C be again ſu<lb></lb>ſtained by a Man; and it <lb></lb>is manifeſt, that this Man in C, needs not (no more than before) <lb></lb>for the ſuſtaining the Weight E, more Force than is requiſite for <lb></lb>the ſuſtaining of 100 pounds: becauſe the Nail at A doth the <lb></lb>ſame Office as the Man which we ſuppoſed there before. </s> <s>In fine, <lb></lb>let us ſuppoſe that this Man in C do pull the Chord to make the <lb></lb>Weight E to riſe, and it is manifeſt, that if he there employeth <lb></lb>the Force which is requiſite for the raiſing of 100 pounds to the <lb></lb>height of two feet, he ſhall raiſe this Weight E of 200 pounds to <lb></lb>the height of one foot: for the Chord A B C being doubled, as it <lb></lb>is, it muſt be pull'd two feet by the end C, to make the Weight E <lb></lb>riſe as much, as if two men did draw it, the one by the end A, <lb></lb>and the other by the end C, each of them the length of one foot <lb></lb>only.</s></p><p type="main"> <s>There is alwaies one thing that hinders the exactneſs of the Cal<lb></lb>culation, that is the ponderoſity of the Chord or Pulley, and the <lb></lb>difficulty that we meet with in making the Chord to ſlip, and in <lb></lb>bearing it: but this is very ſmall in compariſon of that which <pb xlink:href="040/01/1007.jpg" pagenum="313"></pb>raiſeth it, and cannot be eſtimated ſave wthin a ſmall matter.</s></p><p type="main"> <s>Moreover, it is neceſſary to obſerve, that it is nothing but the <lb></lb>redoubling of the Chord, and not the Pulley, that cauſeth this <lb></lb>Force: for if we faſten yet another Pulley towards A, about <lb></lb>which we paſs the Chord A B C H, there will be required no leſs <lb></lb>Force to draw H towards K, and ſo to lift up the Weight E, than <lb></lb>there was before to draw C towards G. </s> <s>But if to theſe two Pul<lb></lb>leys we add yet another towards D, to which we faſten the Weight, <lb></lb>and in which we make the Chord to run or ſlip, juſt as we did in <lb></lb>the firſt, then we ſhall need no more Force to lift up this Weight <lb></lb>of 200 pounds than to lift up 50 pounds without the Pulley: be<lb></lb>cauſe that in drawing four feet of Chord we lift it up but one <lb></lb>foot. </s> <s>And ſo in multiplying of the Pulleys one may raiſe the great<lb></lb>eſt Weights with the leaſt Forces. </s> <s>It is requiſite alſo to obſerve, <lb></lb>that a little more Force is alwaies neceſſary for the raiſing of a <lb></lb>Weight than for the ſuſtaining of it: which is the reaſon why I <lb></lb>have ſpoken here diſtinctly of the one and of the other.</s></p><p type="head"> <s><emph type="italics"></emph>The Inclined<emph.end type="italics"></emph.end> PLANE.</s></p><p type="main"> <s>If not having more Force than ſufficeth to raiſe 100 pounds, one <lb></lb>would nevertheleſs raiſe this Body F, that weigheth 200 pounds, <lb></lb>to the height of the Line B A, there needs no more but to draw <lb></lb>or rowl it along the Inclined Plane C A, which I ſuppoſe to be <lb></lb>twice as long as the Line <lb></lb><figure id="id.040.01.1007.1.jpg" xlink:href="040/01/1007/1.jpg"></figure><lb></lb>A B, for by this means, <lb></lb>for to make it arrive at <lb></lb>the point A, we muſt <lb></lb>there employ the Force <lb></lb>that is neceſſary for the <lb></lb>raiſing 100 pounds twice <lb></lb>as high, and the more inclined this Plane ſhall be made, ſo much <lb></lb>the leſs Force ſhall there need to raiſe the Weight F. </s> <s>But yet there <lb></lb>is to be rebated from this Calculation the difficulty that there is <lb></lb>in moving the Body F, along the Plane A C, if that Plane were <lb></lb>laid down upon the Line B C, all the parts of which I ſuppoſe to <lb></lb>be equidiſtant from the Center of the Earth.</s></p><p type="main"> <s>It is true, that this impediment being ſo much leſs as the Plane is <lb></lb>more united, more hard, more even, and more polite; it cannot <lb></lb>likewiſe be eſtimated but by gueſs, and it is not very conſide<lb></lb>rable.</s></p><p type="main"> <s>We need not neither much to regard that the Line B C being a <lb></lb>part of a Circle that hath the ſame Center with the Earth, the <lb></lb>Plane A C ought to be (though but very little) curved, and to <lb></lb>have the Figure of part of a Spiral, deſcribed between two Circles, <pb xlink:href="040/01/1008.jpg" pagenum="314"></pb>which likewiſe have for their Center that of the Earth, for that it <lb></lb>is not any way ſenſible.</s></p><p type="head"> <s><emph type="italics"></emph>The<emph.end type="italics"></emph.end> WEDGE, <emph type="italics"></emph>Cuneus.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The Force of the Wedge A B C D is eaſily underſtood after <lb></lb>that which hath been ſpoken above of the Inclined Plane, <lb></lb>for the Force wherewith we ſtrike downwards acts as if it <lb></lb>were to make it move according to the Line B D; and the Wood, <lb></lb>or other thing and Body that it cleaveth, openeth not, or the <lb></lb>Weight that it raiſeth doth not riſe, ſave only according to the <lb></lb><figure id="id.040.01.1008.1.jpg" xlink:href="040/01/1008/1.jpg"></figure><lb></lb>Line A C, inſomuch that the Force, <lb></lb>wherewith one driveth or ſtriketh this <lb></lb>Wedge, ought to have the ſame Pro<lb></lb>portion to the Reſiſtance of this <lb></lb>Wood or Weight, that A C hath to <lb></lb>A B. </s> <s>Or elſe again, to be exact, it <lb></lb>would be convenient that B D were <lb></lb>a part of a Circle, and A D and <lb></lb>C D two portions of Spirals that had the ſame Center with the <lb></lb>Earth, and that the Wedge were of a Matter ſo perfectly hard <lb></lb>and polite, and of ſo ſmall weight, as that any little Force would <lb></lb>ſuffice to move it.</s></p><p type="head"> <s><emph type="italics"></emph>The<emph.end type="italics"></emph.end> CRANE, <emph type="italics"></emph>or the<emph.end type="italics"></emph.end> CAPSTEN, <lb></lb><emph type="italics"></emph>Axis in Peritrochio.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>We ſee alſo very eaſily, that the Force wherewith the Wheel <lb></lb>A or Cogg B is turned, which make the Axis or Cylinder C <lb></lb>to move, about which a Chord is rolled, to which the <lb></lb>Weight D, which we would raiſe, is faſtned, ought to have the <lb></lb><figure id="id.040.01.1008.2.jpg" xlink:href="040/01/1008/2.jpg"></figure><lb></lb>ſame proportion to the ſaid <lb></lb>Weight, as the Circumference of <lb></lb>the Cylinder hath to the Cir<lb></lb>cumference of a Circle which <lb></lb>that Force deſcribeth, or that the <lb></lb>Diameter of the one hath unto <lb></lb>the Diameter of the other; for <lb></lb>that the Circumferences have the <lb></lb>ſame proportion as the Diame<lb></lb>ters: inſomuch that the Cylinder C, having no more but one foot <lb></lb>in Diameter, if the Wheel AB be ſix feet in its Diameter, and the <lb></lb>Weight D do weigh 600 pounds, it ſhall ſuffice that the Force in <lb></lb>B ſhall be capable to raiſe 100 pounds, and ſo of others. </s> <s>One may <pb xlink:href="040/01/1009.jpg" pagenum="315"></pb>alſo inſtead of the Chord that rolleth about the Cylinder C, place <lb></lb>there a ſmall Wheel with teeth or Coggs, that may turn another <lb></lb>greater, and by that means multiply the power of the Force as <lb></lb>much as one ſhall pleaſe, without having any thing to deduct of <lb></lb>the ſame, ſave only the difficulty of moving the Machine, as in the <lb></lb>others.</s></p><p type="head"> <s><emph type="italics"></emph>The<emph.end type="italics"></emph.end> SCREW, <emph type="italics"></emph>Cochlea.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>When once the Force of the Capſten and of the In<lb></lb>clined Plane is underſtood, that of the Screw is eaſie <lb></lb>to be computed, for it is compoſed only of a Plane <lb></lb>much inclined, which windeth about a Cylinder: and if this Plane <lb></lb>be in ſuch manner Inclined, as that the Cylinder ought to make <lb></lb><emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> ten turns to advance forwards the length of a foot in the <lb></lb>Screw, and that the bigneſs of the Circumference of the Circle <lb></lb><figure id="id.040.01.1009.1.jpg" xlink:href="040/01/1009/1.jpg"></figure><lb></lb>which the Force that turneth it <lb></lb>about doth deſcribe be of ten <lb></lb>feet; foraſmuch as ten times ten <lb></lb>are one hundred, one Man alone <lb></lb>ſhall be able to preſs as ſtrongly <lb></lb>with this Inſtrument, or Screw, as <lb></lb>one hundred without it, provided <lb></lb>alwaies, that we rebate the Force <lb></lb>that is required to the turning <lb></lb>of it.</s></p><p type="main"> <s>Now I ſpeak here of Preſſing rather than of Raiſing, or Remo<lb></lb>ving, in regard that it is about this moſt commonly that the Screw <lb></lb>is employed, but when we would make uſe of it for the raiſing of <lb></lb>Weights, inſtead of making it to advance into a Female Screw, we <lb></lb>joyn or apply unto it a Wheel of many Coggs, in ſuch ſort <lb></lb>made, that if <emph type="italics"></emph>v. </s> <s>gr.<emph.end type="italics"></emph.end> this <emph type="italics"></emph>W<emph.end type="italics"></emph.end>heel have thirty Coggs, whilſt the Screw <lb></lb>maketh one entire turn, it ſhall not cauſe the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>heel to make more <lb></lb>than the thirtieth part of a turn, and if the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>eight be faſtned to <lb></lb>a Chord that rowling about the Axis of this <emph type="italics"></emph>W<emph.end type="italics"></emph.end>heel ſhall raiſe it but <lb></lb>one foot in the time that the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>heel makes one entire revolution, <lb></lb>and that the greatneſs of the Circumference of the Circle that is <lb></lb>deſcribed by the Force that turneth the Screw about be alſo of ten <lb></lb>ſeet, by reaſon that 10 times 30 make 300, one ſingle Man ſhall be <lb></lb>able to raiſe a <emph type="italics"></emph>W<emph.end type="italics"></emph.end>eight of that bigneſs with this Inſtrument, which <lb></lb>is called the Perpetual Screw, as would require 300 men with<lb></lb>out it.</s></p><p type="main"> <s>Provided, as before, that we thence deduct the difficulty that <lb></lb>we meet with in turning of it, which is not properly cauſed by the <lb></lb>Ponderoſity of the <emph type="italics"></emph>W<emph.end type="italics"></emph.end>eight, but by the Force or Matter of the In<pb xlink:href="040/01/1010.jpg" pagenum="316"></pb>ſtrument: which difficulty is more ſenſible in it than in thoſe afore<lb></lb>going, foraſmuch as it hath greater Force.</s></p><p type="head"> <s>The LEAVER, <emph type="italics"></emph>Vectis.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>I Have deferred to ſpeak of the Leaver until the laſt, in regard <lb></lb>that it is of all Engines for raiſing of Weights, the moſt diffi<lb></lb>cult to be explained.</s></p><p type="main"> <s>Let us ſuppoſe that C H is a Leaver, in ſuch manner ſupported <lb></lb>at the point O, (by means of an Iron Pin that paſſeth thorow it <lb></lb>acroſs, or otherwiſe) that it may turn about on this point O, its <lb></lb>part C deſcribing the Semicircle A B C D E, and its part H the <lb></lb><figure id="id.040.01.1010.1.jpg" xlink:href="040/01/1010/1.jpg"></figure><lb></lb>Semicircle F G H I K; and that <lb></lb>the Weight which we would <lb></lb>raiſe by help of it were in H, <lb></lb>and the Force in C, the Line <lb></lb>C O being ſuppoſed triple of <lb></lb>O H. </s> <s>Then let us conſider that <lb></lb>in the Time whilſt the Force <lb></lb>that moveth this Leaver deſcri<lb></lb>beth the whole Semicircle <lb></lb>A B C D E, and acteth accord<lb></lb>ing to the Line A B C D E, al<lb></lb>though that the Weight deſcri<lb></lb>beth likewiſe the Semicircle <lb></lb>F G H I K, yet it is not raiſed to <lb></lb>the length of this curved Line <lb></lb>F G H I K, but only to that of the Line F O K; inſomuch that the <lb></lb>Proportion that the Force which moveth this Weight ought to <lb></lb>have to its Ponderoſity ought not to be meaſured by that which is <lb></lb>between the two Diameters of theſe Circles, or between their two <lb></lb>Circumferences, as it hath been ſaid above of the Wheel, but ra<lb></lb>ther by that which is betwixt the Circumference of the greater, <lb></lb>and the Diameter of the leſſer. </s> <s>Furthermore let us conſider, that <lb></lb>there is a neceſſity that this Force needeth not to be ſo great, at <lb></lb>ſuch time as it is near to A, or near to E, for the turning of the <lb></lb>Leaver, as then when it is near to B, or to D; nor ſo great when <lb></lb>it is near to B or D, as then when it is near to C: of which the rea<lb></lb>ſon is, that the Weights do there mount leſs: as it is eaſie to un<lb></lb>derſtand, if having ſuppoſed that the Line C O H is parallel to the <lb></lb>Horizon, and that A O F cutteth it at Right Angles, we take the <lb></lb>point G equidiſtant from the points F and H, and the point B equi<lb></lb>diſtant from A and C; and that having drawn G S perpendicular <lb></lb>to F O, we obſerve that the Line F S (which ſheweth how much <lb></lb>the Weight mounteth in the Time that the Force operates along <pb xlink:href="040/01/1011.jpg" pagenum="317"></pb>the Line A B) is much leſſer than the Line S O, which ſheweth <lb></lb>how much it mounteth in the Time that the Force opperates along <lb></lb>the Line B C.</s></p><p type="main"> <s>And to meaſure exactly what his Force ought to be in each Point <lb></lb>of the curved Line A B C D E, it is requiſite to know that it ope<lb></lb>rates there juſt in the ſame manner as if it drew the Weight along <lb></lb>a Plane Circularly Inclined, and that the Inclination of each of the <lb></lb>Points of this circular Plane were to be meaſured by that of the <lb></lb>right Line that toucheth the Circle in this Point. </s> <s>As for example, <lb></lb>when the Force is at the Point B, for to find the proportion that it <lb></lb>ought to have with the ponderoſity of the Weight which is at that <lb></lb>time at the Point G, it is neceſſary to draw the Contingent Line <lb></lb>G M, and to account that the ponderoſity of the Weight is to the <lb></lb>Force which is required to draw it along this Plane, and conſe<lb></lb>quently to raiſe it, according to the Circle F G H, as the Line G M <lb></lb>is to SM Again, for as much as B O is triple of O G, the Force <lb></lb>in B needs to be to the Weight in G but as the third part of the <lb></lb>Line SM is unto the whole Line G M. </s> <s>In the ſelf ſame manner, <lb></lb>when the Force is at the Point D, to know how much the Weight <lb></lb>weigheth at I, it is neceſſary to draw the Contingent Line betwixt <lb></lb>I and P, and the right Line I N perpendicular upon the Horizon, <lb></lb>and from the Point P taken at diſcretion in the Line I P, provided <lb></lb>that it be below the Point I, you muſt draw P N parallel to the <lb></lb>ſame Horizon, to the end you may have the proportion that is be<lb></lb>twixt the Line I P and the third part of the Line I N, for that which <lb></lb>betwixt the ponderoſity of the Weight, and the Force that ought to <lb></lb>be at the Point D for the moving of it: and ſo of others. </s> <s>Where, <lb></lb>nevertheleſs, you muſt except the Point H, at which the Contin<lb></lb>gent Line being perpendicular upon the Horizon, the Weight can <lb></lb>be no other than triple the Force which ought to be in C for the <lb></lb>moving of it: in the Points F and K, at which the Contingent <lb></lb>Line being parallel unto the Horizon it ſelf, the leaſt Force that <lb></lb>one can aſſign is ſufficient to move the Weight. </s> <s>Moreover, that you <lb></lb>may be perfectly exact, you muſt obſerve that the Lines S G and <lb></lb>P N ought to be parts of a Circle that have for their Center that <lb></lb>of the Earth; and GM and I P parts of Spirals drawn between two <lb></lb>ſuch Circles; and, laſtly, that the right Lines S M and I N both <lb></lb>tending towards the Center of the Earth are not exactly Paral<lb></lb>lels: and furthermore, that the Point H where I ſuppoſe the <lb></lb>Contingent Line to be perpendicular unto the Horizon ought <lb></lb>to be ſome ſmall matter nearer to the Point F than to K, at the <lb></lb>which F and K the Contingent Lines are Parallels unto the ſaid <lb></lb>Horizon.</s></p><p type="main"> <s>This done, we may eaſily reſolve all the difficulties of the Ba<lb></lb>lance, and ſhew, That then when it is moſt exact, and for inſtance, <pb xlink:href="040/01/1012.jpg" pagenum="318"></pb>ſuppoſing it's Centre at O by which it is ſuſtained to be no more <lb></lb>but an indiviſible Point, like as I have ſuppoſed here for the Leaver, <lb></lb>if the Armes be declined one way or the other, that which ſhall be <lb></lb>the lowermoſt ought evermore to be adjudged the heavier; ſo that <lb></lb>the Centre of Gravity is not ſixed and immoveable in each ſeveral <lb></lb>Body, as the Ancients have ſuppoſed, which no perſon, that I <lb></lb>know of, hath hitherto obſerved.</s></p><p type="main"> <s>But theſe laſt Conſiderations are of no moment in Practice, and <lb></lb>it would be good for thoſe who ſet themſelves to invent new <lb></lb>Machines, that they knew nothing more of this buſi<lb></lb>neſſe than this little which I have now writ thereof, <lb></lb>for then they would not be in danger of decei<lb></lb>ving themſelves in their Computation, <lb></lb>as they frequently do in ſuppoſing <lb></lb>other Principles.</s></p><p type="head"> <s><emph type="italics"></emph>FINIS.<emph.end type="italics"></emph.end></s></p><figure id="id.040.01.1012.1.jpg" xlink:href="040/01/1012/1.jpg"></figure><pb xlink:href="040/01/1013.jpg" pagenum="319"></pb><p type="head"> <s>A <lb></lb>LETTER <lb></lb>OF <lb></lb>Monſieur Des-Cartes <lb></lb>TO THE <lb></lb>REVEREND FATHER <lb></lb><emph type="italics"></emph>MARIN MERSENNE.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>Reverend Father,<emph.end type="italics"></emph.end></s></p><p type="main"> <s>I Did think to have deferred writing unto you <lb></lb>yet eight or fifteen dayes, to the end I might <lb></lb>not trouble you too often with my Letters, <lb></lb>but I have received yours of the firſt of <emph type="italics"></emph>Sept.<emph.end type="italics"></emph.end><lb></lb>which giveth me to underſtand that it is an <lb></lb>hard matter to admit the Principle which I <lb></lb>have ſuppoſed in my Examination of the <lb></lb>Geoſtatick Queſtion, and in regard that if it <lb></lb>be not true, all the reſt that I have inferred from it would be yet <lb></lb>leſſe true: I would not one onely day defer ſending you a more <lb></lb>particular Explication. </s> <s>It is requiſite above all things to conſider <lb></lb>that I did ſpeak of the Force that ſerveth to raiſe a Weight to ſome <lb></lb>heighth, the which Force hath evermore two Dimenſions, and not <lb></lb>of that which ſerveth in each point to ſuſtain it, which hath never <lb></lb>more than one Dimenſion, inſomuch that theſe two Forces differ <lb></lb>as much the one from the other, as a Superficies differs from a Line: <lb></lb>for the ſame Force which a Nail ought to have for the ſuſtaining of <lb></lb>a Weight of 100 pound one moment of time, doth alſo ſuffice for <lb></lb>to ſuſtain it the ſpace of a year, provided that it do not diminiſh, <lb></lb>but the ſame Quantity of this Force which ſerveth to raiſe the <lb></lb>Weight to the heighth of one foot, ſufficeth not <emph type="italics"></emph>(eadem numero)<emph.end type="italics"></emph.end><lb></lb>to raiſe it two feet; and it is not more manifeſt that two and two <lb></lb>make four, than it's manifeſt that we are to employ double as much <lb></lb>therein.</s></p><p type="main"> <s>Now, foraſmuch as that this is nothing but the ſame thing that <lb></lb>I have ſuppoſed for a Principle, I cannot gueſſe on what the Scruple <lb></lb>ſhould be grounded that men make of receiving it; but I ſhall in <pb xlink:href="040/01/1014.jpg" pagenum="320"></pb>this place ſpeak of all ſuch as I ſuſpect, which for the moſt part <lb></lb>ariſe onely from this, that men are before-hand over-knowing in <lb></lb>the Mechanicks; that is to ſay, that they are pre-occupied with <lb></lb>Principles that others prove touching theſe matters, which not being <lb></lb>abſolutely true, they deceive the more, the more true they ſeem to <lb></lb>be.</s></p><p type="main"> <s>The firſt thing wherewith a man may be pre-occupied in this <lb></lb>buſineſſe, is, that they many times confound the Conſideration of <lb></lb><figure id="id.040.01.1014.1.jpg" xlink:href="040/01/1014/1.jpg"></figure><lb></lb>Space, with that of Time, or of the Ve<lb></lb>locity, ſo that, for Example, in the <lb></lb><emph type="italics"></emph>L<emph.end type="italics"></emph.end>eaver, or (which is the ſame) the Ba<lb></lb>llance A B C D having ſuppoſed that <lb></lb>the Arm A B is double to B C, and the <lb></lb>Weight in C double to the Weight <lb></lb>in A, and alſo that they are in <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> inſtead of ſaying, that <lb></lb>that which cauſeth this <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> is, that if the Weight C did <lb></lb>ſuſtain, or was raiſed up by the Weight A, it did not paſſe more <lb></lb>than half ſo much Space as it, they ſay that it did move ſlower by <lb></lb>the half: which is a fault ſo much the more prejudicial, in that it is <lb></lb>very difficult to be known: for it is not the difference of <lb></lb><figure id="id.040.01.1014.2.jpg" xlink:href="040/01/1014/2.jpg"></figure><lb></lb>the Velocity that is the cauſe why theſe Weights are to be <lb></lb>one double to the other, but the difference of the Space, as <lb></lb>appeareth by this, that to raiſe, for Example, the Weight F <lb></lb>with the hand unto G, it is not neceſſary to employ a Force <lb></lb>that is preciſely double to that which one ſhould have <lb></lb>therein employed the firſt bout, to raiſe it twice as quick<lb></lb>ly, but it is requiſite to employ therein either more or leſs <lb></lb>than the double, according to the different proportion that <lb></lb>this Velocity may have unto the Cauſes that reſiſt it.</s></p><p type="main"> <s>Inſtead of requiring a Force juſt double for the raiſing of it with <lb></lb>the ſame Velocity twice as high, unto H, I ſay that it is juſt dou<lb></lb>ble in counting (as two and two make four) that one and one make <lb></lb>two, for it is requiſite to employ a certain quantity of this Force <lb></lb>to raiſe the Weight from F to G, and again alſo, as much more of <lb></lb>the ſame Force to raiſe it from G to H.</s></p><p type="main"> <s>For if I had had a mind to have joyned the Conſideration of the <lb></lb>Velocity with that of the Space, it had been neceſſary to have <lb></lb>aſſigned three Dimenſions to the Force, whereas I have aſſigned it <lb></lb>no more but two, on purpoſe to exclude it. </s> <s>And if I have teſtified <lb></lb>that there is ſo little of worth in any part of this ſmall Tract of the <lb></lb>Staticks, yet I de ſire that men ſhould know, that there is more in <lb></lb>this alone than in all the reſt: for it's impoſſible to ſay any thing <lb></lb>that is good and ſolid touching Velocity, without having rightly <lb></lb>explained what we are to underſtand by Gravity, as alſo the whole <lb></lb>Syſteme of the World. </s> <s>Now becauſe I would not under take it, <pb xlink:href="040/01/1015.jpg" pagenum="321"></pb>I have thought good to omit this Conſideration, and in this manner <lb></lb>to ſingle out theſe others that I could explain without it: for <lb></lb>though there be no Motion but hath ſome Velocity, nevertheleſs <lb></lb>it is onely the Augmentations and Diminutions of this Velocity <lb></lb>that are conſiderable. </s> <s>And now that ſpeaking of the Motion of a <lb></lb>Body, we ſuppoſe that it is made according to the Velocity which <lb></lb>is moſt naturall to it, which is the ſame as if we did not conſider it <lb></lb>at all.</s></p><p type="main"> <s>The other reaſon that may have hindred men from rightly un<lb></lb>derſtanding my Principle is, that they have thought that they could <lb></lb>demonſtrate without it ſome of thoſe things which I demonſtrate <lb></lb>not without it: As, for example, touching the Pulley A B C, they <lb></lb>have thought that it was enough to know that the Nail in A did <lb></lb><figure id="id.040.01.1015.1.jpg" xlink:href="040/01/1015/1.jpg"></figure><lb></lb>ſuſtain the half of the Weight B; to conclude <lb></lb>that the Hand in C had need but of half ſo much <lb></lb>Force to ſuſtain or raiſe the Weight, thus wound <lb></lb>about the Pulley, as it would need for to ſuſtain <lb></lb>or raiſe it without it. </s> <s>But howbeit that this ex<lb></lb>plaineth very well, how the application of the <lb></lb>Force at C is made unto a Weight double to that <lb></lb>which it could raiſe without a Pulley, and that I <lb></lb>my ſelf did make uſe thereof, yet I deny that <lb></lb>this is ſimply, becauſe that that the Nail A ſu<lb></lb>ſtaineth one part of the Weight B, that the Force <lb></lb>in C, which ſuſtaineth it, might be leſs than if it <lb></lb>had been ſo ſuſtained. </s> <s>For if that had been true, the Rope C E be<lb></lb>ing wound about the Pulley D, the Force in E might by the ſame <lb></lb>reaſon be leſs than the Force in C: for that the Nail A doth not <lb></lb>ſuſtain the Weight leſs than it did before, and that there is alſo <lb></lb>another Nail that ſuſtains it, to wit, that to wich the Pulley D is <lb></lb>faſtned. </s> <s>Thus therefore, that we may not be miſtaken in this, that <lb></lb>the Nail A ſuſtaineth the half of the Weight B, we ought to con<lb></lb>clude no more but this, that by this application the one of the Di<lb></lb>menſions of the Force that ought to be in C <lb></lb><figure id="id.040.01.1015.2.jpg" xlink:href="040/01/1015/2.jpg"></figure><lb></lb>to raiſe up this Weight is diminiſhed the one <lb></lb>half; and that the other, of conſequence, be<lb></lb>cometh double, in ſuch ſort that if the Line <lb></lb>F G repreſent the Force that is required for <lb></lb>the ſuſtaining the Weight B in a point, with<lb></lb>out the help of any Machine, and the <lb></lb>Quadrangle G H that which is required for <lb></lb>the raiſing of it to the height of a foot, the <lb></lb>ſupport of the Nail A diminiſheth the Di<lb></lb>menſion which is repreſented by the Line F G the one half, and the <lb></lb>redoubling of the Rope A B C maketh the other Dimenſion to <pb xlink:href="040/01/1016.jpg" pagenum="322"></pb>double, which is repreſented by the Line FH; and ſo the Force <lb></lb>that ought to be in C for the raiſing of the Weight B to the height <lb></lb>of one foot is repreſented by the Quadrangle IK; and, as we know <lb></lb>in Geometry, that a Line being added to, or taken from a Superfi<lb></lb>cies, neither augmenteth, nor diminiſheth it in the leaſt, ſo the <lb></lb>Force where with the Nail A ſuſtains the Weight B, having but one <lb></lb>ſole Dimenſion, cannot cauſe that the Force in C, conſidered ac<lb></lb>cording to its two Dimenſions, ought to be leſs for the raiſing in <lb></lb>like manner the Weight E, than for the raiſing it without any <lb></lb>Pulley.</s></p><p type="main"> <s>The third thing which may make men imagine ſome Obſcurity <lb></lb>in my Principle is, that they, it may be, have not had regard to all <lb></lb>the words by which I explain it; for I do not ſay ſimply that the <lb></lb>Force that can raiſe a Weight of 50 pounds to the height of four <lb></lb>feet can raiſe one of 200 pounds to the height of one foot; but I <lb></lb>ſay that it may do it, if ſo be that it be applyed to it: now it is <lb></lb>impoſſible to apply the ſame thereto, but by the means of ſome Ma<lb></lb>chine, or other Invention that ſhall cauſe this Weight to aſcend <lb></lb>but one, in the time whilſt the Force paſſeth the whole length <lb></lb>of four feet, and ſo that it do transform the Quandrangle, by <lb></lb>which the Force is repreſented that is required to raiſe this <lb></lb>Weight of 400 pounds to the height of one foot into another <lb></lb>that is equall and like to that which repreſents the Force that is <lb></lb>required for to raiſe a Weight of 50 pounds to the height of four <lb></lb>feet.</s></p><p type="main"> <s>In fine, it may be that men may have thought the worſe of my <lb></lb>Principle, becauſe they have imagined that I have alledged the Ex<lb></lb>amples of the Pulley, of the Inclined Plane, and of the Leaver, to <lb></lb>the end that I might better perſwarde the truth thereof, as if it had <lb></lb>been dubious, or elſe that I had ſo ill diſcourſed as to offer to aſſume <lb></lb>from thence a Principle, which ought of it felf to be ſo clear, as not <lb></lb>to need any proof by things that are ſo difficult to comprehend as <lb></lb>that; it may be, they have never been well demonſtrated by any <lb></lb>man: but neither have I made uſe of them, ſave only with a deſign <lb></lb>to ſhew that this Principle extends it ſelf to all matters of which <lb></lb>one treateth in the Staticks: or, rather, I have made uſe of this oc<lb></lb>caſion for to inſert them into my Treatiſe, for that I conceived <lb></lb>that it would have been too dry and barren if I had therein ſpo<lb></lb>ken of nothing elſe but of this Queſtion, that is of no uſe, as of <lb></lb>that of the Geoſtaticks, which I purpoſed to examine.</s></p><p type="main"> <s>Now one may perceive, by what hath already been ſaid, how <lb></lb>the Forces of the Leaver and Pulley are demonſtrated by my <lb></lb>Principle ſo well, that there only remains the Inclined Plane, of <lb></lb>which you ſhall clearly ſee the Demonſtration by this Figure; in <lb></lb>which G F repreſents the firſt Dimenſion of the Force that the <pb xlink:href="040/01/1017.jpg" pagenum="323"></pb>Rectangle F H deſcribeth whilſt it draweth the Weight D along <lb></lb>the Plane B A, by the means of a Chord parallel to this Plane, and <lb></lb>paſſing about the Pulley E, in ſuch ſort, that H G, that is the height <lb></lb>of this Rectangle, is equal to B A, along which the Weight D is to <lb></lb>move, whilſt it mounteth to the height of the Line C A. </s> <s>And N O <lb></lb>repreſents the firſt Dimenſion of ſuch another Force, that is de<lb></lb>ſcribed by the Rectan<lb></lb>gle N P, in the time that <lb></lb><figure id="id.040.01.1017.1.jpg" xlink:href="040/01/1017/1.jpg"></figure><lb></lb>it is raiſing the Weight <lb></lb>L to M. </s> <s>And I ſuppoſe <lb></lb>that L M is equal to B A, <lb></lb>or double to C A; and <lb></lb>that N O is to F G, as <lb></lb>O P is to G H. </s> <s>This <lb></lb>done, I conſider that at <lb></lb>ſuch time as the Weight <lb></lb>D is moved from B to<lb></lb>wards A, one may ima<lb></lb>gine its Motion to be <lb></lb>compoſed of two others, of which the one carrieth it from B R to<lb></lb>wards C A, (to which operation there is no Force required, as all <lb></lb>thoſe ſuppoſe who treat of the Mechanicks) and the other raiſeth <lb></lb>it from B C towards R A, for which alone the Force is required: <lb></lb>inſomuch that it needs neither more nor leſs Force to move it <lb></lb>along the Inclined Plane B A, than along the Perpendicular C A. <lb></lb></s> <s>For I ſuppoſe that the unevenneſſes, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> of the Plane do not <lb></lb>at all hinder it, like as it is alwaies ſuppoſed in treating of this <lb></lb>matter.</s></p><p type="main"> <s>So then the whole Force F H is employed only about the raiſing <lb></lb>of D to the height of C A: and foraſmuch as it is exactly equal to <lb></lb>the Force N P, that is required for the raiſing of L to the Height <lb></lb>of L M, double to C A, I conclude by my Principle that the <lb></lb>Weight D is double to the Weight L. </s> <s>For in regard that it is <lb></lb>neceſſary to employ as much Force for the one as for the other, <lb></lb>there is as much to be raiſed in the one as in the other; and no <lb></lb>more knowledge is required than to count unto two for the <lb></lb>knowing that it is alike facile to raiſe 200 pounds from C to A, <lb></lb>as to raiſe 100 pounds from L to M: ſince that L M is double <lb></lb>to C A.</s></p><p type="main"> <s>You tell me, moreover, that I ought more particularly to ex<lb></lb>plain the nature of the Spiral Line that repreſenteth the Plane <lb></lb>equally enclined, which hath many qualities that render it ſuffi<lb></lb>ciently knowable.</s></p><pb xlink:href="040/01/1018.jpg" pagenum="324"></pb><p type="main"> <s>For if A be the Center of the Earth, <lb></lb><figure id="id.040.01.1018.1.jpg" xlink:href="040/01/1018/1.jpg"></figure><lb></lb>and A N B C D the Spiral Line, having <lb></lb>drawn the Right Lines A B, A D, and the <lb></lb>like, there is the ſame proportion betwixt <lb></lb>the Curved Line A N B and the Right Line <lb></lb>AB, as is betwixt the Curved Line A N B C, <lb></lb>and the Right Line A C; or betwixt <lb></lb>A N B C D and A D: and ſo of the <lb></lb>reſt.</s></p><p type="main"> <s>And if one draw the Tangents D E, C F, <lb></lb>and B G, the Angles A D E, A C F, A B G, &c. <lb></lb></s> <s>ſhall be equal. </s> <s>As for the reſt 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"></emph>DES-CARTES.<emph.end type="italics"></emph.end></s></p></chap> <chap> <pb xlink:href="040/01/1019.jpg" pagenum="325"></pb><p type="head"> <s>A <lb></lb>LETTER <lb></lb>OF <lb></lb>Monſieur de Robberval <lb></lb>TO <lb></lb>Monſieur de Fermates, <lb></lb>Counſellour of <emph type="italics"></emph>THOULOUSE,<emph.end type="italics"></emph.end><lb></lb>Containing certain Propoſitions in the <lb></lb>MECHANICKS.</s></p><p type="main"> <s>MONSIEUR,</s></p><p type="main"> <s>I have, according to my promiſe, ſent you the <lb></lb>Demonſtration of the Fundamental Propoſi<lb></lb>tion of our Mechanicks, in which I follow the <lb></lb>common method of explaining, in the firſt <lb></lb>place, the Definitions and Principles of which <lb></lb>we make uſe.</s></p><p type="main"> <s>We in general call that Quality a Force or <lb></lb>Power, by means of which any thing whatever <lb></lb>doth tend or aſpire into another place than that in which it is, be it <lb></lb>downwards, upwards, or ſide waies, whether this Quality naturally <lb></lb>belongeth to the Body, or be communicated to it from without. <lb></lb></s> <s>From which definition it followeth, that all Weights are a ſpecies <lb></lb>of Force, in regard that it is a Quality, by means whereof Bodies <lb></lb>do tend downwards. </s> <s>We often alſo aſſign the name of Force to <lb></lb>that very thing to which the Force belongeth, as a ponderous Bo<lb></lb>dy is called a Weight, but with this pre-caution, that this is in re<lb></lb>ference to the true Force, the which augmenting or diminiſhing <lb></lb>ſhall be called a greater or leſſer Force, albeit that the thing to <lb></lb>which it belongeth do remain alwaies the ſame.</s></p><p type="main"> <s>If a Force be ſuſpended or faſtned to a Flexible Line that is <lb></lb>without Gravity, and that is made faſt by one end unto ſome <emph type="italics"></emph>Ful<lb></lb>ciment<emph.end type="italics"></emph.end> or ſtay, in ſuch ſort as that it ſuſtain the Force, drawing <pb xlink:href="040/01/1020.jpg" pagenum="326"></pb>without impediment by this Line, the Force and the Line ſhall <lb></lb>take ſome certain poſition in which they ſhall reſt, and the Line <lb></lb>ſhall of neceſſity be ſtreight, let that Line be termed <emph type="italics"></emph>the Pendant,<emph.end type="italics"></emph.end><lb></lb>or <emph type="italics"></emph>Line of Direction of the Force.<emph.end type="italics"></emph.end> And let the Point by which it is <lb></lb>faſtned to the Fulciment be called <emph type="italics"></emph>the Point of Suſpenſion<emph.end type="italics"></emph.end>: which <lb></lb>may ſometimes be the Arm of a Leaver or Ballance; and then let <lb></lb>the Line drawn from the Center of the Fulciment of the Leaver <lb></lb>or Ballance to the Point of Suſpenſion be named <emph type="italics"></emph>the Diſtance<emph.end type="italics"></emph.end> or <lb></lb><emph type="italics"></emph>the Arm of the Force<emph.end type="italics"></emph.end>: which we ſuppoſe to be a Line fixed, and <lb></lb>conſidered without Gravity. </s> <s>Moreover, let the Angle comprehen<lb></lb>ded betwixt the Arm of the Force and the Line of Direction be <lb></lb>termed <emph type="italics"></emph>the Angle of the Direction of the Force.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>AXIOM I.</s></p><p type="main"> <s>After theſe Definitions we lay down for a Principle, that in the <lb></lb>Leaver, and in the Ballance, Equal Forces drawing by Arms <lb></lb>that are equal, and at equall Angles of Direction, do draw equal<lb></lb>ly. </s> <s>And if in this Poſition they draw one againſt the other they <lb></lb>ſhall make an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end>: but if they draw together, or towards <lb></lb>the ſame part, the Effect ſhall be double.</s></p><p type="main"> <s>If the Forces being equal, and the Augles of Direction alſo <lb></lb>equal, the Arms be unequal, the Force that ſhall be ſuſpended at <lb></lb>the greater Arm ſhall work the greater Effect.</s></p><p type="main"> <s>As in this Figure, the Center of the Ballance or Leaver being A, <lb></lb><figure id="id.040.01.1020.1.jpg" xlink:href="040/01/1020/1.jpg"></figure><lb></lb>if the Arms A B and A C are equal, <lb></lb>as alſo the Angles A B D, and A C E, <lb></lb>the equal Forces D and E ſhall <lb></lb>draw equally, and make an <emph type="italics"></emph>Equili<lb></lb>brium.<emph.end type="italics"></emph.end> So likewiſe the Arm A F be<lb></lb>ing equal to A B, the Angle A F G <lb></lb>to the Angle A B D, and the Force <lb></lb>G to D, theſe two Forces ^{*} G and D <lb></lb><arrow.to.target n="marg1124"></arrow.to.target><lb></lb>draw equally; and in regard that <lb></lb>they draw both one way, the Effect <lb></lb>ſhall be double.</s></p><p type="margin"> <s><margin.target id="marg1124"></margin.target>* In the M. S. <lb></lb></s> <s>Copy it is <emph type="italics"></emph>C and <lb></lb>D.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>In the ſame manner the Forces G and E ſhall make an <emph type="italics"></emph>Equilibri<lb></lb>um<emph.end type="italics"></emph.end>; as alſo I and L ſhall counterpoiſe, if (being equal) the Arms <lb></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 ſame ſhall befall in the Forces P and R, if all things be <lb></lb>diſpoſed as before. </s> <s>And in this caſe we make no other diſtinction <lb></lb>betwixt Weights and other Forces ſave only this, that Weights all <lb></lb>tend towards the Center of Grave Bodies, and Forces may be un<lb></lb>derſtood to tend all towards all parts of the Univerſe, with ſo <lb></lb>much greater or leſſer <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> than Weights. </s> <s>So that Weights and <pb xlink:href="040/01/1021.jpg" pagenum="327"></pb>their parts do draw by Lines of Direction, which all concur in one <lb></lb>and the ſame Point; and Forces and their parts may be underſtood <lb></lb>to draw in ſuch ſort that all the Lines of Direction are parallel to <lb></lb>each other.</s></p><p type="head"> <s>AXIOM II.</s></p><p type="main"> <s>In the ſecond place, we ſuppoſe that a Force and its Line of Di<lb></lb>rection abiding alwaies in the ſame poſition, as alſo the Center <lb></lb>of the Ballance or Leaver, be the Arm what it will that is drawn <lb></lb>from the Center of the Ballance to the Line of Direction, the <lb></lb>Force drawing alwaies in the ſame faſhion, will alwaies produce <lb></lb>the ſame Effect.</s></p><p type="main"> <s>As, in this ſecond Figure, the Center of the Ballance being A, <lb></lb>the Force B, and the Line of Direction <lb></lb><figure id="id.040.01.1021.1.jpg" xlink:href="040/01/1021/1.jpg"></figure><lb></lb>B <emph type="italics"></emph>F<emph.end type="italics"></emph.end> prolonged, as occaſion ſhall re<lb></lb>quire, in which the Arms A G, A C, and <lb></lb>A <emph type="italics"></emph>F<emph.end type="italics"></emph.end> do determine, in this poſition let <lb></lb>the Line B <emph type="italics"></emph>F<emph.end type="italics"></emph.end> be faſtned to the Arm <lb></lb>A <emph type="italics"></emph>F,<emph.end type="italics"></emph.end> or A C, or to another Arm drawn <lb></lb>from the Center A to the Line of Di<lb></lb>rection ^{*} B <emph type="italics"></emph>F<emph.end type="italics"></emph.end>: we ſuppoſe that this <lb></lb><arrow.to.target n="marg1125"></arrow.to.target><lb></lb><emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce B ſhall alwaies work the ſame <lb></lb>Effect upon the Ballance. </s> <s>And if <lb></lb>drawing by the Arm A C it make an <lb></lb><emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> with the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce <emph type="italics"></emph>D<emph.end type="italics"></emph.end> drawing by the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>rm <emph type="italics"></emph>A<emph.end type="italics"></emph.end> E, when <lb></lb>ever it ſhall draw by the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>rms <emph type="italics"></emph>A F<emph.end type="italics"></emph.end> or <emph type="italics"></emph>A<emph.end type="italics"></emph.end> G, it ſhall likewiſe make <lb></lb>an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> with the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce D drawing by the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>rm <emph type="italics"></emph>A E.<emph.end type="italics"></emph.end> This <lb></lb>Principle although it be not expreſly found in <emph type="italics"></emph>A<emph.end type="italics"></emph.end>uthors, yet it is <lb></lb>tacitly ſuppoſed by all thoſe that have writ on this <emph type="italics"></emph>A<emph.end type="italics"></emph.end>rgument, and <lb></lb>Experience conſtantly confirmeth it.</s></p><p type="margin"> <s><margin.target id="marg1125"></margin.target>* In the Original <lb></lb>it is writ, but by <lb></lb>the miſtake of <lb></lb>the Tranſcriber, <lb></lb><emph type="italics"></emph>a la ligue de<emph.end type="italics"></emph.end> di<lb></lb>rection A F.</s></p><p type="head"> <s>AXIOM III.</s></p><p type="main"> <s>I<emph type="italics"></emph>f<emph.end type="italics"></emph.end> the Arms of a Ballance or Leaver are directly placed the one to <lb></lb>the other, and that being equal they ſuſtain equal <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces, of which <lb></lb>the Angles of Direction are Right An<lb></lb><figure id="id.040.01.1021.2.jpg" xlink:href="040/01/1021/2.jpg"></figure><lb></lb>gles, theſe <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces do alwaies weigh <lb></lb>equally upon the Center of the Bal<lb></lb>lance, whether that they be near to the <lb></lb>ſame Center, or far diſtant, or both <lb></lb>conjoyned in the Center it ſelf; as in <lb></lb>this <emph type="italics"></emph>F<emph.end type="italics"></emph.end>igure the Ballance being E D, <lb></lb>the Center A, the equal Arms A D <lb></lb>and <emph type="italics"></emph>A<emph.end type="italics"></emph.end> E, let us ſuſtain equal <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces H and I, of which the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ngles <pb xlink:href="040/01/1022.jpg" pagenum="328"></pb>of Direction <emph type="italics"></emph>A<emph.end type="italics"></emph.end> D H and <emph type="italics"></emph>A<emph.end type="italics"></emph.end> E I are Right <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ngles, we ſuppoſe that <lb></lb>theſe two <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces I and H weigh alike upon the Center <emph type="italics"></emph>A<emph.end type="italics"></emph.end> as if they <lb></lb>were nearer to the Center, at the equal Diſtances <emph type="italics"></emph>A<emph.end type="italics"></emph.end> B and A C, <lb></lb>and we alſo ſuppoſe the ſame if theſe very <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces were ſuſpended <lb></lb>both together in <emph type="italics"></emph>A,<emph.end type="italics"></emph.end> the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ngles of Directions being ſtill Right <lb></lb><emph type="italics"></emph>A<emph.end type="italics"></emph.end>ngles.</s></p><p type="head"> <s>PROPOSITION I.</s></p><p type="main"> <s>Theſe Principles agreed upon, we will eaſily demonſtrate, <lb></lb>in Imitation of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> that upon a ſtraight Balance <lb></lb>the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces, of which and of all their parts the Lines of Dire<lb></lb>ction are parallel to one another, and perpendicular to the Balance, <lb></lb>ſhall couuterpoiſe and make an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> when the ſaid <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces <lb></lb>ſhall be to one another in Reciprocal proportion of their Arms, <lb></lb>which we think to be ſo manifeſt to you, that we thence ſhall de<lb></lb>rive the Demonſtration of this Univerſal Propoſition to which we <lb></lb>haſten.</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"></emph>F<emph.end type="italics"></emph.end>orces is <lb></lb>reciprocal to that of the Perpendicular Lines drawn from the <lb></lb>Center or Point of the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>ulciment unto the Lines of Direction <lb></lb>of the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces, drawing the one againſt the other, they ſhall make <lb></lb>an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> and drawing on one and the ſame ſide, they ſhall <lb></lb>have a like Effect, that is to ſay, that they ſhall have as much <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce <lb></lb>the one as the other, to move the Balance.</s></p><p type="main"> <s>In this <emph type="italics"></emph>F<emph.end type="italics"></emph.end>igure let the Center of the Balance be <emph type="italics"></emph>A,<emph.end type="italics"></emph.end> the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>rm <emph type="italics"></emph>A<emph.end type="italics"></emph.end> B, <lb></lb>bigger than <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C, and firſt let the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ines of Direction B D, and E C <lb></lb>be perpendicular to the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>rms <emph type="italics"></emph>A<emph.end type="italics"></emph.end> B and <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C, by which Lines the <lb></lb><emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces D and E (which may be made of Weights if one will) do <lb></lb>draw; and that there is the ſame rate <lb></lb><figure id="id.040.01.1022.1.jpg" xlink:href="040/01/1022/1.jpg"></figure><lb></lb>of the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce D to the Force E as there <lb></lb>is betwixt the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>rm <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C to the Arm <lb></lb><emph type="italics"></emph>A<emph.end type="italics"></emph.end> B: the Forces drawing one againſt <lb></lb>the other, I ſay, that they will make an <lb></lb><emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> upon the Balance <emph type="italics"></emph>C<emph.end type="italics"></emph.end> A B. <lb></lb></s> <s>For let the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>rm C <emph type="italics"></emph>A<emph.end type="italics"></emph.end> be prolonged <lb></lb>unto F, ſo as that <emph type="italics"></emph>A<emph.end type="italics"></emph.end>F may be equal to <lb></lb><emph type="italics"></emph>A<emph.end type="italics"></emph.end> B: and let C <emph type="italics"></emph>A<emph.end type="italics"></emph.end> F be conſidered as a <lb></lb>ſtreight Balance, of which let the Center be <emph type="italics"></emph>A<emph.end type="italics"></emph.end>: and let there be <lb></lb>ſuppoſed two Forces G and H, of which and of all their parts the <lb></lb>Lines of Direction are parallel to the Line C E, and that the <lb></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"></pb>drawing upon the Arm A <emph type="italics"></emph>F,<emph.end type="italics"></emph.end> and the other, to wit H, upon the Arm <lb></lb>A C: now, by the firſt Propoſition, G and H ſhall make an <emph type="italics"></emph>Equili<lb></lb>brium<emph.end type="italics"></emph.end> upon the Balance C A F: But, by the firſt Principle, the Force <lb></lb>D upon the Arm A B worketh the ſame effect as the Force G on <lb></lb>the Arm A F: Therefore the Force D upon the Arm A B maketh <lb></lb>an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> with the Force H upon A C: And the Force H <lb></lb>drawing in the ſame manner upon the Arm <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C as the Force E, by <lb></lb>the ſame firſt <emph type="italics"></emph>A<emph.end type="italics"></emph.end>xiom, the Force D upon the Arm <emph type="italics"></emph>A<emph.end type="italics"></emph.end> B ſhall make an <lb></lb><emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> with the Force E upon the Arm <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C.</s></p><p type="main"> <s>Now, in the following Figure, let the Center of the Balance be <lb></lb><emph type="italics"></emph>A,<emph.end type="italics"></emph.end> the Arms A B and A C, the Lines of Direction B D and C E <lb></lb>which are not Perpendicular to the Arms, and the Forces D and E <lb></lb>drawing likewiſe by the Lines of Direction, upon which Perpen<lb></lb>diculars are erected unto the Center A, that is A F upon B D, and <lb></lb>A G upon E C, and that as A F is to A G, ſo is the Force E to the <lb></lb>Force D: which Forces draw one <lb></lb><figure id="id.040.01.1023.1.jpg" xlink:href="040/01/1023/1.jpg"></figure><lb></lb>againſt the other: I ſay, that they will <lb></lb>make an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> upon the Balance <lb></lb>C A B: For let the Lines A F and A G <lb></lb>be underſtood to be the two Arms of <lb></lb>a Balance G A F, upon which the For<lb></lb>ces D and E do draw by the Lines of <lb></lb>Direction F D and G E: Theſe Forces <lb></lb>ſhall make an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> by the firſt <lb></lb>part of this ſecond Propoſition; but, by the ſecond Axiom, the Force <lb></lb>D upon the Arm A F hath the ſame Effect as upon the Arm A B: <lb></lb>Therefore the Force D upon the Arm A B maketh an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end><lb></lb>with the Force E upon the Arm A C.</s></p><p type="main"> <s>There are many Caſes, according to the Series of Perpendicu<lb></lb>lars, but it will be eaſie for you to ſee that they have all but one <lb></lb>and the ſame Demonſtration.</s></p><p type="main"> <s>It is alſo eaſie to demonſtrate, that if the Forces draw both on <lb></lb>one ſide they ſhall make the ſame Effect one as another, and that <lb></lb>the Effect of two together ſhall be double to that of one alone.</s></p><p type="head"> <s>OF THE <lb></lb>GEOSTATICKS.</s></p><p type="main"> <s>The Principle which you demand for the <emph type="italics"></emph>Geoſtaticks<emph.end type="italics"></emph.end> is, <lb></lb>That if two equal Weights are conjoyned by a right <lb></lb>Line fixed and void of Gravity, and that being ſo di<lb></lb>ſpoſed they may deſcend freely, they will never reſt till <lb></lb>that the middle of the Line, that is the Center of Gravitation of <lb></lb>the Ancients, unites it ſelf to the common Center of Grave Bodies.</s></p><pb xlink:href="040/01/1024.jpg" pagenum="330"></pb><p type="main"> <s>This Principle ſeems at the firſt very plauſible, but when <lb></lb>the Queſtion concerneth a Principle, you know what Conditions <lb></lb>are required to it, that it may be received, the principal of which are <lb></lb>wanting in the Principle now in controverſie<emph type="italics"></emph>: ſcil.<emph.end type="italics"></emph.end> that we do not <lb></lb>know what is the radical Cauſe why Grave Bodies deſcend; and <lb></lb>whence the Original of this Gravity ariſeth: as alſo that we are to<lb></lb>tally ignorant of that which would arrive at the Center whither <lb></lb>Grave Bodies do tend, nor to other places without the Surface of the <lb></lb>Earth, of which, in regard we inhabit upon it, we have ſome Expe<lb></lb>riments upon which we ground our Principles.</s></p><p type="main"> <s>For it may be, that Gravity is a Quality that reſides in the Body <lb></lb>it ſelf that falleth; it may be that it is in another that attracteth <lb></lb>that which deſcends, as in the Earth: It may be, and it is very likely <lb></lb>that it is a Natural Attraction, or a Natural Deſire of two Bodies to <lb></lb>unite together, as in the Iron and Loadſtone, which are ſuch, that <lb></lb>if the Loadſtone be ſtaid, the Iron, if nothing hinder it, will go find <lb></lb>it out; and if the Iron be ſtaid the Loadſtone will go towards it; <lb></lb>and if they be both at liberty, they will reciprocally approach one <lb></lb>another, yet after ſuch a faſhion, that the ſtrongeſt of the two <lb></lb>will move the leaſt way.</s></p><p type="main"> <s>If the firſt be true, according to the common opinion, we ſee not <lb></lb>how your Principle can ſubſiſt, for Common Senſe tells us, that in <lb></lb>whatever place a Weight is, it alwaies weigheth alike, having ever<lb></lb>more the ſame Quality that maketh it to weigh, and that then a Bo<lb></lb>dy will repoſe at the Common Center of things Grave when the <lb></lb>parts of the Body which ſhall be on each part of the ſaid Center <lb></lb>ſhall be of equal Ponderoſity to counterpoiſe one another, without <lb></lb>having any regard whether they be little or much removed from the <lb></lb>Center. </s> <s>Since therefore that of theſe three poſſible Cauſes of Gra<lb></lb>vitation, we know not which is the right, nay, that we are not cer<lb></lb>tain that it is any of them, it being poſſibly that there is a fourth <lb></lb>from which one may draw Concluſions very different, it ſeemeth to <lb></lb>me impoſſible for us to lay down other Principles in this bufineſs <lb></lb>than thoſe of which we are aſſured by a continual Experience, and <lb></lb>a ſound Judgment. </s> <s>As for our parts, we call thoſe Bodies equally <lb></lb>or unequally Grave which have an equal or unequal Force of mo<lb></lb>ving towards the Common Center: and a Body is ſaid to have the <lb></lb>ſame Weight when it alwaies hath this ſame Force: but if this <lb></lb>Force augmenteth or diminiſheth, then, although it be the ſame Bo<lb></lb>dy, we conſider it no longer as the ſame Weight: Now ſince that <lb></lb>this hapneth to Bodies that recede or approach to the Common <lb></lb>Center, this is it which we deſire to know, but finding nothing that <lb></lb>giveth me content upon this Subject, I will leave the Queſtion un<lb></lb>determined and undeſcribed.</s></p> <p type="head"> <s>>FINIS.</s></p> </chap><pb xlink:href="040/01/1025.jpg"></pb><chap><p type="head"> <s>ARCHIMEDES <lb></lb>HIS TRACT <lb></lb>De Incidentibus Humido, <lb></lb>OR OF THE <lb></lb>NATATION OF BODIES VPON, <lb></lb>OR SVBMERSION IN, <lb></lb>THE <lb></lb>WATER <lb></lb>OR OTHER LIQUIDS.</s></p><p type="head"> <s>IN TWO BOOKS.</s></p><p type="head"> <s>Tranſlated from the Original Greek,</s></p><p type="head"> <s>Firſt into Latine, and afterwards into Italian, by <emph type="italics"></emph>NICOLO <lb></lb>TARTAGLIA,<emph.end type="italics"></emph.end> and by him familiarly demon<lb></lb>ſtrated by way of Dialogue, with <emph type="italics"></emph>Richard Wentworth,<emph.end type="italics"></emph.end><lb></lb>a Noble Engliſh Gentleman, and his Friend.</s></p><p type="head"> <s>Together with the Learned Commentaries of <emph type="italics"></emph>Federico <lb></lb>Commandino,<emph.end type="italics"></emph.end> who hath Reſtored ſuch of the Demonſtrations <lb></lb>as, thorow the Injury of Time, were obliterated.</s></p><p type="head"> <s>Now compared with the ORIGINAL, and Engliſhed <lb></lb>By <emph type="italics"></emph>THOMAS SALVSBVRY,<emph.end type="italics"></emph.end> <expan abbr="Eſq.">Eſque</expan></s></p><p type="head"> <s><emph type="italics"></emph>LONDON,<emph.end type="italics"></emph.end> Printed by <emph type="italics"></emph>W. Leybourn,<emph.end type="italics"></emph.end> 1662.</s></p></chap><chap><pb xlink:href="040/01/1026.jpg"></pb> <pb xlink:href="040/01/1027.jpg" pagenum="335[333]"></pb><p type="head"> <s>ARCHIMEDES <lb></lb>HIS TRACT <lb></lb><emph type="italics"></emph>De <lb></lb>INCIDENTIBUS HUMIDO,<emph.end type="italics"></emph.end><lb></lb>OR OF <lb></lb>The Natation of Bodies upon, or Submerſion in, <lb></lb>the Water, or other Liquids.</s></p></chap> <chap> <pb xlink:href="040/01/1028.jpg"></pb><p type="head"> <s>BOOK I.</s></p><p type="head"> <s>RICARDO.</s></p><p type="main"> <s><emph type="italics"></emph>Dear Companion,<emph.end type="italics"></emph.end> I have peruſed your <emph type="italics"></emph>Induſtrious Invention,<emph.end type="italics"></emph.end><lb></lb>in which I find not any thing that will not certainly hold <lb></lb>true; but, truth is, there are many of your Concluſions <lb></lb>of which I underſtand uot the Cauſe, and therefore, if it <lb></lb>be not a trouble to you, I would deſire you to declare them <lb></lb>to me, for, indeed, nothing pleaſeth me, if the Cauſe <lb></lb>thereof be hid from me.</s></p><p type="main"> <s>NICOLO. </s> <s>My obligations unto you are ſo many and <lb></lb>great, <emph type="italics"></emph>Honoured Campanion,<emph.end type="italics"></emph.end> that no requeſt of yours ought <lb></lb>to be troubleſome to me, and therefore tell me what thoſe Perticulars are of which <lb></lb>you know not the Cauſe, for I ſhall endeavour with the utmoſt of my power and <lb></lb>underſtanding to ſatisfie you in all your demands.</s></p><p type="main"> <s>RIC. </s> <s>In the firſt <emph type="italics"></emph>Direction<emph.end type="italics"></emph.end> of the firſt Book of that your <emph type="italics"></emph>Induſtrious Invention<emph.end type="italics"></emph.end><lb></lb>you conclude, That it is impoſſible that the Water ſhould wholly receive into it <lb></lb>any material Solid Body that is lighter than it ſeif (as to <emph type="italics"></emph>ſpeciæ<emph.end type="italics"></emph.end>) nay, you ſay, That <lb></lb>there will alwaies a part of the Body ſtay or remain above the Waters Surface <lb></lb>(that is uncovered by it;) and, That as the whole Solid Body put into the Water <lb></lb>is in proportion to that part of it that ſhall be immerged, or received, into the Wa<lb></lb>ter, ſo ſhall the Gravity of the Water be to the Gravity <emph type="italics"></emph>(in ſpeciæ)<emph.end type="italics"></emph.end> of that ſame <lb></lb>material Body: And that thoſe Solid Bodies, that are by nature more Grave than the <lb></lb>Water, being put into the Water, ſhall preſently make the ſaid Water give place; <lb></lb>and, That they do not only wholly enter or ſubmerge in the ſame, but go continu<lb></lb>ally deſcending untill they arrive at <emph type="italics"></emph>t<emph.end type="italics"></emph.end>he Bottom; and, That they ſink to the Bot<lb></lb>tom ſo much faſter, by how much they are more Grave than the Water. </s> <s>And, <lb></lb>again, That thoſe which are preciſely of the ſame Gravity with the Water, being <lb></lb>put into the ſame, are of neceſſity wholly received into, or immerged by it, but <lb></lb>yet retained in the Surface of the ſaid Water, and much leſs will the Water con<lb></lb>ſent that it do deſcend to the Bottom: and, now, albeit that all theſe things are <lb></lb>manifeſt to Senſe and Experience, yet nevertheleſs would I be very glad, if it be <lb></lb>poſſible, that you would demonſtrate to me the moſt apt and proper Cauſe of <lb></lb>theſe Effects.</s></p> <pb xlink:href="040/01/1029.jpg" pagenum="334"></pb><p type="main"> <s>NIC. </s> <s>The Cauſe of all theſe Effects is aſſigned by <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> the <emph type="italics"></emph>Siracuſan,<emph.end type="italics"></emph.end> in <lb></lb><arrow.to.target n="marg1126"></arrow.to.target><lb></lb>that Book <emph type="italics"></emph>De Incidentibus (^{*}) Aquæ,<emph.end type="italics"></emph.end> by me publiſhed in Latine, and dedicated to <lb></lb>your ſelf, as I alſo ſaid in the beginning of that my <emph type="italics"></emph>Induſtrions Invention.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1126"></margin.target>* <emph type="italics"></emph>Aquæ,<emph.end type="italics"></emph.end> tanſlated <lb></lb>by me <emph type="italics"></emph>Humido,<emph.end type="italics"></emph.end> as <lb></lb>the more Compre<lb></lb>henſive word, for <lb></lb>his Doctrine holds <lb></lb>true in all Liquids <lb></lb>as well as in Wa<lb></lb>ter, <emph type="italics"></emph>ſoil.<emph.end type="italics"></emph.end> in Wine, <lb></lb>Oyl, Milk, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>RIC. </s> <s>I have ſeen that ſame <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> and have very well underſtood thoſe <lb></lb>two Books in which he treateth <emph type="italics"></emph>De Centro Gravitatis æquerepentibus,<emph.end type="italics"></emph.end> or of the <lb></lb>Center of Gravity in Figures plain, or parallel to the Horizon; and likewiſe thoſe <lb></lb><emph type="italics"></emph>De Quadratura Parabolæ,<emph.end type="italics"></emph.end> or, of Squaring the Parabola; but ^{*}<emph type="italics"></emph>that<emph.end type="italics"></emph.end> in which he treat<lb></lb>eth of Solids that Swim upon, or ſink in Liquids, is ſo obſcure, that, to ſpeak the <lb></lb>truth, there are many things in <emph type="italics"></emph>it<emph.end type="italics"></emph.end> which I do not underſtand, and therefore before <lb></lb><arrow.to.target n="marg1127"></arrow.to.target><lb></lb>we proceed any farther, I ſhould take it for a favour if you would declare it to me <lb></lb>in your Vulgar Tongue, beginning with his firſt <emph type="italics"></emph>Suppoſition,<emph.end type="italics"></emph.end> which ſpeaketh in this <lb></lb>manner.</s></p><p type="margin"> <s><margin.target id="marg1127"></margin.target>* He ſpeaks of but <lb></lb>one Book, <emph type="italics"></emph>Tartag<lb></lb>lia<emph.end type="italics"></emph.end> having tranſla<lb></lb>ted no more.</s></p><p type="head"> <s>SVPPOSITION I.</s></p><p type="main"> <s><emph type="italics"></emph>It is ſuppoſed that the Liquid is of ſuch a nature, that <lb></lb>its parts being equi-jacent and contiguous, the leſs <lb></lb>preſſed are repulſed by the more preſſed. </s> <s>And <lb></lb>that each of its parts is preſſed or repulſed by the <lb></lb>Liquor that lyeth over it, perpendicularly, if the <lb></lb>Liquid be deſcending into any place, or preſſed any <lb></lb>whither by another.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>NIC. </s> <s>Every Science, Art, or Doctrine (as you know, <emph type="italics"></emph>Honoured Companion,<emph.end type="italics"></emph.end>) <lb></lb>hath its firſt undemonſtrable Principles, by which (they being <lb></lb>granted or ſuppoſed) the ſaid Science is proved, maintained, or de<lb></lb>monſtrated. </s> <s>And of theſe Principles, ſome are called <emph type="italics"></emph>Petitions,<emph.end type="italics"></emph.end><lb></lb>and others <emph type="italics"></emph>Demands,<emph.end type="italics"></emph.end> or <emph type="italics"></emph>Suppoſitions.<emph.end type="italics"></emph.end> I ſay, therefore, that the Science or Doctrine <lb></lb>of thoſe Material Solids that Swim or Sink in Liquids, hath only two undemon<lb></lb>ſtrable <emph type="italics"></emph>Suppoſitions,<emph.end type="italics"></emph.end> one of which is that above alledged, the which in compliance <lb></lb>with your deſire I have ſet 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 underſtand the <lb></lb>parts of a Liquid to be <emph type="italics"></emph>Equijacent.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>NIC. </s> <s>When they are equidiſtant from the Center of the World, or of the <lb></lb>Earth (which is the ſame, although ^{*} ſome hold that the Centers of the Earth <lb></lb>and Worldare different.)</s></p><p type="main"> <s>RIC. </s> <s>I underſtand you not unleſs you give me ſome Example thereof in <lb></lb>Figure.<lb></lb><arrow.to.target n="marg1128"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1128"></margin.target>* The Coperni<lb></lb>cans.</s></p><p type="main"> <s>NIC. </s> <s>To exemplifie this particular, Let us ſuppoſe a quantity of Liquor (as <lb></lb>for inſtance of Water) to be upon the Earth; then let us with the Imagination <lb></lb>cut the whole Earth together with that Water into two equal parts, in ſuch a <lb></lb>manner as that the ſaid Section may paſs ^{*} by the Center of the Earth: And let <lb></lb>us ſuppoſe that one part of the Superficies of that Section, as well of the Water <lb></lb>as of the Earth, be the Superficies A B, and that the Center of the Earth be the <lb></lb>point K. </s> <s>This being done, let us in our Imagination deſcribe a Circle upon the </s></p><p type="main"> <s><arrow.to.target n="marg1129"></arrow.to.target><lb></lb>ſaid Center K, of ſuch a bigneſs as that the Circumference may paſs by the Super<lb></lb>ficies of the Section of the Water: Now let this Circumference be E F G: and <lb></lb>let many Lines be drawn from the point K to the ſaid Circumference, cutting the <lb></lb>ſame, as KE, KHO, KFQ KLP, KM. </s> <s>Now I ſay, that all theſe parts of <lb></lb>the ſaid Water, terminated in that Circumference, are Equijacent, as being all <pb xlink:href="040/01/1030.jpg" pagenum="335"></pb>equidiſtant from the point K, the Center of the World, which parts are G M, <lb></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 underſtand you very well, as to this particular: But tell me a little; he <lb></lb>ſaith that each of the parts of the Liquid is preſſed or repulſed by the Liquid that <lb></lb>is above it, according to the Perpendicular: I know not what that Liquid is that <lb></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></lb>thorow ſome Water, each part of the Water that is in that Line he ſuppoſeth to <lb></lb>be preſſed or repulſed by the Water that lieth above it in that ſame Line, and that <lb></lb>that repulſe is made according to the ſame Line, (that is, directly towards the <lb></lb>Center of the World) which Line is called a Perpendicular; becauſe every <lb></lb>Right-Line that departeth from any point, and goeth directly towards the Worlds <lb></lb>Center is called a Perpendicular. </s> <s>And that you may the better underſtand me, let <lb></lb><figure id="id.040.01.1030.1.jpg" xlink:href="040/01/1030/1.jpg"></figure><lb></lb>us imagine <lb></lb>the Line KHO, <lb></lb>and in that <lb></lb>let us imagine <lb></lb>ſeveral parts, <lb></lb>as ſuppoſe RS, <lb></lb>S T, T V, V H, <lb></lb>H O. </s> <s>I ſay, <lb></lb>that he ſup<lb></lb>poſeth that <lb></lb>the part V H <lb></lb>is preſſed by <lb></lb>that placed a<lb></lb>bove it, H O, <lb></lb>according to <lb></lb>the Line OK; <lb></lb>the which <lb></lb>O K, as hath been ſaid above, is called the Perpendicular paſſing thorow thoſe two <lb></lb>parts. </s> <s>In like manner, I ſay that the part T V is expulſed by the part V H, ac<lb></lb>cording to the ſaid Line O K: and ſo the part S T to be preſſed by T V, according <lb></lb>to the ſaid Perpendicular O K, and R S by S T. </s> <s>And this you are to underſtand <lb></lb>in all the other Lines that were protracted from the ſaid Point K, penetrating the <lb></lb>ſaid Water, As for Example, in <emph type="italics"></emph>K<emph.end type="italics"></emph.end> G, <emph type="italics"></emph>K<emph.end type="italics"></emph.end> M, <emph type="italics"></emph>K<emph.end type="italics"></emph.end> L, <emph type="italics"></emph>K<emph.end type="italics"></emph.end> F, <emph type="italics"></emph>K<emph.end type="italics"></emph.end> E, and infinite others of the <lb></lb>like kind.</s></p><p type="main"> <s>RIC. Indeed, <emph type="italics"></emph>Dear Companion,<emph.end type="italics"></emph.end> this your Explanation hath given megreat ſa<lb></lb>tisfaction; for, in my Judgment, it ſeemeth that all the difficulty of this Suppoſition <lb></lb>conſiſts in theſe two particulars which you have declared to me.</s></p><p type="main"> <s>NIC. </s> <s>It doth ſo; for having underſtood that the parts E H, H F, F L, L M, and <lb></lb>MG, determining in the Circumference of the ſaid Circle are equijacent, it is an <lb></lb>eaſie matter to underſtand the foreſaid <emph type="italics"></emph>Suppoſition<emph.end type="italics"></emph.end> in Order, which ſaith, <emph type="italics"></emph>That it is <lb></lb>ſuppoſed that the Liquid is of ſuch a nature, that the part thereof leſs preſſed or thrust is re<lb></lb>pulſed by the more thruſt or preſſed.<emph.end type="italics"></emph.end> As for example, if the part E H were by chance <lb></lb>more thruſt, crowded, or preſſed from above downwards by the Liquid, or ſome <lb></lb>other matter that was over it, than the part H F, contiguous to it, it is ſuppoſed <lb></lb>that the ſaid part H F, leſs preſſed, would be repulſed by the ſaid part E H. </s> <s>And <lb></lb>thus we ought to underſtand of the other parts equijacent, in caſe that they be <lb></lb>contiguous, and not ſevered. </s> <s>That each of the parts thereof is preſſed and repul. <lb></lb></s> <s>ſed by the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid that lieth over it Perpendicularly, is manifeſt by that which was <lb></lb>ſaid above, to wit, that it ſhould be repulſed, in caſe the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid be deſcending into <lb></lb>any place, and thruſt, or driven any whither by another.</s></p><p type="main"> <s>RIC. </s> <s>I underſtand this Suppoſition very well, but yet me thinks that before <lb></lb>the Suppoſition, the Author ought to have defined thoſe two particulars, which <lb></lb>you firſt declared to me, that is, how we are to underſtand the parts of the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid <lb></lb>equijacent, and likewiſe the Perpendicular.</s></p> <pb xlink:href="040/01/1031.jpg" pagenum="336"></pb><p type="main"> <s>NIC. </s> <s>You ſay truth.</s></p><p type="main"> <s>RIC. </s> <s>I have another queſtion to aske you, which is this, Why the Author <lb></lb>uſeth the word <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid, or Humid, inſtead of Water.</s></p><p type="main"> <s>NIC. </s> <s>It may be for two of theſe two Cauſes; the one is, that Water being the <lb></lb>principal of all <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquids, therefore ſaying <emph type="italics"></emph>Humidum<emph.end type="italics"></emph.end> he is to be underſtood to mean <lb></lb>the chief Liquid, that is Water: The other, becauſe that all the Propoſitions of <lb></lb>this Book of his, do not only hold true in Water, but alſo in every other <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid, <lb></lb>as in Wine, Oyl, and the like: and therefore the Author might have uſed the word <lb></lb><emph type="italics"></emph>Humidum,<emph.end type="italics"></emph.end> as being a word more general than <emph type="italics"></emph>Aqua.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>RIC. </s> <s>This I underſtand, therefore let us come to the firſt <emph type="italics"></emph>Propoſition,<emph.end type="italics"></emph.end> which, as <lb></lb>you know, in the Original ſpeaks in this manner.</s></p><p type="head"> <s>PROP. I. THEOR. I.</s></p><p type="main"> <s><emph type="italics"></emph>If any Superficies ſhall be cut by a Plane thorough any <lb></lb>Point, and the Section be alwaies the Circumference <lb></lb>of a Circle, whoſe Center is the ſaid Point: that Su<lb></lb>perficies ſhall be Spherical.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let any Superficies be cut at pleaſure by a Plane thorow the <lb></lb>Point K; and let the Section alwaies deſcribe the Circumfe<lb></lb>rence of a Circle that hath for its Center the Point K: I ſay, <lb></lb>that that ſame Superficies is Sphærical. </s> <s>For were it poſſible that the <lb></lb>ſaid Superficies were not Sphærical, then all the Lines drawn <lb></lb>through the ſaid Point K unto that Superficies would not be equal, <lb></lb>Let therefore A and B be two <lb></lb>Points in the ſaid Superficies, ſo that <lb></lb><figure id="id.040.01.1031.1.jpg" xlink:href="040/01/1031/1.jpg"></figure><lb></lb>drawing the two Lines K A and <lb></lb>K B, let them, if poſſible, be une<lb></lb>qual: Then by theſe two Lines let <lb></lb>a Plane be drawn cutting the ſaid <lb></lb>Superficies, and let the Section in <lb></lb>the Superficies make the Line <lb></lb>D A B G: Now this Line D A B G <lb></lb>is, by our pre-ſuppoſal, a Circle, and <lb></lb>the Center thereof is the Point K, for ſuch the ſaid Superficies was <lb></lb>ſuppoſed to be. </s> <s>Therefore the two Lines K A and K B are equal: <lb></lb>But they were alſo ſuppoſed to be unequal; which is impoſſible: <lb></lb>It followeth therefore, of neceſſity, that the ſaid Superficies be <lb></lb>Sphærical, that is, the Superficies of a Sphære.</s></p><p type="main"> <s>RIC. </s> <s>I underſtand you very well; now let us proceed to the ſecond <emph type="italics"></emph>Propoſition,<emph.end type="italics"></emph.end><lb></lb>which, you know, runs thus.</s></p> <pb xlink:href="040/01/1032.jpg" pagenum="337"></pb><p type="head"> <s>PROP. II. THEOR. II.</s></p><p type="main"> <s><emph type="italics"></emph>The Superficies of every Liquid that is conſiſtant and <lb></lb>ſetled ſhall be of a Sphærical Figure, which Figure <lb></lb>ſhall have the ſame Center with the Earth.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let us ſuppoſe a Liquid that is of ſuch a conſiſtance as that it <lb></lb>is not moved, and that its Superficies be cut by a Plane along <lb></lb>by the Center of the Earth, and let the Center of the Earth <lb></lb>be the Point K: and let the Section of the Superficies be the Line <lb></lb>A B G D. </s> <s>I ſay that the Line A B G D is the Circumference of a <lb></lb><figure id="id.040.01.1032.1.jpg" xlink:href="040/01/1032/1.jpg"></figure><lb></lb>Circle, and that the Center <lb></lb>thereof is the Point K And <lb></lb>if it be poſſible that it may <lb></lb>not be the Circumference <lb></lb>of a Circle, the Right<lb></lb><arrow.to.target n="marg1130"></arrow.to.target><lb></lb>Lines drawn ^{*} by the Point <lb></lb>K to the ſaid Line A B G D <lb></lb>ſhall not be equal. </s> <s>There<lb></lb>fore let a Right-Line be <lb></lb>taken greater than ſome of thoſe produced from the Point K unto <lb></lb>the ſaid Line A B G D, and leſſer than ſome other; and upon the <lb></lb>Point K let a Circle be deſcribed at the length of that Line, <lb></lb>Now the Circumference of this Circle ſhall fall part without the <lb></lb>ſaid Line A B G D, and part within: it having been preſuppoſed <lb></lb>that its Semidiameter is greater than ſome of thoſe Lines that may <lb></lb>be drawn from the ſaid Point K unto the ſaid Line A B G D, and <lb></lb>leſſer than ſome other. </s> <s>Let the Circumference of the deſcribed <lb></lb>Circle be R B G H, and from B to K draw the Right-Line B K: and <lb></lb>drawn alſo the two Lines K R, and K E L which make a Right<lb></lb>Angle in the Point K: and upon the Center K deſcribe the Circum<lb></lb>ference X O P in the Plane and in the Liquid. </s> <s>The parts, there<lb></lb>fore, of the Liquid that are ^{*} according to the Circumference <lb></lb><arrow.to.target n="marg1131"></arrow.to.target><lb></lb>X O P, for the reaſons alledged upon the firſt <emph type="italics"></emph>Suppoſition,<emph.end type="italics"></emph.end> are equi<lb></lb>jacent, or equipoſited, and contiguous to each other; and both <lb></lb>theſe parts are preſt or thruſt, according to the ſecond part of the <lb></lb><emph type="italics"></emph>Suppoſition,<emph.end type="italics"></emph.end> by the Liquor which is above them. </s> <s>And becauſe the <lb></lb>two Angles E K B and B K R are ſuppoſed equal [<emph type="italics"></emph>by the<emph.end type="italics"></emph.end> 26. <emph type="italics"></emph>of<emph.end type="italics"></emph.end> 3. <lb></lb><emph type="italics"></emph>of Euclid,<emph.end type="italics"></emph.end>] the two Circumferences or Arches B E and B R ſhall <lb></lb>be equal (foraſmuch as R B G H was a Circle deſcribed for ſatis<lb></lb>faction of the Oponent, and K its Center:) And in like manner <lb></lb>the whole Triangle B E K ſhall be equal to the whole Triangle <lb></lb>B R K. </s> <s>And becauſe alſo the Triangle O P K for the ſame reaſon <pb xlink:href="040/01/1033.jpg" pagenum="338"></pb>ſhall be equal to the Triangle O X K; Therefore (by common <lb></lb>Notion) ſubſtracting thoſe two ſmall Triangles O P K and O X K <lb></lb>from the two others B E K and B R K, the two Remainders ſhall <lb></lb>be equal: one of which Remainders ſhall be the Quadrangle <lb></lb>B E O P, and the other B R X O. </s> <s>And becauſe the whole Quadran<lb></lb>gle B E O P is full of Liquor, and of the Quadrangle B R X O, <lb></lb>the part B A X O only is full, and the reſidue B R A is wholly void <lb></lb>of Water: It followeth, therefore, that the Quadrangle B E O P <lb></lb>is more ponderous than the Quadrangle B R X O. </s> <s>And if the ſaid <lb></lb>Quadrangle B E O P be more Grave than the Quadrangle <lb></lb>B R X O, much more ſhall the Quadrangle B L O P exceed in Gra<lb></lb>vity the ſaid Quadrangle B R X O: whence it followeth, that the <lb></lb>part O P is more preſſed than the part O X. But, by the firſt part <lb></lb>of the Suppoſition, the part leſs preſſed ſhould be repulſed by the <lb></lb>part more preſſed: Therefore the part O X muſt be repulſed by <lb></lb>the part O P: But it was preſuppoſed that the Liquid did not <lb></lb>move: Wherefore it would follow that the leſs preſſed would not <lb></lb>be repulſed by the more preſſed: And therefore it followeth of <lb></lb>neceſſity that the Line A <emph type="italics"></emph>B<emph.end type="italics"></emph.end> G D is the Circumference of a Circle, <lb></lb>and that the Center of it is the point K. </s> <s>And in like manner ſhall <lb></lb>it be demonſtrated, if the Surface of the Liquid be cut by a Plane <lb></lb>thorow the Center of the Earth, that the Section ſhall be the Cir<lb></lb>cumference of a Circle, and that the Center of the ſame ſhall be <lb></lb>that very Point which is Center of the Earth. </s> <s>It is therefore mani<lb></lb>feſt that the Superficies of a Liquid that is conſiſtant and ſetled <lb></lb>ſhall have the Figure of a Sphære, the Center of which ſhall be <lb></lb>the ſame with that of the Earth, by the firſt <emph type="italics"></emph>Propoſition<emph.end type="italics"></emph.end>; for it is <lb></lb>ſuch that being ever cut thorow the ſame Point, the Section or Di<lb></lb>viſion deſcribes the Circumference of a Circle which hath for Cen<lb></lb>ter the ſelf-ſame Point that is Center of the Earth: Which was to <lb></lb>be demonſtrated.</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"></emph>i.e.<emph.end type="italics"></emph.end> Parallel.</s></p><p type="main"> <s>RIC. </s> <s>I do thorowly underſtand theſe your Reaſons, and ſince there is in them <lb></lb>no umbrage of Doubting, let us proceed to his third <emph type="italics"></emph>Propoſition.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROP. III. THEOR. III.</s></p><p type="main"> <s><emph type="italics"></emph>Solid Magnitudes that being of equal Maſs with the <lb></lb>Liquid are alſo equal to it in Gravity, being demit-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1132"></arrow.to.target><lb></lb><emph type="italics"></emph>ted into the [^{*} ſetled] Liquid do ſo ſubmerge in the <lb></lb>ſame as that they lie or appear not at all above the <lb></lb>Surface of the Liquid, nor yet do they ſink to the <lb></lb>Bottom.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/1034.jpg" pagenum="339"></pb><p type="margin"> <s><margin.target id="marg1132"></margin.target>* I add the word <lb></lb>ſetled, as neceſſary <lb></lb>in making the Ex<lb></lb>periment.</s></p><p type="main"> <s>NIC. </s> <s>In this <emph type="italics"></emph>Propoſition<emph.end type="italics"></emph.end> it is affirmed that thoſe Solid Magnitules that hap<lb></lb>pen to be equal in ſpecifical Gravity with the Liquid being lefeat liber<lb></lb>ty in the ſaid Liquid do ſo ſubmerge in the ſame, as that they lie or ap<lb></lb>pear not at all above the Surface of the Liquid, nor yet do they go or ſink to the <lb></lb>Bottom.</s></p><p type="main"> <s>For ſuppoſing, on the contrary, that it were poſſible for one of <lb></lb>thoſe Solids being placed in the Liquid to lie in part without the <lb></lb>Liquid, that is above its Surface, (alwaies provided that the ſaid <lb></lb>Liquid be ſetled and undiſturbed,) let us imagine any Plane pro<lb></lb>duced thorow the Center of the Earth, thorow the Liquid, and <lb></lb>thorow that Solid Body: and let us imagine that the Section of the <lb></lb>Liquid is the Superficies A B G D, and the Section of the Solid <lb></lb>Body that is within it the Superſicies E Z H T, and let us ſuppoſe <lb></lb>the Center of the Earth to be the Point K: and let the part of the <lb></lb>ſaid Solid ſubmerged in the Liquid be B G H T, and let that above <lb></lb>be B E Z G: and let the Solid Body be ſuppoſed to be comprized in <lb></lb>a Pyramid that hath its Parallelogram Baſe in the upper Surface of <lb></lb>the Liquid, and its Summity or Vertex in the Center of the Earth: <lb></lb>which Pyramid let us alſo ſuppoſe to be cut or divided by the ſame <lb></lb>Plane in which is the Circumference A B G D, and let the Sections <lb></lb><figure id="id.040.01.1034.1.jpg" xlink:href="040/01/1034/1.jpg"></figure><lb></lb>of the Planes of the ſaid <lb></lb>Pyramid be K L and <lb></lb>K M: and in the Liquid <lb></lb>about the Center K let <lb></lb>there be deſcribed a Su<lb></lb>perficies of another <lb></lb>Sphære below E Z H T, <lb></lb>which let be X O P; <lb></lb>and let this be cut by <lb></lb>the Superficies of the Plane: And let there be another Pyramid ta<lb></lb>ken or ſuppoſed equal and like to that which compriſeth the ſaid <lb></lb>Solid Body, and contiguous and conjunct with the ſame; and let <lb></lb>the Sections of its Superficies be K M and K N: and let us ſuppoſe <lb></lb>another Solid to be taken or imagined, of Liquor, contained in that <lb></lb>ſame Pyramid, which let be R S C Y, equal and like to the partial <lb></lb>Solid B H G T, which is immerged in the ſaid Liquid: But the <lb></lb>part of the Liquid which in the firſt Pyramid is under the Super<lb></lb>ficies X O, and that, which in the other Pyramid is under the Su<lb></lb>perficies O P, are equijacent or equipoſited and contiguous, but <lb></lb>are not preſſed equally; for that which is under the Superficies <lb></lb>X O is preſſed by the Solid T H E Z, and by the Liquor that is <lb></lb>contained between the two Spherical Superficies X O and L M <lb></lb>and the Planes of the Pyramid, but that which proceeds accord<lb></lb>ing to F O is preſſed by the Solid R S C Y, and by the Liquid <pb xlink:href="040/01/1035.jpg" pagenum="340"></pb>contained between the Sphærical Superficies that proceed accord<lb></lb>ing to P O and M N and the Planes of the Pyramid; and the Gra<lb></lb>vity of the Liquid, which is according to M N O P, ſhall be leſſer <lb></lb>than that which is according to L M X O; becauſe that Solid of <lb></lb>Liquor which proceeds according to R S C Y is leſs than the Solid <lb></lb>E Z H T (having been ſuppoſed to be equal in quantity to only <lb></lb>the part H B G T of that:) And the ſaid Solid E Z H T hath been <lb></lb>ſuppoſed to be equally grave with the Liquid: Therefore the Gra<lb></lb>vity of the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid compriſed betwixt the two Sphærical Superfi<lb></lb>cies L M and <emph type="italics"></emph>X<emph.end type="italics"></emph.end> O, and betwixt the ſides L <emph type="italics"></emph>X<emph.end type="italics"></emph.end> and M O of the <lb></lb><figure id="id.040.01.1035.1.jpg" xlink:href="040/01/1035/1.jpg"></figure><lb></lb>Pyramid, together with <lb></lb>the whole Solid EZHT, <lb></lb>ſhall exceed the Gravity <lb></lb>of the Liquid compri<lb></lb>ſed betwixt the other <lb></lb>two Sphærical Superfi<lb></lb>cies M N and O P, and <lb></lb>the Sides M O and N P <lb></lb>of the Pyramid, toge<lb></lb>ther with the Solid of Liquor R S C Y by the quantity of the Gra<lb></lb>vity of the part E B Z G, ſuppoſed to remain above the Surface of <lb></lb>the Liquid: And therefore it is manifeſt that the part which pro<lb></lb>ceedeth according to the Circumference O P is preſſed, driven, and <lb></lb>repulſed, according to the <emph type="italics"></emph>Suppoſition,<emph.end type="italics"></emph.end> by that which proceeds ac<lb></lb>cording to the Circumference X O, by which means the Liquid <lb></lb>would not be ſetled and ſtill: But we did preſuppoſe that it was <lb></lb>ſetled, namely ſo, as to be without motion: It followeth, therefore, <lb></lb>that the ſaid Solid cannot in any part of it exceed or lie above the <lb></lb>Superficies of the Liquid: And alſo that being dimerged in the Li<lb></lb>quid it cannot deſcend to the Bottom, for that all the parts of the <lb></lb>Liquid equijacent, or diſpoſed equally, are equally preſſed, becauſe <lb></lb>the Solid is equally grave with the Liquid, by what we preſuppoſed.</s></p><p type="main"> <s>RIC. </s> <s>I do underſtand your Argumentation, but I underſtand not that Phraſe <lb></lb><emph type="italics"></emph>Solid Magnitudes.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>NIC. </s> <s>I will declare this Term unto you. <emph type="italics"></emph>Magnitude<emph.end type="italics"></emph.end> is a general Word that <lb></lb>reſpecteth all the Species of Continual Quantity; and the Species of Continual <lb></lb>Quantity are three, that is, the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine, the Superficies, and the Body; which Body <lb></lb>is alſo called a Solid, as having in it ſelf <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ength, Breadth, and Thickneſs, or Depth: <lb></lb>and therefore that none might equivocate or take that Term <emph type="italics"></emph>Magnitudes<emph.end type="italics"></emph.end> to be <lb></lb>meant of <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ines, or Superficies, but only of Solid <emph type="italics"></emph>Magnitudes,<emph.end type="italics"></emph.end> that is, Bodies, he <lb></lb>did ſpecifie it by that manner of expreſſion, as was ſaid. </s> <s>The truth is, that he <lb></lb>might have expreſt that <emph type="italics"></emph>Propoſition<emph.end type="italics"></emph.end> in this manner: <emph type="italics"></emph>Solids (or Bodies) which being <lb></lb>of equal Gravity with an equal Maſs of the Liquid,<emph.end type="italics"></emph.end> &c. </s> <s>And this <emph type="italics"></emph>Propoſition<emph.end type="italics"></emph.end> would have <lb></lb>been more cleer and intelligible, for it is as ſignificant to ſay, a <emph type="italics"></emph>Solid,<emph.end type="italics"></emph.end> or, a <emph type="italics"></emph>Body,<emph.end type="italics"></emph.end> as <lb></lb>to ſay, a <emph type="italics"></emph>Solid Magnitude:<emph.end type="italics"></emph.end> therefore wonder not if for the future I uſe theſe three <lb></lb>kinds of words indifferently.</s></p><p type="main"> <s>RIC. </s> <s>You have ſufficiently ſatisfied me, wherefore that we may loſe no time <lb></lb>let us go forwards to the fourth <emph type="italics"></emph>Propoſition.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/1036.jpg" pagenum="341"></pb><p type="head"> <s>PROP. IV. THEOR. IV.</s></p><p type="main"> <s><emph type="italics"></emph>Solid Magnitudes that are lighter than the Liquid, <lb></lb>being demitted into the ſetled Liquid, will not total<lb></lb>ly ſubmerge in the ſame, but ſome part thereof will <lb></lb>lie or ſtay above the Surface of the Liquid.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>NIC. </s> <s>In this fourth <emph type="italics"></emph>Propoſition<emph.end type="italics"></emph.end> it is concluded, that every Body or Solid that is <lb></lb>lighter (as to Specifical Gravity) than the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid, being put into the <lb></lb><emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid, will not totally ſubmerge in the ſame, but that ſome part of it <lb></lb>will ſtay and appear without the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid, that is above its Surface.</s></p><p type="main"> <s>For ſuppoſing, on the contrary, that it were poſſible for a Solid <lb></lb>more light than the Liquid, being demitted in the Liquid to ſub<lb></lb>merge totally in the ſame, that is, ſo as that no part thereof re<lb></lb>maineth above, or without the ſaid Liquid, (evermore ſuppoſing <lb></lb>that the Liquid be ſo conſtituted as that it be not moved,) let us <lb></lb>imagine any Plane produced thorow the Center of the Earth, tho<lb></lb>row the Liquid, and thorow that Solid Body: and that the Surface <lb></lb>of the Liquid is cut by this Plane according to the Circumference <lb></lb>A <emph type="italics"></emph>B<emph.end type="italics"></emph.end> G, and the Solid <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ody according to the Figure R; and let the <lb></lb>Center of the Earth be K. </s> <s>And let there be imagined a Pyramid <lb></lb><figure id="id.040.01.1036.1.jpg" xlink:href="040/01/1036/1.jpg"></figure><lb></lb>that compriſeth the Figure <lb></lb>R, as was done in the pre. <lb></lb></s> <s>cedent, that hath its Ver<lb></lb>tex in the Point K, and let <lb></lb>the Superficies of that <lb></lb>Pyramid be cut by the <lb></lb>Superficies of the Plane <lb></lb>A <emph type="italics"></emph>B<emph.end type="italics"></emph.end> G, according to A K <lb></lb>and K <emph type="italics"></emph>B<emph.end type="italics"></emph.end>. </s> <s>And let us ima<lb></lb>gine another Pyramid equal and like to this, and let its Superficies <lb></lb>be cut by the Superficies A <emph type="italics"></emph>B<emph.end type="italics"></emph.end> G according to K <emph type="italics"></emph>B<emph.end type="italics"></emph.end> and K <emph type="italics"></emph>G<emph.end type="italics"></emph.end>; and let <lb></lb>the Superficies of another Sphære be deſcribed in the Liquid, upon <lb></lb>the Center K, and beneath the Solid R; and let that be cut by the <lb></lb>ſame Plane according to <emph type="italics"></emph>X<emph.end type="italics"></emph.end> O P. And, laſtly, let us ſuppoſe ano<lb></lb>ther Solid taken ^{*} from the Liquid, in this ſecond Pyramid, which <lb></lb><arrow.to.target n="marg1133"></arrow.to.target><lb></lb>let be H, equal to the Solid R. </s> <s>Now the parts of the Liquid, name<lb></lb>ly, that which is under the Spherical Superficies that proceeds ac<lb></lb>cording to the Superficies or Circumference <emph type="italics"></emph>X<emph.end type="italics"></emph.end> O, in the firſt Py<lb></lb>ramid, and that which is under the Spherical Superficies that pro<lb></lb>ceeds according to the Circumference O P, in the ſecond Pyramid, <lb></lb>are equijacent, and contiguous, but are not preſſed equally; for <pb xlink:href="040/01/1037.jpg" pagenum="342"></pb>that of the firſt Pyramid is preſſed by the Solid R, and by the Liquid <lb></lb>which that containeth, that is, that which is in the place of the Py<lb></lb>ramid according to A B O X: but that part which, in the other Py<lb></lb>ramid, is preſſed by the Solid H, ſuppoſed to be of the ſame Li<lb></lb>quid, and by the Liquid which that containeth, that is, that which <lb></lb>is in the place of the ſaid Pyramid according to P O B G: and the <lb></lb>Gravity of the Solid R is leſs than the Gravity of the Liquid <lb></lb>H, for that theſe two Magnitudes were ſuppoſed to be equal in <lb></lb>Maſs, and the Solid R was ſuppoſed to be lighter than the Liquid: <lb></lb>and the Maſſes of the two Pyramids of Liquor that containeth theſe <lb></lb><arrow.to.target n="marg1134"></arrow.to.target><lb></lb>two Solids R and H are equal ^{*} by what was preſuppoſed: There<lb></lb>fore the part of the Liquid that is under the Superficies that pro<lb></lb>ceeds according to the Circumference O P is more preſſed; and, <lb></lb>therefore, by the <emph type="italics"></emph>Suppoſition,<emph.end type="italics"></emph.end> it ſhall repulſe that part which is leſs <lb></lb>preſſed, whereby the ſaid Liquid will not be ſetled: But it was be<lb></lb>fore ſuppoſed that it was ſetled: Therefore that Solid R ſhall not <lb></lb>totally ſubmerge, but ſome part thereof will remain without the <lb></lb>Liquid, that is, above its Surface, Which was the <emph type="italics"></emph>Propoſition.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1133"></margin.target>* That is a Maſs of <lb></lb>the Liquid.</s></p><p type="margin"> <s><margin.target id="marg1134"></margin.target>* For that the Py<lb></lb>ramids were ſuppo<lb></lb>ſed equal.</s></p><p type="main"> <s>RIC. </s> <s>I have very well underſtood you, therefore let us come to the fifth <emph type="italics"></emph>Pro<lb></lb>poſition,<emph.end type="italics"></emph.end> which, as you know, doth thus ſpeak.</s></p><p type="head"> <s>PROP. V. THEOR. V.</s></p><p type="main"> <s><emph type="italics"></emph>Solid Magnitudes that are lighter than the Liquid, <lb></lb>being demitted in the (ſetled) Liquid, will ſo far <lb></lb>ſubmerge, till that a Maſs of Liquor, equal to the <lb></lb>Part ſubmerged, doth in Gravity equalize the <lb></lb>whole Magnitude.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>NIC. </s> <s>It having, in the precedent, been demonſtrared that Solids lighter than <lb></lb>the Liquid, being demitted in the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid, alwaies a part of them remains <lb></lb>without the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid, that is above its Surface; In this fifth <emph type="italics"></emph>Propoſition<emph.end type="italics"></emph.end> it is <lb></lb>aſſerted, that ſo much of ſuch a Solid ſhall ſubmerge, as that a Maſs of the <lb></lb><emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid equal to the part ſubmerged, ſhall have equal Gravity with the whole <lb></lb>Solid.</s></p><p type="main"> <s>And to demonſtrate this, let us aſſume all the ſame Schemes <lb></lb>as before, in <emph type="italics"></emph>Propoſition<emph.end type="italics"></emph.end> 3. and likewiſe let the Liquid be ſet<lb></lb>led, and let the Solid E Z H T be lighter than the Liquid. <lb></lb></s> <s>Now if the ſaid Liquid be ſetled, the parts of it that are equija<lb></lb>cent are equally preſſed: Therefore the Liquid that is beneath <pb xlink:href="040/01/1038.jpg" pagenum="343"></pb>the Superficies that proceed according to the Circumferences X O <lb></lb>and P O are equally preſſed; whereby the Gravity preſſed is equal. <lb></lb><figure id="id.040.01.1038.1.jpg" xlink:href="040/01/1038/1.jpg"></figure><lb></lb>But the Gravity of the <lb></lb>Liquid which is in the <lb></lb><arrow.to.target n="marg1135"></arrow.to.target><lb></lb>firſt Pyramid ^{*} without <lb></lb>the Solid B H T G, is <lb></lb>equal to the Gravity of <lb></lb>the Liquid which is in <lb></lb>the other Pyramid with<lb></lb>out the Liquid R S C Y: <lb></lb>It is manifeſt, therefore, <lb></lb>that the Gravity of the Solid E Z H T, is equal to the Gravity of <lb></lb>the Liquid R S C Y: Therefore it is manifeſt that a Maſs of Liquor <lb></lb>equal in Maſs to the part of the Solid ſubmerged is equal in Gra<lb></lb>vity to the whole Solid.</s></p><p type="margin"> <s><margin.target id="marg1135"></margin.target>* <emph type="italics"></emph>Without, i.e.<emph.end type="italics"></emph.end> that <lb></lb>being deducted.</s></p><p type="main"> <s>RIC. </s> <s>This was a pretty Demonſtration, and becauſe I very well underſtand <lb></lb>it, let us loſe no time, but proceed to the ſixth <emph type="italics"></emph>Propoſition,<emph.end type="italics"></emph.end> ſpeaking thus.</s></p><p type="head"> <s>PROP. VI. THEOR. VI.</s></p><p type="main"> <s><emph type="italics"></emph>Solid Magnitudes lighter than the Liquid being thruſt <lb></lb>into the Liquid, are repulſed upwards with a Force <lb></lb>as great as is the exceſs of the Gravity of a Maſs <lb></lb>of Liquor equal to the Magnitude above the Gra<lb></lb>vity of the ſaid Magnitude.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>NIC. </s> <s>This ſixth <emph type="italics"></emph>Propoſition<emph.end type="italics"></emph.end> ſaith, that the Solids lighter than the Liquid <lb></lb>demitted, thruſt, or trodden by Force underneath the Liquids Sur<lb></lb>face, are returned or driven upwards with ſo much Force, by <lb></lb>how much a quantity of the Liquid equal to the. </s> <s>Solid ſhall <lb></lb>exceed the ſaid Solid in Gravity.</s></p><p type="main"> <s>And to delucidate this <emph type="italics"></emph>Propoſition,<emph.end type="italics"></emph.end> let the Solid A be lighter <lb></lb>than the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid, and let us ſuppoſe that the Gravity of the ſaid <lb></lb>Solid A is B: and let the Gravity of a <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid, equal in Maſs to A, <lb></lb>be B G. </s> <s>I ſay, that the Solid A depreſſed or demitted with Force <lb></lb>into the ſaid <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid, ſhall be returned and repulſed upwards with <lb></lb>a Force equal to the Gravity G. </s> <s>And to demonſtrate this <emph type="italics"></emph>Propo<lb></lb>ſition,<emph.end type="italics"></emph.end> take the Solid D, equal in Gravity to the ſaid G. </s> <s>Now <lb></lb>the Solid compounded of the two Solids A and D will be lighter <lb></lb>than the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid: for the Gravity of the Solid compounded of <lb></lb>them both is BG, and the Gravity of as much Liquor as equal<lb></lb>leth in greatneſs the Solid A, is greater than the ſaid Gravity BG, <pb xlink:href="040/01/1039.jpg" pagenum="344"></pb>for that B G is the Gravity of the Liquid equal in Maſs unto it: <lb></lb>Therefore the Solid compounded of thoſe two Solids A and D <lb></lb>being dimerged, it ſhall, by the precedent, ſo much of it ſubmerge, <lb></lb>as that a quantity of the Liquid equal to the ſaid ſubmerged part <lb></lb>ſhall have equal Gravity with the ſaid compounded Solid. </s> <s>And <lb></lb><figure id="id.040.01.1039.1.jpg" xlink:href="040/01/1039/1.jpg"></figure><lb></lb>for an example of that <emph type="italics"></emph>Propoſition<emph.end type="italics"></emph.end> let the Su<lb></lb>perficies of any Liquid be that which pro<lb></lb>ceedeth according to the Circumference <lb></lb>A B G D: Becauſe now a Maſs or quantity <lb></lb>of Liquor as big as the Maſs A hath equal <lb></lb>Gravity with the whole compounded Solid <lb></lb>A D: It is manifeſt that the ſubmerged part <lb></lb>thereof ſhall be the Maſs A: and the remain<lb></lb>der, namely, the part D, ſhall be wholly a<lb></lb>top, that is, above the Surface of the Liquid. <lb></lb></s> <s>It is therefore evident, that the part A hath ſo much virtue or <lb></lb>Force to return upwards, that is, to riſe from below above the Li<lb></lb>quid, as that which is upon it, to wit, the part D, hath to preſs it <lb></lb>downwards, for that neither part is repulſed by the other: But D <lb></lb>preſſeth downwards with a Gravity equal to G, it having been ſup<lb></lb>poſed that the Gravity of that part D was equal to G: Therefore <lb></lb>that is manifeſt which was to be demonſtrated.</s></p><p type="main"> <s>RIC. </s> <s>This was a fine Demonſtration, and from this I perceive that you colle<lb></lb>cted your <emph type="italics"></emph>Induſtrious Invention<emph.end type="italics"></emph.end>; and eſpecially that part of it which you inſert in <lb></lb>the firſt Book for the recovering of a Ship ſunk: and, indeed, I have many Que<lb></lb>ſtions to ask you about that, but I will not now interrupt the Diſcourſe in hand, but <lb></lb>deſire that we may go on to the ſeventh <emph type="italics"></emph>Propoſition,<emph.end type="italics"></emph.end> the purport whereof is this.</s></p><p type="head"> <s>PROP. VII. THEOR. VII.</s></p><p type="main"> <s><emph type="italics"></emph>Solid Magnitudes beavier than the Liquid, being de<lb></lb>mitted into the [ſetled] Liquid, are boren down<lb></lb>wards as far as they can deſcend: and ſhall be lighter <lb></lb>in the Liquid by the Gravity of a Liquid Maſs of <lb></lb>the ſame bigneſs with the Solid Magnitude.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>NIC. </s> <s>This ſeventh <emph type="italics"></emph>Propoſition<emph.end type="italics"></emph.end> hath two parts to be demonſtrated.</s></p><p type="main"> <s>The firſt is, That all Solids heavier than the Liquid, being demit<lb></lb>ted into the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid, are boren by their Gravities downwards as far <lb></lb>as they can deſcend, that is untill they arrive at the Bottom. </s> <s>Which <lb></lb>firſt part is manifeſt, becauſe the Parts of the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid, which ſtill lie <lb></lb>under that Solid, are more preſſed than the others equijacent, <lb></lb>becauſe that that Solid is ſuppoſed more grave than the Liquid. <pb xlink:href="040/01/1040.jpg" pagenum="345"></pb>But now that that Solid is lighter in the Liquid than out of it, as <lb></lb>is affirmed in the ſecond part, ſhall be demonſtrated in this man<lb></lb>ner. </s> <s>Take a Solid, as ſuppoſe A, that is more grave than the Li<lb></lb>quid, and ſuppoſe the Gravity of that ſame Solid A to be BG. <lb></lb></s> <s>And of a Maſs of <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquor of the ſame bigneſs with the Solid A, ſup<lb></lb>poſe the Gravity to be B: It is to be demonſtrated that the Solid <lb></lb>A, immerged in the Liquid, ſhall have a Gravity equal to G. </s> <s>And <lb></lb>to demonſtrate this, let us imagine another Solid, as ſuppoſe D, <lb></lb>more light than the Liquid, but of ſuch a quality as that its Gravi<lb></lb>ty is equal to B: and let this D be of ſuch a Magnitude, that a <lb></lb>Maſs of <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquor equal to it hath its Gravity equal to the Gravity <lb></lb>B G. </s> <s>Now theſe two Solids D and A being compounded toge<lb></lb>ther, all that Solid compounded of theſe two ſhall be equally <lb></lb>Grave with the Water: becauſe the Gravity of theſe two Solids <lb></lb>together ſhall be equal to theſe two Gravities, that is, to B G, and <lb></lb><figure id="id.040.01.1040.1.jpg" xlink:href="040/01/1040/1.jpg"></figure><lb></lb>to B; and the Gravity of a Liquid that hath its <lb></lb>Maſs equal to theſe two Solids A and D, ſhall be <lb></lb>equal to theſe two Gravities B G and B. <emph type="italics"></emph>L<emph.end type="italics"></emph.end>et <lb></lb>theſe two Solids, therefore, be put in the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid, <lb></lb><arrow.to.target n="marg1136"></arrow.to.target><lb></lb>and they ſhall ^{*} remain in the Surface of that <emph type="italics"></emph>L<emph.end type="italics"></emph.end>i<lb></lb>quid, (that is, they ſhall not be drawn or driven <lb></lb>upwards, nor yet downwards:) For if the Solid <lb></lb>A be more grave than the Liquid, it ſhall be <lb></lb>drawn or born by its Gravity downwards to<lb></lb>wards the Bottom, with as much Force as by the Solid D it is thruſt <lb></lb>upwards: And becauſe the Solid D is lighter than the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid, it <lb></lb>ſhall raiſe it upward with a Force as great as the Gravity G: Be<lb></lb>cauſe it hath been demonſtrated, in the ſixth <emph type="italics"></emph>Propoſition,<emph.end type="italics"></emph.end> That So<lb></lb>lid Magnitudes that are lighter than the Water, being demitted in <lb></lb>the ſame, are repulſed or driven upwards with a Force ſo much the <lb></lb>greater by how much a <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid of equal Maſs with the Solid is more <lb></lb>Grave than the ſaid Solid: But the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid which is equal in Maſs <lb></lb>with the Solid D, is more grave than the ſaid Solid D, by the Gra<lb></lb>vity G: Therefore it is manifeſt, that the Solid A is preſſed or <lb></lb>born downwards towards the Centre of the World, with a Force <lb></lb>as great as the Gravity G: Which was to be demonſtrated.</s></p><p type="margin"> <s><margin.target id="marg1136"></margin.target>* Or, according to <lb></lb><emph type="italics"></emph>Commandine,<emph.end type="italics"></emph.end> ſhall <lb></lb>be equall in Gravi<lb></lb>ty to the Liquid, <lb></lb>neither moving up<lb></lb>wards or down<lb></lb>wards.</s></p><p type="main"> <s>RIC. </s> <s>This hath been an ingenuous Demonſtration; and in regard I do ſuffici<lb></lb>ently underſtand it, that we may loſe no time, we will proceed to the ſecond <emph type="italics"></emph>Suppo<lb></lb>ſition,<emph.end type="italics"></emph.end> which, as I need not tell you, ſpeaks thus.</s></p> <pb xlink:href="040/01/1041.jpg" pagenum="346"></pb><p type="head"> <s>SVPPOSITION II.</s></p><p type="main"> <s><emph type="italics"></emph>It is ſuppoſed that thoſe Solids which are moved up<lb></lb>wards, do all aſcend according to the Perpendicular <lb></lb>which is produced thorow their Centre of Gravity.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>COMMANDINE.</s></p><p type="main"> <s><emph type="italics"></emph>And thoſe which are moved downwards, deſcend, likewiſe, according to the Perpendicular <lb></lb>that is produced thorow their Centre of Gravity, which he pretermitted either as known, <lb></lb>or as to be collected from what went before.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>NIC. </s> <s>For underſtanding of this ſecond <emph type="italics"></emph>Suppoſition,<emph.end type="italics"></emph.end> it is requiſite to take notice <lb></lb>that every Solid that is lighter than the Liquid being by violence, or by ſome other <lb></lb>occaſion, ſubmerged in the Liquid, and then left at liberty, it ſhall, by that which <lb></lb>hath been proved in the ſixth <emph type="italics"></emph>Propoſition,<emph.end type="italics"></emph.end> be thruſt or born up wards by the Liquid, <lb></lb>and that impulſe or thruſting is ſuppoſed to be directly according to the Perpendi<lb></lb>cular that is produced thorow the Centre of Gravity of that Solid; which Per<lb></lb>pendicular, if you well remember, is that which is drawn in the Imagination <lb></lb>from the Centre of the World, or of the Earth, unto the Centre of Gravity of <lb></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 ſheweth in that Book, intituled <emph type="italics"></emph>De Centris Gravium, vel de Æqui<lb></lb>ponderantibus<emph.end type="italics"></emph.end>; and therefore repair thither and you ſhall be ſatisfied, for to declare <lb></lb>it to you in this place would cauſe very great confuſion.</s></p><p type="main"> <s>RIC. </s> <s>I underſtand you: ſome other time we will talk of this, becauſe I have <lb></lb>a mind at preſent to proceed to the laſt <emph type="italics"></emph>Propoſition,<emph.end type="italics"></emph.end> the Expoſition of which ſeemeth <lb></lb>to me very confuſed, and, as I conceive, the Author hath not therein ſhewn all <lb></lb>the Subject of that <emph type="italics"></emph>Propoſition<emph.end type="italics"></emph.end> in general, but only a part: which Propoſition <lb></lb>ſpeaketh, as you know, in this form.</s></p><p type="head"> <s>PROP. VIII. THEOR. VIII.<lb></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"></emph>If any Solid Magnitude, lighter than the Liquid, that <lb></lb>hath the Figure of a Portion of a Sphære, ſhall be<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1138"></arrow.to.target><lb></lb><emph type="italics"></emph>demitted into the Liquid in ſuch a manner as that <lb></lb>the Baſe of the Portion touch not the Liquid, the <lb></lb>Figure ſhall ſtand erectly, ſo, as that the Axis of <lb></lb>the ſaid Portion ſhall be according to the Perpen<lb></lb>dicular. </s> <s>And if the Figure ſhall be inclined to any <lb></lb>ſide, ſo, as that the Baſe of the Portion touch the <lb></lb>Liquid, it ſhall not continue ſo inclined as it was de<lb></lb>mitted, but ſhall return to its uprightneſs.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/1042.jpg" pagenum="347"></pb><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"></emph>Propoſition,<emph.end type="italics"></emph.end> let a Solid Magnitude <lb></lb>that hath the Figure of a portion of a Sphære, as hath been ſaid, <lb></lb>be imagined to be de<lb></lb><figure id="id.040.01.1042.1.jpg" xlink:href="040/01/1042/1.jpg"></figure><lb></lb>mitted into the Liquid; and <lb></lb>alſo, let a Plain be ſuppoſed <lb></lb>to be produced thorow the <lb></lb>Axis of that portion, and <lb></lb>thorow the Center of the <lb></lb>Earth: and let the Section <lb></lb>of the Surface of the Liquid <lb></lb>be the Circumference A B <lb></lb>C D, and of the Figure, the <lb></lb>Circumference E F H, & let <lb></lb>E H be a right line, and F T <lb></lb>the Axis of the Portion. </s> <s>If now <lb></lb>it were poſſible, for ſatisfact<lb></lb>ion of the Adverſary, Let <lb></lb>it be ſuppoſed that the ſaid Axis were not according to the <emph type="italics"></emph>(a)<emph.end type="italics"></emph.end> Per<lb></lb><arrow.to.target n="marg1139"></arrow.to.target><lb></lb>pendicular; we are then to demonſtrate, that the Figure will not <lb></lb>continue as it was conſtituted by the Adverſary, but that it will re<lb></lb>turn, as hath been ſaid, unto its former poſition, that is, that the <lb></lb>Axis F T ſhall be according to the Perpendicular. </s> <s>It is manifeſt, by <lb></lb>the <emph type="italics"></emph>Corollary<emph.end type="italics"></emph.end> of the 1. of 3. <emph type="italics"></emph>Euclide,<emph.end type="italics"></emph.end> that the Center of the Sphære <lb></lb>is in the Line F T, foraſmuch as that is the Axis of that Figure. <lb></lb></s> <s>And in regard that the Por<lb></lb><figure id="id.040.01.1042.2.jpg" xlink:href="040/01/1042/2.jpg"></figure><lb></lb>tion of a Sphære, may be <lb></lb>greater or leſſer than an He<lb></lb>miſphære, and may alſo be <lb></lb>an Hemiſphære, let the Cen<lb></lb>tre of the Sphære, in the He<lb></lb>miſphære, be the Point T, <lb></lb>and in the leſſer Portion the <lb></lb>Point P, and in the greater, <lb></lb>the Point K, and let the Cen<lb></lb>tre of the Earth be the Point <lb></lb>L. </s> <s>And ſpeaking, firſt, of <lb></lb>that greater Portion which <lb></lb>hath its Baſe out of, or a<lb></lb>bove, the Liquid, thorew the Points K and L, draw the Line KL <lb></lb>cutting the Circumference E F H in the Point N, Now, becauſe <lb></lb><arrow.to.target n="marg1140"></arrow.to.target><lb></lb>every Portion of a Sphære, hath its Axis in the Line, that from the <lb></lb>Centre of the Sphære is drawn perpendicular unto its Baſe, and hath <lb></lb>its Centre of Gravity in the Axis; therefore that Portion of the Fi<lb></lb>gure which is within the Liquid, which is compounded of two Por <pb xlink:href="040/01/1043.jpg" pagenum="348"></pb>tions of a Sphære, ſhall have its Axis in the Perpendicular, that is <lb></lb>drawn through the point K; and its Centre of Gravity, for the ſame <lb></lb>reaſon, ſhall be in the Line N K: let us ſuppoſe it to be the Point R: <lb></lb><arrow.to.target n="marg1141"></arrow.to.target><lb></lb>But the Centre of Gravity of the whole Portion is in the Line F T, <lb></lb>betwixt the Point R and <lb></lb><figure id="id.040.01.1043.1.jpg" xlink:href="040/01/1043/1.jpg"></figure><lb></lb>the Point F; let us ſuppoſe <lb></lb>it to be the Point <emph type="italics"></emph>X<emph.end type="italics"></emph.end>: The re<lb></lb>mainder, therefore, of that <lb></lb><arrow.to.target n="marg1142"></arrow.to.target><lb></lb>Figure elivated above the <lb></lb>Surface of the Liquid, hath <lb></lb>its Centre of Gravity in <lb></lb>the Line R X produced or <lb></lb>continued right out in the <lb></lb>Part towards X, taken ſo, <lb></lb>that the part prolonged may <lb></lb>have the ſame proportion to <lb></lb>X R, that the Gravity of <lb></lb>that Portion that is demer<lb></lb>ged in the Liquid hath to <lb></lb>the Gravity of that Figure which is above the Liquid; let us ſuppoſe <lb></lb><arrow.to.target n="marg1143"></arrow.to.target><lb></lb>that ^{*} that Centre of the ſaid Figure be the Point S: and thorow that <lb></lb><arrow.to.target n="marg1144"></arrow.to.target><lb></lb>ſame Centre S draw the Perpendicular L S. </s> <s>Now the Gravity of the Fi<lb></lb>gure that is above the Liquid ſhall preſſe from above downwards ac<lb></lb>cording to the Perpendicular S L; & the Gravity of the Portion that <lb></lb>is ſubmerged in the Liquid, ſhall preſſe from below upwards, accor<lb></lb>ding to the Perpendicular R L. </s> <s>Therefore that Figure will not conti<lb></lb>nue according to our Adverſaries Propoſall, but thoſe parts of the <lb></lb>ſaid Figure which are towards E, ſhall be born or drawn downwards, <lb></lb>& thoſe which are towards H ſhall be born or driven upwards, and <lb></lb>this ſhall be ſo long untill that the Axis F T comes to be according <lb></lb>to the Perpendicular.</s></p><p type="margin"> <s><margin.target id="marg1139"></margin.target>(a) <emph type="italics"></emph>Perpendicular <lb></lb>is taken kere, as <lb></lb>in all other places, <lb></lb>by this Author for <lb></lb>the Line K L <lb></lb>drawn thorow the <lb></lb>Centre and Cir<lb></lb>cumference of the <lb></lb>Earth.<emph.end type="italics"></emph.end></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"></emph>i. </s> <s>e,<emph.end type="italics"></emph.end> The Center <lb></lb>of Gravity.</s></p><p type="margin"> <s><margin.target id="marg1144"></margin.target>F</s></p><p type="main"> <s>And this ſame Demonſtration is in the ſame manner verified in <lb></lb>the other <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortions. </s> <s>As, firſt, in the Hæmiſphere that lieth with its <lb></lb>whole Baſe above or without the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid, the Centre of the Sphære <lb></lb>hath been ſuppoſed to be the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>oint T; and therefore, imagining T <lb></lb>to be in the place, in which, in the other above mentioned, the <lb></lb><emph type="italics"></emph>P<emph.end type="italics"></emph.end>oint R was, arguing in all things elſe as you did in that, you ſhall <lb></lb>find that the Figure which is above the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid ſhall preſs from <lb></lb>above downwards according to the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendicular S <emph type="italics"></emph>L<emph.end type="italics"></emph.end>; and the <lb></lb><emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion that is ſubmerged in the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid ſhall preſs from below up<lb></lb>wards according to the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendicular R <emph type="italics"></emph>L.<emph.end type="italics"></emph.end> And therefore it ſhall <lb></lb>follow, as in the other, namely, that the parts of the whole Figure <lb></lb>which are towards E, ſhall be born or preſſed downwards, and thoſe <lb></lb><arrow.to.target n="marg1145"></arrow.to.target><lb></lb>that are towards H, ſhall be born or driven upwards: and this ſhall <lb></lb>be ſo long untill that the Axis F T come to ſtand ^{*} <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendicular <pb xlink:href="040/01/1044.jpg" pagenum="349"></pb>ly. </s> <s>The like ſhall alſo hold true in the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion of the Sphære <lb></lb>leſs than an Hemiſphere that lieth with its whole Baſe above the <lb></lb>Liquid.</s></p><p type="margin"> <s><margin.target id="marg1145"></margin.target>* Or according <lb></lb>to the Perpendi<lb></lb>cular.</s></p><p type="head"> <s>COMMANDINE.</s></p><p type="main"> <s><emph type="italics"></emph>The Demonſtration of this Propoſition is defaced by the Injury of Time, which we have re<lb></lb>ſtored, ſo far as by the Figures that remain, one may collect the Meaning of<emph.end type="italics"></emph.end> Archimedes, <lb></lb><emph type="italics"></emph>for we thought it not good to alter them: and what was wanting to their declaration and ex<lb></lb>planation we have ſupplyed in our Commentaries, as we have alſo determined to do in the ſe<lb></lb>cond Propoſition of the ſecond Book.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>If any Solid Magnitude lighter than the Liquid.] <emph type="italics"></emph>Theſe words, light-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1146"></arrow.to.target><lb></lb><emph type="italics"></emph>er than the Liquid, are added by us, and are not to be found in the Tranſiation; for of theſe <lb></lb>kind of Magnitudes doth<emph.end type="italics"></emph.end> Archimedes <emph type="italics"></emph>ſpeak in this Propoſition.<emph.end type="italics"></emph.end></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 ſuch a manner as that the <lb></lb><arrow.to.target n="marg1147"></arrow.to.target><lb></lb>Baſe of the Portion touch not the Liquid.] <emph type="italics"></emph>That is, ſhall be ſo demitted into <lb></lb>the Liquid as that the Baſe ſhall be upwards, and the<emph.end type="italics"></emph.end> Vertex <emph type="italics"></emph>downwards, which he oppoſeth <lb></lb>to that which he ſaith in the Propoſition following<emph.end type="italics"></emph.end>; Be demitted into the Liquid, ſo, as <lb></lb>that its Baſe be wholly within the Liquid; <emph type="italics"></emph>For theſe words ſignifie the Portion demit<lb></lb>ted the contrary way, as namely, with the<emph.end type="italics"></emph.end> Vertex <emph type="italics"></emph>upwards and the Baſe downwards. </s> <s>The <lb></lb>ſame manner of ſpeech is frequently uſed in the ſecond Book; which treateth of the Portions <lb></lb>of Rectangle Conoids.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1147"></margin.target>B</s></p><p type="main"> <s>Now becauſe every Portion of a Sphære hath its Axis in the Line <lb></lb><arrow.to.target n="marg1148"></arrow.to.target><lb></lb>that from the Center of the Sphære is drawn perpendicular to its <lb></lb>Baſe.] <emph type="italics"></emph>For draw a Line from B to C, and let K L cut the Circumference A B C D in the <lb></lb>Point G, and the Right Line B C in M<emph.end type="italics"></emph.end>: <lb></lb><figure id="id.040.01.1044.1.jpg" xlink:href="040/01/1044/1.jpg"></figure><lb></lb><emph type="italics"></emph>and becauſe the two Circles A B C D, and <lb></lb>E F H do cut one another in the Points <lb></lb>B and C, the Right Line that conjoyneth <lb></lb>their Centers, namely, K L, doth cut the <lb></lb>Line B C in two equall parts, and at <lb></lb>Right Angles; as in our Commentaries <lb></lb>upon<emph.end type="italics"></emph.end> Prolomeys <emph type="italics"></emph>Planiſphære we do <lb></lb>prove: But of the Portion of the Circle <lb></lb>B N C the Diameter is M N; and of the <lb></lb>Portion B G C the Diameter is M G;<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1149"></arrow.to.target><lb></lb><emph type="italics"></emph>for the<emph.end type="italics"></emph.end> (a) <emph type="italics"></emph>Right Lines which are drawn <lb></lb>on both ſides parallel to B C do make<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1150"></arrow.to.target><lb></lb><emph type="italics"></emph>Right Angles with N G; and<emph.end type="italics"></emph.end> (b) <emph type="italics"></emph>for <lb></lb>that cauſe are thereby cut in two equall <lb></lb>parts: Therefore the Axis of the Portion <lb></lb>of the Sphære B N C is N M; and the <lb></lb>Axis of the Portion B G C is M G: <lb></lb>from whence it followeth that the Axis of <lb></lb>the Portion demerged in the Liquid is <lb></lb>in the Line K L, namely N G. </s> <s>And ſince the Center of Gravity of any Portion of a Sphære is <lb></lb>in the Axis, as we have demonstrated in our Book<emph.end type="italics"></emph.end> De Centro Gravitatis Solidorum, <emph type="italics"></emph>the <lb></lb>Centre of Gravity of the Magnitude compounded of both the Portions B N C & B G C, that is, <lb></lb>of the Portion demerged in the Water, is in the Line N G that doth conjoyn the Centers of Gra<lb></lb>vity of thoſe Portions of Sphæres. </s> <s>For ſuppoſe, if poſſible, that it be out of the Line N G, as <lb></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> Becauſe <lb></lb>therefore from the Portion demerged in the Liquid the Portion of the Sphære B N C, not ha<lb></lb>ving the ſame Center of Gravity, is cut off, the Center of Gravity of the Remainder of the <lb></lb>Portion B G C ſhall, by the 8 of the firſt Book of<emph.end type="italics"></emph.end> Archimedes, De Centro Gravitatis <pb xlink:href="040/01/1045.jpg" pagenum="350"></pb>Planotum, <emph type="italics"></emph>be in the Line V Q prolonged: But that is impoſſible; for it is in the Axis <lb></lb>G: It followeth, therefore, that the Center of Gravity of the Portion demerged in <lb></lb>Liquid be in the Line N K: which we propounded to be proved.<emph.end type="italics"></emph.end></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"></emph>(a)<emph.end type="italics"></emph.end> By 29. of the <lb></lb>firſt of <emph type="italics"></emph>Encl.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1150"></margin.target><emph type="italics"></emph>(b)<emph.end type="italics"></emph.end> By 3. of the <lb></lb>third.</s></p><p type="main"> <s>But the Centre of Gravity of the whole Portion is in the Line <lb></lb><arrow.to.target n="marg1151"></arrow.to.target><lb></lb>T, betwixt the Point R and the Point F; let us ſuppoſe it to be<lb></lb>the Point X.] <emph type="italics"></emph>Let the Sphære becompleated, ſo as that there be added of that Portion<lb></lb>the Axis T Y, and the Center of Gravity Z. </s> <s>And becauſe that from the whole Sphære,<lb></lb>whoſe Centre of Gravity is K, as we have alſo demonſtrated in the (c) Book before named, the <lb></lb>is cut off the Portion E Y H, having the Centre of Gravity Z; the Centre of the remaind<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1152"></arrow.to.target><lb></lb><emph type="italics"></emph>of the Portion E F H ſhall be in the Line Z K prolonged: And therefore it muſt of neceſſity<lb></lb>fall betwixt K and F.<emph.end type="italics"></emph.end><lb></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"></emph>By 8 of the <lb></lb>firſt<emph.end type="italics"></emph.end> 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></lb>face of the Liquid, hath its Center of Gravity in the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine R X<lb></lb>prolonged.] <emph type="italics"></emph>By the ſame 8 of the firſt Book of<emph.end type="italics"></emph.end> Archimedes, de Centro Gravita<lb></lb>tis Planorum.</s></p><p type="main"> <s>Now the Gravity of the Figure that is above the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid ſhall<arrow.to.target n="marg1154"></arrow.to.target><lb></lb>preſs from above downwards according to S L; and the Gravit <lb></lb>of the Portion that is ſubmerged in the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid ſhall preſs from be <lb></lb>low upwards, according to the Perpendicular R L.] <emph type="italics"></emph>By the ſecond Sup<lb></lb>poſition of this. </s> <s>For the Magnitude that is demerged in the Liquid is moved upwards with as<lb></lb>much Force along R L, as that which is above the Liquid is moved downwards along S L; as<lb></lb>may be ſhewn by Propoſition 6. of this. </s> <s>And becauſe they are moved along ſeverall other Lines,<lb></lb>neither cauſeth the others being leſs moved; the which it continually doth when the Portion<lb></lb>is ſet according to the Perpendicular: For then the Centers of Gravity of both the Magnitudes<lb></lb>do concur in one and the ſame Perpendicular, namely, in the Axis of the Portion: and look<lb></lb>with what force or<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>that which is in the Lipuid tendeth upwards, and with the like<lb></lb>doth that which is above or without the Liquid tend downwards along the ſame Line: And<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1155"></arrow.to.target><lb></lb><emph type="italics"></emph>therefore, in regard that the one doth not ^{*} exceed the other, the Portion ſhall no longer move <lb></lb>but ſhall ſtay and reſt allwayes in one and the ſame Poſition, unleſs ſome extrinſick Cauſe<lb></lb>chance to intervene.<emph.end type="italics"></emph.end></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"></emph>Or overcome.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROP. IX. THEOR. IX.<lb></lb><arrow.to.target n="marg1156"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1156"></margin.target>* In ſome Greek <lb></lb>Coppies this is no <lb></lb>diſtinct Propoſi<lb></lb>tion, but all <lb></lb>Commentators, <lb></lb>do divide it <lb></lb>from the Prece<lb></lb>dent, as having a <lb></lb>diſtinct demon<lb></lb>ſtration in the <lb></lb>Originall.</s></p><p type="main"> <s>^{*} <emph type="italics"></emph>But if the Figure, lighter than the Liquid, be demit<lb></lb>ted into the Liquid, ſo, as that its Baſe be wholly<lb></lb>within the ſaid Liquid, it ſhall continue in ſuch <lb></lb>manner erect, as that its Axis ſhall ſtand according <lb></lb>to the Perpendicular.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>For ſuppoſe, ſuch a Magnitude as that aforenamed to be de <lb></lb>mitted into the Liquid; and imagine a Plane to be produced<lb></lb>thorow the Axis of the Portion, and thorow the Center of the <lb></lb>Earth: And let the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>ection of the Surface of the Liquid, be the Cir<lb></lb>cumference A B C D, and of the Figure the Circumference E F <emph type="italics"></emph>H<emph.end type="italics"></emph.end><lb></lb>And let E H be a Right Line, and F T the Axis of the Portion. </s> <s>If<lb></lb>now it were poſſible, for ſatisfaction of the Adverſary, let it be <lb></lb>ſuppoſed that the ſaid Axis were not according to the Perpendicu<lb></lb>lar: we are now to demonſtrate that the Figure will not ſo conti <pb xlink:href="040/01/1046.jpg" pagenum="351"></pb>nue, but will return to be according to the <lb></lb><figure id="id.040.01.1046.1.jpg" xlink:href="040/01/1046/1.jpg"></figure><lb></lb>Perpendieular. </s> <s>It is manifeſt that the Gen<lb></lb>tre of the Sphære is in the Line F T. </s> <s>And <lb></lb>again, foraſmuch as the Portion of a Sphære <lb></lb>may be greater or leſſer than an Hemiſ<lb></lb>phære, and may alſo be an Hemiſphære, let <lb></lb>the Centre of the Sphære in the Hemiſ<lb></lb>phære be the Point T, & in the leſſer Por<lb></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></lb>Point R. </s> <s>And ſpeaking firſt of that greater <lb></lb>Portion which hath its Baſe within the <lb></lb>Liquid, thorow R and L, the Earths Cen<lb></lb><figure id="id.040.01.1046.2.jpg" xlink:href="040/01/1046/2.jpg"></figure><lb></lb>tre, draw the line RL. </s> <s>The Portion that is <lb></lb>above the Liquid, hath its Axis in the Per<lb></lb>pendicular paſſing thorow R; and by <lb></lb>what hath been ſaid before, its Centre of <lb></lb>Gravity ſhall be in the Line N R; let it <lb></lb>be the Point R: But the Centre of Gra<lb></lb>vity of the whole Portion is in the line F <lb></lb>T, betwixt R and F; let it be X: The re<lb></lb>mainder therefore of that Figure, which is <lb></lb>within the Liquid ſhall have its Centre in <lb></lb>the Right Line R <emph type="italics"></emph>X<emph.end type="italics"></emph.end> prolonged in the part <lb></lb><figure id="id.040.01.1046.3.jpg" xlink:href="040/01/1046/3.jpg"></figure><lb></lb>towards <emph type="italics"></emph>X,<emph.end type="italics"></emph.end> taken ſo, that the part pro<lb></lb>longed may have the ſame Proportion to <lb></lb>X R, that the Gravity of the Portion that <lb></lb>is above the Liquid hath to the Gravity <lb></lb>of the Figure that is within the Liquid. <lb></lb></s> <s>Let O be the Centre of that ſame Figure: <lb></lb>and thorow O draw the Perpendicular L <lb></lb>O. </s> <s>Now the Gravity of the Portion that <lb></lb>is above the Liquid ſhall preſs according <lb></lb>to the Right Line R L downwards; and <lb></lb>the Gravity of the Figure that is in the <lb></lb>Liquid according to the Right Line O L upwards: There the Figure <lb></lb>ſhall not continue; but the parts of it towards H ſhall move down<lb></lb>wards, and thoſe towards E upwards: & <lb></lb><figure id="id.040.01.1046.4.jpg" xlink:href="040/01/1046/4.jpg"></figure><lb></lb>this ſhall ever be, ſo long as F T is accord<lb></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></lb><arrow.to.target n="marg1158"></arrow.to.target><lb></lb>hath its Axis in the Perpendicular paſſing <lb></lb>thorow K.] <emph type="italics"></emph>For draw B C cutting the Line N K in <lb></lb>M; and let N K out the Circumference<emph.end type="italics"></emph.end> A B <emph type="italics"></emph>C D in G. </s> <s>In <lb></lb>the ſame manner as before me will demonſtrate, that the Axis<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1047.jpg" pagenum="352"></pb><emph type="italics"></emph>of the Portion of the Sphære is N M; and of the Portion B G C the Axis is G M: Wherefore <lb></lb>the Centre of Gravity of them both ſhall be in the Line N M: And becauſe that from the Por<lb></lb>tion B N C the Portion B G C, not having the ſame Centre of Gravity, is cut off, the Centre <lb></lb>of Gravity of the remainder of the Magnitude that is above the Surface of the Liquid ſhall be <lb></lb>in the Line N K; namely, in the Line which conjoyneth the Centres of Gravity of the ſaid <lb></lb>Portions by the foreſaid 8 of<emph.end type="italics"></emph.end> 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 ſome of theſe Figures C is put for X, and ſo it was in <lb></lb>the Greek Copy that I followed.</s></p><p type="main"> <s>RIC. </s> <s>This Demoſtration is very difficult, to my thinking; but I believe that <lb></lb>it is becauſe I have not in memory the Propoſitions of that Book entituled <emph type="italics"></emph>De Cen<lb></lb>tris Gravium.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>NIC. </s> <s>It is ſo.</s></p><p type="main"> <s>RIC. </s> <s>We will take a more convenient time to diſcourſe of that, and now return <lb></lb><arrow.to.target n="marg1159"></arrow.to.target><lb></lb>to ſpeak of the two laſt Propoſitions. </s> <s>And I ſay that the Figures incerted in the <lb></lb>demonſtration would in my opinion, have been better and more intelligble unto <lb></lb>me, drawing the Axis according to its proper Poſition; that is in the half Arch of <lb></lb>theſe Figures, and then, to ſecond the Objection of the Adverſary, to ſuppoſe <lb></lb>that the ſaid Figures ſtood ſomewhat Obliquely, to the end that the ſaid Axis, if it <lb></lb>were poſſible, did not ſtand according to the Perpendicular ſo often mentioned, <lb></lb>which doing, the Propoſition would be proved in the ſame manner as before: <lb></lb>and this way would be more naturall and clear.<lb></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 becauſe thus they were in the Greek Copy, <lb></lb>I thought not fit to alter them, although unto the better.</s></p><p type="main"> <s>RIC. Companion, you have thorowly ſatisfied me in all that in the beginning <lb></lb>of our Diſcourſe I asked of you, to morrow, God permitting, we will treat of <lb></lb>ſome other ingenious Novelties.</s></p><p type="head"> <s>THE TRANSLATOR.</s></p><p type="main"> <s>I ſay 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></lb>me, drawing the Axis Z T according to its proper Poſition, that <lb></lb>is in the half Arch of theſe Figures.] <emph type="italics"></emph>And in this conſideration I have followed <lb></lb>the Schemes of<emph.end type="italics"></emph.end> Commandine, <emph type="italics"></emph>who being the Reſtorer of the Demonſtrations of theſe two laſt <lb></lb>Propoſitions, hath well conſidered what<emph.end type="italics"></emph.end> Ricardo <emph type="italics"></emph>here propoſeth, and therefore hath drawn the <lb></lb>ſaid Axis (which in the Manuſcripts that he had by him is lettered F T, and not as in that of<emph.end type="italics"></emph.end><lb></lb>Tartaylia <emph type="italics"></emph>Z T,) according to that its proper Poſition.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1161"></margin.target>A</s></p><p type="main"> <s>But becauſe thus they were in the Greek Copy, I thought not <lb></lb><arrow.to.target n="marg1162"></arrow.to.target><lb></lb>fit to alter them although unto the better.] <emph type="italics"></emph>The Schemes of thoſe Manu-<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.1047.1.jpg" xlink:href="040/01/1047/1.jpg"></figure><lb></lb><emph type="italics"></emph>ſcripts that<emph.end type="italics"></emph.end> Tartaylia <emph type="italics"></emph>had ſeen were more imperfect then thoſe <lb></lb>in Commandines Copies; but for variety ſake, take here one <lb></lb>of<emph.end type="italics"></emph.end> Tartaylia, <emph type="italics"></emph>it being that of the Portion of a Sphære, equall <lb></lb>to an Hemiſphære, with its Axis oblique, and its Baſe dimitted <lb></lb>into the Liquid, and Lettered as in this Edition.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1162"></margin.target>B</s></p><p type="main"> <s><emph type="italics"></emph>Now Courteous Readers, I hope that you may, amidſt the <lb></lb>great Obſcurity of the Originall in the Demonſtrations of theſe <lb></lb>two laſt Propoſitions, be able from the joynt light of theſe two Famous Commentators of our <lb></lb>more famous Author, to diſcern the truth of the Doctrine affirmed, namely, That Solids of the <lb></lb>Figure of Portions of Sphæres demitted into the Liquid with their Baſes upwards ſhall ſtand <lb></lb>erectly, that is, with their Axis according to the Perpendicular drawn from the Centre of the <lb></lb>Earth unto its Circumference: And that if the ſaid Portions be demitted with their Baſes <lb></lb>oblique and touching the Liquid in one Point, they ſhall not rest in that Obliquity, but ſhall <lb></lb>return to Rectitude: And that laſtly, if theſe Portions be demitted with their Baſes downwards, <lb></lb>they ſhall continue erect with their Axis according to the Perpendicular aforeſaid: ſo that no <lb></lb>more remains to be done, but that weſet before you the 2 Books of this our Admirable Author.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/1048.jpg" pagenum="353"></pb><p type="head"> <s>ARCHIMEDES, <lb></lb>HIS TRACT <lb></lb><emph type="italics"></emph>DE <lb></lb>INSIDENTIBUS HUMIDO,<emph.end type="italics"></emph.end><lb></lb>OR, <lb></lb>Of the NATATION of BODIES Upon, or <lb></lb>Submerſion In the WATER, or other LIQUIDS.</s></p><p type="head"> <s><emph type="italics"></emph>BOOK<emph.end type="italics"></emph.end> II.</s></p><p type="head"> <s>PROP. I. THEOR. I.</s></p><p type="main"> <s><emph type="italics"></emph>If any Magnitude lighter than the Liquid be demitted <lb></lb>into the ſaid Liquid, it ſhall have the ſame proporti<lb></lb>on in Gravity to a Liquid of equal Maſſe, that the <lb></lb>part of the Magnitude demerged hath unto the <lb></lb>whole Magnitude.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>For let any Solid Magnitude, as for in<lb></lb>ſtance F A, lighter than the Liquid, be de<lb></lb>merged in the Liquid, which let be F A: <lb></lb>And let the part thereof immerged be A, <lb></lb>and the part above the Liquid F, It is to <lb></lb>be demonſtrated that the Magnitude F A <lb></lb>hath the ſame proportion in Gravity to a <lb></lb>Liquid of Equall Maſſe that A hath to F <lb></lb>A. </s> <s>Take any Liquid Magnitude, as ſup<lb></lb>poſe N I, of equall Maſſe with F A; and let F be equall to N, and <lb></lb>A to I: and let the Gravity of the whole Magnitude F A be B, and <lb></lb>let that of the Magnitude N I be O, <lb></lb>and let that of I be R. </s> <s>Now the <lb></lb><figure id="id.040.01.1048.1.jpg" xlink:href="040/01/1048/1.jpg"></figure><lb></lb>Magnitude F A hath the ſame pro<lb></lb>portion unto N I that the Gravity B <lb></lb>hath to the Gravity O R: But for <lb></lb>aſmuch as the Magnitude F A demit<lb></lb>ted into the Liquid is lighter than <lb></lb>the ſaid Liquid, it is manifeſt that a Maſſe of the Liquid, I, equall <lb></lb>to the part of the Magnitude demerged, A, hath equall Gravity <lb></lb><arrow.to.target n="marg1163"></arrow.to.target><lb></lb>with the whole Magnitnde, F A: For this was <emph type="italics"></emph>(a)<emph.end type="italics"></emph.end> above demon<lb></lb>ſtrated: But B is the Gravity of the Magnitude F A, and R of I: <pb xlink:href="040/01/1049.jpg" pagenum="354"></pb>Therefore B and R are equall. </s> <s>And becauſe that of the Magni<lb></lb>tude FA the <emph type="italics"></emph>G<emph.end type="italics"></emph.end>ravity is B: Therefore of the Liquid Body <emph type="italics"></emph>N<emph.end type="italics"></emph.end> I the <lb></lb>Gravity is O R. </s> <s>As F A is to N I, ſo is B to O R, or, ſo is R to <lb></lb>O R: But as R is to O R, ſo is I to N I, and A to F A: Therefore <lb></lb><arrow.to.target n="marg1164"></arrow.to.target><lb></lb>I is to N I, as F A to N I: And as I to N I ſo is <emph type="italics"></emph>(b)<emph.end type="italics"></emph.end> A to F A. <lb></lb></s> <s>Therefore F A is to N I, as A is to F A: Which was to be demon<lb></lb>ſtrated.</s></p><p type="margin"> <s><margin.target id="marg1163"></margin.target>(a) <emph type="italics"></emph>By 5. of the <lb></lb>firſt of this.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1164"></margin.target>(b) <emph type="italics"></emph>By 11. of the <lb></lb>fifth of<emph.end type="italics"></emph.end> Eucl.</s></p><p type="head"> <s>PROP. II. THEOR. II.<lb></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"></emph>The Right Portion of a Right angled Conoide, when it <lb></lb>ſhall have its Axis leſſe than<emph.end type="italics"></emph.end> ſeſquialter ejus quæ ad <lb></lb>Axem (<emph type="italics"></emph>or of its<emph.end type="italics"></emph.end> Semi-parameter) <emph type="italics"></emph>having any what <lb></lb>ever proportion to the Liquid in Gravity, being de<lb></lb>mitted into the Liquid ſo as that its Baſe touch not <lb></lb>the ſaid Liquid, and being ſet ſtooping, it ſhall not <lb></lb>remain ſtooping, but ſhall be restored to uprightneſſe. <lb></lb></s> <s>I ſay that the ſaid Portion ſhall ſtand upright when <lb></lb>the Plane that cuts it ſhall be parallel unto the Sur<lb></lb>face of the Liquid.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let there be a Portion of a Rightangled Conoid, as hath been <lb></lb>ſaid; and let it lye ſtooping or inclining: It is to be demon<lb></lb>ſtrated that it will not ſo continue but ſhall be reſtored to re<lb></lb>ctitude. </s> <s>For let it be cut through the Axis by a plane erect upon <lb></lb>the Surface of the Liquid, and let the Section of the Portion be <lb></lb>A PO L, the Section of a Rightangled Cone, and let the Axis <lb></lb><figure id="id.040.01.1049.1.jpg" xlink:href="040/01/1049/1.jpg"></figure><lb></lb>of the Portion and Diameter of the <lb></lb>Section be N O: And let the Sect<lb></lb>ion of the Surface of the Liquid be <lb></lb>I S. </s> <s>If now the Portion be not <lb></lb>erect, then neither ſhall A L be Pa<lb></lb>rallel to I S: Wherefore N O will <lb></lb>not be at Right Angles with I S. </s></p><p type="main"> <s><arrow.to.target n="marg1166"></arrow.to.target><lb></lb>Draw therefore K <foreign lang="grc">ω,</foreign> touching the Section of the Cone I, in the <lb></lb>Point P [that is parallel to I S: and from the Point P unto I S <lb></lb><arrow.to.target n="marg1167"></arrow.to.target><lb></lb>draw P F parallel unto O N, ^{*} which ſhall be the Diameter of the <lb></lb>Section I P O S, and the Axis of the Portion demerged in the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>i<lb></lb><arrow.to.target n="marg1168"></arrow.to.target><lb></lb>quid. </s> <s>In the next place take the Centres of Gravity: ^{*} and of <lb></lb>the Solid Magnitude A P O L, let the Centre of Gravity be R; and <lb></lb><arrow.to.target n="marg1169"></arrow.to.target><lb></lb>of I P O S let the Centre be B: ^{*} and draw a Line from B to R <lb></lb>prolonged unto G; which let be the Centre of Gravity of the <pb xlink:href="040/01/1050.jpg" pagenum="355"></pb>remaining Figure I S L A. </s> <s>Becauſe now that N O is <emph type="italics"></emph>Seſquialter<emph.end type="italics"></emph.end><lb></lb>of R O, but leſs than <emph type="italics"></emph>Seſquialter ejus quæ uſque ad Axem<emph.end type="italics"></emph.end> (or of its <lb></lb><emph type="italics"></emph>Semi-parameter<emph.end type="italics"></emph.end>;) ^{*} R O ſhall be leſſe than <emph type="italics"></emph>quæ uſque ad Axem<emph.end type="italics"></emph.end> (or <lb></lb><arrow.to.target n="marg1170"></arrow.to.target><lb></lb>than the <emph type="italics"></emph>Semi-parameter<emph.end type="italics"></emph.end>;) ^{*} whereupon the Angle R P <foreign lang="grc">ω</foreign> ſhall be <lb></lb><arrow.to.target n="marg1171"></arrow.to.target><lb></lb>acute. </s> <s>For ſince the Line <emph type="italics"></emph>quæ uſque ad Axem<emph.end type="italics"></emph.end> (or <emph type="italics"></emph>Semi-parameter<emph.end type="italics"></emph.end>) <lb></lb>is greater than R O, that Line which is drawn from the Point R, <lb></lb>and perpendicular to K <foreign lang="grc">ω,</foreign> namely RT, meeteth with the line F P <lb></lb>without the Section, and for that cauſe muſt of neceſſity fall be<lb></lb>tween the Points <emph type="italics"></emph>P<emph.end type="italics"></emph.end> and <foreign lang="grc">ω;</foreign> Therefore if <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ines be drawn through <lb></lb>B and G, parallel unto R T, they ſhall contain Right Angles with <lb></lb>the Surface of the Liquid: ^{*} and the part that is within the Li<lb></lb><arrow.to.target n="marg1172"></arrow.to.target><lb></lb>quid ſhall move upwards according to the Perpendicular that is <lb></lb>drawn thorow B, parallel to R T, and the part that is above the Li<lb></lb>quid ſhall move downwards according to that which is drawn tho<lb></lb>row G; and the Solid A P O L ſhall not abide in this Poſition; for <lb></lb>that the parts towards A will move upwards, and thoſe towards <lb></lb>B downwards; Wherefore N O ſhall be conſtituted according to <lb></lb>the Perpendicular.]</s></p><p type="margin"> <s><margin.target id="marg1166"></margin.target>* <emph type="italics"></emph>Supplied by<emph.end type="italics"></emph.end> Fe<lb></lb>derico Comman<lb></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"></emph>The Demonſtration of this propoſition hath been much deſired; which we have (in like man<lb></lb>ner as the 8 Prop. </s> <s>of the firſt Book) reſtored according to<emph.end type="italics"></emph.end> Archimedes <emph type="italics"></emph>his own Schemes, and <lb></lb>illustrated it with Commentaries.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The Right Portion of a Rightangled Conoid, when it ſhall <lb></lb><arrow.to.target n="marg1173"></arrow.to.target><lb></lb>have its Axis leſſe than <emph type="italics"></emph>Seſquialter ejus quæ uſque ad Axem<emph.end type="italics"></emph.end> (or of <lb></lb>its <emph type="italics"></emph>Semi-parameter] In the Tranſlation of<emph.end type="italics"></emph.end> Nicolo Tartaglia <emph type="italics"></emph>it is falſlyread<emph.end type="italics"></emph.end> great<lb></lb>er then Seſquialter, <emph type="italics"></emph>and ſo its rendered in the following Propoſition; but it is the Right <lb></lb>Portion of a Concid cut by a Plane at Right Angles, or erect, unto the Axis: and we ſay <lb></lb>that Conoids are then conſtituted erect when the cutting Plane, that is to ſay, the Plane of the <lb></lb>Baſe, ſhall be parallel to the Surface of the Liquid.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1173"></margin.target>A</s></p><p type="main"> <s>Which ſhall be the Diameter of the Section I P O S, and the <lb></lb><arrow.to.target n="marg1174"></arrow.to.target><lb></lb>Axis of the Portion demerged in the Liquid.] <emph type="italics"></emph>By the 46 of the firſt of <lb></lb>the Conicks of<emph.end type="italics"></emph.end> Apollonious, <emph type="italics"></emph>or by the Corol<lb></lb>lary of the 51 of the ſame.<emph.end type="italics"></emph.end></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"></figure><p type="main"> <s>And of the Solid Magnitude A P <lb></lb><arrow.to.target n="marg1175"></arrow.to.target><lb></lb>O L, let the Centre of Gravity be R; <lb></lb>and of I P O S let the Centre be B.] <lb></lb><emph type="italics"></emph>For the Centre of Gravity of the Portion of a Right<lb></lb>angled Conoid is in its Axis, which it ſo divideth <lb></lb>as that the part thereof terminating in the vertex, <lb></lb>be double to the other part terminating in the Baſe; as <lb></lb>in our Book<emph.end type="italics"></emph.end> De Centro Gravitatis Solidorum Propo. </s> <s>29. <emph type="italics"></emph>we have demonſtrated. </s> <s>And <lb></lb>ſince the Centre of Gravity of the Portion A P O L is R, O R ſhall be double to RN and there<lb></lb>fore N O ſhall be Seſquialter of O R. </s> <s>And for the ſame reaſon, B the Centre of Gravity of the Por<lb></lb>tion I P O S is in the Axis P F, ſo dividing it as that P B is double to B F;<emph.end type="italics"></emph.end></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></lb><arrow.to.target n="marg1176"></arrow.to.target><lb></lb>be the Centre of Gravity of the remaining Eigure I S L A.] <pb xlink:href="040/01/1051.jpg" pagenum="356"></pb><emph type="italics"></emph>For if, the Line B R being prolonged unto G, G R hath the ſame proportion to R B as the Por<lb></lb>tion of the Conoid I P O S hath to the remaining Figure that lyeth above the Surface of the <lb></lb>Liquid, the Toine G ſhall be its Centre of Gravity; by the 8 of the ſecond of<emph.end type="italics"></emph.end> Archimedes <lb></lb>de Centro Gravitatis Planorum, vel de <emph type="italics"></emph>Æ<emph.end type="italics"></emph.end>quiponderantibus.<lb></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 ſhall be leſs than <emph type="italics"></emph>quæ uſque ad Axem<emph.end type="italics"></emph.end> (or than the Semi<lb></lb>parameter.] <emph type="italics"></emph>By the 10 Propofit. </s> <s>of<emph.end type="italics"></emph.end> Euclids <emph type="italics"></emph>fifth Book of Elements. </s> <s>The Line<emph.end type="italics"></emph.end> quæ <lb></lb>uſque ad Axem, <emph type="italics"></emph>(or the Semi-parameter) according to<emph.end type="italics"></emph.end> Archimedes, <emph type="italics"></emph>is the half of that<emph.end type="italics"></emph.end><lb></lb>juxta quam poſſunt, quæ á Sectione ducuntur, (<emph type="italics"></emph>or of the Parameter;) as appeareth <lb></lb>by the 4 Propoſit of his Book<emph.end type="italics"></emph.end> De Conoidibus & Shpæroidibus: <emph type="italics"></emph>and for what reaſon it is <lb></lb>ſo called, we have declared in the Commentaries upon him by us publiſhed.<emph.end type="italics"></emph.end></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="grc">ω</foreign> ſhall be acute.] <emph type="italics"></emph>Let the Line N O be <lb></lb>continued out to H, that ſo RH may be equall to <lb></lb>the Semi-parameter. </s> <s>If now from the Point H<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.1051.1.jpg" xlink:href="040/01/1051/1.jpg"></figure><lb></lb><emph type="italics"></emph>a Line be drawn at Right Angles to N H, it ſhall <lb></lb>meet with FP without the Section; for being <lb></lb>drawn thorow O parallel to A L, it ſhall fall <lb></lb>without the Section, by the 17 of our ſirst Book of<emph.end type="italics"></emph.end><lb></lb>Conicks; <emph type="italics"></emph>Therefore let it meet in V: and <lb></lb>becauſe F P is parallel to the Diameter, and H <lb></lb>V perpendicular to the ſame Diameter, and R H <lb></lb>equall to the Semi-parameter, the Line drawn <lb></lb>from the Point R to V ſhall make Right Angles <lb></lb>with that Line which the Section toucheth in the Point P: that is with K<emph.end type="italics"></emph.end> <foreign lang="grc">ω,</foreign> <emph type="italics"></emph>as ſhall anon be <lb></lb>demonstrated: Wherefore the Perpendidulat R T falleth betwixt A and<emph.end type="italics"></emph.end> <foreign lang="grc">ω;</foreign> <emph type="italics"></emph>and the Argle R<emph.end type="italics"></emph.end><lb></lb>P <foreign lang="grc">ω</foreign> <emph type="italics"></emph>ſhall be an Acute Angle.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let A B C be the Section of a Rightangled Cone, or a Parabola, <lb></lb>and its Diameter B D; and let the Line E F touch the <lb></lb>ſame in the Point G: and in the Diameter B D take the Line <lb></lb>H K equall to the Semi-parameter: and thorow G, G L be<lb></lb>ing drawn parallel to the Diameter, draw KM from the <lb></lb><emph type="italics"></emph>P<emph.end type="italics"></emph.end>oint K at Right Angles to B D cutting G L in M: I ſay <lb></lb>that the Line prolonged thorow Hand Mis perpendicular to <lb></lb>E F, which it cutteth in N.</s></p><p type="main"> <s><emph type="italics"></emph>For from the Point G draw the Line G O at Right Angles to E F cutting the Diameter in <lb></lb>O: and again from the ſame Point draw G P perpendicular to the Diameter: and let the <lb></lb>ſaid Diameter prolonged cut the Line E F in <expan abbr="q.">que</expan> P B ſhall be equall to B Q, by the 35 of<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1179"></arrow.to.target><lb></lb><emph type="italics"></emph>our firſt Book of<emph.end type="italics"></emph.end> Conick <emph type="italics"></emph>Sections,<emph.end type="italics"></emph.end> (a) <emph type="italics"></emph>and G<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.1051.2.jpg" xlink:href="040/01/1051/2.jpg"></figure><lb></lb><emph type="italics"></emph>P a Mean-proportion all betmixt Q P and PO<emph.end type="italics"></emph.end>; <lb></lb><arrow.to.target n="marg1180"></arrow.to.target><lb></lb>(b) <emph type="italics"></emph>and therefore the Square of G P ſhall be e<lb></lb>quall to the Rectangle of O P Q: But it is alſo <lb></lb>equall to the Rectangle comprehended under P B <lb></lb>and the Line<emph.end type="italics"></emph.end> juxta quam poſſunt, <emph type="italics"></emph>or the Par<lb></lb>ameter, by the 11 of our firſt Book of<emph.end type="italics"></emph.end> Conicks: <lb></lb><arrow.to.target n="marg1181"></arrow.to.target><lb></lb>(c) <emph type="italics"></emph>Therefore, look what proportion Q P hath to <lb></lb>P B, and the ſame hath the Parameter unto P O: <lb></lb>But Q P is double unto<emph.end type="italics"></emph.end> P B, <emph type="italics"></emph>for that<emph.end type="italics"></emph.end> P B <emph type="italics"></emph>and B <lb></lb>Q are equall, as hath been ſaid: And therefore <lb></lb>the Parameter ſhall be double to the ſaid P O: <lb></lb>and by the ſame Reaſon P O is equall to that which we call the Semi-parameter, that is, to K H<emph.end type="italics"></emph.end>: <lb></lb><arrow.to.target n="marg1182"></arrow.to.target><lb></lb><emph type="italics"></emph>But<emph.end type="italics"></emph.end> (d) <emph type="italics"></emph>P G is equall to K M, and<emph.end type="italics"></emph.end> (e) <emph type="italics"></emph>the Angle O P G to the Angle H K M; for they are both<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1183"></arrow.to.target><lb></lb><emph type="italics"></emph>Right Angles: And therefore O G alſo is equall to H M, and the Angle P O G unto the<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1052.jpg" pagenum="357"></pb><figure id="id.040.01.1052.1.jpg" xlink:href="040/01/1052/1.jpg"></figure><lb></lb><emph type="italics"></emph>Angle K H M: Therefore<emph.end type="italics"></emph.end> (f) O G <emph type="italics"></emph>and H N are parallel,<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1184"></arrow.to.target><lb></lb><emph type="italics"></emph>and the<emph.end type="italics"></emph.end> (g) <emph type="italics"></emph>Angle H N F equall to the Angle O G F; for <lb></lb>that G O being Perpendicular to E F, H N ſhall alſo be per-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1185"></arrow.to.target><lb></lb><emph type="italics"></emph>pandicnlar to the ſame: Which was to be demon ſtrated.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1179"></margin.target>(a) <emph type="italics"></emph>By Cor. </s> <s>of 8. of <lb></lb>6. of<emph.end type="italics"></emph.end> Euclide.</s></p><p type="margin"> <s><margin.target id="marg1180"></margin.target>(b) <emph type="italics"></emph>By 17. of the<emph.end type="italics"></emph.end><lb></lb>6.</s></p><p type="margin"> <s><margin.target id="marg1181"></margin.target>(c) <emph type="italics"></emph>By 14. of the<emph.end type="italics"></emph.end><lb></lb>6.</s></p><p type="margin"> <s><margin.target id="marg1182"></margin.target>(d) <emph type="italics"></emph>By 33. of the<emph.end type="italics"></emph.end><lb></lb>1.</s></p><p type="margin"> <s><margin.target id="marg1183"></margin.target>(e) <emph type="italics"></emph>By 4. of the<emph.end type="italics"></emph.end> 1.</s></p><p type="margin"> <s><margin.target id="marg1184"></margin.target>(f) <emph type="italics"></emph>By 28. of the<emph.end type="italics"></emph.end><lb></lb>1.</s></p><p type="margin"> <s><margin.target id="marg1185"></margin.target>(g) <emph type="italics"></emph>By 29. of th<emph.end type="italics"></emph.end><lb></lb>1</s></p><p type="main"> <s>And the part which is within the Liquid <lb></lb><arrow.to.target n="marg1186"></arrow.to.target><lb></lb>doth move upwards according to the Per<lb></lb>pendicular that is drawn thorow B parallel <lb></lb>to R T.] <emph type="italics"></emph>The reaſon why this moveth upwards, and that <lb></lb>other downwards, along the Perpendicular Line, hath been ſhewn above in the 8 of the firſt <lb></lb>Book of this; ſo that we have judged it needleſſe to repeat it either in this, or in the reſt <lb></lb>that follow.<emph.end type="italics"></emph.end></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"></emph>In the<emph.end type="italics"></emph.end> Antient <emph type="italics"></emph>Parabola (namely that aſſumed in a Rightangled <lb></lb>Cone) the Line<emph.end type="italics"></emph.end> juxta quam Poſſunt quæ in Sectione ordinatim du<lb></lb>cuntur <emph type="italics"></emph>(which I, following<emph.end type="italics"></emph.end> Mydorgius, <emph type="italics"></emph>do call the<emph.end type="italics"></emph.end> Parameter<emph type="italics"></emph>) is<emph.end type="italics"></emph.end> (a) <lb></lb><arrow.to.target n="marg1187"></arrow.to.target><lb></lb><emph type="italics"></emph>double to that<emph.end type="italics"></emph.end> quæ ducta eſt à Vertice Sectionis uſque ad Axem, <emph type="italics"></emph>or in<emph.end type="italics"></emph.end><lb></lb>Archimedes <emph type="italics"></emph>phraſe,<emph.end type="italics"></emph.end> <foreign lang="grc">τᾱς υσ́χρι τοῡ ἄξον<34>;</foreign> <emph type="italics"></emph>which I for that cauſe, and <lb></lb>for want of a better word, name the<emph.end type="italics"></emph.end> Semiparameter: <emph type="italics"></emph>but in<emph.end type="italics"></emph.end> Modern <lb></lb><emph type="italics"></emph>Parabola's it is greater or leſſer then double. </s> <s>Now that throughout this <lb></lb>Book<emph.end type="italics"></emph.end> Archimedes <emph type="italics"></emph>ſpeaketh of the Parabola in a Rectangled Cone, is mani<lb></lb>feſt both by the firſt words of each Propoſition, & by this that no Parabola <lb></lb>hath its Parameter double to the Line<emph.end type="italics"></emph.end> quæ eſt a Sectione ad Axem, <emph type="italics"></emph>ſave <lb></lb>that which is taken in a Rightangled Cone. </s> <s>And in any other Parabola, for <lb></lb>the Line<emph.end type="italics"></emph.end> <foreign lang="grc">τᾱς μσ́χριτοῡ ἄεον<34></foreign> <emph type="italics"></emph>or<emph.end type="italics"></emph.end> quæ uſque ad Axem <emph type="italics"></emph>to uſurpe the Word<emph.end type="italics"></emph.end> Se<lb></lb>miparameter <emph type="italics"></emph>would be neither proper nor true: but in this caſe it may paſs<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1187"></margin.target>(a) Rîvalt. <emph type="italics"></emph>in<emph.end type="italics"></emph.end> Ar<lb></lb>chimed. <emph type="italics"></emph>de Cunoid <lb></lb>& Sphæroid.<emph.end type="italics"></emph.end> Prop. <lb></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"></emph>The Right Portion of a Rightangled Conoid, when it <lb></lb>ſhall have its Axis leſſe than ſeſquialter of the Se<lb></lb>mi-parameter, the Axis having any what ever pro<lb></lb>portion to the Liquid in Gravity, being demitted into <lb></lb>the Liquid ſo as that its Baſe be wholly within the <lb></lb>ſaid Liquid, and being ſet inclining, it ſhall not re<lb></lb>main inclined, but ſhall be ſo reſtored, as that its Ax<lb></lb>is do ſtand upright, or according to the Perpendicular.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let any Portion be demitted into the Liquid, as was ſaid; and <lb></lb>let its Baſe be in the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid; <lb></lb><figure id="id.040.01.1052.2.jpg" xlink:href="040/01/1052/2.jpg"></figure><lb></lb>and let it be cut thorow the <lb></lb>Axis, by a Plain erect upon the Sur<lb></lb>face of the Liquid, and let the Se<lb></lb>ction be A P O <emph type="italics"></emph>L,<emph.end type="italics"></emph.end> the Section of a <lb></lb>Right angled Cone: and let the Axis <lb></lb>of the Portion and Diameter of the <pb xlink:href="040/01/1053.jpg" pagenum="356"></pb>Section of the Portion be A P O L, the Section of a Rightangled <lb></lb>Cone; and let the Axis of the Portion and Diameter of the Section <lb></lb>be N O, and the Section of the Surface of the Liquid I S. </s> <s>If now <lb></lb>the Portion be not erect, then N O ſhall not be at equall Angles with <lb></lb>I S. </s> <s>Draw R <foreign lang="grc">ω</foreign> touching the Section of the Rightangled Conoid <lb></lb>in P, and parallel to I S: and from the Point P and parall to O N <lb></lb>draw <emph type="italics"></emph>P<emph.end type="italics"></emph.end> F: and take the Centers of Gravity; and of the Solid A <lb></lb><emph type="italics"></emph>P<emph.end type="italics"></emph.end> O L let the Centre be R; and of that which lyeth within the <lb></lb>Liquid let the Centre be B; and draw a Line from B to R pro<lb></lb>longing it to G, that G may be the Centre of Gravity of the Solid <lb></lb>that is above the Liquid. </s> <s>And becauſe N O is ſeſquialter of R <lb></lb>O, and is greater than ſeſquialter of the Semi-Parameter; it is ma<lb></lb><arrow.to.target n="marg1188"></arrow.to.target><lb></lb>nifeſt that <emph type="italics"></emph>(a)<emph.end type="italics"></emph.end> R O is greater than the <lb></lb><figure id="id.040.01.1053.1.jpg" xlink:href="040/01/1053/1.jpg"></figure><lb></lb>Semi-parameter. ^{*}Let therefore R <lb></lb><arrow.to.target n="marg1189"></arrow.to.target><lb></lb>H be equall to the Semi-Parameter, <lb></lb><arrow.to.target n="marg1190"></arrow.to.target><lb></lb>^{*} and O <emph type="italics"></emph>H<emph.end type="italics"></emph.end> double to H M. </s> <s>Foraſ<lb></lb>much therefore as N O is ſeſquialter <lb></lb><arrow.to.target n="marg1191"></arrow.to.target><lb></lb>of R O, and M O of O H, <emph type="italics"></emph>(b)<emph.end type="italics"></emph.end> the <lb></lb>Remainder N M ſhall be ſeſquialter <lb></lb>of the Remainder R H: Therefore <lb></lb>the Axis is greater than ſeſquialter <lb></lb>of the Semi parameter by the quan<lb></lb>tity of the Line M O. </s> <s>And let it be <lb></lb>ſuppoſed that the Portion hath not leſſe proportion in Gravity unto <lb></lb>the Liquid of equall Maſſe, than the Square that is made of the <lb></lb>Exceſſe by which the Axis is greater than ſeſquialter of the Semi<lb></lb>parameter hath to the Square made of the Axis: It is therefore ma<lb></lb>nifeſt that the Portion hath not leſſe proportion in Gravity to the <lb></lb>Liquid than the Square of the Line M O hath to the Square of N <lb></lb>O: But look what proportion the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion hath to the Liquid in <lb></lb>Gravity, the ſame hath the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion ſubmerged to the whole Solid: <lb></lb>for this hath been demonſtrated <emph type="italics"></emph>(c)<emph.end type="italics"></emph.end> above: ^{*}And look what pro<lb></lb><arrow.to.target n="marg1192"></arrow.to.target><lb></lb>portion the ſubmerged Portion hath to the whole <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion, the <lb></lb><arrow.to.target n="marg1193"></arrow.to.target><lb></lb>ſame hath the Square of <emph type="italics"></emph>P<emph.end type="italics"></emph.end> F unto the Square of N O: For it hath <lb></lb>been demonſtrated in <emph type="italics"></emph>(d) Lib. de Conoidibus,<emph.end type="italics"></emph.end> that if from a Right<lb></lb><arrow.to.target n="marg1194"></arrow.to.target><lb></lb>angled Conoid two <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortions be cut by Planes in any faſhion pro<lb></lb>duced, theſe <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortions ſhall have the ſame Proportion to each <lb></lb>other as the Squares of their Axes: The Square of P F, therefore, <lb></lb>hath not leſſe proportion to the Square of N O than the Square of <lb></lb>M O hath to the Square of N O: ^{*}Wherefore P F is not leſſe than <lb></lb><arrow.to.target n="marg1195"></arrow.to.target><lb></lb>M O, ^{*}nor B P than H O. ^{*}If therefore, a Right Line be drawn <lb></lb><arrow.to.target n="marg1196"></arrow.to.target><lb></lb>from H at Right Angles unto N O, it ſhall meet with B <emph type="italics"></emph>P,<emph.end type="italics"></emph.end> and ſhall <lb></lb><arrow.to.target n="marg1197"></arrow.to.target><lb></lb>fall betwixt B and P; let it fall in T: <emph type="italics"></emph>(e)<emph.end type="italics"></emph.end> And becauſe <emph type="italics"></emph>P<emph.end type="italics"></emph.end> F is <lb></lb><arrow.to.target n="marg1198"></arrow.to.target><lb></lb>parallel to the Diameter, and H T is perpendicular unto the ſame <lb></lb>Diameter, and R H equall to the Semi-parameter; a Line drawn <lb></lb>from R to T and prolonged, maketh Right Angles with the Line <pb xlink:href="040/01/1054.jpg" pagenum="360"></pb>contingent unto the Section in the Point P: Wherefore it alſo <lb></lb>maketh Right Angles with the Surface of the Liquid: and that <lb></lb>part of the Conoidall Solid which is within the Liquid ſhall move <lb></lb>upwards according to the Perpendicular drawn thorow B parallel <lb></lb>to R T; and that part which is above the Liquid ſhall move down<lb></lb>wards according to that drawn thorow G, parallel to the ſaid R T: <lb></lb>And thus it ſhall continue to do ſo long untill that the Conoid be <lb></lb>reſtored to uprightneſſe, or to ſtand according to the Perpendicular.</s></p><p type="margin"> <s><margin.target id="marg1188"></margin.target>(a) <emph type="italics"></emph>By 10. of the <lb></lb>fifth.<emph.end type="italics"></emph.end></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"></emph>By 19. of the <lb></lb>fifth.<emph.end type="italics"></emph.end></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"></emph>By 1. of this <lb></lb>ſecond Book.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1194"></margin.target>(d) <emph type="italics"></emph>By<emph.end type="italics"></emph.end> 6. De Co<lb></lb>noilibus & <emph type="italics"></emph>S<emph.end type="italics"></emph.end>phæ<lb></lb>roidibus <emph type="italics"></emph>of<emph.end type="italics"></emph.end> Archi<lb></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"></emph>By 2. of this <lb></lb>ſecond Book.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>COMMANDINE.<lb></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"></emph>So it is to be <lb></lb>read, and not R M, as<emph.end type="italics"></emph.end> Tartaglia's <emph type="italics"></emph>Tranſlation hath is; which may be made appear from <lb></lb>that which followeth.<emph.end type="italics"></emph.end></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"></emph>In the Tranſlation aforenamed it is falſly render<lb></lb>ed,<emph.end type="italics"></emph.end> O N <emph type="italics"></emph>double to<emph.end type="italics"></emph.end> 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></lb>Portion, the ſame hath the Square of P F unto the Square of N O.] <lb></lb><emph type="italics"></emph>This place we have reſtored in our Tranſlation, at the requeſt of ſome friends: But it is demon<lb></lb>ſtrated by<emph.end type="italics"></emph.end> 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 leſſe than M O.] <emph type="italics"></emph>For by 10 of the fifth it followeth <lb></lb>that the Square of P F is not leſſe than the Square of M O: and therefore neither ſhall the <lb></lb>Line P F be leße than the Line M O, by 22 of the<emph.end type="italics"></emph.end></s></p><figure id="id.040.01.1054.1.jpg" xlink:href="040/01/1054/1.jpg"></figure><p type="main"> <s><arrow.to.target n="marg1203"></arrow.to.target><lb></lb><emph type="italics"></emph>ſixth.<emph.end type="italics"></emph.end><lb></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"></emph>By 14. of the <lb></lb>ſixth.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Nor B P than H O,] <emph type="italics"></emph>For as P F is to <lb></lb>P B, ſo is M O to H O: and, by Permutation, as<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1205"></arrow.to.target><lb></lb><emph type="italics"></emph>P F is to M O, ſo is B P to H O; But P F is not <lb></lb>leſſe than M O as hath bin proved; (a) Therefore <lb></lb>neither ſhall B P be leſſe than H O.<emph.end type="italics"></emph.end></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></lb>from H at Right Angles unto N O, it <lb></lb>ſhall meet with B P, and ſhall fall be<lb></lb>twixt B and P.] <emph type="italics"></emph>This Place was corrupt in the <lb></lb>Tranſlation of<emph.end type="italics"></emph.end> Tartaglia<emph type="italics"></emph>: But it is thus demonstra<lb></lb>ted. </s> <s>In regard that P F is not leſſe than O M, nor P B than O H, if we ſuppoſe P F equall to <lb></lb>O M, P B ſhall be likewiſe equall to O H: Wherefore the Line drawn thorow O, parallel to A L <lb></lb>ſhall fall without the Section, by 17 of the firſt of our Treatiſe of Conicks; And in regard that <lb></lb>B P prolonged doth meet it beneath P; Therefore the Perpendicular drawn thorow H doth <lb></lb>alſo meet with the ſame beneath B, and it doth of neceſſity fall betwixt B and P: But the <lb></lb>ſame is much more to follow, if we ſuppoſe P F to be greater than O M.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/1055.jpg" pagenum="361"></pb><p type="head"> <s>PROP. V. THEOR. V.</s></p><p type="main"> <s><emph type="italics"></emph>The Right Portion of a Right-Angled Conoid lighter <lb></lb>than the Liquid, when it ſhall have its Axis great<lb></lb>er than<emph.end type="italics"></emph.end> Seſquialter <emph type="italics"></emph>of the Semi-parameter, if it have <lb></lb>not greater proportion in Gravity to the Liquid [of <lb></lb>equal Maſs] than the Exceſſe by which the Square <lb></lb>made of the Axis is greater than the Square made <lb></lb>of the Exceſſe by which the Axis is greater than<emph.end type="italics"></emph.end><lb></lb>ſeſquialter <emph type="italics"></emph>of the Semi-Parameter hath to the <lb></lb>Square made of the Axis being demitted into the Li<lb></lb>quid, ſo as that its Baſe be wholly within the Liquid, <lb></lb>and being ſet inclining, it ſhall not remain ſo inclined, <lb></lb>but ſhall turn about till that its Axis ſhall be accor<lb></lb>ding to the Perpendicular.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>For let any Portion be demitted into the Liquid, as hath been <lb></lb>ſaid; and let its Baſe be wholly within the Liquid, And being <lb></lb>cut thorow its Axis by a Plain erect upon the Surface of the <lb></lb>Liquid; its Section ſhall be the Section <lb></lb><figure id="id.040.01.1055.1.jpg" xlink:href="040/01/1055/1.jpg"></figure><lb></lb>of a Rightangled Cone: Let it be <lb></lb>A P O L, and let the Axis of the Por<lb></lb>tion and Diameter of the Section be <lb></lb>N O; and the Section of the Surface of <lb></lb>the Liquid I S. </s> <s>And becauſe the Axis <lb></lb>is not according to the Perpendicu<lb></lb>lar, N O will not be at equall angles <lb></lb>with I S. </s> <s>Draw K <foreign lang="grc">ω</foreign> touching the Se<lb></lb>ction A P O L in P, and parallel unto <lb></lb>I S: and thorow P, draw P F parallel unto N O: and take the <lb></lb>Centres of Gravity; and of the Solid A P O L let the Centre be <lb></lb>R; and of that which lyeth above the Liquid let the Centre be B; <lb></lb>and draw a Line from B to R, prolonging it to G; which let be the <lb></lb>Centre of Gravity of the Solid demerged within the Liquid: and <lb></lb>moreover, take R H equall to the Semi-parameter, and let O H be <lb></lb>double to H M; and do in the reſt as hath been ſaid <emph type="italics"></emph>(a)<emph.end type="italics"></emph.end> above. <lb></lb><arrow.to.target n="marg1206"></arrow.to.target><lb></lb>Now foraſmuch as it was ſuppoſed that the Portion hath not greater <lb></lb>proportion in Gravity to the Liquid, than the Exceſſe by which <lb></lb>the Square N O is greater than the Square M O, hath to the ſaid <lb></lb>Square N O: And in regard that whatever proportion in Gravity <pb xlink:href="040/01/1056.jpg" pagenum="362"></pb>the Portion hath to the Liquid of equall Maſſe, the ſame hath the <lb></lb>Magnitude of the Portion ſubmerged unto the whole Portion; as <lb></lb>hath been demonſtrated in the firſt Propoſition; The Magnitude <lb></lb>ſubmerged, therefore, ſhall not have greater proportion to the <lb></lb><arrow.to.target n="marg1207"></arrow.to.target><lb></lb>whole <emph type="italics"></emph>(b)<emph.end type="italics"></emph.end> Portion, than that which hath been mentioned: ^{*}And <lb></lb>therefore the whole Portion hath not greater proportion unto that <lb></lb><arrow.to.target n="marg1208"></arrow.to.target><lb></lb>which is above the Liquid, than the Square N O hath to the Square <lb></lb><arrow.to.target n="marg1209"></arrow.to.target><lb></lb>M O: But the <emph type="italics"></emph>(c)<emph.end type="italics"></emph.end> whole Portion hath the ſame proportion unto <lb></lb>that which is above the Liquid that the Square N O hath to the <lb></lb>Square P F: Therefore the Square N O hath not greater propor<lb></lb><arrow.to.target n="marg1210"></arrow.to.target><lb></lb>tion unto the Square P F, than it hath unto the Square M O: ^{*}And <lb></lb>hence it followeth that P F is not leſſe than O M, nor P B than O <lb></lb><arrow.to.target n="marg1211"></arrow.to.target><lb></lb>H: ^{*} A Line, therefore, drawn from H at Right Angles unto N O <lb></lb>ſhall meet with B P betwixt P and B: Let it be in T: And be<lb></lb>cauſe that in the Section of the Rectangled Cone P F is parallel unto <lb></lb>the Diameter N O; and H T perpendicular unto the ſaid Diame<lb></lb>ter; and R H equall to the Semi-parameter: It is manifeſt that <lb></lb>R T prolonged doth make Right Angles with K P <foreign lang="grc">ω</foreign>: And there<lb></lb>fore doth alſo make Right Angles with I S: Therefore R T is per<lb></lb>pendicular unto the Surface of the Liquid; And if thorow the <lb></lb>Points B and G Lines be drawn parallel unto R T, they ſhall be <lb></lb>perpendicular unto the Liquids Surface. </s> <s>The Portion, therefore, <lb></lb>which is above the Liquid ſhall move downwards in the Liquid ac<lb></lb>cording to the Perpendicular drawn thorow B; and that part <lb></lb>which is within the Liquid ſhall move upwards according to the <lb></lb>Perpendicular drawn thorow G; and the Solid Portion A P O L <lb></lb>ſhall not continue ſo inclined, [<emph type="italics"></emph>as it was at its demerſion<emph.end type="italics"></emph.end>], but ſhall <lb></lb>move within the Liquid untill ſuch time that N O do ſtand accor<lb></lb>ding to the Perpendicular.</s></p><p type="margin"> <s><margin.target id="marg1206"></margin.target>(a) <emph type="italics"></emph>In 4. Prop. of <lb></lb>this.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1207"></margin.target>(a) <emph type="italics"></emph>By 11. of the <lb></lb>fifth.<emph.end type="italics"></emph.end></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"></emph>By 26. of the <lb></lb>Book<emph.end type="italics"></emph.end> De Conoid. <lb></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></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></lb>unto that which is above the Liquid, than the Square N O hath to <lb></lb>the Square M O.] <emph type="italics"></emph>For in regard that the Magnitude of the Portion demerged <lb></lb>within the Liquid hath not greater proportion unto the whole Portion than the Exceſſe by which <lb></lb>the Square N O is greater than the Square M O hath to the ſaid Square N O; Converting of <lb></lb>the Proportion, by the 26. of the fifth of<emph.end type="italics"></emph.end> Euclid, <emph type="italics"></emph>of<emph.end type="italics"></emph.end> Campanus <emph type="italics"></emph>his Tranſlation, the whole <lb></lb>Portion ſhall not have leſſer proportion unto the Magnitude ſubmerged, than the Square N O <lb></lb>hath unto the Exceſſe by which N O is greater than the Square M O. </s> <s>Let a Portion be taken; <lb></lb>and let that part of it which is above the Liquid be the firſt Magnitude; the part of it which <lb></lb>is ſubmerged the ſecond: and let the third Magnitude be the Square M O; and let the Exceſſe <lb></lb>by which the Square N O is greater than the Square M O be the fourth. </s> <s>Now of theſe Mag<lb></lb>nitudes, the proportion of the firſt and ſecond, unto the ſecond, is not leſſe than that of the third & <lb></lb>fourth unto the fourth: For the Square M O together with the Exceſſe by which the Square <lb></lb>N O exceedeth the Square M O is equall unto the ſaid Square N O: Wherefore, by Converſi<lb></lb>on of Proportion, by 30 of the ſaid fifth Book, the proportion of the firſt and ſecond unto the <lb></lb>firſt, ſhall not be greater than that of the third and fourth unto the third: And, for the ſame<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1057.jpg" pagenum="363"></pb><emph type="italics"></emph>the proportion of the whole Portion unto that part thereof which is above the Liquid ſhall not be <lb></lb>greater than that of the Square N O unto the Square M O: Which was to be demonſtrated.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And hence it followeth that P F is not leſſe than O M, nor P B </s></p><p type="main"> <s><arrow.to.target n="marg1213"></arrow.to.target><lb></lb>than O H.] <emph type="italics"></emph>This followeth by the 10 and 14 of the fifth, and by the 22 of the ſixth of<emph.end type="italics"></emph.end><lb></lb>Euclid, <emph type="italics"></emph>as hath been ſaid above.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1213"></margin.target>B</s></p><p type="main"> <s>A <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine, therefore, drawn from Hat Right Angles unto N O ſhall <lb></lb><arrow.to.target n="marg1214"></arrow.to.target><lb></lb>meet with P B betwixt P and B.] <emph type="italics"></emph>Why this ſo falleth out, we will ſhew in the <lb></lb>next.<emph.end type="italics"></emph.end></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"></emph>The Right Portion of a Rightangled Conoid lighter <lb></lb>than the Liquid, when it ſhall have its Axis greater <lb></lb>than ſeſquialter of the Semi-parameter, but leſſe than <lb></lb>to be unto the Semi-parameter in proportion as fifteen <lb></lb>to fower, being demitted into the Liquid ſo as that <lb></lb>its Baſe do touch the Liquid, it ſhall never stand ſo <lb></lb>enclined as that its Baſe toucheth the Liquid in one <lb></lb>Point only.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let there be a Portion, as was ſaid; and demit it into the Li<lb></lb>quid in ſuch faſhion as that its Baſe do touch the Liquid in <lb></lb>one only Point: It is to be demonſtrated that the ſaid Portion <lb></lb><arrow.to.target n="marg1215"></arrow.to.target><lb></lb>ſhall not continue ſo, but ſhall turn about in ſuch manner as that <lb></lb>its Baſe do in no wiſe touch the Surface of the Liquid. </s> <s>For let it be <lb></lb>cut thorow its Axis by a Plane erect <lb></lb><figure id="id.040.01.1057.1.jpg" xlink:href="040/01/1057/1.jpg"></figure><lb></lb>upon the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquids Surface: and let <lb></lb>the Section of the Superficies of the <lb></lb>Portion be A P O L, the Section of <lb></lb>a Rightangled Cone; and the Sect<lb></lb>ion of the Surface of the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid be <lb></lb>A S; and the Axis of the Portion <lb></lb>and Diameter of the Section N O: <lb></lb>and let it be cut in F, ſo as that O <lb></lb>F be double to F N; and in <foreign lang="grc">ω</foreign> ſo, as that N O may be to F <foreign lang="grc">ω</foreign> in the <lb></lb>ſame proportion as fifteen to four; and at Right Angles to N O <lb></lb>draw <foreign lang="grc">ω</foreign> <emph type="italics"></emph>N<emph.end type="italics"></emph.end>ow becauſe N O hath greater proportion unto F <foreign lang="grc">ω</foreign> than <lb></lb>unto the Semi-parameter, let the Semi-parameter be equall to F B: <lb></lb><arrow.to.target n="marg1216"></arrow.to.target><lb></lb>and draw P C parallel unto A S, and touching the Section A P O L <lb></lb>in P; and P I parallel unto <emph type="italics"></emph>N O<emph.end type="italics"></emph.end>; and firſt let P I cut K<foreign lang="grc">ω</foreign> in H. For<lb></lb><arrow.to.target n="marg1217"></arrow.to.target><lb></lb>aſmuch, therefore, as in the Portion A P O L, contained betwixt <lb></lb>the Right <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine and the Section of the Rightangled Cone, K <foreign lang="grc">ω</foreign> is <lb></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"></pb>ſaid K <foreign lang="grc">ω</foreign> in H, and A S is parallel unto the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine that toucheth in <lb></lb>P; It is neceſſary that P I hath unto P H either the ſame proportion <lb></lb>that <emph type="italics"></emph>N<emph.end type="italics"></emph.end> <foreign lang="grc">ω</foreign> hath to <foreign lang="grc">ω</foreign> O, or greater; for this hath already been de<lb></lb>monſtrated: But <emph type="italics"></emph>N<emph.end type="italics"></emph.end> <foreign lang="grc">ω</foreign> is ſeſquialter of <foreign lang="grc">ω</foreign> O; and P I, therefore, is <lb></lb>either Seſquialter of H P, or more than ſeſquialter: Wherefore <lb></lb><arrow.to.target n="marg1218"></arrow.to.target><lb></lb>P H is to H I either double, or leſſe than double. <emph type="italics"></emph>L<emph.end type="italics"></emph.end>et P T be <lb></lb>double to T I: the Centre of Gravity of the part which is within <lb></lb>the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid ſhall be the Point T. </s> <s>Therefore draw a <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine from T <lb></lb>to F prolonging it; and let the Centre of <lb></lb><figure id="id.040.01.1058.1.jpg" xlink:href="040/01/1058/1.jpg"></figure><lb></lb>Gravity of the part which is above the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid <lb></lb>be G: and from the Point B at Right Angles <lb></lb>unto <emph type="italics"></emph>N O<emph.end type="italics"></emph.end> draw B R. </s> <s>And ſeeing that P I is <lb></lb>parallel unto the Diameter <emph type="italics"></emph>N O,<emph.end type="italics"></emph.end> and B R <lb></lb>perpendicular unto the ſaid Diameter, and F <lb></lb>B equall to the Semi-parameter; It is mani<lb></lb>feſt that the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine drawn thorow the Points <lb></lb>F and R being prolonged, maketh equall <lb></lb>Angles with that which toucheth the Section <lb></lb>A P O L in the Point P: and therefore doth alſo make Right An<lb></lb>gles with A S, and with the Surface of the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid: and the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ines <lb></lb>drawn thorow T and G parallel unto F R ſhall be alſo perpendicu<lb></lb>lar to the Surface of the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid: and of the Solid Magnitude A P <lb></lb>O L, the part which is within the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid moveth upwards according <lb></lb>to the Perpendicular drawn thorow T; and the part which is above <lb></lb>the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid moveth downwards according to that drawn thorow G: <lb></lb><arrow.to.target n="marg1219"></arrow.to.target><lb></lb>The Solid A <emph type="italics"></emph>P<emph.end type="italics"></emph.end> O L, therefore, ſhall turn about, and its Baſe ſhall <lb></lb>not in the leaſt touch the Surface of the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid, And if <emph type="italics"></emph>P<emph.end type="italics"></emph.end> I do not <lb></lb>cut the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine K <foreign lang="grc">ω,</foreign> as in the ſecond Figure, it is manifeſt that the <lb></lb><emph type="italics"></emph>P<emph.end type="italics"></emph.end>oint T, which is the Centre of Gravity of the ſubmerged <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion, <lb></lb>falleth betwixt <emph type="italics"></emph>P<emph.end type="italics"></emph.end> and I: And for the other particulars remaining, <lb></lb>they are demonſtrated 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></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 demonſtrated that the ſaid <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion ſhall not continue <lb></lb>ſo, but ſhall turn about in ſuch manner as that its Baſe do in no wiſe <lb></lb>touch the Surface of the Liquid.] <emph type="italics"></emph>Theſe words are added by us, as having been <lb></lb>omitted by<emph.end type="italics"></emph.end> Tartaglia.</s></p><p type="main"> <s><emph type="italics"></emph>N<emph.end type="italics"></emph.end>ow becauſe N O hath greater proportion to F <foreign lang="grc">ω</foreign> than unto </s></p><p type="main"> <s><arrow.to.target n="marg1221"></arrow.to.target><lb></lb>the Semi parameter.] <emph type="italics"></emph>For the Diameter of the Portion N O hath unto F<emph.end type="italics"></emph.end> <foreign lang="grc">ω</foreign> <emph type="italics"></emph>the <lb></lb>ſame proportion as fifteen to fower: But it was ſuppoſed to have leſſe proportion unto the <lb></lb>Semi-parameter than fifteen to fower: Wherefore N O hath greater proportion unto F<emph.end type="italics"></emph.end> <foreign lang="grc">ω</foreign><lb></lb><emph type="italics"></emph>than unto the Semi-parameter: And therefore<emph.end type="italics"></emph.end> (a) <emph type="italics"></emph>the Semi-parameter ſhall be greater<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1222"></arrow.to.target><lb></lb><emph type="italics"></emph>than the ſaid F<emph.end type="italics"></emph.end> <foreign lang="grc">ω.</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"></emph>By 10. of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Foraſmuch, therefore, as in the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion <emph type="italics"></emph>A P O L,<emph.end type="italics"></emph.end> contained, be<lb></lb><arrow.to.target n="marg1223"></arrow.to.target><lb></lb>twixt the Right <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine and the Section of the Rightangled Cone K <lb></lb><foreign lang="grc">ω</foreign> is parallel to A L, and <emph type="italics"></emph>P I<emph.end type="italics"></emph.end> parallel unto the Diameter, and cut by <pb xlink:href="040/01/1059.jpg" pagenum="365"></pb>the ſaid K <foreign lang="grc">ω</foreign> in H, and A S is parallel unto the Line that toucheth <lb></lb>in P; It is neceſſary that P I hath unto P H either the ſame propor<lb></lb>tion that N <foreign lang="grc">ω</foreign> hath to <foreign lang="grc">ω</foreign> O, or greater; for this hath already been <lb></lb>demonſtrated.] <emph type="italics"></emph>Where this is demonſtrated either by<emph.end type="italics"></emph.end> Archimedes <emph type="italics"></emph>himſelf, or by <lb></lb>any other, doth not appear; touching which we will here inſert a Demonſtration, after that <lb></lb>we have explained ſome things that pertaine thereto.<emph.end type="italics"></emph.end></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></lb>the point D, taken in the Line A C, draw D E and D F at <lb></lb>pleaſure unto A B: and in the ſame Line any Points G and L <lb></lb>being taken, draw G H & L M parallel to D E, & G K and <lb></lb>L N parallel unto F D: Then from the Points D & G as farre <lb></lb>as to the Line M L draw D O P, cutting G H in O, and G Q <lb></lb>parallel unto B A. </s> <s>I ſay that the Lines that lye betwixt the Pa<lb></lb>rallels unto F D have unto thoſe that lye betwixt the Par<lb></lb>allels unto D E (namely K N to G Q or to O P; F K to D O; <lb></lb>and F N to D P) the ſame mutuall proportion: that is to ſay, <lb></lb>the ſame that A F hath to A E.</s></p><p type="main"> <s><emph type="italics"></emph>For in regard that the Triangles A F D, A K G, and A N L<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.1059.1.jpg" xlink:href="040/01/1059/1.jpg"></figure><lb></lb><emph type="italics"></emph>are alike, and E F D, H K G, and M N L are alſo alike: There-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1224"></arrow.to.target><lb></lb><emph type="italics"></emph>fore,<emph.end type="italics"></emph.end> (a) <emph type="italics"></emph>as A F is to F D, ſo ſhall A K be to K G; and as F D is to <lb></lb>F E, ſo ſhall K G be to K H: Wherefore,<emph.end type="italics"></emph.end> ex equali, <emph type="italics"></emph>as A F is to F <lb></lb>E, ſo ſhall A K be to K H: And, by Converſion of proportion, as <lb></lb>A F is to A E, ſo ſhall A K be to K H. </s> <s>It is in the ſame manner <lb></lb>proved that, as A F is to A E, ſo ſhall A N be to A M. </s> <s>Now A<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1225"></arrow.to.target><lb></lb><emph type="italics"></emph>N being to A M, as A K is to A H; The<emph.end type="italics"></emph.end> (b) <emph type="italics"></emph>Remainder K N ſhall <lb></lb>be unto the Remainder H M, that is unto G Q, or unto O P, as <lb></lb>A N is to A M; that is, as A F is to A E: Again, A K is to <lb></lb>A H, as A F is to A E; Therefore the Remainder F K ſhall be to <lb></lb>the Remainder E H, namely to D O, as A F is to A E. </s> <s>We might in <lb></lb>like manner demonstrate that ſo is F N to D P: Which is that that <lb></lb>was required to be demonstrated.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1224"></margin.target>(a) <emph type="italics"></emph>By 4. of the <lb></lb>ſixth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1225"></margin.target>(b) <emph type="italics"></emph>By 5. of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>LEMMA II.</s></p><p type="main"> <s>In the ſame Line A B let there be two Points R and S, ſo diſpo<lb></lb>ſed, that A S may have the ſame Proportion to A R that <lb></lb>A F hath to A E; and thorow R draw R T parallel to E D, <lb></lb>and thorow S draw S T parallel to F D, ſo, as that it may <lb></lb>meet with R T in the Point T. </s> <s>I ſay that the Point T fall<lb></lb>eth in the Line A C.</s></p> <pb xlink:href="040/01/1060.jpg" pagenum="366"></pb><figure id="id.040.01.1060.1.jpg" xlink:href="040/01/1060/1.jpg"></figure><p type="main"> <s><emph type="italics"></emph>For if it be poſſible, let it fall ſhort of it: and let R T be pro<lb></lb>longed as farre as to A C in V: and then thorow V draw V X pa<lb></lb>rallel to F D. Now, by the thing we have last demonſtrated, A X <lb></lb>ſhall have the ſame proportion unto A R, as A F hath to A E. <lb></lb></s> <s>But A S hath alſo the ſame proportion to A R: Wherefore<emph.end type="italics"></emph.end> (a) <lb></lb><arrow.to.target n="marg1226"></arrow.to.target><lb></lb>A S <emph type="italics"></emph>is equall to A X, the part to the whole, which is impoſſi<lb></lb>ble. </s> <s>The ſame abſurdity will follow if we ſuppoſe the Toint <lb></lb>T to fall beyond the Line A C: It is therefore neceſſary that <lb></lb>it do fall in the ſaid A C. </s> <s>Which we propounded to be demonstrated.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1226"></margin.target>(a) <emph type="italics"></emph>By 9. of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>LEMMA III.</s></p><p type="main"> <s>Let there be a Parabola, whoſe Diameter <lb></lb><arrow.to.target n="marg1227"></arrow.to.target><lb></lb>let be A B; and let the Right Lines A C and B D be ^{*} con<lb></lb>tingent to it, A C in the Point C, and B D in B: And two <lb></lb>Lines being drawn thorow C, the one C E, parallel unto <lb></lb>the Diameter; the other C F, parallel to B D; take any <lb></lb>Point in the Diameter, as G; and as F B is to B G, ſo let B <lb></lb>G be to B H: and thorow G and H draw G K L, and H E <lb></lb>M, parallel unto B D; and thorow M draw M N O parallel <lb></lb>to <emph type="italics"></emph>A C,<emph.end type="italics"></emph.end> and cutting the Diameter in O: and the Line <emph type="italics"></emph>N P<emph.end type="italics"></emph.end><lb></lb>being drawn thorow <emph type="italics"></emph>N<emph.end type="italics"></emph.end> unto the Diameter let it be parallel <lb></lb>to B D. </s> <s>I ſay 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"></emph>For the Line M N O cutteth the Diameter either in G, or in other Points: and if it do <lb></lb>cut it in G, one and the ſame Point ſhall be noted by the two letters G and O. </s> <s>Therfore F C, <lb></lb>P N, and H E M being Parallels, and A C being Parallels to M N O, they ſhall make the<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.1060.2.jpg" xlink:href="040/01/1060/2.jpg"></figure><lb></lb><emph type="italics"></emph>Triangles A F C, O P N and O H M like to<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1228"></arrow.to.target><lb></lb><emph type="italics"></emph>each other: Wherefore<emph.end type="italics"></emph.end> (a) <emph type="italics"></emph>O H ſhall be to <lb></lb>H M, as A F to FC: and<emph.end type="italics"></emph.end> ^{*} Permutando, <lb></lb><arrow.to.target n="marg1229"></arrow.to.target><lb></lb><emph type="italics"></emph>O H ſhall be to A F, as H M to F C: But <lb></lb>the Square H M is to the Square G L as the Line <lb></lb>H B is to the Line B G, by 20. of our firſt Book <lb></lb>of<emph.end type="italics"></emph.end> Conicks; <emph type="italics"></emph>and the Square G L is unto the <lb></lb>Square F C, as the Line G B is to the Line B F: <lb></lb>and the Lines H B, B G and B F are thereupon<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1230"></arrow.to.target><lb></lb><emph type="italics"></emph>Proportionals: Therefore the<emph.end type="italics"></emph.end> (b) <emph type="italics"></emph>Squares <lb></lb>H M, G L and F C and there Sides, ſhall alſo be <lb></lb>Proportionals: And, therefore, as the (c) <lb></lb>Square H M is to the Square G L, ſo is the Line<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1231"></arrow.to.target><lb></lb><emph type="italics"></emph>H M to the Line F C: But as H M is to F C, ſo <lb></lb>is O H to A F; and as the Square H M is to <lb></lb>the Square G L, ſo is the Line H B to B G; that <lb></lb>is, B G to B F: From whence it followeth that <lb></lb>O H is to A F, as B G to B F: And<emph.end type="italics"></emph.end> Permu<lb></lb>tando, <emph type="italics"></emph>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></lb>are equall, by 35. of our firſt Book of<emph.end type="italics"></emph.end> Conicks: <emph type="italics"></emph>And therefore N O is double to G B: <lb></lb>Which was to be demonſtrated.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/1061.jpg" pagenum="367"></pb><p type="margin"> <s><margin.target id="marg1228"></margin.target>(a) <emph type="italics"></emph>By 4. of the <lb></lb>ſixth.<emph.end type="italics"></emph.end></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"></emph>By 22. of the <lb></lb>ſixth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1231"></margin.target>(c) <emph type="italics"></emph>By<emph.end type="italics"></emph.end> Cor. <emph type="italics"></emph>of 20. <lb></lb>of the ſixth.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>LEMMA IV.</s></p><p type="main"> <s>The ſame things aſſumed again, and M Q being drawn from the <lb></lb>Point M unto the Diameter, let it touch the Section in the <lb></lb>Point M. </s> <s>I ſay that H Q hath to Q O, the ſame proportion <lb></lb>that G H hath to C N.</s></p><p type="main"> <s><emph type="italics"></emph>For make H R equall to G F; and ſeeing that<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.1061.1.jpg" xlink:href="040/01/1061/1.jpg"></figure><lb></lb><emph type="italics"></emph>the Triangles A F C and O P N are alike, and <lb></lb>P N equall to F C, we might in like manner de<lb></lb>monſtrate P O and F A to be equall to each other: <lb></lb>Wherefore P O ſhall be double to F B: But H O <lb></lb>is double to G B: Therefore the Remainder P H <lb></lb>is alſo double to the Remainder F G; that is, to <lb></lb>R H: And therefore is followeth that P R, R H <lb></lb>and F G are equall to one another; as alſo that <lb></lb>R G and P F are equall: For P G is common to <lb></lb>both R P and G F. </s> <s>Since therefore, that H B is <lb></lb>to B G, as G B is to B F, by Converſion of Pro<lb></lb>portion, B H ſhall be to H G, as B G is to G F: <lb></lb>But Q H is to H B, as H O to B G. </s> <s>For by 35 <lb></lb>of our firſt Book of<emph.end type="italics"></emph.end> Conicks, <emph type="italics"></emph>in regard that Q <lb></lb>M toucheth the Section in the Point M, H B and <lb></lb>B Q ſhall be equall, and Q H double to H B: <lb></lb>Therefore,<emph.end type="italics"></emph.end> ex æquali, <emph type="italics"></emph>Q H ſhall be to H G, as <lb></lb>H O to G F; that is, to H R: and,<emph.end type="italics"></emph.end> Permu<lb></lb>tando, <emph type="italics"></emph>Q H ſhall be to H O, as H G to H R: again, by Converſion, H Q ſhall be to Q <lb></lb>O, as H G to G R; that is, to P F; and, by the ſame reaſon, to C N: Whichwas to be de<lb></lb>monſtrated.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Theſe things therefore being explained, we come now to that <lb></lb>which was propounded. </s> <s>I ſay, therefore, firſt that <emph type="italics"></emph>N C<emph.end type="italics"></emph.end> hath <lb></lb>to C K the ſame proportion that H G hath to G B.</s></p><p type="main"> <s><emph type="italics"></emph>For ſince that H Q is to Q O, as H G to C N<emph.end type="italics"></emph.end>; <lb></lb><figure id="id.040.01.1061.2.jpg" xlink:href="040/01/1061/2.jpg"></figure><lb></lb><emph type="italics"></emph>that is, to A O, equall to the ſaid C N: The Re<lb></lb>mainder G Q ſhall be to the Remainder Q A, as <lb></lb>H Q to Q O: and, for the ſame cauſe, the Lines <lb></lb>A C and G L prolonged, by the things that wee <lb></lb>have above demonstrated, ſhall interſect or meet <lb></lb>in the Line Q M. Again, G Q is to Q A, <lb></lb>as H Q to Q O: that is, as H G to F P; as<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1232"></arrow.to.target><lb></lb>(a) <emph type="italics"></emph>was bnt now demonstrated, But unto<emph.end type="italics"></emph.end> (b) <emph type="italics"></emph>G<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1233"></arrow.to.target><lb></lb><emph type="italics"></emph>Q two Lines taken together, Q B that is H B, and <lb></lb>B G are equall: and to Q A H F is equall; for <lb></lb>if from the equall Magnitudes H B and B Q there <lb></lb>be taken the equall Magnitudes F B and B A, the <lb></lb>Re mainder ſhall be equall; Therefore taking H <lb></lb>G from the two Lines H B and B G, there ſhall re<lb></lb>main a Magnitude double to B G; that is, O H: <lb></lb>and P F taken from F H, the Remainder is H P: <lb></lb>Wherefore<emph.end type="italics"></emph.end> (c) <emph type="italics"></emph>O H is to H P, as G Q to Q A:<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1234"></arrow.to.target><lb></lb><emph type="italics"></emph>But as G Q is to Q A, ſo is H Q to Q O;<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1062.jpg" pagenum="368"></pb><arrow.to.target n="marg1235"></arrow.to.target><lb></lb><emph type="italics"></emph>that is, H G to N C: and as<emph.end type="italics"></emph.end> (d) <emph type="italics"></emph>O H is to H P, ſo is G B to C K; For O H is double <lb></lb>to G B, and H P alſo double to G F; that is, to C K; Therefore H G hath the ſame propor<lb></lb>tion to N C, that G B hath to C K: And<emph.end type="italics"></emph.end> Permutando, <emph type="italics"></emph>N C hath to C K the ſame proportion <lb></lb>that H G hath to G B.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1232"></margin.target>(a) <emph type="italics"></emph>By<emph.end type="italics"></emph.end> 2. Lemma.</s></p><p type="margin"> <s><margin.target id="marg1233"></margin.target>(b) <emph type="italics"></emph>By<emph.end type="italics"></emph.end> 4. Lemma.</s></p><p type="margin"> <s><margin.target id="marg1234"></margin.target>(b) <emph type="italics"></emph>By 19. of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1235"></margin.target>(d) <emph type="italics"></emph>By 15. of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Then take ſome other Point at pleaſure in the Section, which <lb></lb>let be S: and thorow S draw two Lines, the one S T paral<lb></lb>lel to D B, and cutting the Diameter in the Point T; the <lb></lb>other S V parallel to A C, and cutting C E in V. </s> <s>I ſay <lb></lb>that V C hath greater proportion to C K, than T G hath <lb></lb>to G B.</s></p><p type="main"> <s><emph type="italics"></emph>For prolong V S unto the Line Q M in X; and from the Point X draw X Y unto the <lb></lb>Diameter parallel to B D: G T ſhall be leſſe than G Y, in regard that V S is leße than V X: <lb></lb>And, by the firſt Lemma, Y G ſhall be to V C, as H G to N C; that is, as G B to C K, which <lb></lb>was demonſtrated but now: And,<emph.end type="italics"></emph.end> Permutando, <emph type="italics"></emph>Y G ſhall be to G B, as V C to C K: But <lb></lb>T G, for that it is leſſe than Y G, hath leſſe proportion to G B, than Y G hath to the ſame; <lb></lb>Therefore V C hath greater proportion to C K. than T G hath to G B: Which was to be de<lb></lb>monſtrated. </s> <s>Therefore a Poſition given G K, there ſhall be in the Section one only Point, to <lb></lb>wit M, from which two Lines M E H and M N O being drawn, N C ſhall have the ſame pro<lb></lb>portion to C K, that H G hath to G B; For if they be drawn from any other, that which fall<lb></lb>eth betwixt A C, and the Line parallel unto it ſhall alwayes have greater proportion to C K, <lb></lb>than that which falleth betwixt G K and the Line parallel unto it hath to G B. That, there<lb></lb>fore, is manifeſt which was affirmed by<emph.end type="italics"></emph.end> Archimedes, <emph type="italics"></emph>to wit, that the Line P I hath unto P H, <lb></lb>either the ſame proportion that N<emph.end type="italics"></emph.end> <foreign lang="grc">ω</foreign> <emph type="italics"></emph>hath to<emph.end type="italics"></emph.end> <foreign lang="grc">ω</foreign> <emph type="italics"></emph>O, or greater.<emph.end type="italics"></emph.end><lb></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 leſſe than double.] <lb></lb><emph type="italics"></emph>If leſſe than double, let P T be double to T I: The Centre of Gravity of that part of the <lb></lb>Portion that is within the Liquid ſhall be the<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.1062.1.jpg" xlink:href="040/01/1062/1.jpg"></figure><lb></lb><emph type="italics"></emph>Point T: But if P H be double to H I, H ſhall <lb></lb>be the Centre of Gravity; And draw H F, and <lb></lb>prolong it unto the Centre of that part of the Por<lb></lb>tion which is above the Liquid, namely, unto G, <lb></lb>and the reſt is demonſtrated as before. </s> <s>And the <lb></lb>ſame is to be underſtood in the Propoſition that <lb></lb>followeth.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The Solid A P O L, therefore, <lb></lb>ſhall turn about, and its Baſe ſhall <lb></lb>not in the leaſt touch the Surface <lb></lb>of the Liquid.] <emph type="italics"></emph>In<emph.end type="italics"></emph.end> Tartaglia's <emph type="italics"></emph>Tranſlation it is rendered<emph.end type="italics"></emph.end> ut Baſis ipſius non tangent <lb></lb>ſuperficiem humidi ſecundum unum ſignum; <emph type="italics"></emph>but we have choſen to read<emph.end type="italics"></emph.end> ut Baſis ipſius <lb></lb>nullo modo humidi ſuperficiem contingent, <emph type="italics"></emph>both here, and in the following Propoſitions, <lb></lb>becauſe the Greekes frequently uſe<emph.end type="italics"></emph.end> <foreign lang="grc">ὡδὲεἶς, ὡδὲ<gap></gap></foreign> <emph type="italics"></emph>pro<emph.end type="italics"></emph.end> <foreign lang="grc">ὠδεὶσ<gap></gap> & οὐδὶν</foreign>: <emph type="italics"></emph>ſo that<emph.end type="italics"></emph.end> <foreign lang="grc">οὐδἔσινουδείς,</foreign> nullus <lb></lb>eſt; <foreign lang="grc">οὐδ<gap></gap>ὑπ̓ἑρὸς</foreign> à nullo, <emph type="italics"></emph>and ſo of others of the like nature.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/1063.jpg" pagenum="369"></pb><p type="head"> <s>PROP. VII. THE OR. VII.</s></p><p type="main"> <s><emph type="italics"></emph>The Right Portion of a Rightangled Conoid lighter <lb></lb>than the Liquid, when it ſhall have its Axis greater <lb></lb>than Seſquialter of the Semi-parameter, but leſſe <lb></lb>than to be unto the ſaid Semi-parameter in proportion <lb></lb>as fiſteen to fower, being demitted into the Liquid ſo <lb></lb>as that its Baſe be wholly within the Liquid, it ſhall <lb></lb>never ſtand ſo as that its Baſe do touch the Surface <lb></lb>of the Liquid, but ſo, that it be wholly within the <lb></lb>Liquid, and ſhall not in the leaſt touch its Surface.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let there be a Portion as hath been ſaid; and let it be de<lb></lb>mitted into the Liquid, as we have ſuppoſed, ſo as that its <lb></lb>Baſe do touch the Surface in one Point only: It is to be de<lb></lb>monſtrated that the ſame ſhall not ſo <lb></lb><figure id="id.040.01.1063.1.jpg" xlink:href="040/01/1063/1.jpg"></figure><lb></lb>continue, but ſhall turn about in <lb></lb>ſuch manner as that its Baſe do in no <lb></lb>wiſe touch the Surface of the Liquid. <lb></lb></s> <s>For let it be cut thorow its Axis by <lb></lb>a Plane erect upon the Liquids Sur<lb></lb>face: and let the Section be A P O L, <lb></lb>the Section of a Rightangled <lb></lb>Cone; the Section of the Liquids <lb></lb>Surface S L; and the Axis of the <lb></lb>Portion and Diameter of the Section P F: and let P F be cut in <lb></lb>R, ſo, as that R P may be double to R F, and in <foreign lang="grc">ω</foreign> ſo as that P F <lb></lb>may be to R <foreign lang="grc">ω</foreign> as fifteen to fower: and draw <foreign lang="grc">ω</foreign> K at Right Angles </s></p><p type="main"> <s><arrow.to.target n="marg1237"></arrow.to.target><lb></lb>to P F: <emph type="italics"></emph>(a)<emph.end type="italics"></emph.end> R <foreign lang="grc">ω</foreign> ſhall be leſſe than the Semi-parameter. </s> <s>There<lb></lb>fore let R H be ſuppoſed equall to the Semi-parameter: and <lb></lb>draw C O touching the Section in O and parallel unto S L; and <lb></lb>let N O be parallel unto P F; and firſt let N O cut K <foreign lang="grc">ω</foreign> in the Point <lb></lb>I, as in the former Schemes: It ſhall be demonſtrated that N O is <lb></lb>to O I either ſeſquialter, or greater than ſeſquialter. </s> <s>Let O I be <lb></lb>leſſe than double to I N; and let O B be double to B N: and let <lb></lb>them be diſpoſed like as before. </s> <s>We might likewiſe demonſtrate <lb></lb>that if a Line be drawn thorow R and T it will make Right Angles <lb></lb>with the Line C O, and with the Surface of the Liquid: Where<lb></lb>fore Lines being drawn from the Points B and G parallels unto <lb></lb>R T, they alſo ſhall be Perpendiculars to the Surface of the Liquid: <lb></lb>The Portion therefore which is above the Liquid ſhall move down <pb xlink:href="040/01/1064.jpg" pagenum="370"></pb><figure id="id.040.01.1064.1.jpg" xlink:href="040/01/1064/1.jpg"></figure><lb></lb>wards according to that ſame Perpendicular <lb></lb>which paſſeth thorow B; and the Portion <lb></lb>which is within the Liquid ſhall move up<lb></lb>wards acording to that paſſing thorow G: <lb></lb>From whence it is manifeſt that the Solid <lb></lb>ſhall turn about in ſuch manner, as that <lb></lb>its Baſe ſhall in no wiſe touch the Surface <lb></lb>of the Liquid; for that now when it touch<lb></lb>eth but in one Point only, it moveth down<lb></lb>wards on the part towards L. </s> <s>And though <lb></lb>N O ſhould not cut <foreign lang="grc">ω</foreign> K, yet ſhall the ſame hold true.</s></p><p type="margin"> <s><margin.target id="marg1237"></margin.target>(a) <emph type="italics"></emph>By 10 of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROP. VIII. THE OR. VIII.</s></p><p type="main"> <s><emph type="italics"></emph>The Right Portion of a Rightangled Conoid, when it <lb></lb>ſhall have its Axis greater than ſeſquialter of the Se<lb></lb>mi-parameter, but leſſe than to be unto the ſaid Semi<lb></lb>parameter, in proportion as fifteen to fower, if it <lb></lb>have a leſſer proportion in Gravity to the Liquid, than <lb></lb>the Square made of the Exceſſe by which the Axis is <lb></lb>greater than Seſquialter of the Semi-parameter hath <lb></lb>to the Square made of the Axis, being demitted into <lb></lb>the Liquid, ſo as that its Baſe touch not the Liquid, <lb></lb>it ſhall neither return to Perpendicularity, nor conti<lb></lb>nue inclined, ſave only when the Axis makes an <lb></lb>Angle with the Surface of the Liquid, equall to that <lb></lb>which we ſhall preſently ſpeak of.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let there be a Portion as hath been ſaid; and let B D be equall <lb></lb>to the Axis: and let B K be double to K D; and R K equall <lb></lb><arrow.to.target n="marg1238"></arrow.to.target><lb></lb>to the Semi-parameter: and let C B be Seſquialter of B R: <lb></lb>C D ſhall be alſo Sefquialter of K R. </s> <s>And as the Portion is to the <lb></lb>Liquid in Gravity, ſo let the Square F Q be to the Square D B; <lb></lb>and let F be double to Q: It is manifeſt, therefore, that F Q hath <lb></lb>to D B, leſs proportion than C B hath to B D; For C B is the <lb></lb>Exceſs by which the Axis is greater than Seſquialter of the Semi<lb></lb><arrow.to.target n="marg1239"></arrow.to.target><lb></lb>parameter: And, therefore, F Q is leſs than B C; and, for the <lb></lb><arrow.to.target n="marg1240"></arrow.to.target><lb></lb>ſame reaſon, F is leſs than B R. </s> <s>Let R <foreign lang="grc">ψ</foreign> be equall to F; and draw <lb></lb><foreign lang="grc">ψ</foreign> E perpendicular to B D; which let be in power or contence the <lb></lb>half of that which the Lines K R and <foreign lang="grc">ψ</foreign> B containeth; and <lb></lb>draw a Line from B to E: It is to be demonſtrated, that the <pb xlink:href="040/01/1065.jpg" pagenum="371"></pb>Portion demitted into the Liquid, like as hath been ſaid, ſhall ſtand <lb></lb>enclined ſo as that its Axis do make an Angle with the Surface of <lb></lb>the Liquid equall unto the Angle E B <foreign lang="grc">Ψ.</foreign> For demit any Portion <lb></lb>into the Liquid ſo as that its Baſe <lb></lb><figure id="id.040.01.1065.1.jpg" xlink:href="040/01/1065/1.jpg"></figure><lb></lb>touch not the Liquids Surface; <lb></lb>and, if it can be done, let the <lb></lb>Axis not make an Angle with the <lb></lb>Liquids Surface equall to the <lb></lb>Angle E B <foreign lang="grc">Ψ</foreign>; but firſt, let it be <lb></lb>greater: and the Portion being <lb></lb>cut thorow the Axis by a Plane e<lb></lb>rect unto [<emph type="italics"></emph>or upon<emph.end type="italics"></emph.end>] the Surface of <lb></lb>the Liquid, let the Section be A P <lb></lb>O L the Section of a Rightangled <lb></lb>Cone; the Section of the Surface of the Liquid X S; and let the <lb></lb>Axis of the Portion and Diameter of the Section be N O: and <lb></lb>draw P Y parallel to X S, and touching the Section A P O L in P; <lb></lb>and P M parallel to N O; and P I perpendicular to N O: and <lb></lb>moreover, let B R be equall to O <foreign lang="grc">ω,</foreign> and R K to T <foreign lang="grc">ω;</foreign> and let <foreign lang="grc">ω</foreign> H <lb></lb>be perpendicular to the Axis. </s> <s>Now becauſe it hath been ſuppoſed <lb></lb><arrow.to.target n="marg1241"></arrow.to.target><lb></lb>that the Axis of the Portion doth make an Angle with the Surface <lb></lb>of the Liquid greater than the Angle B, the Angle P Y I ſhall be <lb></lb>greater than the Angle B: Therefore the Square P I hath greater <lb></lb><arrow.to.target n="marg1242"></arrow.to.target><lb></lb>proportion to the Square Y I, than the Square E <foreign lang="grc">Ψ</foreign> hath to the <lb></lb>Square <foreign lang="grc">Ψ</foreign> B: But as the Square P I is to the Square Y I, ſo is the <lb></lb><arrow.to.target n="marg1243"></arrow.to.target><lb></lb>Line K R unto the Line I Y; and as the Square E <foreign lang="grc">Ψ</foreign> is to the Square <lb></lb><arrow.to.target n="marg1244"></arrow.to.target><lb></lb><foreign lang="grc">Ψ</foreign> B, ſo is half of the Line K R unto the Line <foreign lang="grc">Ψ</foreign> B: Wherefore <lb></lb><emph type="italics"></emph>(a)<emph.end type="italics"></emph.end> K R hath greater proportion to I Y, than the half of K R hath <lb></lb><arrow.to.target n="marg1245"></arrow.to.target><lb></lb>to <foreign lang="grc">Ψ</foreign> B: And, conſequently, I Y isleſſe than the double of <foreign lang="grc">Ψ</foreign> B, <lb></lb>and is the double of O I: Therefore O I is leſſe than <foreign lang="grc">Ψ</foreign> B; and I <foreign lang="grc">ω</foreign><lb></lb><arrow.to.target n="marg1246"></arrow.to.target><lb></lb>greater than <foreign lang="grc">Ψ</foreign> R: but <foreign lang="grc">Ψ</foreign> R is equall to F: Therefore I <foreign lang="grc">ω</foreign> is greater <lb></lb><arrow.to.target n="marg1247"></arrow.to.target><lb></lb>than F. </s> <s>And becauſe that the Portion is ſuppoſed to be in Gra<lb></lb>vity unto the Liquid, as the Square F Q is to the Square B D; and <lb></lb>ſince that as the Portion is to the Liquid in Gravity, ſo is the part <lb></lb>thereof ſubmerged unto the whole Portion; and in regard that as <lb></lb>the part thereof ſubmerged is to the whole, ſo is the Square P M to <lb></lb>the Square O N; It followeth, that the Square P M is to the Square <lb></lb>N O, as the Square F Q is to the Square B D: And therefore F <lb></lb><arrow.to.target n="marg1248"></arrow.to.target><lb></lb>Q is equall to P M: But it hath been demonſtrated that P H is <lb></lb><arrow.to.target n="marg1249"></arrow.to.target><lb></lb>greater than F: It is manifeſt, therefore, that P M is leſſe than <lb></lb>ſeſquialter of P H: And conſequently that P H is greater than <lb></lb>the double of H M. </s> <s>Let P Z be double to Z M: T ſhall be the Cen<lb></lb>tre of Gravity of the whole Solid; the Centre of that part of it <lb></lb>which is within the Liquid, the Point Z; and of the remaining <lb></lb><arrow.to.target n="marg1250"></arrow.to.target><lb></lb>part the Centre ſhall be in the Line Z T prolonged unto G. </s> <s>In <pb xlink:href="040/01/1066.jpg" pagenum="372"></pb>the ſame manner we might demon<lb></lb><figure id="id.040.01.1066.1.jpg" xlink:href="040/01/1066/1.jpg"></figure><lb></lb>ſtrate the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine T H to be perpendi<lb></lb>cular unto the Surface of the Liquid: <lb></lb>and that the Portion demerged with<lb></lb>in the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid moveth or aſcend<lb></lb>eth out of the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid according to <lb></lb>the Perpendicular that ſhall be <lb></lb>drawn thorow Z unto the Surface <lb></lb>of the Liquid; and that the part <lb></lb>that is above the Liquid deſcendeth <lb></lb>into the Liquid according to that <lb></lb>drawn thorow G: therefore the Portion will not continue ſo inclined <lb></lb>as was ſuppoſed: But neither ſhall it return to Rectitude or Per<lb></lb>pendicularity; For that of the Perpendiculars drawn thorow Z and <lb></lb>G, that paſſing thorow Z doth fall on thoſe parts which are to<lb></lb>wards L; and that that paſſeth thorow G on thoſe towards A: <lb></lb>Wherefore it followeth that the Centre Z do move upwards, <lb></lb>and G downwards: Therefore the parts of the whole Solid which <lb></lb>are towards A ſhall move downwards, and thoſe towards L up<lb></lb>wards. </s> <s>Again let the Propoſition run in other termes; and let <lb></lb>the Axis of the Portion make an Angle with the Surface of the <lb></lb><arrow.to.target n="marg1251"></arrow.to.target><lb></lb>Liquid leſſe than that which is at B. </s> <s>Therefore the Square P I <lb></lb>hath leſſer Proportion unto the Square <lb></lb><figure id="id.040.01.1066.2.jpg" xlink:href="040/01/1066/2.jpg"></figure><lb></lb>I Y, than the Square E <foreign lang="grc">Ψ</foreign> hath to the <lb></lb>Square <foreign lang="grc">Ψ</foreign> B: Wherefore K R hath <lb></lb>leſſer proportion to I Y, than the half <lb></lb>of K R hath to <foreign lang="grc">Ψ</foreign> B: And, for the <lb></lb>ſame reaſon, I Y is greater than dou<lb></lb>ble of <foreign lang="grc">Ψ</foreign> B: but it is double of O I: <lb></lb>Therefore O I ſhall be greater than <lb></lb><foreign lang="grc">Ψ</foreign> B: But the Totall O <foreign lang="grc">ω</foreign> is equall <lb></lb>to R B, and the Remainder <foreign lang="grc">ω</foreign> I leſſe <lb></lb>than <foreign lang="grc">ψ</foreign> R: Wherefore P H ſhall alſo <lb></lb>be leſſe than F. And, in regard that <lb></lb>M P is equall to F Q, it is manifeſt that P M is greater than ſeſqui<lb></lb>alter of P H; and that P H is leſſe than double of <emph type="italics"></emph>H<emph.end type="italics"></emph.end> M. <emph type="italics"></emph>L<emph.end type="italics"></emph.end>et P Z <lb></lb>be double to Z M. </s> <s>The Centre of Gravity of the whole Solid ſhall <lb></lb>again be T; that of the part which is within the Liquid Z; and <lb></lb>drawing a Line from Z to T, the Centre of Gravity of that which <lb></lb>is above the Liquid ſhall be found in that Line portracted, that is <lb></lb>in G: Therefore, Perpendiculars being drawn thorow Z and G <lb></lb><arrow.to.target n="marg1252"></arrow.to.target><lb></lb>unto the Surface of the Liquid that are parallel to T H, it followeth <lb></lb>that the ſaid Portion ſhall not ſtay, but ſhall turn about till <lb></lb>that its Axis do make an Angle with the Waters Surface greater than <lb></lb>that which it now maketh. </s> <s>And becauſe that when before we <pb xlink:href="040/01/1067.jpg" pagenum="373"></pb>did ſuppoſe that it made an Angle greater than the Angle B, the <lb></lb>Poriton did not reſt then neither; It is manifeſt that it ſhall ſtay <lb></lb><arrow.to.target n="marg1253"></arrow.to.target><lb></lb>or reſt when it ſhall make an Angle eqnall to B. </s> <s>For ſo ſhall I O <lb></lb>be equall to <foreign lang="grc">Ψ</foreign> <emph type="italics"></emph>B<emph.end type="italics"></emph.end>; and <foreign lang="grc">ω</foreign> I equall to <lb></lb><figure id="id.040.01.1067.1.jpg" xlink:href="040/01/1067/1.jpg"></figure><lb></lb><foreign lang="grc">Ψ</foreign> R; and P H equall to F: There<lb></lb>fore <emph type="italics"></emph>M P<emph.end type="italics"></emph.end> ſhall be ſeſquialter of <emph type="italics"></emph>P H,<emph.end type="italics"></emph.end><lb></lb>and <emph type="italics"></emph>P H<emph.end type="italics"></emph.end> double of H M: And there<lb></lb>fore ſince H is the Centre of Gravity <lb></lb>of that part of it which is within the <lb></lb>Liquid, it ſhall move upwards along <lb></lb>the ſame <emph type="italics"></emph>P<emph.end type="italics"></emph.end>erpendicular according to <lb></lb>which the whole <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion moveth; <lb></lb>and along the ſame alſo ſhall the part <lb></lb>which is above move downwards: <lb></lb>The <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion therefore ſhall reſt; for<lb></lb>aſmuch as the parts are not repulſed 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"></emph>By 13. of the <lb></lb>fifth.<emph.end type="italics"></emph.end></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"></emph>C B<emph.end type="italics"></emph.end> be ſeſquialter of <emph type="italics"></emph>B R<emph.end type="italics"></emph.end>: C D ſhall alſo be ſeſquialter <lb></lb><arrow.to.target n="marg1254"></arrow.to.target><lb></lb>of K R.] <emph type="italics"></emph>In the Tranſlation it is read thus:<emph.end type="italics"></emph.end> Sit autem & CB quidem hemeolia <lb></lb>ipſius B R: C D autem ipſius K R. <emph type="italics"></emph>But we at the reading of this paſſage have thought <lb></lb>fit thus to correctit; for it is not ſuppoſed ſo to be, but from the things ſuppoſed is proved to <lb></lb>be ſo. </s> <s>For if B<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>be double of<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>D, D B ſhall be ſeſquialter of B<emph.end type="italics"></emph.end> <foreign lang="grc">ψ.</foreign> <emph type="italics"></emph>And becauſe E B is <lb></lb>ſeſquialter of B R, it followeth that the<emph.end type="italics"></emph.end> (a) <emph type="italics"></emph>Remainder C D is ſeſquialter of<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>R; that is, of<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1255"></arrow.to.target><lb></lb><emph type="italics"></emph>the Semi-parameter: Wherefore B C ſhall be the Exceſſe by which the Axis is greater than <lb></lb>ſeſquialter of the Semi-parameter.<emph.end type="italics"></emph.end></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"></emph>By 19. of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And therefore F Q is leſſe than <emph type="italics"></emph>B C.] For in regard that the Portion hath<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1256"></arrow.to.target><lb></lb><emph type="italics"></emph>the ſame proportion in Gravity unto the Liquid, as the Square F Q hath to the Square D B; <lb></lb>and hath leſſer proportion than the Square made of the Exceſſe by which the Axis <lb></lb>is greater than Seſquialter of the Semi parameter, hath to the Square made of the Axis; that <lb></lb>is, leßer than the Square C B hath to the Square B D; for the Line B D was ſuppoſed to be <lb></lb>equall unto the Axis: Therefore the Square F Q ſhall have to the Square D B leſſer proporti<lb></lb>on than the Sqnare C B to the ſame Square B D: And therefore the Square<emph.end type="italics"></emph.end> (b) <emph type="italics"></emph>F Q ſhall be<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1257"></arrow.to.target><lb></lb><emph type="italics"></emph>leße than the Square C B: And, for that reaſon, the Line F Q ſhall be leße than B C.<emph.end type="italics"></emph.end></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"></emph>By 8 of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And, for the ſame reaſon, F is leſſe than <emph type="italics"></emph>B R.] For C B being ſeſqui-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1258"></arrow.to.target><lb></lb><emph type="italics"></emph>alter of B R, and F Q ſeſquialter of F<emph.end type="italics"></emph.end>: (c) F <emph type="italics"></emph>Q ſhall be likewiſe leſſe than B C; and F<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1259"></arrow.to.target><lb></lb><emph type="italics"></emph>leße than B R.<emph.end type="italics"></emph.end></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"></emph>By 14 of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Now becauſe it hath been ſuppoſed that the Axis of the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion <lb></lb><arrow.to.target n="marg1260"></arrow.to.target><lb></lb>doth make an Angle with the Surface of the Liquid greater than <lb></lb>the Angle <emph type="italics"></emph>B,<emph.end type="italics"></emph.end> the Angle <emph type="italics"></emph>P Y I<emph.end type="italics"></emph.end> ſhall be greater than the Angle <emph type="italics"></emph>B.] <lb></lb>For the Line P Y being parallel to the Surface of the Liquid, that is, to XS<emph.end type="italics"></emph.end>; (d) <emph type="italics"></emph>the Angle<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1261"></arrow.to.target><lb></lb><emph type="italics"></emph>P Y I ſhall be equall to the Angle contained betwixt the Diameter of the Portion N O, and the <lb></lb>Line X S: And therefore ſhall be greater than the Angle B.<emph.end type="italics"></emph.end></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"></emph>By 29 of the <lb></lb>firſt.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Therefore the Square <emph type="italics"></emph>P I<emph.end type="italics"></emph.end> hath greater proportion to the Square <lb></lb><arrow.to.target n="marg1262"></arrow.to.target><lb></lb>Y I, than the Square E <foreign lang="grc">Ψ</foreign> hath to the Square <foreign lang="grc">Ψ</foreign> <emph type="italics"></emph>B] Let the Triangles P I Y <lb></lb>and E<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>B, be deſcribed apart: And ſeeing that the Angle P Y I is greater <lb></lb>than the Angle E B<emph.end type="italics"></emph.end> <foreign lang="grc">ψ,</foreign> <emph type="italics"></emph>unto the Line I Y, and at the Point Y aſſigned in<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.1067.2.jpg" xlink:href="040/01/1067/2.jpg"></figure><lb></lb><emph type="italics"></emph>the ſame, make the Angle V Y I equall to the Angle E B<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign>; <emph type="italics"></emph>But <lb></lb>the Right Angle at I, is equall unto the Right Angle at<emph.end type="italics"></emph.end> <foreign lang="grc">ψ;</foreign> <emph type="italics"></emph>therefore the<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1068.jpg" pagenum="374"></pb><emph type="italics"></emph>Remaining Angle Y V I is equall to the Remaining Angle B E<emph.end type="italics"></emph.end> <foreign lang="grc">ψ.</foreign> <emph type="italics"></emph>And therefore the<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1263"></arrow.to.target><lb></lb>(e) <emph type="italics"></emph>Line V I hath to the Line I Y the ſame proportion that the Line E<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>hath to<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>B: But <lb></lb>the<emph.end type="italics"></emph.end> (f) <emph type="italics"></emph>Line P I, which is greater than V I, hath unto I Y greater proportion than V I hath un-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1264"></arrow.to.target><lb></lb><emph type="italics"></emph>to the ſame: Therefore<emph.end type="italics"></emph.end> (g) <emph type="italics"></emph>T I ſhall have greater proportion unto I Y, than E<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>hath to<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>B: <lb></lb>And, by the ſame reaſon, the Square T I ſhall have greater proportion to the Square I Y, than<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1265"></arrow.to.target><lb></lb><emph type="italics"></emph>the Square E<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>hath to the Square<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>B.<emph.end type="italics"></emph.end><lb></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"></emph>By 4. of the <lb></lb>ſixth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1264"></margin.target>(f) <emph type="italics"></emph>By 8. of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1265"></margin.target>(g) <emph type="italics"></emph>By 13 of the <lb></lb>fifth.<emph.end type="italics"></emph.end></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, ſo is the Line K R unto <lb></lb>the Line I Y] <emph type="italics"></emph>For by 11. of the firſt of our<emph.end type="italics"></emph.end> Conicks, <emph type="italics"></emph>the Square P I is equall <lb></lb>to the Rectangle contained under the Line I O, and under the Parameter; which <lb></lb>we ſuppoſed to be eqnall to the Semi-parameter; that is, the double of K R<emph.end type="italics"></emph.end>: </s></p><p type="main"> <s><arrow.to.target n="marg1267"></arrow.to.target><lb></lb><emph type="italics"></emph>But I Y is double of I O, by 33 of the ſame: And, therefore, the<emph.end type="italics"></emph.end> (h) <emph type="italics"></emph>Rectangle made of K R <lb></lb>and I Y, is equall to the Rectangle contained under the Line I O, and under the Parameter;<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1268"></arrow.to.target><lb></lb><emph type="italics"></emph>that is, to the Square P I: But as the<emph.end type="italics"></emph.end> (i) <emph type="italics"></emph>Rectangle compounded of K R and I Y is to the <lb></lb>Square I Y, ſo is the Line K R unto the Line I Y: Therefore the Line K R ſhall have unto I <lb></lb>Y, the ſame proportion that the Rectangle compounded of K R and I Y; that is, the Square P I <lb></lb>hath to the Square I Y.<emph.end type="italics"></emph.end><lb></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"></emph>By 26. of the <lb></lb>ſixth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1268"></margin.target>(i) <emph type="italics"></emph>By<emph.end type="italics"></emph.end> Lem. </s> <s>22 <emph type="italics"></emph>of <lb></lb>the tenth.<emph.end type="italics"></emph.end></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="grc">Ψ</foreign> is to the Square <foreign lang="grc">Ψ</foreign> B, ſo is half of the <lb></lb>Line K R unto the Line <foreign lang="grc">ψ</foreign> B.] <emph type="italics"></emph>For the Square E<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>having been ſuppoſed equall <lb></lb>to half the Rectangle contained under the Line K R and<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>B; that is, to that contained under <lb></lb>the half of K R and the Line<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>B; and ſeeing that as the<emph.end type="italics"></emph.end> (k) <emph type="italics"></emph>Rectangle made of half K R<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1270"></arrow.to.target><lb></lb><emph type="italics"></emph>and of B<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>is to the Square<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>B, ſo is half K R unto the Line<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>B; the half of K R ſhall have <lb></lb>the ſame proportion to<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>B, as the Square E<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>hath to the Square<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>B.<emph.end type="italics"></emph.end><lb></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"></emph>By<emph.end type="italics"></emph.end> Lem. </s> <s>22 <emph type="italics"></emph>of <lb></lb>the tenth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1271"></margin.target>H</s></p><p type="main"> <s>And, conſequently, I Y is leſſe than the double of <foreign lang="grc">ψ</foreign> B.] <lb></lb><emph type="italics"></emph>For, as half K R is to<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>B, ſo is K R to another Line: it ſhall be<emph.end type="italics"></emph.end> (1) <emph type="italics"></emph>greater than I Y; that<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1272"></arrow.to.target><lb></lb><emph type="italics"></emph>is, than that to which K R hath leſſer proportion; and it ſhall be double of<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>B: Therefore <lb></lb>I Y is leſſe than the double of<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>B.<emph.end type="italics"></emph.end><lb></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"></emph>By 10 of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1273"></margin.target>K</s></p><p type="main"> <s>And I <foreign lang="grc">ω</foreign> greater than <foreign lang="grc">ψ</foreign> R.] <emph type="italics"></emph>For O having been ſuppoſed equall to B R, <lb></lb>if from B R,<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>B be taken, and from O<emph.end type="italics"></emph.end> <foreign lang="grc">ω,</foreign> <emph type="italics"></emph>O I, which is leſſer than B, be taken; the <lb></lb>Remainder I<emph.end type="italics"></emph.end> <foreign lang="grc">ω</foreign> <emph type="italics"></emph>ſhall be greater than the Remainder<emph.end type="italics"></emph.end> <foreign lang="grc">Ψ</foreign> <emph type="italics"></emph>R.<emph.end type="italics"></emph.end></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"></emph>By the fourteenth of the fifth of<emph.end type="italics"></emph.end><lb></lb>Euclids <emph type="italics"></emph>Elements: For the Line O N is equall to B D.<emph.end type="italics"></emph.end></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 demonſtrated that P H is greater than F.] <lb></lb><emph type="italics"></emph>For it was demonſtrated that I<emph.end type="italics"></emph.end> <foreign lang="grc">ω</foreign> <emph type="italics"></emph>is greater than F: And P H is equall to I<emph.end type="italics"></emph.end> <foreign lang="grc">ω.</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 ſame manner we might demonſtrate the Line T H <lb></lb>to be Perpendicular unto the Surface of the Liquid.] <emph type="italics"></emph>For T<emph.end type="italics"></emph.end> <foreign lang="grc">α</foreign> <emph type="italics"></emph>is equall <lb></lb>to K R; that is, to the Semi-parameter: And, therefore, by the things above demonstrated, <lb></lb>the Line T H ſhall be drawn Perpendicular unto the Liquids Surface.<emph.end type="italics"></emph.end></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 leſſer proportion unto the <lb></lb>Square I Y, than the Square E <foreign lang="grc"><gap></gap></foreign> hath to the Square <foreign lang="grc">ψ</foreign> B.] <lb></lb><emph type="italics"></emph>Theſe, and other particulars of the like nature, that follow both in this and the following <lb></lb>Propoſitions, ſhall be demonſtrated by us no otherwiſe than we have done above.<emph.end type="italics"></emph.end></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></lb>the Surface of the Liquid, that are parallel to T H, it followeth <lb></lb>that the ſaid Portion ſhall not ſtay, but ſhall turn about till that its <lb></lb>Axis do make an Angle with the Waters Surface greater than that <lb></lb>which it now maketh.] <emph type="italics"></emph>For in that the Line drawn thorow G, doth fall perpendicu<lb></lb>larly towards thoſe parts which are next to L; but that thorow Z, towards thoſe next to A; <lb></lb>It is neceſſary that the Centre G do move downwards, and Z upwards: and, therefore, the <lb></lb>parts of the Solid next to L ſhall move downwards, and thoſe towards A upwards, that the <lb></lb>Axis may makea greater Angle with the Surface of the Liquid.<emph.end type="italics"></emph.end></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 ſo ſhall I O be equall to <foreign lang="grc">ψ</foreign> B; and <foreign lang="grc">ω</foreign> I equall to I R; and <lb></lb>P H equall to F.] <emph type="italics"></emph>This plainly appeareth in the third Figure, which is added by us.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/1069.jpg" pagenum="375"></pb><p type="head"> <s>PROP. IX. THE OR. IX.</s></p><p type="main"> <s><emph type="italics"></emph>The Right Portion of a Rightangled Conoid, when it <lb></lb>ſhall have its Axis greater than Seſquialter of the <lb></lb>Semi-parameter, but leſſer than to be unto the ſaid <lb></lb>Semi-parameter in proportion as fifteen to four, and <lb></lb>hath greater proportion in Gravity to the Liquid, than <lb></lb>the exceſs by which the Square made of the Axis is <lb></lb>greater than the Square made of the Exceſs, by which <lb></lb>the Axis is greater than Seſquialter of the Semi<lb></lb>parameter, hath to the Square made of the Axis, <lb></lb>being demitted into the Liquid, ſo as that its Baſe <lb></lb>be wholly within the Liquid, and being ſet inclining<lb></lb>it ſhall neither turn about, ſo as that its Axis ſtand <lb></lb>according to the Perpendicular, nor remain inclined, <lb></lb>ſave only when the Axis makes an Angle with <lb></lb>the Surface of the Liquid, equall to that aßigned <lb></lb>as before.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let there be a Portion as was ſaid; and ſuppoſe D B equall to <lb></lb>the Axis of the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion: and let B K be double to K D; and <lb></lb>K R equall to the Semi-parameter: and C B Seſquialter of <lb></lb>B R. </s> <s>And as the Portion is to the Liquid in Gravity, ſo let the Ex<lb></lb>ceſſe by which the Square B D exceeds the Square F Q be to the <lb></lb>Square B D: and let F be double to Q: It is manifeſt, therefore, <lb></lb>that the Exceſſe by which the <lb></lb><figure id="id.040.01.1069.1.jpg" xlink:href="040/01/1069/1.jpg"></figure><lb></lb>Square B D is greater than the <lb></lb>Square B C hath leſser proportion <lb></lb>to the Square B D, than the Exceſs <lb></lb>by which the Square B D is greater <lb></lb>than the Square F Q hath to the <lb></lb>Square B D; for B C is the Exceſs <lb></lb>by which the Axis of the Portion is <lb></lb>greater than Seſquialter of the <lb></lb>Semi-parameter: And, therefore, </s></p><p type="main"> <s><arrow.to.target n="marg1280"></arrow.to.target><lb></lb>the Square B D doth more exceed <lb></lb>the Square F Q, than doth the <lb></lb>Square B C: And, conſequently, the Line F Q is leſs than B C; <pb xlink:href="040/01/1070.jpg" pagenum="376"></pb>and F leſs than B R. </s> <s>Let R <foreign lang="grc">Ψ</foreign> be equall to F; and draw <foreign lang="grc">Ψ</foreign> E <lb></lb>perpendicular to B D; which let be in power the half of that <lb></lb>which the Lines K R and <foreign lang="grc">Ψ</foreign> B containeth; and draw a Line from <lb></lb>B to E: I ſay that the Portion demitted into the Liquid, ſo as that <lb></lb>its Baſe be wholly within the Liquid, ſhall ſo ſtand, as that its Axis <lb></lb>do make an Angle with the Liquids Surface, equall to the Angle B. <lb></lb></s> <s>For let the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion be demitted into the Liquid, as hath been ſaid; <lb></lb>and let the Axis not make an Angle with the Liquids Surface, equall <lb></lb>to B, but firſt a greater: and the ſame being cut thorow the Axis <lb></lb>by a Plane erect unto the Surface of the Liquid, let the Section of <lb></lb>the Portion be A P O L, the Section of a Rightangled Cone; the <lb></lb>Section of the Surface of the Liquid <foreign lang="grc">Γ</foreign> I; and the Axis of the <lb></lb>Portion and Diameter of the Section N O; which let be cut in <lb></lb>the Points <foreign lang="grc">ω</foreign> and T, as before: and draw Y P, parallelto <foreign lang="grc">Γ</foreign> I, and <lb></lb>touching the Section in P, and MP parallel to N O, and P S perpen<lb></lb>dicular to the Axis. </s> <s>And becauſe now that the Axis of the Portion <lb></lb>maketh an <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ngle with the Liquids Surface greater than the Angle <lb></lb>B, the Angle S Y P ſhall alſo be greater than the Angle B: And, <lb></lb>therefore, the Square P S hath greater proportion to the Square <lb></lb><arrow.to.target n="marg1281"></arrow.to.target><lb></lb>S Y, than the Square <foreign lang="grc">Ψ</foreign> E hath to the Square <foreign lang="grc">Ψ</foreign> B: And, for that <lb></lb>cauſe, K R hath greater proportion to S Y, than the half of K R <lb></lb>hath to <foreign lang="grc">Ψ</foreign> B: Therefore, S Y is leſs than the double of <foreign lang="grc">Ψ</foreign> B; and <lb></lb><arrow.to.target n="marg1282"></arrow.to.target><lb></lb>S O leſs than <foreign lang="grc">ψ</foreign> B: <emph type="italics"></emph>A<emph.end type="italics"></emph.end>nd, therefore, S <foreign lang="grc">ω</foreign> is greater than R <foreign lang="grc">ψ</foreign>; and <lb></lb><arrow.to.target n="marg1283"></arrow.to.target><lb></lb>P H greater than F. <emph type="italics"></emph>A<emph.end type="italics"></emph.end>nd, becauſe that the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion hath the <lb></lb>ſame proportion in Gravity unto the Liquid, that the Exceſs by <lb></lb>which the Square B D, is greater than the Square F Q, hath unto <lb></lb>the Square B D; and that as the Portion is in proportion to the <lb></lb>Liquid in Gravity, ſo is the part thereof ſubmerged unto the whole <lb></lb>Portion; It followeth that the part ſubmerged, hath the ſame <lb></lb>proportion to the whole <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion, that the Exceſs by which the <lb></lb>Square B D is greater than the Square F Q hath unto the Square <lb></lb>B D: <emph type="italics"></emph>A<emph.end type="italics"></emph.end>nd, therefore, the whole <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion ſhall have the ſame propor<lb></lb><arrow.to.target n="marg1284"></arrow.to.target><lb></lb>tion to that part which is above the <lb></lb><figure id="id.040.01.1070.1.jpg" xlink:href="040/01/1070/1.jpg"></figure><lb></lb>Liquid, that the Square B D hath to <lb></lb>the Square F Q: But as the whole <lb></lb>Portion is to that part which is above <lb></lb>the Liquid, ſo is the Square N O unto <lb></lb>the Square P M: Therefore, P M <lb></lb>ſhall be equall to F Q: But it <lb></lb>hath been demonſtrated, that P H is <lb></lb>greater than F. And, therefore, <lb></lb>MH ſhall be leſs than <expan abbr="q;">que</expan> and P H <lb></lb>greater than double of H M. </s> <s>Let <lb></lb>therefore, P Z be double to Z M: <pb xlink:href="040/01/1071.jpg" pagenum="377"></pb>and drawing a Line from Z to T pro<lb></lb><figure id="id.040.01.1071.1.jpg" xlink:href="040/01/1071/1.jpg"></figure><lb></lb>long it unto G. </s> <s>The Centre of <lb></lb>Gravity of the whole Portion ſhall <lb></lb>be T; of that part which is above <lb></lb>the Liquid Z; and of the Remain<lb></lb>der which is within the Liquid, the <lb></lb>Centre ſhall be in the Line Z T pro<lb></lb>longed; let it be in G: It ſhall be <lb></lb>demonſtrated, as before, that T H <lb></lb>is perpendicular to the Surface of <lb></lb>the Liquid, and that the Lines <lb></lb>drawn thorow Z and G parallel to the ſaid T H, are alſo perpen<lb></lb>diculars unto the ſame: Therefore, the Part which is above the <lb></lb>Liquid ſhall move downwards, along that which paſseth thorow Z; <lb></lb>and that which is within it, ſhall move upwards, along that which <lb></lb>paſseth thorow G: And, therefore, the Portion ſhall not remain <lb></lb>ſo inclined, nor ſhall ſo turn about, as that its Axis be perpendicular <lb></lb><arrow.to.target n="marg1285"></arrow.to.target><lb></lb>unto the Surface of the Liquid; for the parts towards L ſhall move <lb></lb>downwards, and thoſe towards <emph type="italics"></emph>A<emph.end type="italics"></emph.end> upwards; as may appear by <lb></lb>the things already demonſtrated. </s> <s>And, if the Axis ſhould make <lb></lb>an Angle with the Surface of the Liquid, leſs than the Angle B; <lb></lb>it ſhall in like manner be demonſtrated, that the Portion will not <lb></lb><arrow.to.target n="marg1286"></arrow.to.target><lb></lb>reſt, but incline untill that its Axis do make an Angle with the <lb></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></lb><arrow.to.target n="marg1287"></arrow.to.target><lb></lb>F Q, than doth the Square B C: And, conſequently, the Line <lb></lb>F Q, is leſs than B C; and F leſs than B R.] <emph type="italics"></emph>Becauſe the Exceſs by <lb></lb>which the Square B D exceedeth the Square B C; having leſs proportion unto the Square B D, <lb></lb>than the Exceſs by which the Square B D exceedeth the Square F Q, hath to the ſaid Square<emph.end type="italics"></emph.end>; <lb></lb>(a) <emph type="italics"></emph>the Exceſs by which the Square B D exceedeth the Square B C ſhall be leſs than the Exceſs<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1288"></arrow.to.target><lb></lb><emph type="italics"></emph>by which it exceedeth the Square F Q: Therefore, the Square F Q is leſs than the Square B C: <lb></lb>and, conſquently, the Line F Q leſs than the Line BC: But F Q hath the ſameproportion <lb></lb>to F, that B C hath to B R; for the Antecedents are each Seſquialter of their conſequents: <lb></lb>And<emph.end type="italics"></emph.end> (b) <emph type="italics"></emph>F Q being leſs than B C, F ſhall alſo be leſs than B R.<emph.end type="italics"></emph.end><lb></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"></emph>By 8. of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1289"></margin.target>(b) <emph type="italics"></emph>By 14. of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And, for that cauſe, K R hath greater proportion to S Y, than <lb></lb>the half of K R hath to <foreign lang="grc">ψ</foreign> B.] <emph type="italics"></emph>For K R is to S Y, as the Square P S is to the Square<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1290"></arrow.to.target><lb></lb><emph type="italics"></emph>S Y: and the half of the Line K R is to the Line<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>B, as the Square E<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>is to the Square<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>B.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1290"></margin.target>B</s></p><p type="main"> <s>And S O leſs than <foreign lang="grc">ψ</foreign> B.] <emph type="italics"></emph>For S Y is double of S O.<emph.end type="italics"></emph.end><lb></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"></emph>For P H is equall to S<emph.end type="italics"></emph.end> <foreign lang="grc">ω,</foreign> <emph type="italics"></emph>and R<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>equall to F.<emph.end type="italics"></emph.end></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 ſhall have the ſame propor</s></p><p type="main"> <s><arrow.to.target n="marg1293"></arrow.to.target><lb></lb>tion to that part which is above the Liquid, that the Square B D <lb></lb>hath to the Square F Q] <emph type="italics"></emph>Becauſe that the part ſubmerged, being to the whole Portion <lb></lb>as the Exceſs by which the Square B D is greater than the Square F Q, is to the Square B D; <lb></lb>the whole Portion, Converting, ſhall be to the part thereof ſubmerged, as the Square B D is to<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1072.jpg" pagenum="378"></pb><emph type="italics"></emph>the Exceſs by which it exceedeth the Square F Q: And, therefore, by Converſion of Proportion, <lb></lb>the whole Portion is to the part thereof above the Liquid, as the Square B D is to the Square, <lb></lb>F <expan abbr="q;">que</expan> for the Square B D is ſo much greater than the Exceſs by which it exceedeth the Squar, <lb></lb>F Q as is the ſaid Square F <expan abbr="q.">que</expan><emph.end type="italics"></emph.end><lb></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 ſhall move downwards, and thoſe to<lb></lb>wards A upwards.] <emph type="italics"></emph>We thus carrect theſe words, for in<emph.end type="italics"></emph.end> Tartaglia's <emph type="italics"></emph>Tranſlation it <lb></lb>is falſly, as I conceive, read<emph.end type="italics"></emph.end> Quoniam quæ ex parte L ad ſuperiora ferentur, <emph type="italics"></emph>becauſe <lb></lb>the Line thàt paſſeth thorow Z falls perpendicularly on the parts towards L, and that thorow<lb></lb>G falleth perpendicularly on the parts towards A: Whereupon the Centre Z, together with thoſe <lb></lb>parts which are towards L ſhall move downwards; and the Centre G, together with the parts <lb></lb>which are towards A upwards.<emph.end type="italics"></emph.end></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 ſhall in like manner be demonſtrated that the Portion ſhall not <lb></lb>reſt, but incline untill that its Axis do make an Angle with the <lb></lb>Surface of the Liquid, equall to the Angle B.] <emph type="italics"></emph>This may be eaſily demon<lb></lb>ſtratred, as nell from what hath been ſaid in the precedent Propoſition, as alſo from the two <lb></lb>latter Figures, by us inſerted<emph.end type="italics"></emph.end></s></p><p type="head"> <s>PROP. X. THEOR. X.</s></p><p type="main"> <s><emph type="italics"></emph>The Right Portion of a Rightangled Conoid, lighter <lb></lb>than the Liquid, when it ſhall have its Axis greater <lb></lb>than to be unto the Semiparameter, in proportion as <lb></lb>fifteen to four, being demitted into the Liquid, ſo as<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1296"></arrow.to.target><lb></lb><emph type="italics"></emph>that its Baſe touch not the ſame, it ſhall ſometimes<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1297"></arrow.to.target><lb></lb><emph type="italics"></emph>ſtand perpendicular; ſometimes inclined; and ſome<lb></lb>times ſo inclined, as that its Baſe touch the Surface <lb></lb>of the Liquid in one Point only, and that in two Po-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1298"></arrow.to.target><lb></lb><emph type="italics"></emph>ſitions; ſometimes ſo that its Baſe be more ſubmer-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1299"></arrow.to.target><lb></lb><emph type="italics"></emph>ged in the Liquid; and ſometimes ſo as that it doth <lb></lb>not in the leaſt touch the Surface of the Liquid;<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1300"></arrow.to.target><lb></lb><emph type="italics"></emph>according to the proportion that it hath to the Liquid <lb></lb>in Gravity. </s> <s>Every one of which Caſes ſhall be anon <lb></lb>demonſtrated.<emph.end type="italics"></emph.end></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 ſaid; and it being cut <lb></lb>thorow its Axis, by a Plane erect unto the Superficies of the <lb></lb>Liquid, let the Section be A P O L, the Section of a Right <lb></lb>angled Cone; and the Axis of the Portion and Diameter of the <lb></lb>Section B D: and let B D be cut in the Point K, ſo as that B K <lb></lb>be double of K D; and in C, ſo as that B D may have the ſame <lb></lb><arrow.to.target n="marg1301"></arrow.to.target><lb></lb>proportion to K C, as fifteen to four: It is manifeſt, therefore, <lb></lb><arrow.to.target n="marg1302"></arrow.to.target><lb></lb>that K C is greater than the Semi-parameter: Let the Semi <pb xlink:href="040/01/1073.jpg" pagenum="379"></pb>parameter be equall to K R: and <lb></lb><figure id="id.040.01.1073.1.jpg" xlink:href="040/01/1073/1.jpg"></figure><lb></lb><arrow.to.target n="marg1303"></arrow.to.target><lb></lb>let D S be Seſquialter of K R: but <lb></lb>S B is alſo Seſquialter of B R: <lb></lb>Therefore, draw a Line from A to <lb></lb>B; and thorow C draw C E Per<lb></lb>pendicular to B D, cutting the Line <lb></lb>A B in the Point E; and thorow E <lb></lb>draw E Z parallel unto B D. Again, <lb></lb>A B being divided into two equall <lb></lb>parts in T, draw T H parallel to the <lb></lb>ſame B D: and let Sections of <lb></lb>Rightangled Cones be deſcribed, A E I about the Diameter E Z; <lb></lb>and A T D about the Diameter T H; and let them be like to the <lb></lb><arrow.to.target n="marg1304"></arrow.to.target><lb></lb>Portion A B L: Now the Section of the Cone A E I, ſhall paſs <lb></lb><arrow.to.target n="marg1305"></arrow.to.target><lb></lb>thorow K; and the Line drawn from R perpendicular unto B D, <lb></lb>ſhall cut the ſaid A E I; let it cut it in the Points Y G: and <lb></lb>thorow Y and G draw P Y Q and O G N parallels unto B D, and <lb></lb>cutting A T D in the Points F and X: laſtly, draw P <foreign lang="grc">Φ</foreign> and O X <lb></lb>touching the Section A P O L in the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>oints P and O. </s> <s>In regard, <lb></lb><arrow.to.target n="marg1306"></arrow.to.target><lb></lb>therefore, that the three <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortions A P O L, A E I, and A T D are <lb></lb>contained betwixt Right Lines, and the Sections of Rightangled <lb></lb>Cones, and are right alike and unequall, touching one another, upon <lb></lb>one and the ſame Baſe; and N X G O being drawn from the <lb></lb><emph type="italics"></emph>P<emph.end type="italics"></emph.end>oint N upwards, and Q F Y P from Q: O G ſhall have to G X <lb></lb>a proportion compounded of the proportion, that I L hath to L A, <lb></lb>and of the proportion that A D hath to DI: But I L is to L A, <lb></lb>as two to five: And C B is to B D, as ſix to fifteen; that is, as two <lb></lb><arrow.to.target n="marg1307"></arrow.to.target><lb></lb>to five: And as C B is to B D, ſo is <emph type="italics"></emph>E B to B A<emph.end type="italics"></emph.end>; and D Z to <lb></lb><arrow.to.target n="marg1308"></arrow.to.target><lb></lb>D A: And of D Z and D A, L I and L A are double: and A D <lb></lb><arrow.to.target n="marg1309"></arrow.to.target><lb></lb>is to D I, as five to one: <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ut the proportion compounded of the <lb></lb>proportion of two to five, and of the proportion of five to one, is <lb></lb><arrow.to.target n="marg1310"></arrow.to.target><lb></lb>the ſame with that of two to one: and two is to one, in double <lb></lb>proportion: Therefore, O G is double of GX: and, in the ſame <lb></lb>manner is P Y proved to be double of Y F: Therefore, ſince that <lb></lb>D S is Seſquialter of K R; <emph type="italics"></emph>B S<emph.end type="italics"></emph.end> ſhall be the Exceſs by which the <lb></lb>Axis is greater than Seſquialter of the Semi-parameter. </s> <s>If there<lb></lb>fore, the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion have the ſame proportion in Gravity unto the <lb></lb>Liquid, as the Square made of the Line <emph type="italics"></emph>B S,<emph.end type="italics"></emph.end> hath to the Square <lb></lb>made of <emph type="italics"></emph>B D,<emph.end type="italics"></emph.end> or greater, being demitted into the Liquid, ſo as hat <lb></lb>its <emph type="italics"></emph>B<emph.end type="italics"></emph.end>aſe touch not the Liquid, it ſhall ſtand erect, or perpendicular: <lb></lb>For it hath been demonſtrated above, that the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion whoſe <lb></lb><arrow.to.target n="marg1311"></arrow.to.target><lb></lb>Axis is greater than Seſquialter of the Semi-parameter, if it have <lb></lb>not leſser proportion in Gravity unto the Liquid, than the Square <pb xlink:href="040/01/1074.jpg" pagenum="380"></pb>made of the Exceſs by which the Axis is greater than Seſquialter <lb></lb>of the Semi-parameter, hath to the Square made of the Axis, being <lb></lb>demitted into the Liquid, ſo as hath been ſaid, it ſhall ſtand erect, <lb></lb>or <emph type="italics"></emph>P<emph.end type="italics"></emph.end>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"></emph>The particulars contained in this Tenth Propoſition, are divided by<emph.end type="italics"></emph.end> Archimedes <lb></lb><emph type="italics"></emph>into five Parts and Concluſions, each of which he proveth by a diſtinct Demonſtration.<emph.end type="italics"></emph.end><lb></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 ſhall ſometimes ſtand perpendicular.] <emph type="italics"></emph>This is the firſt Concluſion, the <lb></lb>Demonstration of which he hath ſubjoyned to the Propoſition.<emph.end type="italics"></emph.end></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 ſometimes ſo inclined, as that its Baſe touch the Surface <lb></lb>of the Liquid, in one Point only.] <emph type="italics"></emph>This is demonſtrated in the third Con<lb></lb>cluſion.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Sometimes, ſo that its Baſe be moſt ſubmerged in the Liquid.] </s></p><p type="main"> <s><arrow.to.target n="marg1314"></arrow.to.target><lb></lb><emph type="italics"></emph>This pertaineth unto the fourth Concluſion.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1314"></margin.target>C</s></p><p type="main"> <s><emph type="italics"></emph>A<emph.end type="italics"></emph.end>nd, ſometimes, ſo as that it doth not in the leaſt touch the Sur<lb></lb><arrow.to.target n="marg1315"></arrow.to.target><lb></lb>face of the Liquid.] <emph type="italics"></emph>This it doth hold true two wayes, one of which is explained is <lb></lb>the ſecond, and the other in the fifth Concluſion.<emph.end type="italics"></emph.end></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></lb><arrow.to.target n="marg1316"></arrow.to.target><lb></lb>vity. </s> <s>Every one of which Caſes ſhall be anon demonſtrated.] <lb></lb><emph type="italics"></emph>In<emph.end type="italics"></emph.end> Tartaglia's <emph type="italics"></emph>Verſion it is rendered, to the confuſion of the ſence,<emph.end type="italics"></emph.end> Quam autem pro<lb></lb>portionem habeant ad humidum in Gravitate fingula horum demonſtrabuntur.</s></p><p type="margin"> <s><margin.target id="marg1316"></margin.target>E</s></p><p type="main"> <s>It is manifeſt, therefore, that K C is greater than the Semi<lb></lb><arrow.to.target n="marg1317"></arrow.to.target><lb></lb>parameter] <emph type="italics"></emph>For, ſince B D hath to K C the ſame proportion, as fifteen to four, and <lb></lb>hath unto the Semi-parameter greater proportion; (a) the Semi-parameter ſhall be leſs<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1318"></arrow.to.target><lb></lb><emph type="italics"></emph>than K C.<emph.end type="italics"></emph.end></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"></emph>By 10. of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the Semi-parameter be equall to KR.] <emph type="italics"></emph>We have added theſe words,<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1319"></arrow.to.target><lb></lb><emph type="italics"></emph>which are not to be found in<emph.end type="italics"></emph.end> Tartaglia.</s></p><p type="margin"> <s><margin.target id="marg1319"></margin.target>G</s></p><p type="main"> <s>But S B is alſo Seſquialter of BR.] <emph type="italics"></emph>For, D B is ſuppoſed Seſquialter of<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1320"></arrow.to.target><lb></lb><emph type="italics"></emph>B K; and D S alſo is Seſquialter of K R: Wherefore as<emph.end type="italics"></emph.end> (b) <emph type="italics"></emph>the whole D B, is to the whole <lb></lb>B K, ſo is the part D S to the part K R. Therefore, the Remainder S B, is alſo to the<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1321"></arrow.to.target><lb></lb><emph type="italics"></emph>Remainder B R, as D B is to B K.<emph.end type="italics"></emph.end></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"></emph>By 19 of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>A<emph.end type="italics"></emph.end>nd let them be like to the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion <emph type="italics"></emph>A B L.<emph.end type="italics"></emph.end>] Apollonius <emph type="italics"></emph>thus defineth<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1322"></arrow.to.target><lb></lb><emph type="italics"></emph>like Portions of the Sections of a Cone, in<emph.end type="italics"></emph.end> Lib. 6. Conicornm, <emph type="italics"></emph>as<emph.end type="italics"></emph.end> Eutocius <emph type="italics"></emph>writeth<emph.end type="italics"></emph.end> ^{*}; <lb></lb><arrow.to.target n="marg1323"></arrow.to.target><lb></lb><foreign lang="grc">ὄν οἱ̄ς ἀχ δεισω̄ν ὄν ἑχάσῳ ωαραλλήλων τη̄ <35>ὰσει, ἵσων τὸ πλη̄ο<34>, αἱ παράλληλος, καὶ ἁι <35>άσεις ωρὸς τάς αποτρμ<gap></gap><lb></lb>νομένας ἀπὸ <gap></gap> διαμέτσων τω̄ς κορυφαῑς ἐν τοῑς ἀντοῑς λόγοις εἰσι, καὶ αἱ ἀποτεμνόμεναι ωρὸς τὰς ἀ τεμνομίνασ<gap></gap></foreign><lb></lb><emph type="italics"></emph>that is,<emph.end type="italics"></emph.end> In both of which an equall number of Lines being drawn parallel to the <lb></lb>Baſe; the parallel and the Baſes have to the parts of the Diameters, cut off from <lb></lb>the Vertex, the ſameproportion: as alſo, the parts cut off, to the parts cut off. <lb></lb><emph type="italics"></emph>Now the Lines parallel to the Baſes are drawn, as I ſuppoſe, by making a Rectilineall Figure (cal-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1324"></arrow.to.target><lb></lb><emph type="italics"></emph>led)<emph.end type="italics"></emph.end> Signally inſcribed [<foreign lang="grc">χη̄μα γιωρίμως ἐγν̀<36>ρόμενον</foreign>] <emph type="italics"></emph>in both portions, having an equall num<lb></lb>ber of Sides in both. </s> <s>Therefore, like Portions are cut off from like Sections of a Cone; and <lb></lb>their Diameters, whether they be perpendicular to their Baſes, or making equall Angles with their <lb></lb>Baſes, have the ſame proportion unto their Baſes.<emph.end type="italics"></emph.end><lb></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"></emph>Upon prop. 3 lib.<emph.end type="italics"></emph.end> 2 <lb></lb>Archim. <emph type="italics"></emph>Æqui<lb></lb>pond.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1324"></margin.target><emph type="italics"></emph>Vide<emph.end type="italics"></emph.end> Archim, <emph type="italics"></emph>ante <lb></lb>prop. 2. lib. 2. <lb></lb>Æquipond.<emph.end type="italics"></emph.end></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"></emph>A E I<emph.end type="italics"></emph.end> ſhall paſs thorow K.] <lb></lb><emph type="italics"></emph>For, if it be poſſible, let it not paſs thorow K, but thorow ſome other Point of the Line D B, as <lb></lb>thorow V. Inregard, therefore, that in the Section of the Right-angled Cone A E I, whoſe <lb></lb>Diameter is E Z, A E is drawn and prolonged; and D B parallel unto the Diameter, cutteth <lb></lb>both A E and A I; A E in B, and A I in D; D B ſhall have to B V, the ſame proportion<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1075.jpg" pagenum="381"></pb><emph type="italics"></emph>that A Z hath to Z D; by the fourth Propoſition of<emph.end type="italics"></emph.end> Archimedes, De quadratura Para<lb></lb>bolæ: <emph type="italics"></emph>But A Z is Seſquialter of Z D; for it is as three to two, as we ſhallanon demon-<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1326"></arrow.to.target><lb></lb><emph type="italics"></emph>ſtrate: Therefore D B is Seſquialter of B V; but D B and B K are Seſquialter: <lb></lb>And, therefore, the Lines<emph.end type="italics"></emph.end> (c) <emph type="italics"></emph>B V and B K are equall: Which is imposſible: <lb></lb>Therefore the Section of the Right-angled Cone A E I, ſhall paſs thorow the Point K; which <lb></lb>we would demonstrate.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1326"></margin.target>(c) <emph type="italics"></emph>By 9 of the <lb></lb>fifth,<emph.end type="italics"></emph.end></s></p><p type="main"> <s>In regard, therefore, that the three <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortions A P O L, A E I <lb></lb><arrow.to.target n="marg1327"></arrow.to.target><lb></lb>and A T D are contained betwixt Right Lines and the Sections <lb></lb>of Right-angled Cones, and are Right, alike and unequall, <lb></lb>touching one another, upon one and the ſame Baſe.] <emph type="italics"></emph>After theſe words,<emph.end type="italics"></emph.end><lb></lb>upon one and the ſame Baſe, <emph type="italics"></emph>we may ſee that ſomething is obliterated, that is to be <lb></lb>deſired: and for the Demonſtration of theſe particulars, it is requiſite in this place to <lb></lb>premiſe ſome things: which will alſo be neceſſary unto the things that follow.<emph.end type="italics"></emph.end></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"></emph>L<emph.end type="italics"></emph.end>ine A B; and let it be cut by two <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ines, <lb></lb>parallel to one another, A C and D E, ſo, that as <emph type="italics"></emph>A B<emph.end type="italics"></emph.end> is to <lb></lb>B D. ſo <emph type="italics"></emph>A C<emph.end type="italics"></emph.end> may be to D E. </s> <s>I ſay that the Line that con<lb></lb>joyneth the Points C and B ſhall likewiſe paſs by E.</s></p><figure id="id.040.01.1075.1.jpg" xlink:href="040/01/1075/1.jpg"></figure><p type="main"> <s><emph type="italics"></emph>For, if poſſible, let it not paſs by E, but either <lb></lb>above or below it. </s> <s>Let it first paſs below it, <lb></lb>as by F. </s> <s>The Triangles A B C and D B F ſhall <lb></lb>be alike: And, therefore, as<emph.end type="italics"></emph.end> (a) <emph type="italics"></emph>A B is to B D,<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1328"></arrow.to.target><lb></lb><emph type="italics"></emph>ſo is A C to D F: But as A B is to B D, ſo was <lb></lb>A C to D E: Therefore<emph.end type="italics"></emph.end> (b) <emph type="italics"></emph>D F ſhall be equall to<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1329"></arrow.to.target><lb></lb><emph type="italics"></emph>D E: that is, the part to the whole: Which is <lb></lb>abſurd. </s> <s>The ſame abſurditie will follow, if the <lb></lb>Line C B be ſuppoſed to paſs above the Point E: <lb></lb>And, therefore, C B muſt of necesſity paſs thorow <lb></lb>E: Which was required to be demonſtrated.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1328"></margin.target>(a) <emph type="italics"></emph>By 4. of the <lb></lb>ſixth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1329"></margin.target>(b) <emph type="italics"></emph>By 9. of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>LEMMA. II.</s></p><p type="main"> <s>Let there be two like <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortions, contained betwixt Right Lines, <lb></lb>and the Sections of Right-angled Cones; A B C the great<lb></lb>er, whoſe Diameter let be B D; and E F C the leſser, whoſe <lb></lb>Diameter let be F G: and, let them be ſo applyed to one <lb></lb>another, that the greater include the leſser; and let their <lb></lb>Baſes A C and E C be in the ſame Right Line, that the ſame <lb></lb>Point C, may be the term or bound of them both: And, <lb></lb>then in the Section A B C, take any Point, as H; and draw <lb></lb>a Line from H to C. </s> <s>I ſay, that the Line H C, hath to that <lb></lb>part of it ſelf, that lyeth betwixt C and the Section E F C, the <lb></lb>ſame proportion that A C hath to C E.</s></p><p type="main"> <s><emph type="italics"></emph>Draw B C, which ſhall paſs thorow F, For, in regard, that the Portions are alike, the <lb></lb>Diameters with the Baſes contain equall Angles: And, therefore, B D and F G are parallel <lb></lb>to one another: and B D is to A C, as F G it to E C: and,<emph.end type="italics"></emph.end> Permutando, <emph type="italics"></emph>B D is to F G, as <lb></lb>A C is to C E; that is,<emph.end type="italics"></emph.end> (a) <emph type="italics"></emph>as their halfes D C to C G; therefore, it followeth, by the<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1330"></arrow.to.target><lb></lb><emph type="italics"></emph>preceding Lemma, that the Line B C ſhall paſs by the Point F. Moreover, from the Point <lb></lb>H unto the Diameter B D, draw the Line H K, parallel to the Baſe A C: and, draw a Line<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1076.jpg" pagenum="382"></pb><figure id="id.040.01.1076.1.jpg" xlink:href="040/01/1076/1.jpg"></figure><lb></lb><emph type="italics"></emph>from K to C, cutting the Diameter F G in L: <lb></lb>and, thorow L, unto the Section E F. G, on the <lb></lb>part E, draw the Line L M, parallel unto the <lb></lb>ſame Baſe A C. And, of the Section A B C, <lb></lb>let the Line B N be the Parameter; and, of the <lb></lb>Section E F C, let F O be the Parameter. </s> <s>And, <lb></lb>becauſe the Triangles C B D and C F G are alike<emph.end type="italics"></emph.end>; <lb></lb>(b) <emph type="italics"></emph>therefore, as B C is to C F, ſo ſhall D C be<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1331"></arrow.to.target><lb></lb><emph type="italics"></emph>to C G, and B D to F G. Again, becauſe the <lb></lb>Triangles C K B and C L F, are alſo alike to <lb></lb>one another; therefore, as B C is to C F, that is, <lb></lb>as B D is to F G, ſo ſhall K C be to C L, and B K to F L: Wherefore, K C to C L, and,<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1332"></arrow.to.target><lb></lb><emph type="italics"></emph>B K to F L, are as D C to C G; that is,<emph.end type="italics"></emph.end> (c) <emph type="italics"></emph>as their duplicates A C and C E: But as <lb></lb>B D is to F G, ſo is D C to C G; that is, A D to E G: And,<emph.end type="italics"></emph.end> Permutando, <emph type="italics"></emph>as B D is to <lb></lb>A D, ſo is F G to E G: But the Square A D, is equall to the Rectangle D B N, by the 11 <lb></lb>of our firſt of<emph.end type="italics"></emph.end> Conicks: <emph type="italics"></emph>Therefore, the<emph.end type="italics"></emph.end> (d) <emph type="italics"></emph>three Lines B D, A D and B N are<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1333"></arrow.to.target><lb></lb><emph type="italics"></emph>Proportionalls. </s> <s>By the ſame reaſon, likewiſe, the Square E G being equall to the Rectangle <lb></lb>G F O, the three other Lines F G, E G and F O, ſhall be alſo Proportionals: And, as B D is <lb></lb>to A D, ſo is F G to E G: And, therefore, as A D is to B N, ſo is E G to F O:<emph.end type="italics"></emph.end> Ex equali, <lb></lb><emph type="italics"></emph>therefore, as D B is to B N, ſo is G F to F O: And,<emph.end type="italics"></emph.end> Permutando, <emph type="italics"></emph>as D B is to G F, ſo is <lb></lb>B N to F O: But as D B is to G F, ſo is B K to F L: Therefore, B K is to F L, as <lb></lb>B N is to F O: And,<emph.end type="italics"></emph.end> Permutando, <emph type="italics"></emph>as B K is to B N, ſo is F L to F O. Again, <lb></lb>becauſe the<emph.end type="italics"></emph.end> (e) <emph type="italics"></emph>Square H K is equall to the Rectangle B N; and the Square M L, equall<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1334"></arrow.to.target><lb></lb><emph type="italics"></emph>to the Rectangle L F O, therefore, the three Lines B K, K H and B N ſhall be Proportionals: <lb></lb>and F L, L M, and F O ſhall alſo be Proportionals: And, therefore,<emph.end type="italics"></emph.end> (f) <emph type="italics"></emph>as the Line<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1335"></arrow.to.target><lb></lb><emph type="italics"></emph>B K is to the Line B N, ſo ſhall the Square B K, be to the Square H K: And, as the <lb></lb>Line F L is to the Line F O, ſo ſhall the Square F L be to the Square L M: <lb></lb>Therefore, becauſe that as B K is to B N, ſo is F L to F O; as the Square<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1336"></arrow.to.target><lb></lb><emph type="italics"></emph>B K is to the Square K H, ſo ſhall the Square F L be to the Square L M: Therefore,<emph.end type="italics"></emph.end><lb></lb>(g) <emph type="italics"></emph>as the Line B K is to the Line K H, ſo is the Line F L to L M: And,<emph.end type="italics"></emph.end> Permutando, <lb></lb><emph type="italics"></emph>as B K is to F L, ſo is K H to L M: But B K was to F L, as K C to C L: Therefore, <lb></lb>K H is to L M, as K C to C L: And, therefore, by the preceding Lemma, it is manifeſt that <lb></lb>the Line H C alſo ſhall paſs thorow the Point M: As K C, therefore, is to C L, that is, <lb></lb>as A C to C E, ſo is H C to C M; that is, to the ſame part of it ſelf, that lyeth betwixt C and <lb></lb>the Section E F C. And, in like manner might we demonſtrate, that the ſame happeneth <lb></lb>in other Lines, that are produced from the Point C, and the Sections E B C. And, that <lb></lb>B C hath the ſame proportion to C F, plainly appeareth; for B C is to C F, as D C to C G; <lb></lb>that is, as their Duplicates A C to C E.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1330"></margin.target>(a) <emph type="italics"></emph>By 15. of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1331"></margin.target>(b) <emph type="italics"></emph>By 4. of the <lb></lb>ſixth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1332"></margin.target>(c) <emph type="italics"></emph>By 15. of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1333"></margin.target>(d) <emph type="italics"></emph>By 17. of the <lb></lb>ſixth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1334"></margin.target>(e) <emph type="italics"></emph>By 11 of our <lb></lb>firſt of<emph.end type="italics"></emph.end> Conicks.</s></p><p type="margin"> <s><margin.target id="marg1335"></margin.target>(f) <emph type="italics"></emph>By<emph.end type="italics"></emph.end> Cor. <emph type="italics"></emph>of 20. <lb></lb>of the ſixth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1336"></margin.target>(g) <emph type="italics"></emph>By 23. of the <lb></lb>ſixth.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>From whence it is manifeſt, that all Lines ſo drawn, ſhall be cut by the <lb></lb>ſaid Section in the ſame proportion. </s> <s>For, by Diviſion and Converſion, <lb></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 alſo be proved, that the Lines which are <lb></lb>drawn in like Portions, ſo, as that with the Baſes, they con<lb></lb>tain equall Angles, ſhall alſo cut off like Portions; that is, <lb></lb>as in the foregoing Figure, the Portions H B C and M F C, <lb></lb>which the Lines C H and C M do cut off, are alſo alike to <lb></lb>each other.</s></p><p type="main"> <s><emph type="italics"></emph>For let C H and C M be divided in the midst in the Points P and <expan abbr="q;">que</expan> and thorow thoſe <lb></lb>Points draw the Lines R P S and T Q V parallel to the Diameters. </s> <s>Of the Portion <lb></lb>H S C the Diameter ſhall be P S, and of the Portion M V C the Diameter ſhall be<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1077.jpg" pagenum="383"></pb><emph type="italics"></emph>Q V. And, ſuppoſe that as the Square C R is to the Square C P, ſo is the Line B N unto <lb></lb>another Line; which let be S X: And, as the Square C T is to the Square C Q ſo let F O <lb></lb>be to V Y. </s> <s>Now it is manifeſt, by the things which we have demonſtrated, in our Commentaries, <lb></lb>upon the fourth Propoſition of<emph.end type="italics"></emph.end> Archimedes, De Conoidibus & Spheæroidibus, <emph type="italics"></emph>that the <lb></lb>Square C P is equall to the Rectangle P S X; and alſo, that the Square C Q is equall to <lb></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></lb>and M V C: But ſince the Triangles C P R and C Q T are alike; C R ſhall have to C P, the <lb></lb>ſame Proportion that C T hath to C Q: And, therefore, the<emph.end type="italics"></emph.end> (a) <emph type="italics"></emph>Square C R ſhall have<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1337"></arrow.to.target><lb></lb><emph type="italics"></emph>to the Square C P, the ſame proportion that the<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.1077.1.jpg" xlink:href="040/01/1077/1.jpg"></figure><lb></lb><emph type="italics"></emph>Square C T hath to the Square C Q: There<lb></lb>fore, alſo, the Line B N ſhall be to the Line <lb></lb>S X, as the Line F O is to V Y: But H C was <lb></lb>to C M, as A C to C E: And, therefore, alſo, <lb></lb>their halves C P and C Q, are alſo to one <lb></lb>another, as A D and E G: And.<emph.end type="italics"></emph.end> Permu<lb></lb>tando, <emph type="italics"></emph>C P is to A D, as C Q is to E G: <lb></lb>But it hath been proved, that A D is to B N, <lb></lb>as E G to F O; and B N to S X, as F O to <lb></lb>V Y: Therefore,<emph.end type="italics"></emph.end> exæquali, <emph type="italics"></emph>C P ſhall be <lb></lb>to S X, as C Q is to V Y. And, ſince the <lb></lb>Square C P is equall to the Rectangle P S X, and the Square C Q to the Rectangle Q V Y, <lb></lb>the three Lines S P, PC and S X ſhall be proportionalls, and V Q, Q C and V Y ſhal be <lb></lb>Proportionalls alſo: And therefore alſo S P ſhall be to P C as V Q to Q C And as P C <lb></lb>is to C H, ſo ſhall Q C. be to C M: Therefore,<emph.end type="italics"></emph.end> ex æquali, <emph type="italics"></emph>as S P the Diameter of the <lb></lb>Portion H S C is to its Baſe C H, ſo is V Q the Diameter of the portion M V S the <lb></lb>Baſe C M; and the Angles which the Diameter with the Baſes do contain, are equall; and the <lb></lb>Lines S P and V Q are parallel: Therefore the Portions, alſo, H S C and M V C ſhall be alike: <lb></lb>Which was propoſed to be demonſtrated<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1337"></margin.target>(a) <emph type="italics"></emph>By 22. of the <lb></lb>ſixth.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>LEMMA. IV.</s></p><p type="main"> <s><emph type="italics"></emph>L<emph.end type="italics"></emph.end>et there be two <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ines A <emph type="italics"></emph>B<emph.end type="italics"></emph.end> and C D; and let them be cut in the <lb></lb>Points E and F, ſo that as A E is to E B, C F may be to F D: <lb></lb>and let them be cut again in two other Points G and H; and <lb></lb>let C H be to H D, as A G is to G B. </s> <s>I ſay that C F ſhall be to <lb></lb>F H as A E is E G.</s></p><p type="main"> <s><emph type="italics"></emph>For in regard that as A E is to E B, ſo is C F to F D; it followeth that, by Compounding, <lb></lb>as A B is to E B, ſo ſhall C D be to F D. Again, ſince that as A G is to G B, ſo is C H, to <lb></lb>H D; it followeth that, by Compounding and Converting, as G B is to A B, ſo ſhall H D be<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.1077.2.jpg" xlink:href="040/01/1077/2.jpg"></figure><lb></lb><emph type="italics"></emph>C D: Therefore,<emph.end type="italics"></emph.end> ex æquali, <emph type="italics"></emph>and Converting as E B <lb></lb>is to G B, ſo ſhall F D be to H D; And, by Conver<lb></lb>ſion of Propoſition, as E B is to E G, ſo ſhall F D <lb></lb>be to F H: But as A E is to E B, ſo is C F to F D:<emph.end type="italics"></emph.end><lb></lb>Ex æquali, <emph type="italics"></emph>therefore, as A E is to E G, ſo <lb></lb>ſhall CF be to F H.<emph.end type="italics"></emph.end> Again, another way. <emph type="italics"></emph>Let <lb></lb>the Lines A B and C D be applyed to one another, <lb></lb>ſo as that they doe make an Angle at the parts A and C; <lb></lb>and let A and C be in one and the ſame Point: then <lb></lb>draw Lines from D to B, from H to G, and from F to E. </s> <s>And ſince that as A E is to E B, <lb></lb>ſo is C F, that is A F to F D; therefore F E ſhall be parallel to D B<emph.end type="italics"></emph.end>; (a) <emph type="italics"></emph>and likewiſe<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1338"></arrow.to.target><lb></lb><emph type="italics"></emph>H G ſhall be parallel to D B; for that A H is to H D, as A G to G B<emph.end type="italics"></emph.end>: (b) <emph type="italics"></emph>Therefore F E <lb></lb>and H G are parallel to each other: And conſequently, as A E is to E G, ſo is A H, that is,<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1339"></arrow.to.target><lb></lb><emph type="italics"></emph>C F to F H: Which was to be demonſtrated.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/1078.jpg" pagenum="384"></pb><p type="margin"> <s><margin.target id="marg1338"></margin.target>(a) <emph type="italics"></emph>By 2. of the <lb></lb>ſixth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1339"></margin.target>(b) <emph type="italics"></emph>By 30 of the <lb></lb>firſt.<emph.end type="italics"></emph.end></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></lb>Lines and the Sections of Right-angled Cones, as in the fore<lb></lb>going figure, A B C, whoſe Diameter is B D; and E F C, <lb></lb>whoſe Diameter is F G; and from the Point E, draw the <lb></lb>Line E H parallel to the Diameters B D and F G; and let it <lb></lb>cut the Section A B C in K: and from the Point C draw C H <lb></lb>touching the Section A B C in C, and meeting with the Line <lb></lb>E H in H; which alſo toucheth the Section E F C in the ſame <lb></lb>Point C, as ſhall be demonſtrated: I ſay that the Line drawn <lb></lb>from C <emph type="italics"></emph>H<emph.end type="italics"></emph.end> unto the Section E F C ſo as that it be parallel to <lb></lb>the Line E H, ſhall be divided in the ſame proportion by the <lb></lb>Section A B C, in which the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine C A is divided by the Section <lb></lb>E F C; and the part of the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine C A which is betwixt the <lb></lb>two Sections, ſhall anſwer in proportion to the part of the Line <lb></lb>drawn, which alſo falleth betwixt the ſame Sections: that is, <lb></lb>as in the foregoing Figure, if D B be produced untill it meet <lb></lb>with C H in L, that it may interſect the Section E F C in the <lb></lb>Point M, the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine <emph type="italics"></emph>L<emph.end type="italics"></emph.end> B ſhall have to B M the ſame proportion <lb></lb>that C E hath to E A.</s></p><p type="main"> <s><emph type="italics"></emph>For let G F be prolonged untill it meet the ſame Line C H in N, cutting the Section A B C <lb></lb>in O; and drawing a Line from B to C, which ſhall paſſe by F, as hath been ſhewn, the<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.1078.1.jpg" xlink:href="040/01/1078/1.jpg"></figure><lb></lb><emph type="italics"></emph>Triangles C G F and C D B ſhall be alike; as <lb></lb>alſo the Triangles C F N and C B L: Wherefore<emph.end type="italics"></emph.end><lb></lb>(a) <emph type="italics"></emph>as G F is to D B, ſo ſhall C F b to C B:<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1340"></arrow.to.target><lb></lb><emph type="italics"></emph>And as<emph.end type="italics"></emph.end> (b) <emph type="italics"></emph>C F is to C B, ſo ſhall F N be <lb></lb>to B L: Therefore G F ſhall be to D B, as F N<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1341"></arrow.to.target><lb></lb><emph type="italics"></emph>to B L: And,<emph.end type="italics"></emph.end> Permutando, <emph type="italics"></emph>G F ſhall be to <lb></lb>F N, as D B to B L: But D B is equall to <lb></lb>B L, by 35 of our Firſt Book of<emph.end type="italics"></emph.end> Conicks: <lb></lb><emph type="italics"></emph>Therefore<emph.end type="italics"></emph.end> (c) <emph type="italics"></emph>G F alſo ſhall be equall to F N:<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1342"></arrow.to.target><lb></lb><emph type="italics"></emph>And by 33 of the ſame, the Line C H touch<lb></lb>eth the Section E F C in the ſame Point. </s> <s>There<lb></lb>fore, drawing a Line from C to M, prolong it <lb></lb>untill it meet with the Section A B C in P; and <lb></lb>from P unto A C draw P Q parallel to B D. <lb></lb>Becauſe, now, that the Line C H toucheth the <lb></lb>Section E F C in the Point C; L M ſhall have <lb></lb>the ſame proportion to M D that C D hath to D E, <lb></lb>by the Fifth Propoſition of<emph.end type="italics"></emph.end> Archimedes <emph type="italics"></emph>in his <lb></lb>Book<emph.end type="italics"></emph.end> De Quadratura Patabolæ: <emph type="italics"></emph>And by <lb></lb>reaſon of the Similitude of the Triangles C M D <lb></lb>and C P Q, as C M is to C D, ſo ſhall C P <lb></lb>be to C Q: And,<emph.end type="italics"></emph.end> Permutando, <emph type="italics"></emph>as C M is to <lb></lb>C P, ſo ſhall C D be to C Q: But as C M is to C P, ſo is C E to C A,; as we have but <lb></lb>even now demonſtrated: And therefore, as C E is to C A, ſo is C D to C <expan abbr="q;">que</expan> that is as the <lb></lb>whole is to the whole, ſo is the part to the part: The remainder, therefore, D E is to the <lb></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"></emph.end> Permutando, <emph type="italics"></emph>C D <lb></lb>is to D E, as C Q is to Q A: And L M is alſo to M D, as C D to D E: Therefore L M is<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1079.jpg" pagenum="385"></pb><emph type="italics"></emph>to M D, as C Q to Q A: But L B is to B D, by 5 of<emph.end type="italics"></emph.end> Archimedes, <emph type="italics"></emph>before recited, as C D <lb></lb>to D A: It is manifeſt therefore, by the precedent Lemma, that C D is to D Q, as L B is to <lb></lb>B M: But as C D is to D Q, ſo is C M to M P: Therefore L B is to B M, as C M to M P:<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1343"></arrow.to.target><lb></lb><emph type="italics"></emph>And it haveing been demonſtrated, that C M is to M P, as C E to E A; L B ſhall be to B M,<lb></lb>as C E to E A. </s> <s>And in like manner it ſhall be demonstrated that ſo is N O to O F; as alſo the <lb></lb>Remainders. </s> <s>And that alſo H K is to K E, as C E to E A, doth plainly appeare by the ſame<emph.end type="italics"></emph.end><lb></lb>5. <emph type="italics"></emph>of<emph.end type="italics"></emph.end> Archimedes<emph type="italics"></emph>: Which is that that we propounded to be demonſtrated.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1340"></margin.target>(a) <emph type="italics"></emph>By 4. of the <lb></lb>ſixth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1341"></margin.target>(b) <emph type="italics"></emph>By 11 of the <lb></lb>fifth,<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1342"></margin.target>(c) <emph type="italics"></emph>By 14 of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1343"></margin.target><emph type="italics"></emph>By 2. of the ſixth<emph.end type="italics"></emph.end></s></p><p type="head"> <s>LEMMA. VI.</s></p><p type="main"> <s>And, therefore, let the things ſtand as above; and deſcribe <lb></lb>yet another like Portion, contained betwixt a Right Line, and <lb></lb>the Section of the Rightangled Cone D R C, whoſe Diameter <lb></lb>is R S, that it may cut the Line F G in T; and prolong S R <lb></lb>unto the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine C H in V, which meeteth the Section A B C in <lb></lb>X, and E F C in Y. </s> <s>I ſay, that B M hath to M D, a propor<lb></lb>tion compounded of the proportion that E A hath to A C; <lb></lb>and of that which C D hath to D E.</s></p><p type="main"> <s><emph type="italics"></emph>For, we ſhall firſt demonſtrate, that the Line C H toucheth the Section D R C in the <lb></lb>Point C; and that L M is to M D, as alſo N F to F T, and V Y to Y R, as C D is to E D. <lb></lb>And, becauſe now that L B is to B M, as C E is to E A; therefore, Compounding and Conver<lb></lb>ting, B M ſhall be to L M, as E A to A C: And, as L M is to M D, ſo ſhall C D be to <lb></lb>D E: The proportion, therefore, of B M to M D, is compounded of the proportion that <lb></lb>B M hath to L M, and of the proportion that L M hath to M D: Therefore, the proportion <lb></lb>of B M to M D, ſhall alſo be compounded of the proportion that E A hath to A C, and of <lb></lb>that which C D hath to D E. </s> <s>In the ſame manner it ſhal be demonſtrated, that O F hath to <lb></lb>F T, and alſo X Y to Y R, a proportion compounded of thoſe ſame proportions; and ſo in <lb></lb>the reſt: Which was to be demonstrated.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>By which it appeareth that the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ines ſo drawn; which fall betwixt <lb></lb>the Sections A B C and D R C, ſhall be divided by the Section E F C <lb></lb>in the ſame Proportion.</s></p><p type="main"> <s>And C B is to B D, as ſix to fifteen.] <emph type="italics"></emph>For we have ſuppoſed that B K is<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1344"></arrow.to.target><lb></lb><emph type="italics"></emph>double of K D: Wherefore, by Compoſition B D ſhall be to K D as three to one; that is, as <lb></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></lb>And, by Converſion of proportion and Convert<lb></lb>ing, C B is to B D, as ſix to ſifteen.<emph.end type="italics"></emph.end></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"></figure><p type="main"> <s>And as C B is to B D, ſo is <lb></lb><arrow.to.target n="marg1345"></arrow.to.target><lb></lb>E B to B A; and D Z to D A.] <lb></lb><emph type="italics"></emph>For the Triangles C B E and D B A being <lb></lb>alike; As C B is to B E, ſo ſhall D B be to B A: <lb></lb>And,<emph.end type="italics"></emph.end> Permutando, <emph type="italics"></emph>as C B is to B D, ſo ſhall <lb></lb>E B be to B A: Againe, as B C is to C E ſo <lb></lb>ſhall B D be to D A, And,<emph.end type="italics"></emph.end> Permutando, <emph type="italics"></emph>as <lb></lb>C B is to B D, ſo ſhall C E, that is, D Z <lb></lb>equall to it, be to D A.<emph.end type="italics"></emph.end></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></lb><arrow.to.target n="marg1346"></arrow.to.target><lb></lb>L A are double.] <emph type="italics"></emph>That the Line L A is <lb></lb>double of D A, is manifeſt, for that B D is the Diameter of the Portion. </s> <s>And that L I is <lb></lb>dovble to D Z ſhall be thus demonſtrated. </s> <s>For as much as ZD is to D A, as two to five: <lb></lb>therefore, Converting and Dividing, A Z, that is, I Z, ſhall be to Z D, as three to two:<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1080.jpg" pagenum="386"></pb><emph type="italics"></emph>Again, by dividing, I D ſhall be to D Z, as one to two: But Z D was to D A, that is, to D L, <lb></lb>as two to five: Therefore,<emph.end type="italics"></emph.end> ex equali, <emph type="italics"></emph>and Converting, L D is to D I, as five to one: and, by <lb></lb>Converſion of Proportion, D L is to D I, as five to four: But D Z was to D L, as two to <lb></lb>five: Therefore, again,<emph.end type="italics"></emph.end> ex equali, <emph type="italics"></emph>D Z is to L I, as two to four: Therefort L I is double <lb></lb>of D Z: Which was to be demonſtrated.<emph.end type="italics"></emph.end><lb></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"></emph>This we have but juſt now demon<lb></lb>ſtrated.<emph.end type="italics"></emph.end></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 demonſtrated, above, that the Portion whoſe <lb></lb>Axis is greater than Seſquialter of the Semi-parameter, if it have <lb></lb>not leſſer proportion in Gravity to the Liquid, &c.] <emph type="italics"></emph>He hath demonstra<lb></lb>ted this in the fourth Propoſition of this Book.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>CONCLVSION II.</s></p><p type="main"> <s><emph type="italics"></emph>If the Portion have leſſer proportion in Gravity to the<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1349"></arrow.to.target><lb></lb><emph type="italics"></emph>Liquid, than the Square S B hath to the Square <lb></lb>B D, but greater than the Square X O hath to the <lb></lb>Square B D, being demitted into the Liquid, ſo in<lb></lb>clined, as that its Baſe touch not the Liquid, it ſhall <lb></lb>continue inclined, ſo, as that its Baſe ſhall not in the <lb></lb>leaſt touch the Surface of the Liquid, and its Axis <lb></lb>ſhall make an Angle with the Liquids Surface, greater <lb></lb>than the Angle X.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1349"></margin.target>A</s></p><p type="main"> <s>Therfore repeating the firſt figure, let the Portion have unto <lb></lb>the Liquid in Gravitie a proportion greater than the Square <lb></lb>X O hath to the ſquare B D, but leſſer than the Square made of <lb></lb>the Exceſſe by which the Axis is greater than Seſquialter of the Semi<lb></lb><figure id="id.040.01.1080.1.jpg" xlink:href="040/01/1080/1.jpg"></figure><lb></lb>Parameter, that is, of S B, hath to <lb></lb>the Square B D: and as the Portion <lb></lb>is to the Liquid in Gravity, ſo let <lb></lb>the Square made of the Line <foreign lang="grc">ψ</foreign> be <lb></lb>to the Square B D: <foreign lang="grc">ψ</foreign> ſhall be great<lb></lb><arrow.to.target n="marg1350"></arrow.to.target><lb></lb>er than X O, but leſſer than the <lb></lb>Exceſſe by which the Axis is grea<lb></lb>ter than Seſquialter of the Semi<lb></lb>parameter, that is, than S B. </s> <s>Let <lb></lb>a Right Line M N be applyed to <lb></lb>fall between the Conick-Sections <lb></lb>A M Q L and A <emph type="italics"></emph>X<emph.end type="italics"></emph.end> D, [<emph type="italics"></emph>parallel to <lb></lb>B D falling betwixt O X and B D,<emph.end type="italics"></emph.end>] and equall to the Line <foreign lang="grc">ψ</foreign>: and let <lb></lb>it cut the remaining Conick Section A H I in the point H, and the <lb></lb><arrow.to.target n="marg1351"></arrow.to.target><lb></lb>Right Line R G in V. </s> <s>It ſhall be demonſtrated that M H is double to <lb></lb>H N, like as it was demonſtrated that O G is double to G X. <pb xlink:href="040/01/1081.jpg" pagenum="387"></pb><figure id="id.040.01.1081.1.jpg" xlink:href="040/01/1081/1.jpg"></figure><lb></lb>And from the Point M draw M Y <lb></lb>touching the Section A M Q L in M; <lb></lb>and M C perpendicular to B D: and <lb></lb>laſtly, having drawn A N & prolong<lb></lb>ed it to Q, the Lines A N & N Q ſhall <lb></lb>be equall to each other. </s> <s>For in <lb></lb>regard that in the Like Portions <lb></lb><arrow.to.target n="marg1352"></arrow.to.target><lb></lb>A M Q L and A <emph type="italics"></emph>X<emph.end type="italics"></emph.end> D the Lines A Q <lb></lb>and A N are drawn from the Baſes <lb></lb>unto the Portions, which Lines <lb></lb>contain equall Angles with the ſaid <lb></lb>Baſes, Q A ſhall have the ſame proportion to A M that L A hath <lb></lb>to A D: Therefore A N is equall to N Q, and A Q parallel to M Y. <lb></lb><arrow.to.target n="marg1353"></arrow.to.target><lb></lb>It is to be demonſtrated that the Portion being demitted into the <lb></lb>Liquid, and ſo inclined as that its Baſe touch not the Liquid, it <lb></lb>ſhall continue inclined ſo as that its Baſe ſhall not in the leaſt touch <lb></lb>the Surface of the Liquid, and its Axis ſhall make an Angle with <lb></lb>the Liquids Surface greater than the Angle X. </s> <s>Let it be demitted <lb></lb>into the Liquid, and let it ſtand, ſo, as that its Baſe do touch the <lb></lb>Surface of the Liquid in one Point only; and let the Portion be cut <lb></lb>thorow the Axis by a Plane erect unto the Surface of the Liquid, <lb></lb><figure id="id.040.01.1081.2.jpg" xlink:href="040/01/1081/2.jpg"></figure><lb></lb>and Let the Section of the Super<lb></lb>ficies of the Portion be A P O L, <lb></lb>the Section of a Rightangled Cone, <lb></lb>and let the Section of the Liquids <lb></lb>Surface be A O; And let the Axis <lb></lb>of the Portion and Diameter of the <lb></lb>Section be <emph type="italics"></emph>B<emph.end type="italics"></emph.end> D: and let B D be <lb></lb><arrow.to.target n="marg1354"></arrow.to.target><lb></lb>cut in the Points K and R as hath <lb></lb>been ſaid; alſo draw P G Parallel to <lb></lb>A O and touching the Section <lb></lb>A P O L in P; and from that Point <lb></lb>draw P T Parallel to B D, and P S perpendicular to the ſame B D. <lb></lb>Now, foraſmuch as the Portion is unto the Liquid in Gravity, as <lb></lb>the Square made of the Line <foreign lang="grc">ψ</foreign> is to the Square B D; and ſince that <lb></lb>as the portion is unto the Liquid in Gravitie, ſo is the part thereof <lb></lb>ſubmerged unto the whole Portion; and that as the part ſubmerged <lb></lb>is to the whole, ſo is the Square T P to the Square B D; It follow<lb></lb>eth that the Line <foreign lang="grc">ψ</foreign> ſhall be equall to T P: And therefore the Lines <lb></lb>M N and P T, as alſo the Portions A M Q and A P O ſhall like<lb></lb>wiſe be equall to each other. </s> <s>And ſeeing that in the Equall and <lb></lb>Like Portions A P O L and A M Q L the Lines A O and A Q <lb></lb><arrow.to.target n="marg1355"></arrow.to.target><lb></lb>are drawn from the extremites of their Baſes, ſo, as that the Portions <lb></lb>cut off do make Equall Angles with their Diameters; as alſo the <pb xlink:href="040/01/1082.jpg" pagenum="388"></pb>Angles at Y and G being equall; therefore the Lines Y B and G B, <lb></lb>and B C and B S ſhall alſo be equall: And therefore C R and S R, <lb></lb>and M V and P Z, and V N and Z T, ſhall be equall likewiſe. <lb></lb><arrow.to.target n="marg1356"></arrow.to.target><lb></lb>Since therefore M V is Leſſer than double of V N, it is manifeſt that <lb></lb>P Z is leſſer than double of Z T. <emph type="italics"></emph>L<emph.end type="italics"></emph.end>et P <foreign lang="grc">ω</foreign> be double of <foreign lang="grc">ω</foreign> T; and <lb></lb>drawing a <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine from <foreign lang="grc">ω</foreign> to K, prolong it to E. </s> <s>Now the Centre of <lb></lb>Gravity of the whole Portion ſhall be the point K; and the Centre <lb></lb>of that part which is in the Liquid ſhall be <foreign lang="grc">ω,</foreign> and of that which is <lb></lb>above the Liquid ſhall be in the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine K E, which let be E: But the <lb></lb><emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine K Z ſhall be perpendicular unto the Surface of the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid: <lb></lb>And therefore alſo the Lines drawn thorow the Points E and <foreign lang="grc">ω</foreign> parall<lb></lb><arrow.to.target n="marg1357"></arrow.to.target><lb></lb>lell unto K Z, ſhall be perpendicular sunto the ſame: Therefore the <lb></lb>Portion ſhall not abide, but ſhall turn about ſo, as that its <emph type="italics"></emph>B<emph.end type="italics"></emph.end>aſe <lb></lb>do not in the leaſt touch the Surface of the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquid; in regard that <lb></lb>now when it toucheth in but one Point only, it moveth upwards, on <lb></lb><arrow.to.target n="marg1358"></arrow.to.target><lb></lb>the part towards A: It is therefore perſpicuous, that the Portion <lb></lb>ſhall conſiſt ſo, as that its Axis ſhall make an Angle with the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>iquids <lb></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></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 leſſer proportion in Gravity to the Liquid, <lb></lb>than the Square S B hath to the Square B D, but greater than the <lb></lb>Square X O hath to the Square B D.] <emph type="italics"></emph>This is the ſecond part of the Tenth <lb></lb>propoſition; and the other pat is with their Demonſtrations, ſhall hereafter follow in the ſame Order.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><foreign lang="grc">Ψ</foreign> ſhall be greater than <emph type="italics"></emph>X<emph.end type="italics"></emph.end> O, but leſſer than the Exceſs by </s></p><p type="main"> <s><arrow.to.target n="marg1360"></arrow.to.target><lb></lb>which the Axis is greater than Seſquialter of the Semi-parameter, <lb></lb>that is than S B.] <emph type="italics"></emph>This followeth from the 10 of the fifth Book of<emph.end type="italics"></emph.end> Euclids <emph type="italics"></emph>Elements.<emph.end type="italics"></emph.end><lb></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 ſhall be demonſtrated, that M H is double to H N, like as it <lb></lb>was demonſtrated, that O G is double to G X.] <emph type="italics"></emph>As in the firſt Concluſion <lb></lb>of this Propoſition, and from what we have but even now written, thereupon appeareth:<emph.end type="italics"></emph.end></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></lb>Lines A Q and A N are drawn from the Baſes unto the Portions, <lb></lb>which Lines contain equall Angles with the ſaid Baſes, Q A ſhall <lb></lb>have the ſame proportion to A N, that L A hath to A D.] <lb></lb><emph type="italics"></emph>This we have demonstrated above.<emph.end type="italics"></emph.end></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"></emph>For ſince that Q A is to A N, as L A to <lb></lb>A D; Dividing and Converting, A N ſhall be to N Q as A D to D L: But A D <lb></lb>is equall to D L; for that D B is ſuppoſed to be the Diameter of the Portion: Therefore<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1364"></arrow.to.target><lb></lb><emph type="italics"></emph>alſo<emph.end type="italics"></emph.end> (a) <emph type="italics"></emph>A N is equall to N <expan abbr="q.">que</expan><emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1364"></margin.target>(a) <emph type="italics"></emph>By 14 of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And A Q parallel to M Y.] <emph type="italics"></emph>By the fifth of the ſecond Book of<emph.end type="italics"></emph.end> Apollonius <emph type="italics"></emph>his Conicks.<emph.end type="italics"></emph.end><lb></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 ſaid.] </s></p><p type="main"> <s><arrow.to.target n="marg1366"></arrow.to.target><lb></lb><emph type="italics"></emph>In the firſt Conciuſion of this Propoſition: And let it be cut in K, ſo, as that B K be double to <lb></lb>K D, and in R ſo, as that K R may be equall to the Semi-parameter.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1366"></margin.target>G</s></p><p type="main"> <s>And, ſeeing that in the Equall and Like Portions A P O L and <lb></lb><arrow.to.target n="marg1367"></arrow.to.target><lb></lb>A <emph type="italics"></emph>M<emph.end type="italics"></emph.end> Q L, the Lines A O and A Q are drawn from the Extremities <lb></lb>of their Baſes, ſo, as that the Portions cut off, do make equall Angles <pb xlink:href="040/01/1083.jpg" pagenum="389"></pb>with their Diameters; as alſo, the Angles at Y and G being equall; <lb></lb>Therefore, the Lines Y B and G B, & B C & B S, ſhall alſo be equall.] <lb></lb><emph type="italics"></emph>Let the Line A Q cut the Diameter D B in<emph.end type="italics"></emph.end> <foreign lang="grc">γ,</foreign> <emph type="italics"></emph>and let it cut A O in<emph.end type="italics"></emph.end> <foreign lang="grc">δ.</foreign> <emph type="italics"></emph>Now becauſe that in<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.1083.1.jpg" xlink:href="040/01/1083/1.jpg"></figure><lb></lb><emph type="italics"></emph>the equall and like Portions A P O L & A M Q L, <lb></lb>from the Extremities of their Baſes, A O and <lb></lb>A Q are drawn, that contain equall Angles with <lb></lb>thoſe Baſes; and ſince the Angles at D, are both <lb></lb>Right; Therefore, the Remaining Angles A<emph.end type="italics"></emph.end> <foreign lang="grc">δ</foreign> <emph type="italics"></emph>D <lb></lb>and A<emph.end type="italics"></emph.end> <foreign lang="grc">γ</foreign> D <emph type="italics"></emph>ſhall be equall to one another: But <lb></lb>the Line P G is parallel unto the Line A O; alſo <lb></lb>M Y is parallel to A <expan abbr="q;">que</expan> and P S and M C to <lb></lb>A D: Therefore the Triangles P G S and M Y C, <lb></lb>as alſo the Triangles A<emph.end type="italics"></emph.end> <foreign lang="grc">δ</foreign> <emph type="italics"></emph>D and A<emph.end type="italics"></emph.end> <foreign lang="grc">γ</foreign> <emph type="italics"></emph>D, are all <lb></lb>alike to each other<emph.end type="italics"></emph.end>: (b) <emph type="italics"></emph>And as A D is to A<emph.end type="italics"></emph.end> <foreign lang="grc">δ,</foreign><lb></lb><arrow.to.target n="marg1368"></arrow.to.target><lb></lb><emph type="italics"></emph>ſo is A D to A<emph.end type="italics"></emph.end> <foreign lang="grc">γ</foreign><emph type="italics"></emph>: and,<emph.end type="italics"></emph.end> Permutando, <emph type="italics"></emph>the Lines <lb></lb>A D and A D are equall to each other: Therefore, <lb></lb>A<emph.end type="italics"></emph.end> <foreign lang="grc">δ</foreign> <emph type="italics"></emph>and A<emph.end type="italics"></emph.end> <foreign lang="grc">γ</foreign> <emph type="italics"></emph>are alſo equall: But A O and <lb></lb>A Q are equall to each other; as alſo their halves <lb></lb>A T and A N: Therefore the Remainders T<emph.end type="italics"></emph.end> <foreign lang="grc">δ</foreign> <emph type="italics"></emph>and N<emph.end type="italics"></emph.end> <foreign lang="grc">γ</foreign><emph type="italics"></emph>; that is, TG and MY, are alſo<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1369"></arrow.to.target><lb></lb><figure id="id.040.01.1083.2.jpg" xlink:href="040/01/1083/2.jpg"></figure><lb></lb><emph type="italics"></emph>equall. </s> <s>And, as<emph.end type="italics"></emph.end> (c) <emph type="italics"></emph>P G is to G S, ſo is M Y to <lb></lb>Y C: and<emph.end type="italics"></emph.end> Permutando, <emph type="italics"></emph>as P G is to M Y, ſo is <lb></lb>G S to Y C: And, therefore, G S and Y C are <lb></lb>equall; as alſo their halves B S and B C: From <lb></lb>whence it followeth, that the Remainders S R and C R <lb></lb>are alſo equall: And, conſequently, that P Z and <lb></lb>M V, and V N and Z T, are lkiewiſe equall to one <lb></lb>another.<emph.end type="italics"></emph.end></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"></emph>By 4. of the <lb></lb>ſixth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1369"></margin.target>(c) <emph type="italics"></emph>By 34 of the <lb></lb>firſt,<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Since, therefore, that N V is leſſer <lb></lb><arrow.to.target n="marg1370"></arrow.to.target><lb></lb>than double of V N.] <emph type="italics"></emph>For M H is double of <lb></lb>H N, and M V is leſſer than M H: Therefore, M V <lb></lb>is leſſer than double of H N, and much leſſer than <lb></lb>double of V N.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1370"></margin.target>K</s></p><p type="main"> <s>Therefore, the Portion ſhall not abide, but ſhall turn about, <lb></lb><arrow.to.target n="marg1371"></arrow.to.target><lb></lb>ſo, as that its Baſe do not in the leaſt touch the Surface of <lb></lb>the Liquid; in regard that now when it toucheth in but one Point <lb></lb>only, it moveth upwards on the part towards A.] Tartaglia's <emph type="italics"></emph>his Tranſla<lb></lb>tion hath it thus,<emph.end type="italics"></emph.end> Non ergo manet Portio ſed inclinabitur ut Baſis ipſius, nec ſecundum <lb></lb>unum tangat Superficiem Humidi, quon am nunc ſecundum unum tacta ipſa reclina<lb></lb>tur<emph type="italics"></emph>: Which we have thought fit in this manner to correct, from other Places of<emph.end type="italics"></emph.end><lb></lb>Archimedes, <emph type="italics"></emph>that the ſenſe might be the more perſpicuous. </s> <s>For in the ſixth Propoſition of this, <lb></lb>he thus writeth (as we alſo have it in the Tranſlation,)<emph.end type="italics"></emph.end> The Solid A P O L, therefore, ſhall <lb></lb>turn about, and its Baſe ſhall not in the leaſt touch the Surface of the Liquid. <emph type="italics"></emph>Again, <lb></lb>in the ſeventh Propoſition<emph.end type="italics"></emph.end>; From whence it is manifeſt, that its Baſe ſhall turn about in <lb></lb>ſuch manner, a that its Baſe doth in no wiſe touch the Surface of the Liquid; For <lb></lb>that now when it toucheth but in one Point only, it moveth downwards on the part <lb></lb>towards L. <emph type="italics"></emph>And that the Portion moveth upwards, on the part towards A, doth plainly ap<lb></lb>pear: For ſince that the Perpendiculars unto the Surface of the Liquid, that paſs thorow <foreign lang="grc">ω</foreign>, de <lb></lb>fall on the part towards A, and thoſe that paſs thorow E, on the part towards L; it is neceſſary <lb></lb>that the Centre<emph.end type="italics"></emph.end> <foreign lang="grc">ω</foreign> <emph type="italics"></emph>do move upwards, and the Centre E downwards.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1371"></margin.target>L</s></p><p type="main"> <s>It is therefore perſpicuous, that the Portion ſhall conſiſt, ſo, as that <lb></lb>its Axis ſhall make an Angle with the Liquids Surface greater than <lb></lb>the Angle <emph type="italics"></emph>X.] For dræwing a Line from A to X, prolong it untill it do cut the Diamter<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1084.jpg" pagenum="390"></pb><figure id="id.040.01.1084.1.jpg" xlink:href="040/01/1084/1.jpg"></figure><lb></lb><emph type="italics"></emph>B D in<emph.end type="italics"></emph.end> <foreign lang="grc">λ</foreign><emph type="italics"></emph>; and from the Point O, and parallel to <lb></lb>A<emph.end type="italics"></emph.end> <foreign lang="grc">λ,</foreign> <emph type="italics"></emph>draw O X; and let it touch the Section in O, <lb></lb>as in the first Figure: And the<emph.end type="italics"></emph.end> (d) <emph type="italics"></emph>Angle at X,<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1372"></arrow.to.target><lb></lb><emph type="italics"></emph>ſhall be equall alſo to the angle<emph.end type="italics"></emph.end> <foreign lang="grc">λ</foreign><emph type="italics"></emph>: But the angle at Y <lb></lb>is equall to the Angle at<emph.end type="italics"></emph.end> <foreign lang="grc">γ;</foreign> <emph type="italics"></emph>and the<emph.end type="italics"></emph.end> (e) <emph type="italics"></emph>Angle<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1373"></arrow.to.target><lb></lb>A <foreign lang="grc">Γ</foreign> D <emph type="italics"></emph>greater than the Angle A<emph.end type="italics"></emph.end> <foreign lang="grc">λ</foreign> <emph type="italics"></emph>D, which falleth <lb></lb>without it: Therefore the Angle at Y ſhall be great<lb></lb>er than that at X. </s> <s>And becauſe now the Portion <lb></lb>turneth about, ſo, as that the Baſe doth not touch <lb></lb>the Liquid, the Axis ſhall make an Angle with its <lb></lb>Surface greater than the Angle G; that is, than the <lb></lb>Angle Y: And, for that reaſon, much greater than <lb></lb>the Angle X.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1372"></margin.target>(d) <emph type="italics"></emph>By 29 of the <lb></lb>firſt.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1373"></margin.target>(e) <emph type="italics"></emph>By 16. of the <lb></lb>firſt.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>CONCLUSION III.</s></p><p type="main"> <s><emph type="italics"></emph>If the Portion have the ſame proportion in Gravity to the <lb></lb>Liquid, that the Square X O hath to the Square<emph.end type="italics"></emph.end><lb></lb>BD, <emph type="italics"></emph>being demitted into the Liquid, ſo inclined, as that <lb></lb>its Baſe touch not the Liquid, it ſhall ſtand and <lb></lb>continue inclined, ſo, as that its Baſe touch the Sur<lb></lb>face of the Liquid, in one Point only, and its Axis ſhall <lb></lb>make an Angle with the Liquids Surface equall to the <lb></lb>Angle X. And, if the Portion have the ſame proportion <lb></lb>in Gravity to the Liquid, that the Square P F hath <lb></lb>to the Square B D, being demitted into the Liquid, <lb></lb>& ſet ſo inclined, as that its Baſe touch not the Liquid, <lb></lb>it ſhall ſtand inclined, ſo, as that its Baſe touch the <lb></lb>Surface of the Liquid in one Point only, & its Axis ſhall <lb></lb>make an Angle with it, equall to the Angle<emph.end type="italics"></emph.end> <foreign lang="grc">Φ.</foreign></s></p><p type="main"> <s>Let the Portion have the ſame proportion in Gravity to tho <lb></lb>Liquid that the Square <emph type="italics"></emph>X<emph.end type="italics"></emph.end>O hath to the Square B D; and let <lb></lb>it be demitted into the Liquid ſo inclined, as that its Baſe touch <lb></lb><figure id="id.040.01.1084.2.jpg" xlink:href="040/01/1084/2.jpg"></figure><lb></lb>not the Liquid. </s> <s>And cutting it by <lb></lb>a Plane thorow the Axis, erect unto <lb></lb>the Surface of the Liquid, let the <lb></lb>Section of the Solid, be the Section <lb></lb>of a Right-angled Cone, A P M L; <lb></lb>let the Section of the Surface of the <lb></lb>Liquid be I M; and the Axis of the <lb></lb>Portion and Diameter of the Section <lb></lb>B D; and let B D be divided as be<lb></lb>fore; and draw PN parallel to IM <pb xlink:href="040/01/1085.jpg" pagenum="391"></pb>and touching the Section in P, and T P parallel to B D; and P S perpen<lb></lb>dicular unto B D. </s> <s>It is to be demonſtrated that the Portion ſhall <lb></lb><figure id="id.040.01.1085.1.jpg" xlink:href="040/01/1085/1.jpg"></figure><lb></lb>not ſtand ſo, but ſhall encline until <lb></lb>that the Baſe touch the Surface of <lb></lb>the Liquid, in one Point only, for let <lb></lb>the ſuperior figure ſtand as it was, <lb></lb>and draw O C, Perpendicular to B D; <lb></lb>and drawing a <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ine from A to <emph type="italics"></emph>X,<emph.end type="italics"></emph.end><lb></lb>prolong it to Q: A X ſhalbe equall <lb></lb>to <emph type="italics"></emph>X<emph.end type="italics"></emph.end> <expan abbr="q.">que</expan> Then draw O X parallel <lb></lb>to A <expan abbr="q.">que</expan> And becauſe the Portion <lb></lb>is ſuppoſed to have the ſame pro<lb></lb>portion in Gravity to the Liquid <lb></lb>that the ſquare X O hath to the <lb></lb>Square B D; the part thereof ſubmerged ſhall alſo have the ſame <lb></lb>proportion to the whole; that is, the Square T P to the Square <lb></lb><arrow.to.target n="marg1374"></arrow.to.target><lb></lb>B D; and ſo T P ſhall be equal to <emph type="italics"></emph>X<emph.end type="italics"></emph.end> O: And ſince that of the <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortions <lb></lb>I P M and A O Q the Diameters are equall, the portions ſhall alſo be <lb></lb><arrow.to.target n="marg1375"></arrow.to.target><lb></lb>equall. <emph type="italics"></emph>A<emph.end type="italics"></emph.end>gain, becauſe that in the Equall and <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ike <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortions A O Q L <lb></lb><arrow.to.target n="marg1376"></arrow.to.target><lb></lb>and AP ML the Lines A Q and I M, which cut off equall <emph type="italics"></emph>P<emph.end type="italics"></emph.end>or<lb></lb>tions, are drawn, that, from the Extremity of the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>aſe, and this <lb></lb>not from the Extremity; it appeareth that that which is drawn from <lb></lb>the end or Extremity of the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>aſe, ſhall make the Acute Angle with <lb></lb>the Diameter of the whole <emph type="italics"></emph>P<emph.end type="italics"></emph.end>ortion leſset. <emph type="italics"></emph>A<emph.end type="italics"></emph.end>nd the Angle at <emph type="italics"></emph>X<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1377"></arrow.to.target><lb></lb>being leſſe than the Angle at N, B C ſhall be greater than B S; and <lb></lb>C R leſſer than S R: <emph type="italics"></emph>A<emph.end type="italics"></emph.end>nd, therfore O G ſhall be leſſer than P Z; <lb></lb>and G <emph type="italics"></emph>X<emph.end type="italics"></emph.end> greater than Z T: Therfore P Z is greater than double of <lb></lb>Z T; being that O G is double of G X. </s> <s>Let P H be double to H T; <lb></lb>and drawing a Line from H to K, prolong it to <foreign lang="grc">ω.</foreign> The Center of <lb></lb>Gravity of the whole Portion ſhall be K; the Center of the part <lb></lb>which is within the Liquid H, and that of the part which is above <lb></lb>the Liquid in the Line K <foreign lang="grc">ω</foreign>; which ſuppoſed to be <foreign lang="grc">ω.</foreign> Therefore it <lb></lb>ſhall be demonſtrated, both, that K H is perpendicular to the Surface <lb></lb>of the Liquid, and thoſe Lines alſo that are drawn thorow the Points <lb></lb>Hand <foreign lang="grc">ω</foreign> parallel to K H: And therfore the Portion ſhall not reſt, but <lb></lb>ſhall encline untill that its Baſe do touch the Surface of the Liquid <lb></lb>in one Point; and ſo it ſhall continue. </s> <s>For in the Equall Portions <lb></lb>A O Q L and A P M L, the <lb></lb><figure id="id.040.01.1085.2.jpg" xlink:href="040/01/1085/2.jpg"></figure><lb></lb>Lines A Q and A M, that cut off <lb></lb>equall Portions, ſhall be dawn <lb></lb>from the Ends or Terms of the Baſes; <lb></lb>and A O Q and A P M ſhall be <lb></lb>demonſtrated, as in the former, to <lb></lb><arrow.to.target n="marg1378"></arrow.to.target><lb></lb>be equall: Therfore A Q and A M, <lb></lb>do make equall Acute Angles with <lb></lb>the Diameters of the Portions; and <pb xlink:href="040/01/1086.jpg" pagenum="392"></pb>the Angles at X and N are equall. </s> <s>And, therefore, if drawing HK, <lb></lb>it be prolonged to <foreign lang="grc">ω,</foreign> the Centre of Gravity of the whole Portion ſhall <lb></lb>be K; of the part which is within the Liquid H; and of the part which <lb></lb>is above the Liquid in K <foreign lang="grc">ὠ</foreign> as ſuppoſe in <foreign lang="grc">ω;</foreign> and H K perpendicular to <lb></lb><figure id="id.040.01.1086.1.jpg" xlink:href="040/01/1086/1.jpg"></figure><lb></lb>the Surface of the Liquid. </s> <s>Therfore <lb></lb>along the ſame Right Lines ſhall the <lb></lb>part which is within the Liquid move <lb></lb>upwards, and the part above it down<lb></lb>wards: And therfore the Portion <lb></lb>ſhall reſt with one of its Points <lb></lb>touching the Surface of the Liquid, <lb></lb>and its Axis ſhall make with the <lb></lb><arrow.to.target n="marg1379"></arrow.to.target><lb></lb>ſame an Angle equall to X. </s> <s>It is <lb></lb>to be demonſtrated in the ſame <lb></lb>manner that the Portion that hath <lb></lb>the ſame proportion in Gravity to the Liquid, that the Square P F hath <lb></lb>to the Square B D, being demitted into the Liquid, ſo, as that its <lb></lb>Baſe touch not the Liquid, it ſhall ſtand inclined, ſo, as that its Baſe <lb></lb>touch the Surface of the Liquid in one Point only; and its Axis ſhall <lb></lb>make therwith an Angle equall to the Angle <foreign lang="grc">φ.</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></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"></emph>By the twenty ſixth of the Book<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1381"></arrow.to.target><lb></lb><emph type="italics"></emph>of<emph.end type="italics"></emph.end> Archimedes, De Conoidibus & Sphæroidibus: <emph type="italics"></emph>Therefore, (a) the Square T P <lb></lb>ſhall be equall to the Square X O: And for that reaſon, the Line T P equall to the <lb></lb>Line X O.<emph.end type="italics"></emph.end><lb></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"></emph>By 9 of the <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1382"></margin.target>B</s></p><p type="main"> <s>The Portions ſhall alſo be equall.] <emph type="italics"></emph>By the twenty fifth of the ſame Book.<emph.end type="italics"></emph.end></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, becauſe that in the Equall and Like Portions, A O Q L <lb></lb>and A P M L.] <emph type="italics"></emph>For, in the Portion A P M L, deſcribe the Portion A O Q equall <lb></lb>to the Portion I P M: The Point Q falleth beneath M; for otherwiſe, the Whole would be <lb></lb>equall to the Part. </s> <s>Then draw I V parallel to A Q, and cutting the Diameter is<emph.end type="italics"></emph.end> <foreign lang="grc">ψ;</foreign> <emph type="italics"></emph>and <lb></lb>let I M cut the ſame<emph.end type="italics"></emph.end> <foreign lang="grc">ς;</foreign> <emph type="italics"></emph>and A Q in<emph.end type="italics"></emph.end> <foreign lang="grc">ς.</foreign> <emph type="italics"></emph>I ſay <lb></lb>that the Angle A<emph.end type="italics"></emph.end> <foreign lang="grc">υ</foreign> <emph type="italics"></emph>D, is leſſer than the Angle<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.1086.2.jpg" xlink:href="040/01/1086/2.jpg"></figure><lb></lb><emph type="italics"></emph>I<emph.end type="italics"></emph.end> <foreign lang="grc">σ</foreign> <emph type="italics"></emph>D. </s> <s>For the Angle I<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>D is equall to the <lb></lb>Angle A<emph.end type="italics"></emph.end> <foreign lang="grc">υ</foreign> <emph type="italics"></emph>D: (b) But the interiour Angle<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1384"></arrow.to.target><lb></lb><emph type="italics"></emph>I<emph.end type="italics"></emph.end> <foreign lang="grc">ψ</foreign> <emph type="italics"></emph>D is leſſer than the exteriour I<emph.end type="italics"></emph.end> <foreign lang="grc">σ</foreign> <emph type="italics"></emph>D: There-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1385"></arrow.to.target><lb></lb><emph type="italics"></emph>fore, (c) A<emph.end type="italics"></emph.end> <foreign lang="grc">υ</foreign> <emph type="italics"></emph>D ſhall alſo be lefter than I<emph.end type="italics"></emph.end> <foreign lang="grc">σ</foreign> <emph type="italics"></emph>D.<emph.end type="italics"></emph.end><lb></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"></emph>By 29 of the <lb></lb>firſt.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1385"></margin.target><emph type="italics"></emph>(c) By 16 of the <lb></lb>firſt.<emph.end type="italics"></emph.end></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 leſſe <lb></lb>than the Angle at N.] <emph type="italics"></emph>Thorow O draw twe <lb></lb>Lines, O C perpendicular to the Diameter B D, and <lb></lb>O X touching the Section in the Point O, and cutting<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1387"></arrow.to.target><lb></lb><emph type="italics"></emph>the Diameter in X: (d) O X ſhall be parallel <lb></lb>to A <expan abbr="q;">que</expan> and the<emph.end type="italics"></emph.end> (e) <emph type="italics"></emph>Angle at X, ſhall be equall to<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1388"></arrow.to.target><lb></lb><emph type="italics"></emph>that at<emph.end type="italics"></emph.end> <foreign lang="grc">υ</foreign>: <emph type="italics"></emph>Therefore, the<emph.end type="italics"></emph.end> (f) <emph type="italics"></emph>Angle at X,<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1389"></arrow.to.target><lb></lb><emph type="italics"></emph>ſhall be leſſer than the Angle at<emph.end type="italics"></emph.end> <foreign lang="grc">ς;</foreign> <emph type="italics"></emph>that is, to <lb></lb>that at N: And, conſequently, X ſhall fall beneath N: Therefore, the Line X B is greater than <lb></lb>N B. And, ſince B C is equall to X B, and B S equall to N B; B C ſhall be greater than B S.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/1087.jpg" pagenum="397"></pb><p type="margin"> <s><margin.target id="marg1387"></margin.target><emph type="italics"></emph>(d) By 5 of our ſe<lb></lb>cond of<emph.end type="italics"></emph.end> Conicks.</s></p><p type="margin"> <s><margin.target id="marg1388"></margin.target>(e) <emph type="italics"></emph>By 29 of the <lb></lb>firſt.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1389"></margin.target>(f) <emph type="italics"></emph>By 39 of our <lb></lb>firſt of<emph.end type="italics"></emph.end> Conicks.</s></p><p type="main"> <s>Therefore, A Q and A M do make equall Acute Angles with <lb></lb><arrow.to.target n="marg1390"></arrow.to.target><lb></lb>the Diameters of the Portions.] <emph type="italics"></emph>We demonſtrate this as in the Commentaries <lb></lb>upon the ſecond Concluſion.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1390"></margin.target>E</s></p><p type="main"> <s>It is to be demonſtrated in the ſame manner, that the Portion <lb></lb><arrow.to.target n="marg1391"></arrow.to.target><lb></lb>that hath the ſame proportion in Gravity to the Liquid, that the <lb></lb>Square P F hath to the Square B D, <lb></lb>being demitted into the Liquid, ſo, <lb></lb><figure id="id.040.01.1087.1.jpg" xlink:href="040/01/1087/1.jpg"></figure><lb></lb>as that its Baſe touch not the Li<lb></lb>quid, it ſhall ſtand inclined, ſo, as <lb></lb>that its Baſe touch the Surface of the <lb></lb>Liquid in one point only; and its Axis <lb></lb>ſhall make therewith an angle equall <lb></lb>to the Angle <foreign lang="grc">φ.</foreign>] <emph type="italics"></emph>Let the Portion be to the <lb></lb>Liquid in Gravity, as the Square P F to the <lb></lb>Square B D: and being demitted into the <lb></lb>Liquid, ſo inclined, as that its Baſe touch not <lb></lb>the Liquid, let it be cut thorow the Axis by a <lb></lb>Plane erect to the Surface of the Liquid, that <lb></lb>that the Section may be A M O L, the Section <lb></lb>of a Rightangled Cone; and, let the Section of the Liquids Surface be I O; and the Axit <lb></lb>of the Portion and Diameter of the Section B D; which let be cut into the ſame parts as <lb></lb>we ſaid before, and draw M N parallel to I O, that it may touch the Section in the Point <lb></lb>M; and M T parallel to B D, and P M S perpe ndicular to the ſame. </s> <s>It is to be demon<lb></lb>strated, that the Portion ſhall not reſt, but ſhall incline, ſo, as that it touch the Liquids <lb></lb>Surface, in one Point of its Baſe only. </s> <s>For,<emph.end type="italics"></emph.end><lb></lb><figure id="id.040.01.1087.2.jpg" xlink:href="040/01/1087/2.jpg"></figure><lb></lb><emph type="italics"></emph>draw P C perpendicular to B D; and drawing <lb></lb>a Line from A to F, prolong it till it meet with <lb></lb>the Section in <expan abbr="q;">que</expan> and thorow P draw P<emph.end type="italics"></emph.end> <foreign lang="grc">φ</foreign> <emph type="italics"></emph>pa<lb></lb>rallel to A Q: Now, by the things allready de<lb></lb>monſtrated by us, A F and F Q ſhall be equall <lb></lb>to one another. </s> <s>And being that the Portion hath <lb></lb>the ſame proportion in Gravity unto the Liquid, <lb></lb>that the Square P F hath to the Square B D; and <lb></lb>ſeeing that the part ſubmerged, hath the ſame pro-<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg1392"></arrow.to.target><lb></lb><emph type="italics"></emph>partion to the whole Portion; that is, the Squàre <lb></lb>M T to the Square B D; (g) the Square M T <lb></lb>ſhall be equall to the Square P F; and, by the <lb></lb>ſame reaſon, the Line M T equall to the Line <lb></lb>P F. </s> <s>So that there being drawn in the equall & like <lb></lb>portions A P Q Land A M O L, the Lines A Q and I O which cut off equall Portions, the <lb></lb>firſt from the Extreme term of the Baſe, the laſt not from the Extremity; it followeth, that <lb></lb>A Q drawn from the Extremity, containeth a leſſer Acute Angle with the Diameter of the <lb></lb>Portion, than I O: But the Line P<emph.end type="italics"></emph.end> <foreign lang="grc">φ</foreign> <emph type="italics"></emph>is parallel to the Line A Q, and M N to I O: There<lb></lb>fore, the Angle at<emph.end type="italics"></emph.end> <foreign lang="grc">φ</foreign> <emph type="italics"></emph>ſhall be leſſer than the Angle at N; but the Line B C greater than B S; <lb></lb>and S R, that is, M X, greater than C R, that is, than P Y: and, by the ſame reaſon, X T <lb></lb>leſſer than Y F. And, ſince P Y is double to Y F, M X ſhall be greater than double to <lb></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></lb>Line from H to K, prolonging it. </s> <s>Now, the Centre of Gravity of the whole Portion <lb></lb>ſhall be the Point K; of the part within the Liquid H; and of the Remaining part above <lb></lb>the Liquid in the Line H K produced, as ſuppoſe in<emph.end type="italics"></emph.end> <foreign lang="grc">ω</foreign> <emph type="italics"></emph>It ſhall be demonſtrated in the ſame <lb></lb>manner, as before, that both the Line K H and thoſe that are drawn thorow the Points H <lb></lb>and<emph.end type="italics"></emph.end> <foreign lang="grc">ω</foreign> <emph type="italics"></emph>parallel to the ſaid K H, are perpendicular to the Surface of the Liquid: The <lb></lb>Portion therefore, ſhall not reſt; but when it ſhall be enclined ſo far as to touch the Sur<lb></lb>face of the Liquid in one Point and no more, then it ſhall ſtay. </s> <s>For the Angle at N<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1088.jpg" pagenum="398"></pb><figure id="id.040.01.1088.1.jpg" xlink:href="040/01/1088/1.jpg"></figure><lb></lb><emph type="italics"></emph>ſhall be equall to the Angle at<emph.end type="italics"></emph.end> <foreign lang="grc">φ;</foreign> <emph type="italics"></emph>and the Line B S <lb></lb>equall to the Line B C; and S R to C R: Where<lb></lb>fore, M H ſhall be likewiſe equall to P Y. There<lb></lb>fore, having drawn HK and prolonged it; the <lb></lb>Centre of Gravity of the whole Portion ſhall be <lb></lb>K; of that which is in the Liquid H; and of <lb></lb>that which is above it, the Centre ſhall be in <lb></lb>the Line prolonged: let it be in<emph.end type="italics"></emph.end> <foreign lang="grc">ω.</foreign> <emph type="italics"></emph>There<lb></lb>fore, along that ſame Line K H, which is per<lb></lb>pendicular to the Surface of the Liquid, ſhall <lb></lb>the part which is within the Liquid move up<lb></lb>wards, and that which is above the Liquld <lb></lb>downwards: And, for this cauſe, the Portion, <lb></lb>ſhall be no longer moved, but ſhall ſtay, and <lb></lb>reſt, ſo, as that its Baſe do touch the Liquids Surface in but one Point; and its Axis <lb></lb>maketh an Angle therewith equall to the Angle<emph.end type="italics"></emph.end> <foreign lang="grc">φ</foreign><emph type="italics"></emph>; And, this is that which we were to <lb></lb>demonſtrate.<emph.end type="italics"></emph.end></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"></emph>By 9 of t <lb></lb>fifth.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>CONCLVSION IV.</s></p><p type="main"> <s><emph type="italics"></emph>If the Portion have greater proportion in Gravity <lb></lb>to the Liquid, than the Square F P to the Square <lb></lb>B D, but leſſer than that of the Square X O to the <lb></lb>Square B D, being demitted into the Liquid, <lb></lb>and inclined, ſo, as that its Baſe touch not the <lb></lb>Liquid, it ſhall ſtand and reſt, ſo, as that its Baſe <lb></lb>ſhall be more ſubmerged in the Liquid.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Again, let the Portion have greater proportion in <lb></lb>Gravity to the Liquid, than the Square F P to the <lb></lb>Square B D, but leſſer than that of the Square X O to <lb></lb>the Square B D; and as the Portion is in Gravity to the Liquid, <lb></lb>ſo let the Square made of the Line <foreign lang="grc">ψ</foreign> be to the Square B D. <foreign lang="grc">Ψ</foreign><lb></lb>ſhall be greater than F P, and leſſer than X O. Apply, therefore, <lb></lb>the right Line I V to fall betwixt the Portions A V Q L and A X D; <lb></lb>and let it be equall to <foreign lang="grc">ψ,</foreign> and parallel to B D; and let it meet <lb></lb>the Remaining Section in Y: V Y ſhall alſo be proved double <lb></lb>to Y I, like as it hath been demonſtrated, that O G is double off <lb></lb>G X. And, draw from V, the Line V <foreign lang="grc">ω,</foreign> touching the Section <lb></lb>A V Q L in V; and drawing a Line from A to I, prolong it unto <lb></lb><expan abbr="q.">que</expan> We prove in the ſame manner, that the Line A I is equall <lb></lb>to I <expan abbr="q;">que</expan> and that A Q is parallel to V <foreign lang="grc">ω.</foreign> It is to be demonſtrated, <lb></lb>that the Portion being demitted into the Liquid, and ſo inclined, <lb></lb>as that its Baſe touch not the Liquid, ſhall ſtand, ſo, that its Baſe <lb></lb>ſhall be more ſubmerged in the Liquid, than to touch it Surface in <pb xlink:href="040/01/1089.jpg" pagenum="399"></pb>but one Point only. </s> <s>For let it be de<lb></lb><figure id="id.040.01.1089.1.jpg" xlink:href="040/01/1089/1.jpg"></figure><lb></lb>mitted into the Liquid, as hath been <lb></lb>ſaid; and let it firſt be ſo inclined, as <lb></lb>that its Baſe do not in the leaſt <lb></lb>touch the Surface of the Liquid. </s> <s>And <lb></lb>then it being cut thorow the Axis, <lb></lb>by a Plane erect unto the Surface of <lb></lb>the Liquid, let the Section of the <lb></lb>Portion be A N Z G; that of the <lb></lb>Liquids Surface E Z; the Axis of <lb></lb>the Portion and Diameter of the <lb></lb>Section B D; and let B D be cut in <lb></lb>the Points K and R, as before; and <lb></lb>draw N L parallel to E Z, and touching the Section A N Z G <lb></lb>in N, and N S perpendicular to <lb></lb><figure id="id.040.01.1089.2.jpg" xlink:href="040/01/1089/2.jpg"></figure><lb></lb>B D. Now, ſeeing that the Por<lb></lb>tion is in Gravity unto the Liquid, <lb></lb>as the Square made of the Line <lb></lb>is to the Square B D; <foreign lang="grc">ψ</foreign> ſhall <lb></lb>be equall to N T: Which is to <lb></lb>be demonſtrated as above: And, <lb></lb>therefore, N T is alſo equall to <lb></lb>V I: The Portions, therefore, <lb></lb>A V Q and E N Z are equall to <lb></lb>one another. </s> <s>And, ſince that in <lb></lb>the Equall and like Portions A V <lb></lb>Q L and A N Z G, there are drawn A Q and E Z, cutting off <lb></lb>equall Portions, that from the <lb></lb><figure id="id.040.01.1089.3.jpg" xlink:href="040/01/1089/3.jpg"></figure><lb></lb>Extremity of the Baſe, this not <lb></lb>from the Extreme, that which is <lb></lb>drawn from the Extremity of the <lb></lb>Baſe, ſhall make the Acute Angle <lb></lb>with the Diameter of the Portion <lb></lb>leſſer: and in the Triangles N L S <lb></lb>and V <foreign lang="grc">ω</foreign> C, the Angle at L is <lb></lb>greater than the Angle at <foreign lang="grc">ω</foreign>: <lb></lb>Therefore, B S ſhall be leſſer <lb></lb>than B C; and S R leſſer than <lb></lb>C R: and, conſequently, N X <lb></lb>greater than V H; and X T leſſer than H I. Seeing, therefore, <lb></lb>that V Y is double to Y I; It is manifeſt, that N X is greater than <lb></lb>double to X T. </s> <s>Let N M be double to M T: It is manifeſt, from what <lb></lb>hath been ſaid, that the Portion ſhall not reſt, but will incline, untill <lb></lb>that its Bafe do touch the Surface of the Liquid: and it toucheth it in <lb></lb>one Point only, as appeareth in the Figure: And other things <pb xlink:href="040/01/1090.jpg" pagenum="400"></pb><figure id="id.040.01.1090.1.jpg" xlink:href="040/01/1090/1.jpg"></figure><lb></lb>ſtanding as before, we will again <lb></lb>demonſtrate, that N T is equall to <lb></lb>V I; and that the Portions A V Q <lb></lb>and A N Z are equall to each other. <lb></lb></s> <s>Therefore, in regard, that in the <lb></lb>Equall and Like Portions A V Q L <lb></lb>and A N Z G, there are drawn <lb></lb>A Q and A Z cutting off equall Por<lb></lb>tions, they ſhall with the Diameters <lb></lb>of the Portions, contain equall <lb></lb>Angles. </s> <s>Therefore, in the Triangles <lb></lb>N L S and V <foreign lang="grc">ω</foreign> C, the Angles at <lb></lb>the Points <emph type="italics"></emph>L<emph.end type="italics"></emph.end> and <foreign lang="grc">ω</foreign> are equall; and the Right Line B S equall to <lb></lb>B C; S R to C R; N X to V H; and X T to H I: And, ſince <lb></lb>V Y is double to Y I, N X ſhall be greater than double of X T. <lb></lb></s> <s>Let therefore, N M be double to M T. </s> <s>It is hence again manifeſt, <lb></lb>that the Portion will not remain, but ſhall incline on the part <lb></lb>towards A: But it was ſuppoſed, that the ſaid Portion did <lb></lb>touch the Surface of the Liquid in one ſole Point: Therefore, <lb></lb>its Baſe muſt of neceſſity ſubmerge farther into the Liquid.</s></p><p type="head"> <s>CONCLVSION V.</s></p><p type="main"> <s><emph type="italics"></emph>If the Portion have leſſer proportion in Gravity to <lb></lb>the Liquid, than the Square F P to the Square <lb></lb>B D, being demitted into the Liquid, and in<lb></lb>clined, ſo, as that its Baſe touch not the Liquid, <lb></lb>it ſhall ſtand ſo inclined, as that its Axis ſhall <lb></lb>make an Angle with the Surface of the Liquid, <lb></lb>leſſe than the Angle<emph.end type="italics"></emph.end> <foreign lang="grc">ψ;</foreign> <emph type="italics"></emph>And its Baſe ſhall <lb></lb>not in the leaſt touch the Liquids Surface.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Finally, let the Portion have leſſer proportion to the Liquid <lb></lb>in Gravity, than the Square F P hath to the Square B D; and <lb></lb>as the Portion is in Gravity to the Liquid, ſo let the <lb></lb>Square made of the Line <foreign lang="grc">ψ</foreign> be to the Square B D. <foreign lang="grc">ψ</foreign> ſhall be <lb></lb>leſſer than P F. Again, apply any Right Line as G I, falling <lb></lb>betwixt the Sections A G Q L and A X D, and parallel to B D; <lb></lb>and let it cut the Middle Conick Section in the Point H, and <pb xlink:href="040/01/1091.jpg" pagenum="401"></pb>the Right Line R Y in Y. </s> <s>We <lb></lb><figure id="id.040.01.1091.1.jpg" xlink:href="040/01/1091/1.jpg"></figure><lb></lb>ſhall demonſtrate G H to be double <lb></lb>to H I, as it hathbeen demonſtra<lb></lb>ted, that O G is double to G X. <lb></lb></s> <s>Then draw G <foreign lang="grc">ω</foreign> touching the Section <lb></lb>A G Q L in G; and G C perpen di<lb></lb>cular to B D; and drawing a Line <lb></lb>from A to I, prolong it to <expan abbr="q.">que</expan> Now <lb></lb>A I ſhall be equall to I <expan abbr="q;">que</expan> and <lb></lb>A Q parallel to G <foreign lang="grc">ω.</foreign> It is to be <lb></lb>demonſtrated, that the Portion being <lb></lb>demitted into the Liquid, and inclined, ſo, as that its Baſe touch <lb></lb>the Liquid, it ſhall ſtand ſo incli<lb></lb><figure id="id.040.01.1091.2.jpg" xlink:href="040/01/1091/2.jpg"></figure><lb></lb>ned, as that its Axis ſhall make <lb></lb>an Angle with the Surface of the <lb></lb>Liquid leſſe than the Angle <foreign lang="grc">φ;</foreign><lb></lb>and its Baſe ſhall not in the leaſt <lb></lb>touch the Liquids Surface. </s> <s>For <lb></lb>let it be demitted into the Liquid, <lb></lb>and let it ſtand, ſo, as that its Baſe <lb></lb>do touch the Surface of the Liquid <lb></lb>in one Point only: and the Portion <lb></lb>being cut thorow the Axis by a <lb></lb>Plane erect unto the Surface of the Liquid, let the Section of <lb></lb><figure id="id.040.01.1091.3.jpg" xlink:href="040/01/1091/3.jpg"></figure><lb></lb>the Portion be A N Z L, the Section <lb></lb>of a Rightangled Cone; that of <lb></lb>the Surface of the Liquid A Z; and <lb></lb>the Axis of the Portion and Dia<lb></lb>meter of the Section B D; and let <lb></lb>B D be cut in the Points K and R <lb></lb>as hath been ſaid above; and draw <lb></lb>N F parallel to A Z, and touching <lb></lb>the Section of the Cone in the Point <lb></lb>N; and N T parallel to B D; and <lb></lb>N S perpendicular to the ſame. </s> <s>Be<lb></lb>cauſe, now, that the Portion is in Gravity to the Liquid, as <lb></lb>the Square made of <foreign lang="grc">ψ</foreign> is to the Square B D; and ſince that as the <lb></lb>Portion is to the Liquid in Gravity, ſo is the Square N T to the <lb></lb>Square B D, by the things that have been ſaid; it is plain, that <lb></lb>N T is equall to the Line <foreign lang="grc">ψ</foreign>: And, therefore, alſo, the Portions <lb></lb>A N Z and A G Q are equall. </s> <s>And, ſeeing that in the Equall and <lb></lb>Like Portions A G Q L and A N Z L; there are drawn from the <lb></lb>Extremities of their Baſes, A Q and A Z which cut off equall Porti<lb></lb>ons: It is obvious, that with the Diameters of the Portions they <pb xlink:href="040/01/1092.jpg" pagenum="402"></pb>make equall Angles; and that in the Triangles N F S and G <foreign lang="grc">ω</foreign> C <lb></lb>the Angles at F and <foreign lang="grc">ω</foreign> are equall; as alſo, that S B and B C, and<lb></lb>S R and C R are equall to one another: And, therefore, N X and<lb></lb>G Y are alſo equall; and X T and Y I. </s> <s>And ſince G H is double<lb></lb>to H I, N X ſhall be leſſer than double of X T. </s> <s>Let N M therefore<lb></lb>be double to M T; and drawing a Line from M to K, prolong it<lb></lb>unto E. </s> <s>Now the Centre of Gravity of the whole ſhall be the<lb></lb>Point K; of the part which is in the Liquid the Point M; and<lb></lb>that of the part which is above the Liquid in the Line prolonged <lb></lb>as ſuppoſe in E. Therefore, by what was even now demonſtrated <lb></lb>it is manifeſt that the Portion ſhall not ſtay thus, but ſhall incline, ſo <lb></lb>as that its Baſe do in no wiſe touch the Surface of the Liquid <lb></lb>And that the Portion will ſtand, ſo, as to make an Angle with the<lb></lb>Surface of the Liquid leſſer than<lb></lb><figure id="id.040.01.1092.1.jpg" xlink:href="040/01/1092/1.jpg"></figure><lb></lb>the Angle <foreign lang="grc">φ,</foreign> ſhall thus be demon <lb></lb>ſtrated. </s> <s>Let it, if poſſible, ſtand,<lb></lb>ſo, as that it do not make an Angle<lb></lb>leſſer than the Angle <foreign lang="grc">φ;</foreign> and diſpoſe<lb></lb>all things elſe in the ſame manner a <lb></lb>before; as is done in the preſet <lb></lb>Figure. </s> <s>We are to demonſtrat <lb></lb>in the ſame method, that N T is e<lb></lb>quall to <foreign lang="grc">ψ;</foreign> and by the ſame reaſor <lb></lb>equall alſo to G I. </s> <s>And ſince that in<lb></lb>the Triangles P <foreign lang="grc">φ</foreign> C and N F S, the Angle F is not leſſer than the<lb></lb>Angle <foreign lang="grc">φ,</foreign> B F ſhall not be greater than B C: And, therefore, neither<lb></lb>ſhall S R be leſſer than C R; nor N X than P Y: But ſince P F is<lb></lb>greater than N T, let P F be Seſquialter of P Y: N T ſhall be leſſer<lb></lb>than Seſquialter of N X: And, therefore, N X ſhall be greate <lb></lb>than double of X T. </s> <s>Let N M be double of M T; and drawing <lb></lb>Line from M to K prolong it. </s> <s>It is manifeſt, now, by what hath<lb></lb>been ſaid, that the Portion ſhall not continue in this poſition, but ſhall<lb></lb>turn about, ſo, as that its Axis do make an Angle with the Surface<lb></lb>of the Liquid, leſſer than the Angle <foreign lang="grc">φ.</foreign> </s></p><p type="head"> <s><emph type="italics"></emph>FINIS.<emph.end type="italics"></emph.end></s></p></chap><pb xlink:href="040/01/1093.jpg"></pb> <chap> <p type="head"> <s>A <lb></lb>DISCOURSE <lb></lb><emph type="italics"></emph>PRESENTED<emph.end type="italics"></emph.end><lb></lb>TO THE MOST SERENE <lb></lb>Don Coſimo II. <lb></lb>GREAT DUKE <lb></lb><emph type="italics"></emph>OF<emph.end type="italics"></emph.end><lb></lb>TUSCANY, <lb></lb>CONCERNING <lb></lb>The <emph type="italics"></emph>NATATION<emph.end type="italics"></emph.end> of BODIES Vpon, <lb></lb>And <emph type="italics"></emph>SUBMERSION<emph.end type="italics"></emph.end> In, <lb></lb>THE <lb></lb>WATER.</s></p><p type="head"> <s>By GALILEUS GALILEI: Philoſopher and <lb></lb>Mathematician, unto His moſt Serene Highneſſe.</s></p><p type="head"> <s>Engliſhed from the Second Edition of the ITALIAN, <lb></lb>compared with the Manuſcript Copies, and reduced <lb></lb>into PROPOSITIONS: <lb></lb>By <emph type="italics"></emph>THOMAS SALUSBURY,<emph.end type="italics"></emph.end> <expan abbr="Eſq;">Eſque</expan></s></p><p type="head"> <s><emph type="italics"></emph>LONDON<emph.end type="italics"></emph.end>: <lb></lb>Printed by WILLIAM LEYBOURN: <lb></lb><emph type="italics"></emph>M D C LXIII.<emph.end type="italics"></emph.end></s></p></chap><chap> <pb xlink:href="040/01/1094.jpg" pagenum="401"></pb><p type="head"> <s>A DISCOVRSE <lb></lb>Preſented to the Moſt Serene DON COSIMO II. <lb></lb>GREATDUKE of <emph type="italics"></emph>TUSC ANY:<emph.end type="italics"></emph.end><lb></lb>CONCERNING<lb></lb><emph type="italics"></emph>The Natation of BODIES Upon, or Submerſion <lb></lb>In, the WATER.<emph.end type="italics"></emph.end></s> </p></chap> <chap><p type="main"> <s>Conſidering (Moſt Serene Prince) that the <lb></lb>publiſhing this preſent Treatiſe, of ſo <lb></lb>different an Argument from that which <lb></lb><arrow.to.target n="marg1393"></arrow.to.target><lb></lb>many expect, and which according to the <lb></lb>intentions I propoſed in my ^{*} Aſtronomi<lb></lb>call <emph type="italics"></emph>Adviſo,<emph.end type="italics"></emph.end> I ſhould before this time <lb></lb>have put forth, might peradventure make <lb></lb>ſome thinke, either that I had wholly <lb></lb>relinquiſhed my farther imployment <lb></lb>about the new Celeſtiall Obſervations, <lb></lb>or that, at leaſt, I handled them very <lb></lb>remiſſely; I have judged fit to render an account, aſwell of my <lb></lb>deferring that, as of my writing, and publiſhing this treatiſe.</s></p><p type="margin"> <s><margin.target id="marg1393"></margin.target>His Nuncio Sl<lb></lb>derio.</s></p><p type="main"> <s>As to the firſt, the laſt diſcoveries of <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> to be tricorporeall, and <lb></lb>of the mutations of Figure in <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> like to thoſe that are ſeen in the <lb></lb>Moon, together with the Conſequents depending thereupon, have <lb></lb>not ſo much occaſioned the demur, as the inveſtigation of the times <lb></lb>of the Converſions of each of the Four Medicean Planets about <emph type="italics"></emph>Ju <lb></lb>piter,<emph.end type="italics"></emph.end> which I lighted upon in <emph type="italics"></emph>April<emph.end type="italics"></emph.end> the year paſt, 1611, at my being in <lb></lb><emph type="italics"></emph>Rome<emph.end type="italics"></emph.end>; where, in the end, I aſſertained my ſelfe, that the firſt and neereſt <lb></lb>to <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> moved about 8 <emph type="italics"></emph>gr.<emph.end type="italics"></emph.end> & 29 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> of its Sphere in an houre, make <lb></lb>ing its whole revolution in one naturall day, and 18 hours, and almoſt <lb></lb>an halfe. </s><s>The ſecond moves in its Orbe 14 <emph type="italics"></emph>gr. </s><s>13 min.<emph.end type="italics"></emph.end> or very neer, <lb></lb>in an hour, and its compleat converſion is conſummate in 3 dayes, 13 <lb></lb>hours, and one third, or thereabouts. </s><s>The third paſſeth in an hour, <lb></lb>2 <emph type="italics"></emph>gr. </s><s>6 min.<emph.end type="italics"></emph.end> little more or leſs of its Circle, and meaſures it all in 7 <lb></lb>dayes, 4 hours, or very neer. </s><s>The fourth, and more remote than the <lb></lb>reſt, goes in one houre, o <emph type="italics"></emph>gr 54 min.<emph.end type="italics"></emph.end> and almoſt an halfe of its Sphere, <lb></lb>and finiſheth it all in 16 dayes, and very neer 18 hours. </s><s>But be <lb></lb>cauſe the exceſſive velocity of their returns or reſtitutions, requires a <lb></lb>moſt ſcrupulous preciſeneſſe to calculate their places, in times paſt <pb xlink:href="040/01/1095.jpg" pagenum="402"></pb>and future, eſpecially if the time be for many Moneths or Years; I <lb></lb>am therefore forced, with other Obſervations, and more exact than <lb></lb>the former, and in times more remote from one another, to correct <lb></lb>the Tables of ſuch Motions, and limit them even to the ſhorteſt mo <lb></lb>ment: for ſuch exactneſſe my firſt Obſervations ſuffice not; not only <lb></lb>in regard of the ſhort intervals of Time, but becauſe I had not as then <lb></lb>found out a way to meaſure the diſtances between the ſaid Planets <lb></lb>by any Inſtrument: I Obſerved ſuch Intervals with ſimple relation <lb></lb>to the Diameter of the Body of <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end>; taken, as we have ſaid, by <lb></lb>the eye, the which, though they admit not errors of above a Minute, <lb></lb>yet they ſuffice not for the determination of the exact greatneſs of the <lb></lb>Spheres of thoſe Stars. </s><s>But now that I have hit upon a way of ta <lb></lb>king ſuch meaſures without failing, ſcarce in a very few Seconds, I will <lb></lb>continue the obſervation to the very occultation of <emph type="italics"></emph>JVPITER,<emph.end type="italics"></emph.end> <lb></lb>which ſhall ſerve to bring us to the perfect knowledge of the Moti <lb></lb>ons, and Magnitudes of the Orbes of the ſaid Planets, together <lb></lb><arrow.to.target n="marg1394"></arrow.to.target> <lb></lb>alſo with ſome other conſequences thence ariſing. </s><s>I adde to theſe <lb></lb>things the obſervation of ſome obſcure Spots, which are diſcover <lb></lb>ed in the Solar Body, which changing, poſition in that, propounds <lb></lb>to our conſideration a great argument either that the Sun revolves in <lb></lb>it ſelfe, or that perhaps other Starts, in like manner as <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> and <lb></lb><emph type="italics"></emph>Mercury,<emph.end type="italics"></emph.end> revolve about it, inviſible in other times, by reaſon of their <lb></lb>ſmall digreſſions, leſſe than that of <emph type="italics"></emph>Mercury,<emph.end type="italics"></emph.end> and only viſible when <lb></lb>they interpoſe between the Sun and our eye, or elſe hint the truth <lb></lb>of both this and that; the certainty of which things ought not to be <lb></lb>contemned, nor omitted.</s></p><p type="margin"> <s><margin.target id="marg1394"></margin.target>The Authors <lb></lb>Obſervations of <lb></lb>the Solar Spots.</s></p><p type="main"> <s><emph type="italics"></emph>Continuall obſervation hath at laſt aſſured me that theſe Spots are <lb></lb>matters contiguous to the Body of the Sun, there continually produced <lb></lb>in great number, and afterwards diſſolved, ſome in a ſhorter, ſome in a <lb></lb>longer time, and to be by the Converſion or Revolution of the Sun in it <lb></lb>ſelfe, which in a Lunar Moneth, or thereabouts, finiſheth its Period, <lb></lb>caried about in a Circle, an accident great of it ſelfe, and greater for <lb></lb>its Conſequences.<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1395"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1395"></margin.target>The occaſion in <lb></lb>ducing the Au <lb></lb>thor to write <lb></lb>this Treatiſe.</s></p><p type="main"> <s>As to the other particular in the next place. ^{*} Many cauſes have <lb></lb>moved me to write the preſent Tract, the ſubject whereof, is the <lb></lb>Diſpute which I held ſome dayes ſince, with ſome learned men of <lb></lb>this City, about which, as your Highneſſe knows, have followed <lb></lb>many Diſcourſes: The principall of which Cauſes hath been the <lb></lb>Intimation of your Highneſſe, having commended to me Writing, <lb></lb>as a ſingular means to make true known from falſe, reall from appa <lb></lb>rent Reaſons, farr better than by Diſputing vocally, where the <lb></lb>one or the other, or very often both the Diſputants, through too <pb xlink:href="040/01/1096.jpg" pagenum="403"></pb>greate heate, or exalting of the voyce, either are not underſtood, <lb></lb>or elſe being tranſported by oſtentation of not yeilding to one ano <lb></lb>ther, farr from the firſt Propoſition, with the novelty, of the <lb></lb>various Propoſals, confound both themſelves and their Auditors.</s></p><p type="main"> <s>Moreover, it ſeemed to me convenient to informe your High <lb></lb>neſſe of all the ſequell, concerning the Controverſie of which I <lb></lb>treat, as it hath been advertiſed often already by others: and becauſe <lb></lb>the Doctrine which I follow, in the diſcuſſion of the point in hand, <lb></lb>is different from that of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end>; and interferes with his Principles, <lb></lb>I have conſidered that againſt the Authority of that moſt famous <lb></lb>Man, which amongſt many makes all ſuſpected that comes not from <lb></lb>the Schooles of the Peripateticks, its farr better to give ones Reaſons <lb></lb>by the Pen than by word of mouth and therfore I reſolved to write the <lb></lb>preſent diſcourſe: in which yet I hope to demonſtrate that it was not <lb></lb>out of capritiouſneſſe, or for that I had not read or underſtood <lb></lb><emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> that I ſometimes ſwerve from his opinion, but becauſe <lb></lb>ſeverall Reaſons perſwade me to it, and the ſame <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> hath </s></p><p type="main"> <s><arrow.to.target n="marg1396"></arrow.to.target> <lb></lb>tought me to fix my judgment on that which is grounded upon <lb></lb>Reaſon, and not on the bare Authority of the Maſter; and it is <lb></lb>moſt certaine according to the ſentence of <emph type="italics"></emph>Alcinoos,<emph.end type="italics"></emph.end> that philoſopha <lb></lb><arrow.to.target n="marg1397"></arrow.to.target> <lb></lb>ting ſhould be free. </s><s>Nor is the reſolution of our Queſtion in my <lb></lb>judgment without ſome benefit to the Univerſall, foraſmuch as <lb></lb>treating whether the figure of Solids operates, or not, in their going, <lb></lb>or not going to the bottome in Water, in occurrences of building <lb></lb>Bridges or other Fabricks on the Water, which happen commonly <lb></lb>in affairs of grand import, it may be of great availe to know the <lb></lb>truth.</s></p><p type="margin"> <s><margin.target id="marg1396"></margin.target><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> prefers <lb></lb>Reaſon to the <lb></lb>Authority ofan <lb></lb>Author.</s></p><p type="margin"> <s><margin.target id="marg1397"></margin.target>The benefit of <lb></lb>this Argument.</s></p><p type="main"> <s>I ſay therfore, that being the laſt Summer in company with certain <lb></lb><arrow.to.target n="marg1398"></arrow.to.target> <lb></lb>Learned men, it was ſaid in the argumentation; That Condenſation <lb></lb>was the propriety of Cold, and there was alledged for inſtance, the <lb></lb>example of Ice: now I at that time ſaid, that, in my judgment, <lb></lb>the Ice ſhould be rather Water rarified than condenſed, and my <lb></lb><arrow.to.target n="marg1399"></arrow.to.target> <lb></lb>reaſon was, becauſe Condenſation begets diminution of Maſs, and <lb></lb>augmentation of gravity, and Rarifaction cauſeth greater Lightneſs, <lb></lb>and augmentarion of Maſſe: and Water in freezing, encreaſeth in <lb></lb>Maſſe, and the Ice made thereby is lighter than the Water on which <lb></lb>it ſwimmeth.</s></p><p type="margin"> <s><margin.target id="marg1398"></margin.target>Condenſation <lb></lb>the Propriety of <lb></lb>Cold, according <lb></lb>to the Peripate <lb></lb>ticks.</s></p><p type="margin"> <s><margin.target id="marg1399"></margin.target>Ice rather water <lb></lb>rarified, than <lb></lb>condenſed, and <lb></lb>why:</s></p><p type="main"> <s><emph type="italics"></emph>What I ſay, is manifeſt, becauſe, the medium ſubtracting from the <lb></lb>whole Gravity of Sollids the weight of ſuch another Maſſe of the ſaid<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1400"></arrow.to.target> <lb></lb><emph type="italics"></emph>Medium; was<emph.end type="italics"></emph.end> Archimedes <emph type="italics"></emph>proves in his ^{*} Firſt Booke<emph.end type="italics"></emph.end> De Inſidentibus <lb></lb>Humido; <emph type="italics"></emph>when ever the Maſſe of the ſaid Solid encreaſeth by Diſtraction, <lb></lb>the more ſhall the<emph.end type="italics"></emph.end> Medium <emph type="italics"></emph>detract from its entire Gravity; and leſſe, <lb></lb>when by Compreſſion it ſhall be condenſed and reduced to a leſſe Maſſe.<emph.end type="italics"></emph.end></s></p><p type="margin"> <pb xlink:href="040/01/1097.jpg" pagenum="404"></pb> <s><margin.target id="marg1400"></margin.target>In lib: 1. of Na <lb></lb>tation of Bodies <lb></lb>Prop. </s><s>7.</s></p><p type="margin"> <s><margin.target id="marg1401"></margin.target>Figure operates <lb></lb>not in the Nata <lb></lb>tion of Sollids.</s></p><p type="main"> <s>It was anſwered me, that that proceeded not from the greater Levity; <lb></lb><arrow.to.target n="marg1401"></arrow.to.target> <lb></lb>but from the Figure, large and flat, which not being able to pene <lb></lb>trate the Reſiſtance of the Water, is the cauſe that it ſubmergeth not. <lb></lb></s><s>I replied, that any piece of Ice, of whatſoever Figure, ſwims upon <lb></lb>the Water, a manifeſt ſigne, that its being never ſo flat and broad, <lb></lb>hath not any part in its floating: and added, that it was a manifeſt <lb></lb>proofe hereof to ſee a piece of Ice of very broad Figure being thruſt <lb></lb>to the botome of the Water, ſuddenly return to flote atoppe, which <lb></lb>had it been more grave, and had its ſwimming proceeded from its <lb></lb>Forme, unable to penetrate the Reſiſtance of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> that <lb></lb>would be altogether impoſſible; I concluded therefore, that the Figure <lb></lb>was in ſort a Cauſe of the Natation or Submerſion of Bodies, <lb></lb>but the greater or leſſe Gravity in reſpect of the Water: and there <lb></lb>fore all Bodyes heavier than it of what Figure ſoever they be, indiffe <lb></lb>rently go to the bottome, and the lighter, though of any figure, float <lb></lb>indifferently on the top: and I ſuppoſe that thoſe which hold other <lb></lb>wiſe, were induced to that beliefe, by ſeeing how that diverſity <lb></lb>of Formes or Figures, greatly altereth the Veloſity, and Tardity <lb></lb>of Motion; ſo that Bodies of Figure broad and thin, deſcend <lb></lb>far more leaſurely into the Water, than thoſe of a more compacted <lb></lb>Figure, though both made of the ſame Matter: by which ſome <lb></lb>might be induced to believe that the Dilatation of the Figure might <lb></lb>reduce it to ſuch ampleneſſe that it ſhould not only retard but wholly <lb></lb>impede and take away the Motion, which I hold to be falſe. </s><s>Upon <lb></lb>this Concluſion, in many dayes diſcourſe, was ſpoken much, and <lb></lb>many things, and divers Experiments produced, of which your <lb></lb>Highneſſe heard, and ſaw ſome, and in this diſcourſe ſhall have <lb></lb>all that which hath been produced againſt my Aſſertion, and what <lb></lb>hath been ſuggeſted to my thoughts on this matter, and for con <lb></lb>firmation of my Concluſion: which if it ſhall ſuffice to remove that <lb></lb>(as I eſteem hitherto falſe) Opinion, I ſhall thinke I have not <lb></lb>unprofitably ſpent my paynes and time. </s><s>and although that come <lb></lb>not to paſſe, yet ought I to promiſe another benefit to my ſelfe, <lb></lb>namely, of attaining the knowledge of the truth, by hearing my <lb></lb>Fallacyes confuted, and true demonſtrations produced by thoſe <lb></lb>of the contrary opinion.</s></p><p type="main"> <s>And to proceed with the greateſt plainneſs and perſpicuity that <lb></lb>I can poſſible, it is, I conceive, neceſſary, firſt of all to declare <lb></lb>what is the true, intrinſecall, and totall Cauſe, of the aſcending of <lb></lb>ſome Sollid Bodyes in the Water, and therein floating; or on the <lb></lb>contrary, of their ſinking. </s><s>and ſo much the rather in aſmuch as I <lb></lb>cannot ſatisfie my ſelfe in that which <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> hath left written on <lb></lb>this Subject.</s></p><p type="margin"> <s><margin.target id="marg1402"></margin.target>The cauſe of the <lb></lb>Natation & ſub</s></p> <p type="main"> <s>I ſay then the Cauſe why ſome Sollid Bodyes deſcend to the <lb></lb><arrow.to.target n="marg1402"></arrow.to.target> <pb xlink:href="040/01/1098.jpg" pagenum="405"></pb>Bottom of Water, is the exceſſe of their Gravity, above the <lb></lb><arrow.to.target n="marg1403"></arrow.to.target> <lb></lb>Gravity of the Water; and on the contrary, the exceſs of the <lb></lb>Waters Gravity above the Gravity of thoſe, is the Cauſe that others <lb></lb>do not deſcend, rather that they riſe from the Bottom, and aſcend <lb></lb>to the Surface. </s><s>This was ſubtilly demonſtrated by <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> in <lb></lb>his Book Of the NATATION of BODIES: Conferred afterwards <lb></lb>by a very grave Author, but, if I erre not inviſibly, as below for <lb></lb>defence of him, I ſhall endeavour to prove.</s></p><p type="margin"> <s><margin.target id="marg1403"></margin.target>merſion of Sol <lb></lb>ids in the Wa <lb></lb>ter.</s></p><p type="main"> <s>I, with a different Method, and by other meanes, will endeavour <lb></lb>to demonſtrate the ſame, reducing the Cauſes of ſuch Effects to <lb></lb>more intrinſecall and immediate Principles, in which alſo are diſco <lb></lb>vered the Cauſes of ſome admirable and almoſt incredible Acci <lb></lb>dents, as that would be, that a very little quantity of Water, ſhould <lb></lb>be able, with its ſmall weight, to raiſe and ſuſtain a Solid Body, an <lb></lb>hundred or a thouſand times heavier than it.</s></p><p type="main"> <s>And becauſe demonſtrative Order ſo requires, I ſhall define cer <lb></lb>tain Termes, and afterwards explain ſome Propoſitions, of which, <lb></lb>as of things true and obvious, I may make uſe of to my preſent pur <lb></lb>poſe.</s></p><p type="head"> <s>DEFINITION I.</s></p><p type="main"> <s><emph type="italics"></emph>I then call equally Grave<emph.end type="italics"></emph.end> in ſpecie, <emph type="italics"></emph>thoſe Matters <lb></lb>of which equall Maſſes weigh equally.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>As if for example, two Balls, one of Wax, and the other of ſome <lb></lb>Wood of equall Maſſe, were alſo equall in Weight, we ſay, that <lb></lb>ſuch Wood, and the Wax are <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> equally grave.</s></p><p type="head"> <s>DEFINITION II.</s></p><p type="main"> <s><emph type="italics"></emph>But equally grave in Abſolute Gravity, we call two <lb></lb>Sollids, weighing equally, though of Maſs they be <lb></lb>unequall.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>As for example, a Maſs of Lead, and another of Wood, that <lb></lb>weigh each ten pounds, I call equall in Abſolute Gravity, though <lb></lb>the Maſs of the Wood be much greater then that of the Lead.</s></p><p type="main"> <s><emph type="italics"></emph>And, conſequently, leſs Grave<emph.end type="italics"></emph.end> in ſpecie.</s></p><p type="head"> <s>DEFINITION III.</s></p><p type="main"> <s><emph type="italics"></emph>I call a Matter more Grave<emph.end type="italics"></emph.end> in ſpecie <emph type="italics"></emph>than another, of <lb></lb>which a Maſs, equall to a Maſs of the other, ſhall <lb></lb>weigh more.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/1099.jpg" pagenum="406"></pb><p type="main"> <s>And ſo I ſay, that Lead is more grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than Tinn, becauſe <lb></lb>if you take of them two equall Maſſes, that of the Lead weigheth <lb></lb>more.</s></p><p type="head"> <s>DEFINITION IV.</s></p><p type="main"> <s><emph type="italics"></emph>But I call that Body more grave abſolutely than this, if <lb></lb>that weigh more than this, without any reſpect had to <lb></lb>the Maſſes.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And thus a great piece of Wood is ſaid to weigh more than a <lb></lb>little lump of Lead, though the Lead be <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> more heavy than <lb></lb>the Wood. </s><s>And the ſame is to be underſtood of the leſs grave <emph type="italics"></emph>in <lb></lb>ſpecie,<emph.end type="italics"></emph.end> and the leſs grave abſolutely.</s></p><p type="main"> <s>Theſe Termes defined, I take from the Mechanicks two Princi <lb></lb>ples: the firſt is, that</s></p><p type="head"> <s>AXIOME. I.</s></p><p type="main"> <s><emph type="italics"></emph>Weights abſolutely equall, moved with equall Velocity, <lb></lb>are of equall Force and Moment in their operations.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>DEFINITION V.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Moment, amongſt Mechanicians, ſigrifieth that <lb></lb>Vertue, that Force, or that Efficacy, with which <lb></lb>the Mover moves, and the Moveable reſiſts.</s></p><p type="main"> <s><emph type="italics"></emph>Which Vertue dependes not only on the ſimple Gravity, but on the <lb></lb>Velocity of the Motion, and on the diverſe Inclinations of the Spaces <lb></lb>along which the Motion is made: For a deſcending Weight makes a <lb></lb>greater<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>in a Space much declining, than in one leſs declining; <lb></lb>and in ſumme, what ever is the occaſion of ſuch Vertue, it ever retaines <lb></lb>the name of<emph.end type="italics"></emph.end> Moment; <emph type="italics"></emph>nor in my Judgement, is this ſence new in our <lb></lb>Idiome, for, if I mistake not, I think we often ſay; This is a weighty <lb></lb>buſineſſe, but the other is of ſmall moment: and we conſider lighter mat <lb></lb>ters and let paſs thoſe of Moment; a Metaphor, I ſuppoſe, taken from <lb></lb>the Mechanicks.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>As for example, two weights equall in abſolute Gravity, being <lb></lb>put into a Ballance of equall Arms, they ſtand in <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> nei <lb></lb>ther one going down, nor the other up: becauſe the equality of the <lb></lb>Diſtances of both, from the Centre on which the Ballance is ſuppor <lb></lb>ted, and about which it moves, cauſeth that thoſe weights, the ſaid <lb></lb>Ballance moving, ſhall in the ſame Time move equall Spaces, that is, <lb></lb>ſhall move with equall Velocity, ſo that there is no reaſon for which <pb xlink:href="040/01/1100.jpg" pagenum="407"></pb>this Weight ſhould deſcend more than that, or that more than this; <lb></lb>and therefore they make an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> and their Moments continue <lb></lb>of ſemblable and equall Vertue.</s></p><p type="main"> <s>The ſecond Principle is; That</s></p><p type="head"> <s>AXIOME II.</s></p><p type="main"> <s><emph type="italics"></emph>The Moment and Force of the Gravity, is encreaſed by <lb></lb>the Velocity of the Motion.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>So that Weights abſolutely equall, but conjoyned with Velocity <lb></lb>unequall, are of Force, Moment and Vertue unequall: and the <lb></lb>more potent, the more ſwift, according to the proportion of the Ve <lb></lb>locity of the one, to the Velocity of the other. </s><s>Of this we have a <lb></lb>very pertinent example in the Balance or Stiliard of unequall Arms, <lb></lb>at which Weights abſolutely equall being ſuſpended, they do not <lb></lb>weigh down, and gravitate equally, but that which is at a greater <lb></lb>diſtance from the Centre, about which the Beam moves, deſcends, <lb></lb>raiſing the other, and the Motion of this which aſcends is ſlow, and <lb></lb>the other ſwift: and ſuch is the Force and Vertue, which from the <lb></lb>Velocity of the Mover, is conferred on the Moveable, which receives <lb></lb>it, that it can exquiſitely compenſate, as much more Weight added to <lb></lb>the other ſlower Moveable: ſo that if of the Arms of the Balance, <lb></lb>one were ten times as long as the other, whereupon in the Beames <lb></lb>moving about the Centre, the end of that would go ten times as far <lb></lb>as the end of this, a Weight ſuſpended at the greater diſtance, may <lb></lb>ſuſtain and poyſe another ten times more grave abſolutely than it: <lb></lb>and that becauſe the Stiliard moving, the leſſer Weight ſhall move <lb></lb>ten times faſter than the bigger. </s><s>It ought alwayes therefore to be <lb></lb>underſtood, that Motions are according to the ſame Inclinations, <lb></lb>namely, that if one of the Moveables move perpendicularly to the <lb></lb>Horizon, then the other makes its Motion by the like Perpendicular; <lb></lb>and if the Motion of one were to be made Horizontally; that then <lb></lb>the other is made along the ſame Horizontall plain: and in ſumme, <lb></lb>alwayes both in like Inclinations. </s><s>This proportion between the <lb></lb>Gravity and Velocity is found in all Mechanicall Inſtruments: and <lb></lb>is conſidered by <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> as a Principle in his <emph type="italics"></emph>Mechanicall Queſtions<emph.end type="italics"></emph.end>; <lb></lb>whereupon we alſo may take it for a true Aſſumption, That</s></p><p type="head"> <s>AXIOME III.</s></p><p type="main"> <s><emph type="italics"></emph>Weights abſolutely unequall, do alternately counterpoyſe <lb></lb>and become of equall Moments, as oft as their Gravi <lb></lb>ties, with contrary proportion, anſwer to the Velocity of <lb></lb>their Motions.<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/1101.jpg" pagenum="408"></pb><p type="main"> <s>That is to ſay, that by how much the one is leſs grave than the other, <lb></lb>by ſo much is it in a conſtitution of moving more ſwiftly than that.</s></p><p type="main"> <s>Having prefatically explicated theſe things, we may begin to en <lb></lb>quire, what Bodyes thoſe are which totally ſubmerge in Water, and <lb></lb>go to the Bottom, and which thoſe that by conſtraint float on the <lb></lb>top, ſo that being thruſt by violence under Water, they return to <lb></lb>ſwim, with one part of their Maſs viſible above the Surface of the <lb></lb>Water: and this we will do by conſidering the reſpective operati <lb></lb>on of the ſaid Solids, and of Water: Which operation followes <lb></lb>the Submerſion and ſinking; and this it is, That in the Submerſion <lb></lb><arrow.to.target n="marg1404"></arrow.to.target> <lb></lb>that the Solid maketh, being depreſſed downwards by its proper <lb></lb>Gravity, it comes to drive away the water from the place where it <lb></lb>ſucceſſively ſubenters, and the water repulſed riſeth and aſcends <lb></lb>above its firſt levell, to which Aſcent on the other ſide it, as being a <lb></lb>grave Body of its own nature, reſiſts: And becauſe the deſcending <lb></lb>Solid more and more immerging, greater and greater quantity of <lb></lb>Water aſcends, till the whole Sollid be ſubmerged; its neceſſary to <lb></lb>compare the Moments of the Reſiſtance of the water to Aſcenſion, <lb></lb>with the Moments of the preſſive Gravity of the Solid: And if the <lb></lb>Moments of the Reſiſtance of the water, ſhall equalize the Moments <lb></lb><arrow.to.target n="marg1405"></arrow.to.target> <lb></lb>of the Solid, before its totall Immerſion; in this caſe doubtleſs there <lb></lb>ſhall be made an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> nor ſhall the Body ſink any farther. <lb></lb></s><s>But if the Moment of the Solid, ſhall alwayes exceed the Moments <lb></lb><arrow.to.target n="marg1406"></arrow.to.target> <lb></lb>wherewith the repulſed water ſucceſſively makes Reſiſtance, that <lb></lb>Solid ſhall not only wholly ſubmerge under water, but ſhall deſcend <lb></lb>to the Bottom. </s><s>But if, laſtly, in the inſtant of totall Submerſion, <lb></lb><arrow.to.target n="marg1407"></arrow.to.target> <lb></lb>the equality ſhall be made between the Moments of the prement <lb></lb>Solid, and the reſiſting Water; then ſhall reſt enſue, and the ſaid <lb></lb>Solid ſhall be able to reſt indifferently, in whatſoever part of the <lb></lb>water. </s><s>By this time is manifeſt the neceſſity of comparing the <lb></lb><arrow.to.target n="marg1408"></arrow.to.target> <lb></lb>Gravity of the water, and of the Solid; and this compariſon might <lb></lb>at firſt ſight ſeem ſufficient to conclude and determine which are the <lb></lb>Solids that float a-top, and which thoſe that ſink to the Bottom in the <lb></lb>water, aſſerting that thoſe ſhall float which are leſſe grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> <lb></lb>than the water, and thoſe ſubmerge, which are <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> more grave. <lb></lb></s><s>For it ſeems in appearance, that the Sollid in ſinking continually, <lb></lb>raiſeth ſo much Water in Maſs, as anſwers to the parts of its own <lb></lb>Bulk ſubmerged: whereupon it is impoſſible, that a Solid leſs grave <lb></lb><emph type="italics"></emph>in ſpecie,<emph.end type="italics"></emph.end> than water, ſhould wholly ſink, as being unable to raiſe a <lb></lb>weight greater than its own, and ſuch would a Maſs of water equall <lb></lb>to its own Maſs be. </s><s>And likewiſe it ſeems neceſſary, that the graver <lb></lb>Solids do go to the Bottom, as being of a Force more than ſufficient <lb></lb>for the raiſing a Maſſe of water, equall to its own, though inferiour <lb></lb>in weight. </s><s>Nevertheleſs the buſineſs ſucceeds otherwiſe: and <pb xlink:href="040/01/1102.jpg" pagenum="409"></pb>though the Concluſions are true, yet are the Cauſes thus aſſigned <lb></lb>deficient, nor is it true, that the Solid in ſubmerging, raiſeth and <lb></lb>repulſeth Maſſes of Water, equall to the parts of it ſelf ſubmerged; <lb></lb>but the Water repulſed, is alwayes leſs than the parts of the Solid <lb></lb><arrow.to.target n="marg1409"></arrow.to.target> <lb></lb>ſubmerged: and ſo much the more by how much the Veſſell in <lb></lb>which the Water is contained is narrower: in ſuch manner that it <lb></lb>hinders not, but that a Solid may ſubmerge all under Water, with <lb></lb>out raiſing ſo much Water in Maſs, as would equall the tenth or <lb></lb>twentieth part of its own Bulk: like as on the contrary, a very <lb></lb><arrow.to.target n="marg1410"></arrow.to.target> <lb></lb>ſmall quantity of Water, may raiſe a very great Solid Maſs, though <lb></lb>ſuch Solid ſhould weigh abſolutely a hundred times as much, or <lb></lb>more, than the ſaid Water, if ſo be that the Matter of that ſame <lb></lb>Solid be <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> leſs grave than the Water. </s><s>And thus a great <lb></lb>Beam, as ſuppoſe of a 1000 weight, may be raiſed and born afloat <lb></lb>by Water, which weighs not 50: and this happens when the Mo <lb></lb>ment of the Water is compenſated by the Velocity of its Motion.</s></p><p type="margin"> <s><margin.target id="marg1404"></margin.target>How the ſub <lb></lb>merſion of So <lb></lb>lids in the Wa <lb></lb>ter, is effected.</s></p><p type="margin"> <s><margin.target id="marg1405"></margin.target>What Solids <lb></lb>ſhall float on the <lb></lb>Water.</s></p><p type="margin"> <s><margin.target id="marg1406"></margin.target>What Solids <lb></lb>ſhall ſinke to the <lb></lb>botome.</s></p><p type="margin"> <s><margin.target id="marg1407"></margin.target>What Solids <lb></lb>ſhall reſt in all <lb></lb>places of the Wa <lb></lb>ter.</s></p><p type="margin"> <s><margin.target id="marg1408"></margin.target>The Gravitie of <lb></lb>the Water and <lb></lb><emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid muſt be <lb></lb>compared in all <lb></lb>Problems, of Na <lb></lb>tation of Bodies.</s></p><p type="margin"> <s><margin.target id="marg1409"></margin.target>The water re <lb></lb>pulſed is ever leſs <lb></lb>than the parts of <lb></lb>the Sollid ſub <lb></lb>merged.</s></p><p type="margin"> <s><margin.target id="marg1410"></margin.target><emph type="italics"></emph>A<emph.end type="italics"></emph.end> ſmall quantity <lb></lb>of water, may <lb></lb>float a very <lb></lb>great Solid Maſs.</s></p><p type="main"> <s>But becauſe ſuch things, propounded thus in abſtract, are ſome <lb></lb>what difficult to be comprehended, it would be good to demonſtrate <lb></lb>them by particular examples; and for facility of demonſtration, we <lb></lb>will ſuppoſe the Veſſels in which we are to put the Water, and place <lb></lb>the Solids, to be inviron'd and included with ſides erected perpendi <lb></lb>cular to the Plane of the Horizon, and the Solid that is to be put <lb></lb>into ſuch veſſell to be either a ſtreight Cylinder, or elſe an upright <lb></lb>Priſme</s></p><p type="main"> <s><emph type="italics"></emph>The which propoſed and declared, I proceed to demonstrate the truth <lb></lb>of what hath been hinted, forming the enſuing Theoreme.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>THEOREME I.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The Maſs of the Water whichaſcends in the ſub <lb></lb><arrow.to.target n="marg1411"></arrow.to.target> <lb></lb>merging of a Solid, Priſme or Cylinder, or that <lb></lb>abaſeth in taking it out, is leſs than the Maſs of <lb></lb>the ſaid Solid, ſo depreſſed or advanced: and <lb></lb>hath to it the ſame proportion, that the Surface <lb></lb>of the Water circumfuſing the Solid, hath to the <lb></lb>ſame circumfuſed Surface, together with the Baſe <lb></lb>of the Solid.</s></p><p type="margin"> <s><margin.target id="marg1411"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he Proportion <lb></lb>of the water rai <lb></lb>ſed to the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid <lb></lb>ſubmerged.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Veſſell be A B C D, and in it the Water raiſed up to the <lb></lb>Levell E F G, before the Solid Priſme H I K be therein immerged; <lb></lb>but after that it is depreſſed under Water, let the Water be raiſed as <lb></lb>high as the Levell L M, the Solid H I K ſhall then be all under Water, <lb></lb>and the Maſs of the elevated Water ſhall be L G, which is leſs than the<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1103.jpg" pagenum="410"></pb><figure id="id.040.01.1103.1.jpg" xlink:href="040/01/1103/1.jpg"></figure> <lb></lb><emph type="italics"></emph>Maſſe of the Solid depreſſed, namely of <lb></lb>H I K, being equall to the only part E I K, <lb></lb>which is contained under the firſt Levell <lb></lb>E F G. </s><s>Which is manifeſt, becauſe if <lb></lb>the Solid H I K be taken out, the Water <lb></lb>I G ſhall return into the place occupied by <lb></lb>the Maſs E I K, where it was continuate be <lb></lb>fore the ſubmerſion of the Priſme. </s><s>And <lb></lb>the Maſs L G being equall to the Maſs <lb></lb>E K: adde thereto the Maſs E N, and it <lb></lb>ſhall be the whole Maſs E M, compoſed of the parts of the Priſme E N, <lb></lb>and of the Water N F, equall to the whole Solid H I K: And, there <lb></lb>fore, the Maſs L G ſhall have the ſame proportion to E M, as to the <lb></lb>Maſs H I K: But the Maſs L G hath the ſame proportion to the Maſs <lb></lb>E M, as the Surface L M hath to the Surface M H: Therefore it is ma <lb></lb>nifeſt, that the Maſs of Water repulſed L G, is in proportion to the Maſs <lb></lb>of the Solid ſubmerged H I K; as the Surface L M, namely, that of the <lb></lb>Water ambient about the Sollid, to the whole Surface H M, compounded <lb></lb>of the ſaid ambient water, and the Baſe of the Priſme H N. </s><s>But if we <lb></lb>ſuppoſe the firſt Levell of the Water the according to the Surface H M, <lb></lb>and the Priſme allready ſubmerged H I K; and after to be taken out and <lb></lb>raiſed to E A O, and the Water to be faln from the firſt Levell H L M as <lb></lb>low as E F G; It is manifeſt, that the Priſme E A O being the ſame with <lb></lb>H I K, its ſuperiour part H O, ſhall be equall to the inferiour E I K: <lb></lb>and remove the common part E N, and, conſequently, the Maſs of the <lb></lb>Water L G is equall to the Maſs H O; and, therefore, leſs than the <lb></lb>Solid, which is without the Water, namely, the whole Priſme E A O, to <lb></lb>which likewiſe, the ſaid Maſs of Water abated L G, hath the ſame propor <lb></lb>tion, that the Surface of the Waters circumfuſed L M hath to the ſame <lb></lb>circumfuſed Surface, together with the Baſe of the Priſme A O: which <lb></lb>hath the ſame demonſtration with the former caſe above.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>And from hence is inferred, that the Maſs of the Water, that riſeth in <lb></lb>the immerſion of the Solid, or that ebbeth in elevating it, is not equall to <lb></lb>all the Maſs of the Solid, which is ſubmerged or elevated, but to that <lb></lb>part only, which in the immerſion is under the firſt Levell of the Water, <lb></lb>and in the elevation remaines above the firſt Levell: Which is that <lb></lb>which was to be demonſtrated. </s><s>We will now purſue the things that <lb></lb>remain.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And firſt we will demonſtrate that,</s></p> <pb xlink:href="040/01/1104.jpg" pagenum="411"></pb><p type="head"> <s>THEOREME II.</s></p><p type="main"> <s><emph type="italics"></emph>When in one of the above ſaid Veſſels, of what ever<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1412"></arrow.to.target> <lb></lb><emph type="italics"></emph>breadth, whether wide or narrow, there is placed ſuch <lb></lb>a Priſme or Cylinder, inviron'd with Water, if we ele <lb></lb>vate that Solid perpendicularly, the Water circumfu <lb></lb>ſed ſhall abate, and the Abatement of the Water, <lb></lb>ſhall have the ſame proportion to the Elevation of the <lb></lb>Priſme, as one of the Baſes of the Priſme, hath to <lb></lb>the Surface of the Water Circumfuſed.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1412"></margin.target>The proportion <lb></lb>of the water aba <lb></lb>ted, to the Solid <lb></lb>raiſed.</s></p><p type="main"> <s>Imagine in the Veſſell, as is aforeſaid, the <lb></lb><figure id="id.040.01.1104.1.jpg" xlink:href="040/01/1104/1.jpg"></figure> <lb></lb>Priſme A C D B to be placed, and in the <lb></lb>reſt of the Space the Water to be dif <lb></lb>fuſed as far as the Levell E A: and rai <lb></lb>ſing the Solid, let it be transferred to <lb></lb>G M, and let the Water be abaſed from <lb></lb>E A to N O: I ſay, that the deſcent of <lb></lb>the Water, meaſured by the Line A O, <lb></lb>hath the ſame proportion to the riſe of the <lb></lb>Priſme, meaſured by the Line G A, as the Baſe of the Solid G H <lb></lb>hath to the Surface of the Water N O. </s><s>The which is manifeſt: <lb></lb>becauſe the Maſs of the Solid G A B H, raiſed above the firſt Levell <lb></lb>E A B, is equall to the Maſs of Water that is abaſed E N O A. <lb></lb>Therefore, E N O A and G A B H are two equall Priſmes; for of <lb></lb>equall Priſmes, the Baſes anſwer contrarily to their heights: There <lb></lb>fore, as the Altitude A O is to the Altitude A G, ſo is the Superfi <lb></lb>cies or Baſe G H to the Surface of the Water N O. </s><s>If therefore, <lb></lb>for example, a Pillar were erected in a waſte Pond full of Water, <lb></lb>or elſe in a Well, capable of little more then the Maſs of the ſaid <lb></lb>Pillar, in elevating the ſaid Pillar, and taking it out of the Water, <lb></lb>according as it riſeth, the Water that invirons it will gradually abate, <lb></lb>and the abaſement of the Water at the inſtant of lifting out the <lb></lb>Pillar, ſhall have the ſame proportion, that the thickneſs of the Pillar <lb></lb>hath to the exceſs of the breadth of the ſaid Pond or Well, above <lb></lb>the thickneſs of the ſaid Pillar: ſo that if the breadth of the Well <lb></lb>were an eighth part larger than the thickneſs of the Pillar, and the <lb></lb><arrow.to.target n="marg1413"></arrow.to.target> <lb></lb>breadth of the Pond twenty five times as great as the ſaid thickneſs, <lb></lb>in the Pillars aſcending one foot, the water in the Well ſhall deſcend <lb></lb>ſeven 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></lb>leſs grave <emph type="italics"></emph>in ſpe <lb></lb>cie<emph.end type="italics"></emph.end> than water, <lb></lb>ſtayeth not un <lb></lb>der water, in ve <lb></lb>ry ſmall depthst.</s></p><p type="main"> <s>This Demonſtrated, it will not be difficult to ſhew the true <lb></lb>cauſe, how it comes to paſs, that,</s></p> <pb xlink:href="040/01/1105.jpg" pagenum="412"></pb><p type="head"> <s>THEOREME III.</s></p><p type="main"> <s><emph type="italics"></emph>A Priſme or regular Cylinder, of a ſubſtance ſpecifically <lb></lb>leſs grave than Water, if it ſhould be totally ſubmerged <lb></lb>in Water, ſtayes not underneath, but riſeth, though the <lb></lb>Water circumfuſed be very little, and in abſolute <lb></lb>Gravity, never ſo much inferiour to the Gravity of the <lb></lb>ſaid Priſme.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let then the Priſme A E F B, be put into the Veſſell C D F B, the <lb></lb>ſame being leſs grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than the Water: and let the <lb></lb>Water infuſed riſe to the height of the Priſme: I ſay, that the <lb></lb>Priſme left at liberty, it ſhall riſe, being born up <lb></lb>by the Water circumfuſed C D E A. </s><s>For the <lb></lb><figure id="id.040.01.1105.1.jpg" xlink:href="040/01/1105/1.jpg"></figure> <lb></lb>Water C E being ſpecifically more grave than <lb></lb>the Solid A F, the abſolute weight of the water <lb></lb>C E, ſhall have greater proportion to the abſo <lb></lb>lute weight of the Priſme A F, than the Maſs <lb></lb>C E hath to the Maſs A F (in regard the Maſs <lb></lb>hath the ſame proportion to the Maſs, that the <lb></lb>weight abſolute hath to the weight abſolute, <lb></lb>in caſe the Maſſes are of the ſame Gravity <emph type="italics"></emph>in ſpecie.<emph.end type="italics"></emph.end>) But <lb></lb>the Maſs C E is to the Maſs A F, as the Surface of the water A C, is <lb></lb>to the Superficies, or Baſe of the Priſme A B; which is the ſame pro <lb></lb>portion as the aſcent of the Priſme when it riſeth, hath to the deſcent <lb></lb>of the water circumfuſed C E.</s></p><p type="main"> <s>Therefore, the abſolute Gravity of the water C E, hath greater <lb></lb>proportion to the abſolute Gravity of the Priſme A F; than the <lb></lb>Aſcent of the Priſme A F, hath to the deſcent of the ſaid <lb></lb>water C E. </s><s>The Moment, therefore, compounded of the abſolute <lb></lb>Gravity of the water C E, and of the Velocity of its deſcent, whilſt <lb></lb>it forceably repulſeth and raiſeth the Solid A F, is greater than the <lb></lb>Moment compounded of the abſolute Gravity of the Priſme A F, and <lb></lb>of the Tardity of its aſcent, with which Moment it contraſts and re <lb></lb>fiſts the repulſe and violence done it by the Moment of the water: <lb></lb>Therefore, the Priſme ſhall be raiſed. <lb></lb><arrow.to.target n="marg1414"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1414"></margin.target>The Proportion <lb></lb>according to <lb></lb>which the Sub <lb></lb>merſion & Na <lb></lb>tation of Solids <lb></lb>is made.</s></p><p type="main"> <s>It followes, now, that we proceed forward to demonſtrate more <lb></lb>particularly, how much ſuch Solids ſhall be inferiour in Gravity to <lb></lb>the water elevated; namely, what part of them ſhall reſt ſubmerged, <lb></lb>and what ſhall be viſible above the Surface of the water: but firſt <lb></lb>it is neceſſary to demonſtrate the ſubſequent Lemma.</s></p> <pb xlink:href="040/01/1106.jpg" pagenum="413"></pb><p type="head"> <s>LEMMA I.</s></p><p type="main"> <s><emph type="italics"></emph>The abſolute Gravities of Solids, have a proportion com-<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1415"></arrow.to.target> <lb></lb><emph type="italics"></emph>pounded of the proportions of their ſpecificall Gravities, <lb></lb>and of their Maſſes.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1415"></margin.target>The abſolute <lb></lb>Gravity of So <lb></lb>lids, are in a pro <lb></lb>portion com <lb></lb>pounded of their <lb></lb>Specifick Gravi <lb></lb>ties, and of their <lb></lb>Maſſes.</s></p><p type="main"> <s>Let A and B be two Solids. </s><s>I ſay, that the Abſolute Gravity <lb></lb>of A, hath to the Abſolute Gravity of B, a proportion com <lb></lb>pounded of the proportions of the ſpecificall Gravity of A, to <lb></lb>the Specificall Gravity of B, and of the Maſs <lb></lb>A to the Maſs B. </s><s>Let the Line D have the <lb></lb><figure id="id.040.01.1106.1.jpg" xlink:href="040/01/1106/1.jpg"></figure> <lb></lb>ſame proportion to E, that the ſpecifick <lb></lb>Gravity of A, hath to the ſpecifick Gravity <lb></lb>of B; and let E be to F, as the Maſs A to the <lb></lb>Maſs B: It is manifeſt, that the proportion <lb></lb>of D to F, is compounded of the proportions <lb></lb>D and E; and E and F. </s><s>It is requiſite, <lb></lb>therefore, to demonſtrate, that as D is to F, ſo the abſolute Gravity <lb></lb>of A, is to the abſolute Gravity of B. </s><s>Take the Solid C, equall in <lb></lb>Maſs to the Solid A, and of the ſame Gravity <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> with the Solid <lb></lb>B. Becauſe, therefore, A and C are equall in Maſs, the abſolute <lb></lb>Gravity of A, ſhall have to the abſolute Gravity of C, the ſame pro <lb></lb>portion, as the ſpecificall Gravity of A, hath to the ſpecificall Gravity <lb></lb>of C, or of B, which is the ſame <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end>; that is, as D is to E. And, be <lb></lb>cauſe, C and B are of the ſame Gravity <emph type="italics"></emph>in ſpecie,<emph.end type="italics"></emph.end> it ſhall be, that as <lb></lb>the abſolute weight of C, is to the abſolute weight of B, ſo the Maſs <lb></lb>C, or the Maſs A, is to the Maſs B; that is, as the Line E to the Line <lb></lb>F. </s><s>As therefore, the abſolute Gravity of A, is to the abſolute <lb></lb>Gravity of C, ſo is the Line D to the Line E: and, as the abſolute <lb></lb>Gravity of C, is to the abſolute Gravity of B, ſo is the Line E to the <lb></lb>Line F: Therefore, by Equality of proportion, the abſolute Gra <lb></lb>vity of A, is to the abſolute Gravity of B, as the Line D to the <lb></lb>Line F: which was to be demonſtrated. </s><s>I proceed now to demon <lb></lb>ſtrate, how that,</s></p> <pb xlink:href="040/01/1107.jpg" pagenum="414"></pb><p type="head"> <s>THEOREME IV. <lb></lb><arrow.to.target n="marg1416"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1416"></margin.target>The proportion <lb></lb>of water requi <lb></lb>ſite to make a <lb></lb>Solid ſwim.</s></p><p type="main"> <s><emph type="italics"></emph>If a Solid, Cylinder, or Priſme, leſſe grave ſpecifically <lb></lb>than the Water, being put into a Veſſel, as above, of <lb></lb>whatſoever greatneſſe, and the Water, be afterwards <lb></lb>infuſed, the Solid ſhall reſt in the bottom, unraiſed, till <lb></lb>the Water arrive to that part of the Altitude, of the <lb></lb>ſaid Priſme, to which its whole Altitude hath the <lb></lb>ſame proportion, that the Specificall Gravity of the <lb></lb>Water, hath to the Specificall Gravity of the ſaid <lb></lb>Solid: but infuſing more Water, the Solid ſhall aſcend.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the Veſſell be M L G N of any bigneſs, and let there be pla <lb></lb>ced in it the Solid Priſme D F G E, leſs grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than the <lb></lb>water; and look what proportion the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>pecificall Gravity of <lb></lb>the water, hath to that of the Priſme, ſuch let the Altitude D F, have <lb></lb>to the Altitude F B. </s><s>I ſay, that infuſing water to the Altitude F B, <lb></lb>the Solid D G ſhall not float, but ſhall ſtand in <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> ſo, that <lb></lb>that every little quantity of water, that is infuſed, ſhall raiſe it. </s><s>Let <lb></lb>the water, therefore, be infuſed to the Levell A B C, and, becauſe <lb></lb>the Specifick Gravity of the Solid D G, is to the Specifick Gravity of <lb></lb>the water, as the altitude B F is to the altitude F D; that is, as the Maſs <lb></lb>B G to the Maſs G D; as the proportion of the Maſs B G is to the <lb></lb>Maſs G D, as the proportion of the Maſs G D is to the Maſs A F, they <lb></lb>compoſe the Proportion of the Maſs B G to the Maſs A F. Therefore, <lb></lb>the Maſs B G is to the Maſs A F, in a proportion compounded of the <lb></lb>proportions of the Specifick Gravity of the Solid G D, to the Speci <lb></lb>fick Gravity of the water, and of the Maſs G D <lb></lb>to the Maſs A F: But the ſame proportions <lb></lb><figure id="id.040.01.1107.1.jpg" xlink:href="040/01/1107/1.jpg"></figure> <lb></lb>of the Specifick Gravity of G D, to the Specifick <lb></lb>Gravity of the water, and of the Maſs G D to <lb></lb>the Maſs A F, do alſo by the precedent <emph type="italics"></emph>Lemma,<emph.end type="italics"></emph.end> <lb></lb>compound the proportion of the abſolute Gra <lb></lb>vity of the Solid D G, to the abſolute Gravity <lb></lb>of the Maſs of the water A F: Therefore, <lb></lb>as the Maſs B G is to the Maſs A F, ſo is the <lb></lb>Abſolute Gravity of the Solid D G, to the Ab <lb></lb>ſolute Gravity of the Maſs of the water A F. </s><s>But as the Maſs B G <lb></lb>is to the Maſs A F; ſo is the Baſe of the Priſme D E, to the Surface <lb></lb>of the water AB; and ſo is the deſcent of the water A B, to the <lb></lb>Elevation of the Priſme D G; Therefore, the deſcent of the <pb xlink:href="040/01/1108.jpg" pagenum="415"></pb>water is to the elevation of the Priſme, as the abſolute Gravity of <lb></lb>the Priſme, is to the abſolute Gravity of the water: Therefore, the <lb></lb>Moment reſulting from the abſolute Gravity of the water A F, and <lb></lb>the Velocity of the Motion of declination, with which Moment it <lb></lb>forceth the Priſme D G, to riſe and aſcend, is equall to the Moment <lb></lb>that reſults from the abſolute Gravity of the Priſme D G, and from <lb></lb>the Velocity of the Motion, wherewith being raiſed, it would aſcend: <lb></lb>with which Moment it reſiſts its being raiſed: becauſe, therefore, <lb></lb>ſuch Moments are equall, there ſhall be an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> between the <lb></lb>water and the Solid. </s><s>And, it is manifeſt, that putting a little more <lb></lb>water unto the other A F, it will increaſe the Gravity and Moment, <lb></lb>whereupon the Priſme D G, ſhall be overcome, and elevated till that <lb></lb>the only part B F remaines ſubmerged. </s><s>Which is that that was to <lb></lb>be demonſtrated.</s></p><p type="head"> <s>COROLLARY I.</s></p><p type="main"> <s><emph type="italics"></emph>By what hath been demonſtrated, it is manifeſt, that Solids leſs grave<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1417"></arrow.to.target> <lb></lb>in ſpecie <emph type="italics"></emph>than the water, ſubmerge only ſo far, that as much water in <lb></lb>Maſs, as is the part of the Solid ſubmerged, doth weigh abſolutely as <lb></lb>much as the whole Solid.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1417"></margin.target><emph type="italics"></emph>H<emph.end type="italics"></emph.end>ow far Solids <lb></lb>leſs grave <emph type="italics"></emph>in ſpe <lb></lb>cie<emph.end type="italics"></emph.end> than water, <lb></lb>do ſubmerge.</s></p><p type="main"> <s>For, it being ſuppoſed, that the Specificall Gravity of the water, <lb></lb>is to the Specificall Gravity of the Priſme D G, as the Altitude <lb></lb>D F, is to the Altitude F B; that is, as the Solid D G is to the <lb></lb>Solid B G; we might eaſily demonſtrate, that as much water in Maſs <lb></lb>as is equall to the Solid B G, doth weigh abſolutely as much as the <lb></lb>whole Solid D G; For, by the <emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> foregoing, the Abſolute <lb></lb>Gravity of a Maſs of water, equall to the Maſs B G, hath to the Ab <lb></lb>ſolute Gravity of the Priſme D G, a proportion compounded of the <lb></lb>proportions, of the Maſs B G to the Maſs G D, and of the Specifick <lb></lb>Gravit 7 of the water, to the Specifick Gravity of the Priſme: But <lb></lb>the Gravity <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> of the water, to the Gravity <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> of the <lb></lb>Priſme, is ſuppoſed to be as the Maſs G D to the Maſs G B. There <lb></lb>fore, the Abſolute Gravity of a Maſs of water, equall to the Maſs <lb></lb>B G, is to the Abſolute Gravity of the Solid D G, in a proportion <lb></lb>compounded of the proportions, of the Maſs B G to the Maſs G D, <lb></lb>and of the Maſs D G to the Maſs G B; which is a proportion of <lb></lb>equalitie. </s><s>The Abſolute Gravity, therefore, of a Maſs of Water <lb></lb>equall to the part of the Maſs of the Priſme B G, is equall to the Ab <lb></lb>ſolute Gravity of the whole Solid D G.</s></p> <pb xlink:href="040/01/1109.jpg" pagenum="416"></pb><p type="head"> <s>COROLLARY II. <lb></lb><arrow.to.target n="marg1418"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1418"></margin.target><emph type="italics"></emph>A<emph.end type="italics"></emph.end> Rule to equi <lb></lb>librate <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olids in <lb></lb>the water.</s></p><p type="main"> <s><emph type="italics"></emph>It followes, moreover, that a Solid leſs grave than the water, being put <lb></lb>into a Veſſell of any imaginable greatneſs, and water being circumfuſed <lb></lb>about it to ſuch a height, that as much water in Maſs, as is the part of <lb></lb>the Solid ſubmerged, doth/> weigh abſolutely as much as the whole Solid; <lb></lb>it ſhall by that water be juſtly ſuſtained, be the circumfuſed Water in <lb></lb>quantity greater or leſſer.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>For, if the Cylinder or Priſme M, leſs grave than the water, <emph type="italics"></emph>v. <lb></lb></s><s>gra.<emph.end type="italics"></emph.end> in Subſequiteriall proportion, ſhall be put into the capaci <lb></lb>ous Veſſell A B C D, and the water raiſed about it, to three <lb></lb>quarters of its height, namely, to its Levell A D: it ſhall be ſuſtained <lb></lb>and exactly poyſed in <emph type="italics"></emph>Equi <lb></lb>librium.<emph.end type="italics"></emph.end> The ſame will hap <lb></lb>pen, if the Veſſell E N S F <lb></lb><figure id="id.040.01.1109.1.jpg" xlink:href="040/01/1109/1.jpg"></figure> <lb></lb>were very ſmall, ſo, that be <lb></lb>tween the Veſſell and the So <lb></lb>lid M, there were but a very <lb></lb>narrow ſpace, and only capable of ſo much water, as the hundredth <lb></lb>part of the Maſs M, by which it ſhould be likewiſe raiſed and erected, <lb></lb>as before it had been elevated to three fourths of the height of the <lb></lb>Solid: which to many at the firſt ſight, may ſeem a notable Paradox, <lb></lb>and beget a conceit, that the Demonſtration of theſe effects, were <lb></lb>ſophiſticall and fallacious: but, for thoſe who ſo repute it, the Ex <lb></lb>periment is a means that may fully ſatisfie them. </s><s>But he that ſhall <lb></lb>but comprehend of what Importance Velocity of Motion is, and how <lb></lb>it exactly compenſates the defect and want of Gravity, will ceaſe to <lb></lb>wonder, in conſidering that at the elevation of the Solid M, the great <lb></lb>Maſs of water A B C D abateth very little, but the little Maſs of <lb></lb>water E N S F decreaſeth very much, and in an inſtant, as the Solid <lb></lb>M before did liſe, howbeit for a very ſhort ſpace: Whereupon the <lb></lb>Moment, compounded of the ſmall Abſolute Gravity of the water <lb></lb>E N S F, and of its great Velocity in ebbing, equalizeth the Force and <lb></lb>and Moment, that reſults from the compoſicion of the immenſe Gra <lb></lb>vity of the water A B C D, with its great ſlowneſſe of ebbing; <lb></lb>ſince that in the Elevation of the Sollid M, the abaſement of the leſ</s></p><p type="main"> <s><arrow.to.target n="marg1419"></arrow.to.target> <lb></lb>ſer water E S, is performed juſt ſo much more ſwiftly than the great <lb></lb>Maſs of water A C, as this is more in Maſs than that which we thus <lb></lb>demonſtrate.</s></p><p type="margin"> <s><margin.target id="marg1419"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he proportion <lb></lb>according to <lb></lb>which water ri <lb></lb>ſeth and falls in <lb></lb>different Veſſels <lb></lb>at the Immerſi <lb></lb>on and Elevati <lb></lb>on of <emph type="italics"></emph>s<emph.end type="italics"></emph.end>olids.</s></p><p type="main"> <s>In the riſing of the Solid M, its elevation hath the ſame proportion <lb></lb>to the circumfuſed water E N S F, that the Surface of the ſaid water, <lb></lb>hath to the Superficies or Baſe of the ſaid Solid M; which Baſe hath <lb></lb>the ſame proportion to the Surface of the water A D, that the abaſe <pb xlink:href="040/01/1110.jpg" pagenum="417"></pb>ment or ebbing of the water A C, hath to the riſe or elevation of <lb></lb>the ſaid Solid M. Therefore, by Perturbation of proportion, in the <lb></lb>aſcent of the ſaid Solid M, the abaſement of the water A B C D, to <lb></lb>the abaſement of the water E N S F, hath the ſame proportion, that the <lb></lb>Surface of the water E F, hath to the Surface of the water A D; <lb></lb>that is, that the whole Maſs of the water E N S F, hath to the whole <lb></lb>Maſs A B C D, being equally high: It is manifeſt, therefore, that <lb></lb>in the expulſion and elevation of the Solid M, the water E N S F <lb></lb>ſhall exceed in Velocity of <emph type="italics"></emph>M<emph.end type="italics"></emph.end>otion the water A B C D, aſmuch as it <lb></lb>on the other ſide is exceeded by that in quantity: whereupon their <lb></lb>Moments in ſuch operations, are mutually equall.</s></p><p type="main"> <s><emph type="italics"></emph>And, for ampler confirmation, and clearer explication of this, let us <lb></lb>conſider the preſent Figure, (which if I be not deceived, may ſerve to <lb></lb>detect the errors of ſome Practick Mechanitians, who upon a falſe founda <lb></lb>tion ſome times attempt impoſſible enterprizes,) in which, unto the large <lb></lb>Veſſell E I D F, the narrow Funnell or Pipe I C A B is continued, and ſup <lb></lb>poſe water infuſed into them, unto the Levell L G H, which water ſhall <lb></lb>reſt in this poſition, not without admiration in ſome, who cannot conceive<emph.end type="italics"></emph.end> <lb></lb><figure id="id.040.01.1110.1.jpg" xlink:href="040/01/1110/1.jpg"></figure> <lb></lb><emph type="italics"></emph>how it can be, that the heavie charge of the great <lb></lb>Maſs of water G D, preſſing downwards, ſhould <lb></lb>not elevate and repulſe the little quantity of the <lb></lb>other, contained in the Funnell or Pipe C L, by <lb></lb>which the deſcent of it is reſisted and hindered: <lb></lb>But ſuch wonder ſhall ceaſe, if we begin to ſuppoſe <lb></lb>the water G D to be abaſed only to Q D, and <lb></lb>ſhall afterwards conſider, what the water C L <lb></lb>hath done, which to give place to the other, which <lb></lb>is deſcended from the Levell G H, to the Levell <lb></lb>Q O, ſhall of neceſſity have aſcended in the ſame <lb></lb>time, from the Levell Lunto A B. </s><s>And the <lb></lb>aſcent L B, ſhall be ſo much greater than the de <lb></lb>ſcent G Q, by how much the breadth of the Veſſell <lb></lb>G D, is greater than that of the Funnell I C; <lb></lb>which, in ſumme, is as much as the water G D, <lb></lb>is more than the water L C: but in regard that the Moment of the Velocity <lb></lb>of the Motion, in one Moveable, compenſates that of the Gravity of ano <lb></lb>ther, what wonder is it, if the ſwift aſcent of the leſſer Water C L, ſhall <lb></lb>reſiſt the ſlow deſcent of the greater G D<emph.end type="italics"></emph.end>?</s></p><p type="main"> <s>The ſame, therefore, happens in this operation, as in the Stilliard, <lb></lb>in which a weight of two pounds counterpoyſeth an other of 200, <lb></lb>asoften as that ſhall move in the ſame time, a ſpace 100 times great <lb></lb>er than this: which falleth out when one Arme of the Beam is an <pb xlink:href="040/01/1111.jpg" pagenum="418"></pb>hundred times as long as the other. </s><s>Let the erroneous opinion o <lb></lb><arrow.to.target n="marg1420"></arrow.to.target> <lb></lb>thoſe therefore ceaſe, who hold that a Ship is better, and eaſter born <lb></lb>up in a great abundance of water, then in a leſſer quantity, (<emph type="italics"></emph>this was <lb></lb>believed by<emph.end type="italics"></emph.end> Ariſtotle <emph type="italics"></emph>in his Problems, Sect. </s><s>23, Probl.<emph.end type="italics"></emph.end> 2.) it being or <lb></lb>the contrary true, that its poſſible, that a Ship may as well float in <lb></lb>ten Tun of water, as in an Ocean. <lb></lb><arrow.to.target n="marg1421"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1420"></margin.target>A ſhip flotes as <lb></lb>well in ten Tun <lb></lb>of water as in an <lb></lb>Ocean.</s></p><p type="margin"> <s><margin.target id="marg1421"></margin.target>A Solid ſpeci <lb></lb>fiaclly graver <lb></lb>than the water, <lb></lb>cannot be born <lb></lb>up by any quan <lb></lb>tity of it.</s></p><p type="main"> <s>But following our matter, I ſay, that by what hath been hitherto <lb></lb>demonſtrated, we may underſtand how, that</s></p><p type="head"> <s>COROLLARY III.</s></p><p type="main"> <s><emph type="italics"></emph>One of the above named Solids, when more grave<emph.end type="italics"></emph.end> in ſpecie <emph type="italics"></emph>than the water, <lb></lb>can never be ſuſtained, by any whatever quantity of it.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>For having ſeen how that the Moment wherewith ſuch a Solid <lb></lb>as grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> as the water, contraſts with the Moment of any Maſs <lb></lb>of water whatſoever, is able to retain it, even to its totall Submerſion: <lb></lb>without its ever aſcending; it remaineth, manifeſt, that the water is <lb></lb>far leſs able to raiſe it up, when it exceeds the ſame <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end>: ſo, <lb></lb>that though you infuſe water till its totall Submerſion, it ſhall ſtill <lb></lb>ſtay at the Bottome, and with ſuch Gravity, and Reſiſtance to Eleva <lb></lb>tion, as is the exceſs of its Abſolute Gravity, above the Abſolute Gra <lb></lb>vity of a Maſs equall to it, made of water, or of a Matter <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> <lb></lb>equally grave with the water: and, though you ſhould moreover <lb></lb>adde never ſo much water above the Levell of that which equalizeth <lb></lb>the Altitude of the Solid, it ſhall not, for all that, encreaſe the Preſſion <lb></lb>or Gravitation, of the parts circumfuſed about the ſaid Solid, by <lb></lb>which greater preſſion, it might come to be repulſed, becauſe, the <lb></lb>Reſiſtance is not made, but only by thoſe parts of the water, which <lb></lb>at the Motion of the ſaid Solid do alſo move, and theſe are thoſe <lb></lb>only, which are comprehended by the two Superficies equidiſtant to <lb></lb>the Horizon, and their parallels, that comprehend the Altitude of the <lb></lb>Solid immerged in the water.</s></p><p type="main"> <s>I conceive, I have by this time ſufficiently declared and opened <lb></lb>the way to the contemplation of the true, intrinſecall and proper <lb></lb>Cauſes of diverſe Motions, and of the Reſt of many Solid Bodies in <lb></lb>diverſe <emph type="italics"></emph>Mediums,<emph.end type="italics"></emph.end> and particularly in the water, ſhewing how all ii <lb></lb>effect, depend on the mutuall exceſſes of the Gravity of the Movea <lb></lb>bles and of the <emph type="italics"></emph>Mediums<emph.end type="italics"></emph.end>: and, that which did highly import, re <lb></lb>moving the Objection, which peradventure would have begotter <lb></lb>much doubting, and ſcruple in ſome, about the verity of my Con <lb></lb>cluſion, namely, how that notwithſtanding, that the exceſs of the <lb></lb>Gravity of the water, above the Gravity of the Solid, demitted into <lb></lb>it, be the cauſe of its floating and riſing from the Bottom to the Sur <lb></lb>face, yet a quantity of water, that weighs not ten pounds, can raiſe <pb xlink:href="040/01/1112.jpg" pagenum="419"></pb>Solid that weighs above 100 pounds: in that we have demonſtra <lb></lb>ted, That it ſufficeth, that ſuch difference be found between the <lb></lb>Specificall Gravities of the <emph type="italics"></emph>Mediums<emph.end type="italics"></emph.end> and Moveables, let the particular <lb></lb>and abſolute Gravities be what they will: inſomuch, that a Solid, <lb></lb>provided that it be Specifically leſs grave than the water, although <lb></lb>its abſolute weight were 1000 pounds, yet may it be born up and <lb></lb>elevated by ten pounds of water, and leſs: and on the contrary, a <lb></lb>nother Solid, ſo that it be Specifically more grave than the water, <lb></lb>though in abſolute Gravity it were not above a pound, yet all the <lb></lb>water in the Sea, cannot raiſe it from the Bottom, or float it. </s><s>This <lb></lb>ſufficeth me, for my preſent occaſion, to have, by the above declared <lb></lb>Examples, diſcovered and demonſtrated, without extending ſuch <lb></lb>matters farther, and, as I might have done, into a long Treatiſe: <lb></lb>yea, but that there was a neceſſity of reſolving the above propoſed <lb></lb>doubt, I ſhould have contented my ſelf with that only, which is <lb></lb>demonſtrated by <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> in his firſt Book <emph type="italics"></emph>De Inſidentibus hu <lb></lb>mido<emph.end type="italics"></emph.end>: where in generall termes he infers and confirms the ſame </s></p><p type="main"> <s><arrow.to.target n="marg1422"></arrow.to.target> <lb></lb><arrow.to.target n="marg1423"></arrow.to.target> <lb></lb>Concluſions, namely, that Solids (<emph type="italics"></emph>a<emph.end type="italics"></emph.end>) leſs grave than water, ſwim or <lb></lb><arrow.to.target n="marg1424"></arrow.to.target> <lb></lb>float upon it, the (<emph type="italics"></emph>b<emph.end type="italics"></emph.end>) more grave go to the Bottom, and the (<emph type="italics"></emph>c<emph.end type="italics"></emph.end>) e <lb></lb><arrow.to.target n="marg1425"></arrow.to.target> <lb></lb>qually grave reſt indifferently in all places, yea, though they ſhould <lb></lb>be wholly under water.</s></p><p type="margin"> <s><margin.target id="marg1422"></margin.target><emph type="italics"></emph>Of Natation<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1423"></margin.target>(a) <emph type="italics"></emph>Lib. 1. Prop.<emph.end type="italics"></emph.end> 4.</s></p><p type="margin"> <s><margin.target id="marg1424"></margin.target>(b) <emph type="italics"></emph>Id. </s><s>Lib. </s><s>1. <lb></lb>Prop.<emph.end type="italics"></emph.end> 3.</s></p><p type="margin"> <s><margin.target id="marg1425"></margin.target>(c) <emph type="italics"></emph>Id. </s><s>Lib. 1. <lb></lb>Prop.<emph.end type="italics"></emph.end> 3.</s></p><p type="main"> <s>But, becauſe that this Doctrine of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> peruſed, tranſcri <lb></lb><arrow.to.target n="marg1426"></arrow.to.target> <lb></lb>bed and examined by <emph type="italics"></emph>Signor Franceſco Buonamico,<emph.end type="italics"></emph.end> in his <emph type="italics"></emph>fifth Book <lb></lb>of Motion, Chap.<emph.end type="italics"></emph.end> 29, and afterwards by him confuted, might by the <lb></lb>Authority of ſo renowned, and famous a Philoſopher, be rendered <lb></lb>dubious, and ſuſpected of falſity; I have judged it neceſſary to de <lb></lb>fend it, if I am able ſo to do, and to clear <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> from thoſe <lb></lb>cenſures, with which he appeareth to be charged. <emph type="italics"></emph>Buonamico<emph.end type="italics"></emph.end> re <lb></lb><arrow.to.target n="marg1427"></arrow.to.target> <lb></lb>jecteth the Doctrine of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> firſt, as not conſentaneous with <lb></lb>the Opinion of <emph type="italics"></emph>Aristotle,<emph.end type="italics"></emph.end> adding, that it was a ſtrange thing to him, <lb></lb><arrow.to.target n="marg1428"></arrow.to.target> <lb></lb>that the Water ſhould exceed the Earth in Gravity, ſeeing on the <lb></lb>contrary, that the Gravity of water, increaſeth, by means of the parti <lb></lb><arrow.to.target n="marg1429"></arrow.to.target> <lb></lb>cipation of Earth. </s><s>And he ſubjoyns preſently after, that he was <lb></lb>not ſatisfied with the Reaſons of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> as not being able with <lb></lb>that Doctrine, to aſſign the cauſe whence it comes, that a Boat and <lb></lb>a Veſſell, which otherwiſe, floats above the water, doth ſink to the <lb></lb>Bottom, if once it be filled with water; that by reaſon of the e <lb></lb>quality of Gravity, between the water within it, and the other water <lb></lb>without, it ſhould ſtay a top; but yet, nevertheleſs, we ſee it to go to <lb></lb>the Bottom. <lb></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"></emph>Authors<emph.end type="italics"></emph.end> <lb></lb>defence of <emph type="italics"></emph>Ar <lb></lb>chimedes<emph.end type="italics"></emph.end> his Do <lb></lb>ctrine, againſt <lb></lb>the oppoſitions <lb></lb>of <emph type="italics"></emph>Buonamico.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1427"></margin.target>His firſt Objecti <lb></lb>on againſt the <lb></lb>Doctrine of <emph type="italics"></emph>Ar <lb></lb>chimedes.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1428"></margin.target>His Second Ob <lb></lb>jection.</s></p><p type="margin"> <s><margin.target id="marg1429"></margin.target>His third Obje <lb></lb>ction.</s></p><p type="margin"> <s><margin.target id="marg1430"></margin.target>His ſourth Ob <lb></lb>jection.</s></p><p type="main"> <s>He farther addes, that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> had clearly confuted the Ancients, <lb></lb>who ſaid, that light Bodies moved upwards, driven by the impulſe </s></p><p type="main"> <s><arrow.to.target n="marg1431"></arrow.to.target> <lb></lb>of the more grave Ambient: which if it were ſo, it ſhould ſeem of <lb></lb>neceſſity to follow, that all naturall Bodies are by nature heavy, <pb xlink:href="040/01/1113.jpg" pagenum="420"></pb>and none light: For that the ſame would befall the Fire and Air, <lb></lb>if put in the Bottom of the water. </s><s>And, howbeit, <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> grants <lb></lb>a Pulſion in the Elements, by which the Earth is reduced into a Sphe <lb></lb>ricall Figure, yet nevertheleſs, in his judgement, it is not ſuch that it <lb></lb>can remove grave Bodies from their naturall places, but rather, that <lb></lb>it ſend them toward the Centre, to which (as he ſomewhat obſcurely <lb></lb>continues to ſay,) the water principally moves, if it in the interim <lb></lb>meet not with ſomething that reſiſts it, and, by its Gravity, thruſts <lb></lb>it out of its place: in which caſe, if it cannot directly, yet at leaſt <lb></lb>as well as it can, it tends to the Centre: but it happens, that light <lb></lb>Bodies by ſuch Impulſion, do all aſcend upward: but this properly <lb></lb>they have by nature, as alſo, that other of ſwimming. </s><s>He concludes, <lb></lb><arrow.to.target n="marg1432"></arrow.to.target> <lb></lb>laſtly, that he concurs with <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> in his Concluſions; but not <lb></lb>in the Cauſes, which he would referre to the facile and difficult Sepa <lb></lb>ration of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> and to the predominance of the Elements, ſo <lb></lb>that when the Moveable ſuperates the power of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end>; as for <lb></lb>example, Lead doth the Continuity of water, it ſhall move thorow it, <lb></lb>elſe not.</s></p><p type="margin"> <s><margin.target id="marg1431"></margin.target>The <emph type="italics"></emph>Ancients<emph.end type="italics"></emph.end> <lb></lb>denved <emph type="italics"></emph>Aoſolute<emph.end type="italics"></emph.end> <lb></lb>Levity.</s></p><p type="margin"> <s><margin.target id="marg1432"></margin.target>The cauſes of <lb></lb>Natation & Sub <lb></lb>merſion, accord <lb></lb>ing to the Peri <lb></lb>pateticks.</s></p><p type="main"> <s>This is all that I have been able to collect, as produced againſt <lb></lb><emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> by <emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end>: who hath not well obſerved the <lb></lb>Principles and Suppoſitions of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end>; which yet muſt be <lb></lb>falſe, if the Doctrine be falſe, which depends upon them; but is <lb></lb>contented to alledge therein ſome Inconveniences, and ſome Repug <lb></lb>nances to the Doctrine and Opinion of <emph type="italics"></emph>Ariſtotle.<emph.end type="italics"></emph.end> In anſwer to which <lb></lb>Objections, I ſay, firſt, That the being of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> Doctrine, ſim <lb></lb><arrow.to.target n="marg1433"></arrow.to.target> <lb></lb>ply different from the Doctrine of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> ought not to move any <lb></lb>to ſuſpect it, there being no cauſe, why the Authority of this ſhould <lb></lb>be preferred to the Authority of the other: but, becauſe, where the <lb></lb>decrees of Nature are indifferently expoſed to the intellectuall eyes of <lb></lb>each, the Authority of the one and the other, loſeth all anthentical <lb></lb>neſs of Perſwaſion, the abſolute power reſiding in Reaſon; therefore <lb></lb>I paſs to that which he alledgeth in the ſecond place, as an abſurd con <lb></lb><arrow.to.target n="marg1434"></arrow.to.target> <lb></lb>ſequent of the Doctrine of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> namely, That water ſhould <lb></lb>be more grave than Earth. </s><s>But I really find not, that ever <emph type="italics"></emph>Archi <lb></lb>medes<emph.end type="italics"></emph.end> ſaid ſuch a thing, or that it can be rationally deduced from his <lb></lb>Concluſions: and if that were manifeſt unto me, I verily believe, I <lb></lb>ſhould renounce his Doctrine, as moſt erroneous. </s><s>Perhapsthis Dedu <lb></lb>ction of <emph type="italics"></emph>Buonamico,<emph.end type="italics"></emph.end> is founded upon that which he citeth of the Ve <lb></lb>ſſel, which ſwims as long as its voyd of water, but once full it ſinks to <lb></lb>the Bottom, and underſtanding it of a Veſſel of Earth, he infers againſt <lb></lb><emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> thus: Thou ſayſt that the Solids which ſwim, are leſs grave <lb></lb>than water: this Veſſell ſwimmeth: therefore, this Veſſell is leſſe grave <lb></lb>than water. </s><s>If this be the Illation. </s><s>I eaſily anſwer, granting that this <lb></lb>Veſſell is leſſe grave than water, and denying the other conſequence, <pb xlink:href="040/01/1114.jpg" pagenum="421"></pb>namely, that Earth is leſs Grave than Water. </s><s>The Veſſel that ſwims <lb></lb>occupieth in the water, not only a place equall to the Maſs of the <lb></lb>Earth, of which it is formed; but equall to the Earth and to the Air <lb></lb>together, contained in its concavity. </s><s>And, if ſuch a Maſs compoun <lb></lb>ded of Earth and Air, ſhall be leſs grave than ſuch another quantity <lb></lb>of water, it ſhall ſwim, and ſhall accord with the Doctrine of <emph type="italics"></emph>Archi <lb></lb>medes<emph.end type="italics"></emph.end>; but if, again, removing the Air, the Veſſell ſhall be filled <lb></lb>with water, ſo that the Solid put in the water, be nothing but <lb></lb>Earth, nor occupieth other place, than that which is only poſſeſt by <lb></lb>Earth, it ſhall then go to the Bottom, by reaſon that the Earth is <lb></lb>heavier than the water: and this correſponds well with the meaning <lb></lb>of <emph type="italics"></emph>Archimedes.<emph.end type="italics"></emph.end> See the ſame effect illuſtrated, with ſuch another <lb></lb>Experiment, In preſſing a Viall Glaſs to the Bottom of the water, <lb></lb>when it is full of Air, it will meet with great reſiſtance, becauſe it is <lb></lb>not the Glaſs alone, that is preſſed under water, but together with <lb></lb>the Glaſs a great Maſs of Air, and ſuch, that if you ſhould take as <lb></lb>much water, as the Maſs of the Glaſs, and of the Air contained in it, <lb></lb>you would have a weight much greater than that of the Viall, and of <lb></lb>its Air: and, therefore, it will not ſubmerge without great violence: <lb></lb>but if we demit only the Glaſs into the water, which ſhall be when <lb></lb>you ſhall fill the Glaſs with water, then ſhall the Glaſs deſcend to <lb></lb>the Bottom; as ſuperiour in Gravity to the water.</s></p><p type="margin"> <s><margin.target id="marg1433"></margin.target>The Authors an <lb></lb>ſwer to the firſt <lb></lb>Objection.</s></p><p type="margin"> <s><margin.target id="marg1434"></margin.target>The Authors an <lb></lb>ſwer to the ſe <lb></lb>cond Objection.</s></p><p type="main"> <s>Returning, therefore, to our firſt purpoſe; I ſay, that Earth is <lb></lb>more grave than water, and that therefore, a Solid of Earth goeth to <lb></lb>the bottom of it; but one may poſſibly make a compoſition of Earth <lb></lb>and Air, which ſhall be leſs grave than a like Maſs of Water; and <lb></lb>this ſhall ſwim: and yet both this and the other experiment ſhall <lb></lb>very well accord with the Doctrine of <emph type="italics"></emph>Archimedes.<emph.end type="italics"></emph.end> But becauſe that <lb></lb>in my judgment it hath nothing of difficulty in it, I will not poſitive <lb></lb>ly affirme that <emph type="italics"></emph>Signor Buonamico,<emph.end type="italics"></emph.end> would by ſuch a diſcourſe object <lb></lb>unto <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> the abſurdity of inferring by his doctrine, that Earth <lb></lb>was leſs grave than Water, though I know not how to conceive what <lb></lb>other accident he could have induced thence.</s></p><p type="main"> <s>Perhaps ſuch a Probleme (in my judgement falſe) was read by <lb></lb><emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end> in ſome other Author, by whom peradventure it <lb></lb>was attributed as a ſingular propertie, of ſome particular Water, and <lb></lb>ſo comes now to be uſed with a double errour in confutation of <emph type="italics"></emph>Ar <lb></lb>chimedes,<emph.end type="italics"></emph.end> ſince he ſaith no ſuch thing, nor by him that did ſay it was it <lb></lb>meant of the common Element of Water.</s></p><p type="main"> <s>The third difficulty in the doctrine of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> was, that he <lb></lb><arrow.to.target n="marg1435"></arrow.to.target> <lb></lb>could not render a reaſon whence it aroſe, that a piece of Wood, <lb></lb>and a Veſſell of Wood, which otherwiſe floats, goeth to the bottom, <lb></lb>if filled with Water. <emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end> hath ſuppoſed that a Verſſell <lb></lb>of Wood, and of Wood that by nature ſwims, as before is ſaid, <pb xlink:href="040/01/1115.jpg" pagenum="422"></pb>goes to the bottom, if it be filled with water; of which he in the fol <lb></lb>lowing Chapter, which is the 30 of the fifth Book copiouſly diſcourſ <lb></lb>eth: but I (ſpeaking alwayes without diminution of his ſingular <lb></lb>Learning) dare in defence of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> deny this experiment, being <lb></lb>certain that a piece of Wood which by its nature ſinks not in Water, <lb></lb>ſhall not ſinke though it be turned and converted into the forme of a <lb></lb>ny Veſſell whatſoever, and then filled with Water: and he that would <lb></lb>readily ſee the Experiment in ſome other tractable Matter, and that is <lb></lb>eaſily reduced into ſeveral Figures, may take pure Wax, and ma <lb></lb>king it firſt into a Ball or other ſolid Figure, let him adde to it ſo <lb></lb>much Lead as ſhall juſt carry it to the bottome, ſo that being a graine <lb></lb>leſs it could not be able to ſinke it, and making it afterwards into <lb></lb>the forme of a Diſh, and filling it with Water, he ſhall finde that with <lb></lb>out the ſaid Lead it ſhall not ſinke, and that with the Lead it ſhall de <lb></lb>ſcend with much ſlowneſs: & in ſhort he ſhall ſatisfie himſelf, that the <lb></lb>Water included makes no alteration. </s><s>I ſay not all this while, but that <lb></lb>its poſſible of Wood to make Barkes, which being filled with water, <lb></lb>ſinke; but that proceeds not through its Gravity, encreaſed by the <lb></lb>Water, but rather from the Nailes and other Iron Workes, ſo that <lb></lb>it no longer hath a Body leſs grave than Water, but one mixt of Iron <lb></lb>and Wood, more grave than a like Maſſe of Water. </s><s>Therefore let <lb></lb><emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end> deſiſt from deſiring a reaſon of an effect, that is <lb></lb>not in nature: yea if the ſinking of the Woodden Veſſell when its full <lb></lb>of Water, may call in queſtion the Doctrine of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> which <lb></lb>he would not have you to follow, is on the contrary conſonant and a <lb></lb>greeable to the Doctrine of the Peripateticks, ſince it aptly aſſignes a <lb></lb>reaſon why ſuch a Veſſell muſt, when its full of Water, deſcend to the <lb></lb>bottom; converting the Argument the other way, we may with <lb></lb>ſafety ſay that the Doctrine of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> is true, ſince it aptly agre <lb></lb>eth with true experiments, and queſtion the other, whoſe Deducti <lb></lb>ons are faſtened upon etroneouſs Concluſions. </s><s>As for the other point <lb></lb>hinted in this ſame Inſtance, where it ſeemes that <emph type="italics"></emph>Benonamico<emph.end type="italics"></emph.end> under <lb></lb>ſtands the ſame not only of a piece of wood, ſhaped in the forme of a <lb></lb>Veſſell, but alſo of maſſie Wood, which filled, <emph type="italics"></emph>ſcilicet,<emph.end type="italics"></emph.end> as I believe, he <lb></lb>would ſay, ſoaked and ſteeped in Water, goes finally to the bottom <lb></lb>that happens in ſome poroſe Woods, which, while their Poroſity is re <lb></lb>pleniſhed with Air, or other Matter leſs grave than Water, are Maſ <lb></lb>ſes ſpecificially leſs grave than the ſaid Water, like as is that Viall of <lb></lb>Glaſs whileſt it is full of Air: but when, ſuch light Matter depart <lb></lb>ing, there ſucceedeth Water into the ſame Poroſities and Cavities, <lb></lb>there reſults a compound of Water and Glaſs more grave than a like <lb></lb>Maſs of Water: but the exceſs of its Gravity conſiſts in the Matter <lb></lb>of the Glaſs, and not in the Water, which cannot be graver than it <lb></lb>ſelf: ſo that which remaines of the Wood, the Air of its Cavi <pb xlink:href="040/01/1116.jpg" pagenum="423"></pb>ties departing, if it ſhall be more grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than Water, fil but its <lb></lb>Poroſities with Water, and you ſhal have a Compoſt of Water and <lb></lb>of Wood more grave than Water, but not by vertue of the Water re <lb></lb>ceived into and imbibed by the Poroſities, but of that Matter of the <lb></lb>Wood which remains when the Air is departed: and being ſuch it <lb></lb>ſhall, according to the Doctrine of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> goe to the bottom, <lb></lb>like as before, according to the ſame Doctrine it did ſwim.</s></p><p type="margin"> <s><margin.target id="marg1435"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he Authors an <lb></lb>ſwer to the third <lb></lb>Objection.</s></p><p type="main"> <s>As to that finally which preſents it ſelf in the fourth place, namely, <lb></lb><arrow.to.target n="marg1436"></arrow.to.target> <lb></lb>that the <emph type="italics"></emph>Ancients<emph.end type="italics"></emph.end> have been heretofore confuted by <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> who <lb></lb>denying Poſitive and Abſolute Levity, and truely eſteeming all Bo <lb></lb>dies to be grave, ſaid, that that which moved upward was driven by <lb></lb>the circumambient Air, and therefore that alſo the Doctrine of <lb></lb><emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> as an adherent to ſuch an Opinion was con <lb></lb>victed and confuted: I anſwer firſt, that <emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end> in my <lb></lb>judgement hath impoſed upon <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> and deduced from his <lb></lb>words more than ever he intended by them, or may from his Propo <lb></lb>ſitions be collected, in regard that <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> neither denies, nor ad <lb></lb>mitteth Poſitive Levity, nor doth he ſo much as mention it: ſo that <lb></lb>much leſs ought <emph type="italics"></emph>Buonamico<emph.end type="italics"></emph.end> to inferre, that he hath denyed that it <lb></lb>might be the Cauſe and Principle of the Aſcenſion of Fire, and other <lb></lb>Light Bodies: having but only demonſtrated, that Solid Bodies <lb></lb><arrow.to.target n="marg1437"></arrow.to.target> <lb></lb>more grave than Water deſcend in it, according to the exceſs of their <lb></lb>Gravity above the Gravity of that, he demonſtrates likewiſe, how the <lb></lb><arrow.to.target n="marg1438"></arrow.to.target> <lb></lb>leſs grave aſcend in the ſame Water, accordng to its exceſs of Gra <lb></lb>ty, above the Gravity of them. </s><s>So that the moſt that can be gather <lb></lb>ed from the Dem onſtration of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> is, that like as the exceſs <lb></lb>of the Gravity of the Moveable above the Gravity of the Water, is <lb></lb>the Cauſe that it deſcends therein, ſo the exceſs of the Gravity of <lb></lb>the water above that of the Moveable, is a ſufficient Cauſe why it deſ <lb></lb>cends not, but rather betakes it ſelf to ſwim: not enquiring whe <lb></lb>ther of moving upwards there is, or is not any other Cauſe contrary <lb></lb>to Gravity: nor doth <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> diſcourſe leſs properly than if one <lb></lb>ſhould ſay: If the South Winde ſhall aſſault the Barke with greater <lb></lb><emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> than is the violence with which the Streame of the River car <lb></lb>ries it towards the South, the motion of it ſhall be towards the North: <lb></lb>but if the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the Water ſhall overcome that of the Winde, its <lb></lb>motion ſhall be towards the South. </s><s>The diſcourſe is excellent and <lb></lb>would be unworthily contradicted by ſuch as ſhould oppoſe it, ſaying: <lb></lb>Thou miſ-alledgeſt as Cauſe of the motion of the Bark towards the <lb></lb>South, the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the Stream of the Water above that of the <lb></lb>South Winde; miſ-alledgeſt I ſay, for it is the Force of the North <lb></lb>Winde oppoſite to the South, that is able to drive the Bark towards <lb></lb>the South. </s><s>Such an Objection would be ſuperfluous, becauſe he which <lb></lb>alledgeth for Cauſe of the Motion the ſtream of the Water, denies not <pb xlink:href="040/01/1117.jpg" pagenum="424"></pb>but that the Winde oppoſite to the South may do the ſame, but only <lb></lb>affirmeth that the force of the Water prevailing over the South <lb></lb>Wind, the Bark ſhall move towards the South: and ſaith no more <lb></lb>than is true. </s><s>And juſt thus when <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> ſaith, that the Gravity <lb></lb>of the Water prevailing over that by which the moveable deſcends to <lb></lb>the Bottom, ſuch moveable ſhall be raiſed from the Bottom to the Sur <lb></lb>face alledgeth a very true Cauſe of ſuch an Accident, nor doth he af <lb></lb>firm or deny that there is, or is not, a vertue contrary to Gravity, called <lb></lb>by ſome Levity, that hath alſo a power of moving ſome Matters up <lb></lb>wards. </s><s>Let therefore the Weapons of <emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end> be directed a <lb></lb><arrow.to.target n="marg1439"></arrow.to.target> <lb></lb>gainſt <emph type="italics"></emph>Plato,<emph.end type="italics"></emph.end> and other <emph type="italics"></emph>Ancients,<emph.end type="italics"></emph.end> who totally denying <emph type="italics"></emph>Levity,<emph.end type="italics"></emph.end> and taking <lb></lb>all Bodies to be grave, ſay that the Motion upwards is made, not <lb></lb>from an intrinſecal Principle of the Moveable, but only by the Im <lb></lb>pulſe of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end>; and let <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> and his Doctrine eſcape <lb></lb>him, ſince he hath given him no Cauſe of quarelling with him <lb></lb>But if this Apologie, produced in defence of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> ſhould ſeen <lb></lb>to ſome inſufficient to free him from the Objections and Arguments <lb></lb>produced by <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> againſt <emph type="italics"></emph>Plato,<emph.end type="italics"></emph.end> and the other <emph type="italics"></emph>Ancients,<emph.end type="italics"></emph.end> as if they <lb></lb>did alſo fight againſt <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> alledging the Impulſe of the Water <lb></lb><arrow.to.target n="marg1440"></arrow.to.target> <lb></lb>as the Cauſe of the ſwimming of ſome Bodies leſs grave than it, I would <lb></lb>not queſtion, but that I ſhould be able to maintaine the Doctrine of <lb></lb><emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> and thoſe others to be moſt true, who abſolutely deny Levity, <lb></lb>and affirm no other Intrinſecal Principle of Motion to be in Elemen <lb></lb>tary Bodies ſave only that towards the Centre of the Earth, nor no <lb></lb><arrow.to.target n="marg1441"></arrow.to.target> <lb></lb>other Cauſe of moving upwards, ſpeaking of that which hath the re <lb></lb>ſemblance of natural Motion, but only the repulſe of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> ſluid, <lb></lb>and exceeding the Gravity of the Moveable: and as to the Reaſons <lb></lb>of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> on the contrary, I believe that I could be able fully to <lb></lb><arrow.to.target n="marg1442"></arrow.to.target> <lb></lb>anſwer them, and I would aſſay to do it, if it were abſolutely neceſſa <lb></lb>ry to the preſent Matter, or were it not too long a Digreſſion for this <lb></lb>ſhort Treatiſe. </s><s>I will only ſay, that if there were in ſome of our Elle <lb></lb>mentary Bodies an Intrinſecall Principle and Naturall Inclination <lb></lb>to ſhun the Centre of the Earth, and to move towards the Concave <lb></lb>of the Moon, ſuch Bodies, without doubt, would more ſwiftly aſcend <lb></lb>through thoſe <emph type="italics"></emph>Mediums<emph.end type="italics"></emph.end> that leaſt oppoſe the Velocity of the Moveable, <lb></lb>and theſe are the more tenuous and ſubtle; as is, for example, the <lb></lb>Air in compariſon of the Water, we daily proving that we can with <lb></lb><arrow.to.target n="marg1443"></arrow.to.target> <lb></lb>farre more expeditious Velocity move a Hand or a Board to and a <lb></lb>gain in one than in the other: nevertheleſs, we never could finde any <lb></lb>Body, that did not aſcend much more ſwiftly in the water than in the <lb></lb><arrow.to.target n="marg1444"></arrow.to.target> <lb></lb>Air. </s><s>Yea of Bodies which we ſee continually to aſcend in the Water, <lb></lb>there is none that having arrived to the confines of the Air, do not whol <lb></lb>ly loſe their Motion; even the Air it ſelf, which riſing with great Ce <lb></lb>lerity through the Water, being once come to its Region it loſeth all</s></p> <pb xlink:href="040/01/1118.jpg" pagenum="425"></pb><p type="margin"> <s><margin.target id="marg1436"></margin.target>The Authors <lb></lb>anſwer to the <lb></lb>fourth Object <lb></lb>ion.</s></p><p type="margin"> <s><margin.target id="marg1437"></margin.target>Of Natation, <lb></lb>Lib. 1. Prop. </s><s>7.</s></p><p type="margin"> <s><margin.target id="marg1438"></margin.target>Of Natation, <lb></lb>Lib. </s><s>1. Prop. </s><s>4.</s></p><p type="margin"> <s><margin.target id="marg1439"></margin.target><emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> denyeth <lb></lb>Poſitive Levi <lb></lb>ty.</s></p><p type="margin"> <s><margin.target id="marg1440"></margin.target>The Authors <lb></lb>defence of the <lb></lb>doctrine of <emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> <lb></lb>and the <emph type="italics"></emph>Ancients,<emph.end type="italics"></emph.end> <lb></lb>who abſolutely <lb></lb>deny Levity:</s></p><p type="margin"> <s><margin.target id="marg1441"></margin.target>According to <lb></lb><emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> there is no <lb></lb>Principle of the <lb></lb>Motion of de <lb></lb>ſcent in Naturall <lb></lb>Bodies, ſave that <lb></lb>to the Centre.</s></p><p type="margin"> <s><margin.target id="marg1442"></margin.target>No cauſe of <lb></lb>the motion of <lb></lb><emph type="italics"></emph>A<emph.end type="italics"></emph.end> cent, ſave the <lb></lb>Impulſe of the <lb></lb><emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> exceed <lb></lb>ing the Move <lb></lb>able in Gravi <lb></lb>tie.</s></p><p type="margin"> <s><margin.target id="marg1443"></margin.target>Bodies aſcend <lb></lb>much ſwifter in <lb></lb>the Water, than <lb></lb>in the Air.</s></p><p type="margin"> <s><margin.target id="marg1444"></margin.target>All Bodies aſ <lb></lb>cending through <lb></lb>Water, loſe <lb></lb>their Motion, <lb></lb>comming to the <lb></lb>confines of the <lb></lb>Air.</s></p><p type="main"> <s>And, howbeit, Experience ſhewes, that the Bodies, ſucceſſively <lb></lb><arrow.to.target n="marg1445"></arrow.to.target> <lb></lb>leſs grave, do moſt expeditiouſly aſcend in water, it cannot be doubt <lb></lb>ed, but that the Ignean Exhalations do aſcend more ſwiftly <lb></lb><arrow.to.target n="marg1446"></arrow.to.target> <lb></lb>through the water, than doth the Air: which Air is ſeen by Experi <lb></lb>ence to aſcend more ſwiftly through the Water, than the Fiery Exha <lb></lb>lations through the Air: Therefore, we muſt of neceſſity conclude, <lb></lb>that the ſaid Exhalations do much more expeditiouſly aſcend through <lb></lb>the Water, than through the Air; and that, conſequently, they are <lb></lb>moved by the Impulſe of the Ambient <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> and not by an intrin <lb></lb>ſick Principle that is in them, of avoiding the Centre of the Earth; <lb></lb>to which other grave Bodies tend.</s></p><p type="margin"> <s><margin.target id="marg1445"></margin.target>The lighter <lb></lb>Bodies alſend <lb></lb>more ſwiftly <lb></lb>through Water.</s></p><p type="margin"> <s><margin.target id="marg1446"></margin.target>Fiery Exhalati <lb></lb>ons ascend tho <lb></lb>row the Water <lb></lb>more ſwiftly <lb></lb>than doth the <lb></lb>Air; & the Air <lb></lb>aſcends more <lb></lb>ſwiftly thorow <lb></lb>the Water, than <lb></lb><emph type="italics"></emph>F<emph.end type="italics"></emph.end>ire thorow the <lb></lb>Air.</s></p><p type="main"> <s>To that which for a finall concluſion, <emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end> produceth <lb></lb><arrow.to.target n="marg1447"></arrow.to.target> <lb></lb>of going about to reduce the deſcending or not deſcending, to the <lb></lb>eaſie and uneaſie Diviſion of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> and to the predominancy <lb></lb>of the Elements: I anſwer, as to the firſt part, that that cannot in any <lb></lb>manner be admitted as a Cauſe, being that in none of the Fluid <lb></lb><emph type="italics"></emph>Mediums,<emph.end type="italics"></emph.end> as the Air, the Water, and other Liquids, there is any <lb></lb><arrow.to.target n="marg1448"></arrow.to.target> <lb></lb>Reſiſtance againſt Diviſion, but all by every the leaſt Force, are di <lb></lb>vided and penetrated, as I will anon demonſtrate: ſo, that of ſuch <lb></lb>Reſiſtance of Diviſion there can be no Act, ſince it ſelf is not in be <lb></lb>ing. </s><s>As to the other part, I ſay, that the predominancy of the Ele <lb></lb><arrow.to.target n="marg1449"></arrow.to.target> <lb></lb>ments in Moveables, is to be conſidered, as far as to the exceſſe or <lb></lb>defect of Gravity, in relation to the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end>: for in that Action, <lb></lb>the Elements operate not, but only, ſo far as they are grave or light: <lb></lb>therefore, to ſay that the Wood of the Firre ſinks not, becauſe Air <lb></lb>predominateth in it, is no more than to ſay, becauſe it is leſs grave <lb></lb>than the Water. </s><s>Yea, even the immediate Cauſe, is its being leſs <lb></lb>grave than the Water: and it being under the predominancy of the <lb></lb><arrow.to.target n="marg1450"></arrow.to.target> <lb></lb>Air, is the Cauſe of its leſs Gravity: Therefore, he that alledgeth the <lb></lb>predominancy of the Element for a Cauſe, brings the Cauſe of the <lb></lb>Cauſe, and not the neereſt and immediate Cauſe. </s><s>Now, who knows <lb></lb>not that the true Cauſe is the immediate, and not the mediate? <lb></lb><arrow.to.target n="marg1451"></arrow.to.target> <lb></lb>Moreover, he that alledgeth Gravity, brings a Cauſe moſt perſpicuous <lb></lb>to Sence: The cauſe we may very eaſily aſſertain our ſelves; <lb></lb>whether Ebony, for example, and Firre, be more or leſs grave than <lb></lb>water: but whether Earth or Air predominates in them, who ſhall <lb></lb><arrow.to.target n="marg1452"></arrow.to.target> <lb></lb>make that manifeſt? </s><s>Certainly, no Experiment can better do it <lb></lb>than to obſerve whether they ſwim or ſink. </s><s>So, that he who knows, <lb></lb>not whether ſuch a Solid ſwims, unleſs when he knows that Air pre <lb></lb>dominates in it, knows not whether it ſwim, unleſs he ſees it ſwim, <lb></lb>for then he knows that it ſwims, when he knows that it is Air that <lb></lb>predominates, but knows not that Air hath the predominance, unleſs <lb></lb>he ſees it ſwim: therefore, he knows not if it ſwims, till ſuch time <lb></lb>as he hath ſeen it ſwim.</s></p> <pb xlink:href="040/01/1119.jpg" pagenum="426"></pb><p type="margin"> <s><margin.target id="marg1447"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he Authors <lb></lb>confutation of <lb></lb>the Peripateticks <lb></lb>Cauſes of Nata <lb></lb>tion & Submerſi <lb></lb>on.</s></p><p type="margin"> <s><margin.target id="marg1448"></margin.target>Water & other <lb></lb>fluids void of <lb></lb>Reſiſtance a <lb></lb>gainſt Diviſion.</s></p><p type="margin"> <s><margin.target id="marg1449"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he predomi <lb></lb>nancy of Ele <lb></lb>ments in Move <lb></lb>ables to be con <lb></lb>ſidered only in <lb></lb>relation to their <lb></lb>excefs or defect <lb></lb>of Gravity in <lb></lb>reference to the <lb></lb><emph type="italics"></emph>Medium.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1450"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he immedi <lb></lb>ate Cauſe of Na <lb></lb>tation is that the <lb></lb>Moveable is leſs <lb></lb>grave than the <lb></lb>Water.</s></p><p type="margin"> <s><margin.target id="marg1451"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he <emph type="italics"></emph>P<emph.end type="italics"></emph.end>eripate <lb></lb>ticks alledge for <lb></lb>the reaſon of <lb></lb>Natation the <lb></lb>Cauſe of the <lb></lb>Cauſe.</s></p><p type="margin"> <s><margin.target id="marg1452"></margin.target>Gravity a <lb></lb>Cauſe moſt per <lb></lb>ſpicuous to <lb></lb>ſence:</s></p><p type="main"> <s>Let us not then deſpiſe thoſe Hints, though very dark, which <lb></lb>Reaſon, after ſome contemplation, offereth to our Intelligence, and <lb></lb>lets be content to be taught by <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> that then any Body ſhall <lb></lb><arrow.to.target n="marg1453"></arrow.to.target> <lb></lb>ſubmerge in water, when it ſhall be ſpecifically more grave than it <lb></lb>and that if it ſhall be leſs grave, it ſhall of neceſſity ſwim, and <lb></lb><arrow.to.target n="marg1454"></arrow.to.target> <lb></lb>that it will reſt indifferently in any place under water, if its Gravity <lb></lb>be perfectly like to that of the water. <lb></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></lb>tation Prop. </s><s>7.</s></p><p type="margin"> <s><margin.target id="marg1454"></margin.target>Id. </s><s>Lib. 1. <lb></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></lb>Prop. </s><s>3.</s></p><p type="main"> <s>Theſe things explained and proved, I come to conſider that which <lb></lb>offers it ſelf, touching what the Diverſity of figure given unto the <lb></lb>ſaid Moveable hath to do with theſe Motions and Reſts; and pro <lb></lb>ceed to affirme, that,</s></p><p type="head"> <s>THEOREME V.</s></p><p type="main"> <s><emph type="italics"></emph>The diverſity of Figures given to this or that Solid<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1456"></arrow.to.target> <lb></lb><emph type="italics"></emph>cannot any way be a Cauſe of its abſolute Sinking or <lb></lb>Swimming.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1456"></margin.target>Diverſity of <lb></lb>Figure no Cauſe <lb></lb>of its abſolute <lb></lb>Natation or Sub <lb></lb>merſion.</s></p><p type="main"> <s>So that if a Solid being formed, for example, into a Spherical <lb></lb>Figure, doth ſink or ſwim in the water, I ſay, that being formed <lb></lb>into any other Figure, the ſame figure in the ſame water, ſhall <lb></lb>ſink or ſwim: nor can ſuch its Motion by the Expanſion or by o <lb></lb>ther mutation of Figure, be impeded or taken away. <lb></lb><arrow.to.target n="marg1457"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1457"></margin.target>The Expanſi <lb></lb>on of <emph type="italics"></emph>F<emph.end type="italics"></emph.end>igure, re <lb></lb>tards the Veloci <lb></lb>ty of the aſcent <lb></lb>or deſcent of the <lb></lb>Moveable in the <lb></lb>water; but doth <lb></lb>not deprive it of <lb></lb>all Motion.</s></p><p type="main"> <s>The Expanſion of the Figure may indeed retard its Velocity, aſ <lb></lb>well of aſcent as deſcent, and more and more according as the ſaid Fi <lb></lb>gure is reduced to a greater breadth and thinneſs: but that it may bere <lb></lb>duced to ſuch a form as that that ſame matter be wholly hindred from <lb></lb>moving in the ſame water, that I hold to be impoſſible. </s><s>In this I have <lb></lb>met with great contradictors, who producing ſome Experiments, and <lb></lb>in perticular a thin Board of Ebony, and a Ball of the ſame Wood <lb></lb>and ſhewing how the Ball in Water deſcended to the bottom, and <lb></lb>the Board being put lightly upon the Water ſubmerged not, but reſt <lb></lb>ed; have held, and with the Authority of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> confirmed them <lb></lb>ſelves in their Opinions, that the Cauſe of that Reſt was the breadth <lb></lb>of the Figure, u able by its ſmall weight to pierce and penetrate the <lb></lb>Reſiſtance of the Waters Craſſitude, which Reſiſtance is readily o <lb></lb>vercome by the other Sphericall Figure.</s></p><p type="main"> <s>This is the Principal point in the preſent Queſtion, in which I per <lb></lb>ſwade my ſelf to be on the right ſide.</s></p><p type="main"> <s>Therefore, beginning to inveſtigate with the examination of ex <lb></lb>quiſite Experiments that really the Figure doth not a jot alter the deſ <lb></lb>cent or Aſcent of the ſame Solids, and having already demonſtra <lb></lb>ted that the greater or leſs Gravity of the Solid in relation to the Gra <lb></lb>vity of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> is the cauſe of Deſcent or Aſcent: when ever we <pb xlink:href="040/01/1120.jpg" pagenum="427"></pb>would make proof of that, which about this Effect the diverſity of Fi <lb></lb>gure worketh, its neceſſary to make the Experiment with Matter <lb></lb>wherein variety of Gravities hath no place. </s><s>For making uſe of Mat <lb></lb>ters which may be different in their Specifical Gravities, and meeting <lb></lb>with varieties of effects of Aſcending and Deſcending, we ſhall al <lb></lb>wayes be left unſatisfied whether that diverſity derive it ſelf really <lb></lb>from the ſole Figure, or elſe from the divers Gravity alſo. </s><s>We may <lb></lb>remedy this by takeing one only Matter, that is tractable and eaſily <lb></lb>reduceable into every ſort of Figure. </s><s>Moreover, it wil be an excellent <lb></lb>expedient to take a kinde of Matter, exactly alike in Gravity unto the <lb></lb>Water: for that Matter, as far as pertaines to the Gravity, is in <lb></lb>different either to Aſcend or Deſcend; ſo that we may preſently ob <lb></lb>ſerve any the leaſt difference that derives it ſelf from the diverſity of <lb></lb>Figure.</s></p><p type="main"> <s>Now to do this, Wax is moſt apt, which, beſides its incapacity of </s></p><p type="main"> <s><arrow.to.target n="marg1458"></arrow.to.target> <lb></lb>receiveing any ſenſible alteration from its imbibing of Water, is duct <lb></lb>ile or pliant, and the ſame piece is eaſily reduceable into all Figures: <lb></lb>and being <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> a very inconſiderable matter inferiour in Gravity <lb></lb>to the Water, by mixing therewith a little of the fileings of Lead it is <lb></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></lb>ment in Wax, <lb></lb>that proveth Fi <lb></lb>gute to have no <lb></lb>Operation in <lb></lb>Natation & Sub <lb></lb>merſion.</s></p><p type="main"> <s>This Matter prepared, and, for example, a Ball being made there <lb></lb>of as bigge as an Orange or biger, and that made ſo grave as to <lb></lb>ſink to the bottom, but ſo lightly, that takeing thence one only Grain <lb></lb>of Lead, it returnes to the top, and being added, it ſubmergeth to <lb></lb>the bottom, let the ſame Wax afterwards be made into a very broad <lb></lb>and thin Flake or Cake; and then, returning to make the ſame Ex <lb></lb>periment, you ſhall ſee that it being put to the bottom, it ſhall, with the <lb></lb>Grain of Lead reſt below, and that Grain deducted, it ſhall aſcend to <lb></lb>the very Surface, and added again it ſhall dive to the bottom. </s><s>And <lb></lb>this ſame effect ſhall happen alwaies in all ſort of Figures, as wel re <lb></lb>gular as irregular: nor ſhall you ever finde any that will ſwim with <lb></lb>out the removall of the Grain of Lead, or ſinke to the bottom unleſs <lb></lb>it be added: and, in ſhort, about the going or not going to the Bot <lb></lb>tom, you ſhall diſcover no diverſity, although, indeed, you ſhall about <lb></lb>the quick and ſlow deſcent: for the more expatiated and diſtended <lb></lb>Figures move more ſlowly aſwel in the diveing to the bottom as in <lb></lb>the riſing to the top; and the other more contracted and compact Fi <lb></lb>gures, more ſpeedily. </s><s>Now I know not what may be expected from <lb></lb>the diverſity of Figures, if the moſt contrary to one another operate <lb></lb>not ſo much as doth a very ſmall Grain of Lead, added or removed.</s></p><p type="main"> <s>Me thinkes I hear ſome of the Adverſaries to raiſe a doubt upon <lb></lb><arrow.to.target n="marg1459"></arrow.to.target> <lb></lb>my produced Experiment. </s><s>And firſt, that they offer to my conſidera <lb></lb>tion, that the Figure, as a Figure ſimply, and disjunct from the Matter <lb></lb>workes not any effect, but requires to be conjoyned with the Matter <pb xlink:href="040/01/1121.jpg" pagenum="428"></pb>and, furthermore, not with every Matter, but with thoſe only, <lb></lb>wherewith it may be able ro execute the deſired operation. </s><s>Like <lb></lb>as we ſee it verified by Experience, that the Acute and ſharp Angle is <lb></lb>more apt to cut, than the Obtuſe; yet alwaies provided, that both <lb></lb>the one and the other, be joyned with a Matter apt to cut, as for <lb></lb>example, with Steel. </s><s>Therefore, a Knife with a fine and ſharp <lb></lb>edge, cuts Bread or Wood with much eaſe, which it will not do, if <lb></lb>the edge be blunt and thick: but he that will inſtead of Steel, take <lb></lb>Wax, and mould it into a Knife, undoubtedly ſhall never know the <lb></lb>effects of ſharp and blunt edges: becauſe neither of them will cut, <lb></lb>the Wax being unable by reaſon of its flexibility, to overcome the <lb></lb>hardneſs of the Wood and Bread. </s><s>And, therefore, applying the <lb></lb>like diſcourſe to our purpoſe, they ſay, that the difference of Figure <lb></lb>will ſhew different effects, touching Natation and Submerſion, but <lb></lb>not conjoyned with any kind of Matter, but only with thoſe Matters <lb></lb>which, by their Gravity, are apt to reſiſt the Velocity of the water, <lb></lb>whence he that would elect for the Matter, Cork or other light wood <lb></lb>unable, through its Levity, to ſuperate the Craſſitude of the water, <lb></lb>and of that Matter ſhould forme Solids of divers Figures, woulld in <lb></lb>vain ſeek to find out what operation Figure hath in Natation or Sub <lb></lb>merſion; becauſe all would ſwim, and that not through any property <lb></lb>of this or that Figure, but through the debility of the Matter, want <lb></lb>ing ſo much Gravity, as is requiſite to ſuperate and overcome the <lb></lb>Denſity and Craſſitude of the water.</s></p><p type="margin"> <s><margin.target id="marg1459"></margin.target>An objection a <lb></lb>gainſt the Expe <lb></lb>riment in Wax.</s></p><p type="main"> <s>Its needfull, therefore, if wee would ſee the effect wrought by the <lb></lb>Diverſity of Figure, firſt to make choice of a Matter of its nature <lb></lb>apt to penetrate the Craſſitude of the water. </s><s>And, for this effect, <lb></lb><arrow.to.target n="marg1460"></arrow.to.target> <lb></lb>they have made choice of ſuch a Matter, as fit, that being readily re <lb></lb>duced into Sphericall Figure, goes to the Bottom; and it is Ebony <lb></lb>of which they afterwards making a ſmall Board or Splinter, as thin as <lb></lb>a Lath, have illuſtrated how that this, put upon the Surface of the <lb></lb>water, reſts there without deſcending to the Bottom: and making, on <lb></lb>the otherſide, of the ſame wood a Ball, no leſs than a hazell Nut, <lb></lb>they ſhew, that this ſwims not, but deſcendes. </s><s>From which Experi <lb></lb>ment, they think they may frankly conclude, that the Breadth ofthe <lb></lb>Figure in the flat Lath or Board, is the cauſe of its not deſcendingto <lb></lb>the Bottom, foraſmuch as a Ball of the ſame Matter, not different <lb></lb>from the Board in any thing but in Figure, ſubmergeth in the ſame <lb></lb>water to the Bottom. </s><s>The diſcourſe and the Experiment hath really <lb></lb>ſo much of probability and likely hood of truth in it, that it would be <lb></lb>no wonder, if many perſwaded by a certain curſory obſervation, <lb></lb>ſhould yield credit to it; nevertheleſs, I think I am able to diſcover, <lb></lb>how that it is not free from falacy.</s></p><p type="margin"> <s><margin.target id="marg1460"></margin.target>An Experi <lb></lb>ment in Ebany, <lb></lb>brought to diſ <lb></lb>prove the Expe <lb></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"></pb>have been produced, I ſay, that Figures, as ſimple Figures, not only <lb></lb><arrow.to.target n="marg1461"></arrow.to.target> <lb></lb>operate not in naturall things, but neither are they ever ſeperated <lb></lb>from the Corporeall ſubſtance: nor have I ever alledged them ſtript <lb></lb>of ſenſible Matter, like as alſo I freely admit, that in our endeavour <lb></lb>ing to examine the Diverſity of Accidents, dependant upon the va <lb></lb>riety of Figures, it is neceſſary to apply them to Matters, which ob <lb></lb>ſtruct not the various operations of thoſe various Figures: and I ad <lb></lb>mit and grant, that I ſhould do very ill, if I would experiment the in <lb></lb>fluence of Acuteneſſe of edge with a Knife of Wax, applying it to cut <lb></lb>an Oak, becauſe there is no Acuteneſs in Wax able to cut that <lb></lb>very hard wood. </s><s>But yet ſuch an Experiment of this Knife, would <lb></lb>not be beſides the purpoſe, to cut curded Milk, or other very yielding <lb></lb>Matter: yea, in ſuch like Matters, the Wax is more commodious <lb></lb>than Steel; for finding the diverſity depending upon Angles, more or <lb></lb>leſs Acute, for that Milk is indifferently cut with a Raiſor, and with <lb></lb>a Knife, that hath a blunt edge. </s><s>It needs, therefore, that regard be <lb></lb>had, not only to the hardneſs, ſolidity or Gravity of Bodies, which <lb></lb>under divers figures, are to divide and penetrate ſome Matters, but it <lb></lb>forceth alſo, that regard be had, on the other ſide, to the Reſiſtance <lb></lb>of the Matters, to be divided and penetrated. </s><s>But ſince I have in <lb></lb>making the Experiment concerning our Conteſt, choſen a Matter <lb></lb>which penetrates the Reſiſtance of the water; and in all figures deſ <lb></lb>cendes to the Bottome, the Adverſaries can charge me with no defect; <lb></lb>yea, I have propounded ſo much a more excellent Method than they, <lb></lb>in as much as I have removed all other Cauſes, of deſcending or <lb></lb>not deſcending to the Bottom, and retained the only ſole and pure <lb></lb>variety of Figures, demonſtrating that the ſame Figures all deſcende <lb></lb>with the only alteration of a Grain in weight: which Grain being <lb></lb>removed, they return to float and ſwim; it is not true, therefore, <lb></lb>(reſuming the Example by them introduced) that I have gon about <lb></lb>to experiment the efficacy of Acuteneſs, in cutting with Matters un <lb></lb>able to cut, but with Matters proportioned to our occaſion; ſince <lb></lb>they are ſubjected to no other variety, then that alone which depends <lb></lb>on the Figure more or leſs a cute. <lb></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></lb>ſeperable from <lb></lb>Corporeall Sub <lb></lb>ſtance.</s></p><p type="margin"> <s><margin.target id="marg1462"></margin.target>The anſwer to <lb></lb>the Objection a <lb></lb>gainſt the Expe <lb></lb>riment of the <lb></lb>Wax.</s></p><p type="main"> <s>But let us proceed a little farther, and obſerve, how that indeed <lb></lb>the Conſideration, which, they ſay, ought to be had about the Election <lb></lb>of the Matter, to the end, that it may be proportionate for the ma <lb></lb>king of our experiment, is needleſly introduced, declaring by the ex <lb></lb>ample of Cutting, that like as Acuteneſs is inſufficient to cut, unleſs <lb></lb>when it is in a Matter hard and apt to ſuperate the Reſiſtance of the <lb></lb>wood or other Matter, which we intend to cut; ſo the aptitude of <lb></lb>deſcending or notdeſcending in water, ought and can only be known <lb></lb>in thoſe Matters, that are able to overcome the Renitence, and ſupe <lb></lb>rate the Craſſitude of the water. </s><s>Unto which, I ſay, that to make <lb></lb>diſtinction and election, more of this than of that Matter, on which to <pb xlink:href="040/01/1123.jpg" pagenum="430"></pb>impreſs the Figures for cutting or penetrating this or that Body, <lb></lb>as the ſolidity or obdurateneſs of the ſaid Bodies ſhall be greater <lb></lb>or leſs, is very neceſſary: but withall I ſubjoyn, that ſuch diſtinct <lb></lb>ion, election and caution would be ſuperfluous and unprofitable, if <lb></lb>the Body to be cut or penetrated, ſhould have no Reſiſtance, or <lb></lb>ſhould not at all withſtand the Cutting or Penitration: and if the <lb></lb>Knife were to be uſed in cutting a Miſt or Smoak, one of Paper <lb></lb>would be equally ſerviceable with one of <emph type="italics"></emph>Damaſcus<emph.end type="italics"></emph.end> Steel: and ſo <lb></lb>by reaſon the water hath not any Reſiſtance againſt the Penitration <lb></lb>of any Solid Body, all choice of Matter is ſuperfluous and needleſs, <lb></lb>and the Election which I ſaid above to have been well made of a <lb></lb>Matter reciprocall in Gravity to water, was not becauſe it was ne <lb></lb>ceſſary, for the overcoming of the craſſiitude of the water, but its <lb></lb>Gravity, with which only it reſiſts the ſinking of Solid Bodies: and <lb></lb>for what concerneth the Reſiſtance of the craſſitude, if we narrowly <lb></lb>conſider it, we ſhall find that all Solid Bodies, as well thoſe that <lb></lb>ſink, as thoſe that ſwim, are indifferently accomodated and apt to <lb></lb>bring us to the knowledge of the truth in queſtion. </s><s>Nor will I <lb></lb>be frighted out of the belief of theſe Concluſions, by the Experi <lb></lb>ments which may be produced againſt me, of many ſeverall Woods, <lb></lb>Corks, Galls, and, moreover, of ſubtle ſlates and plates of all ſorts <lb></lb>of Stone and Mettall, apt by means of their Naturall Gravity, to <lb></lb>move towards the Centre of the Earth, the which, nevertheleſs, be <lb></lb>ing impotent, either through the Figure (as the Adverſaries thinke) <lb></lb>or through Levity, to break and penetrate the Continuity of the <lb></lb>parts of the water, and to diſtract its union, do continue to ſwimm <lb></lb>without ſubmerging in the leaſt: nor on the other ſide, ſhall the <lb></lb>Authority of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> move me, who in more than one place, aſſir <lb></lb>meth the contrary to this, which Experience ſhews 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></lb>ſuch Levity, nor <lb></lb>of ſuch Figure, <lb></lb>but that it doth <lb></lb>penetrate the <lb></lb>Craſſitude of <lb></lb>the Water.</s></p><p type="main"> <s>I return, therefore, to aſſert, that there is not any Solid of ſuch <lb></lb>Levity, nor of ſuch Figure, that being put upon the water, doth not <lb></lb>divide and penetrate its Craſſitude: yea if any with a more per <lb></lb>ſpicatious eye, ſhall return to obſerve more exactly the thin Boards <lb></lb>of Wood, he ſhall ſee them to be with part of their thickneſs under </s></p><p type="main"> <s><arrow.to.target n="marg1464"></arrow.to.target> <lb></lb>water, and not only with their inferiour Superficies, to kiſſe the <lb></lb>Superiour of the water, as they of neceſſity muſt have believed, who <lb></lb>have ſaid, that ſuch Boards ſubmerge not, as not being able to di <lb></lb>vide the Tenacity of the parts of the water: and, moreover, he <lb></lb>ſhall ſee, that ſubtle ſhivers of Ebony, Stone or Metall, when they <lb></lb>float, have not only broak the Continuity of the water, but are with <lb></lb>all their thickneſs, under the Surface of it; and more and more, <lb></lb>according as the Matters are more grave: ſo that a thin Plate of <lb></lb>Lead, ſhall be lower than the Surface of the circumfuſed water, by <lb></lb>at leaſt twelve times the thickneſs of the Plate, and Gold ſhall dive <pb xlink:href="040/01/1124.jpg" pagenum="431"></pb>below the Levell of the water, almoſt twenty times the thickneſs <lb></lb>of the Plate, as I ſhall anon declare.</s></p><p type="margin"> <s><margin.target id="marg1464"></margin.target>Bodies of all <lb></lb>Figures, laid up <lb></lb>on the water, do <lb></lb>penetrate its <lb></lb>Craſſitude, and <lb></lb>in what propor <lb></lb>tion.</s></p><p type="main"> <s>But let us proceed to evince, that the water yields and ſufters it <lb></lb>ſelf to be penetrated by every the lighteſt Body; and therewithall <lb></lb>demonſtrate, how, even by Matters that ſubmerge not, we may <lb></lb>come to know that Figure operates nothing about the going or <lb></lb>not going to the Bottom, ſeeing that the water ſuffers it ſelf to be <lb></lb>penetrated equally by every Figure.</s></p><p type="main"> <s>Make a Cone, or a Piramis of Cypreſs, of Firre, or of other <lb></lb><arrow.to.target n="marg1465"></arrow.to.target> <lb></lb>Wood of like Gravity, or of pure Wax, and let its height be ſome <lb></lb>what great, namely a handfull, or more, and put it into the water <lb></lb>with the Baſe downwards: firſt, you ſhall ſee that it will penetrate <lb></lb>the water, nor ſhall it be at all impeded by the largeneſs of the Baſe, <lb></lb>nor yet ſhall it ſink all under water, but the part towards the point <lb></lb>ſhall lye above it: by which ſhall be manifeſt, firſt, that that Solid <lb></lb>forbeares not to ſink out of an inabillity to divide the Continuity <lb></lb>of the water, having already divided it with its broad part, that in <lb></lb>the opinion of the Adverſaries is the leſs apt to make the diviſion. <lb></lb></s><s>The Piramid being thus fixed, note what part of it ſhall be ſub <lb></lb>merged, and revert it afterwards with the point downwards, and <lb></lb>you ſhall ſee that it ſhall not dive into the water more than before, <lb></lb>but if you obſerve how far it ſhall ſink, every perſon expert in <lb></lb>Geometry, may meaſure, that thoſe parts that remain out of the <lb></lb>water, both in the one and in the other Experiment are equall to <lb></lb>an hair: whence he may manifeſtly conclude, that the acute Figure <lb></lb>which ſeemed moſt apt to part and penetrate the water, doth not <lb></lb>part or penetrate it more than the large and ſpacious.</s></p><p type="margin"> <s><margin.target id="marg1465"></margin.target>The Experi <lb></lb>ment of a Cone, <lb></lb>demitted with <lb></lb>its Baſe, and af <lb></lb>ter with its <lb></lb>Point down <lb></lb>wards.</s></p><p type="main"> <s>And he that would have a more eaſie Experiment, let him take <lb></lb>two Cylinders of the ſame Matter, one long and ſmall, and the o <lb></lb>ther ſhert, but very broad, and let him put them in the water, not <lb></lb>diſtended, but erect and endways: he ſhall ſee, if he diligently <lb></lb>meaſure the parts of the one and of the other, that in each of them <lb></lb>the part ſubmerged, retains exactly the ſame proportion to that <lb></lb>out of the water, and that no greater part is ſubmerged of that <lb></lb>long and ſmall one, than of the other more ſpacious and broad: <lb></lb>howbeit, this reſts upon a very large, and that upon a very little <lb></lb>Superficies of water: therefore the diverſity of Figure, occaſioneth <lb></lb>neither facility, nor difficulty, in parting and penetrating the Con <lb></lb>tinuity of the water; and, conſequently, cannot be the Cauſe of the <lb></lb>Natation or Submerſion. </s><s>He may likewiſe diſcover the non <lb></lb>operating of variety of Figures, in ariſing from the Bottom of the <lb></lb>water, towards the Surface, by taking Wax, and tempering it with <lb></lb>a competent quantity of the filings of Lead, ſo that it may become <lb></lb>a conſiderable matter graver than the water: then let him make <pb xlink:href="040/01/1125.jpg" pagenum="432"></pb>it into a Ball, and thruſt it unto the Bottom of the water; and <lb></lb>faſten to it as much Cork, or other light matter, as juſt ſerveth to <lb></lb>raiſe it, and draw it towards the Surface: for afterwards changing <lb></lb>the ſame Wax into a thin Cake, or into any other Figure, that <lb></lb>ſame Cork ſhall raiſe it in the ſame manner to a hair.</s></p><p type="main"> <s>This ſilenceth not my Antagoniſts, but they ſay, that all the <lb></lb>diſcourſe hitherto made by me little importeth to them, and that it <lb></lb>ſerves their turn, that they have demonſtrated in one only parti <lb></lb>cular, and in what matter, and under what Figure pleaſeth them, <lb></lb>namely, in a Board and in a Ball of Ebony, that this put in the <lb></lb>water, deſcends to the Bottom, and that ſtays atop to ſwim: <lb></lb>and the Matter being the ſame, and the two Bodies differing in no <lb></lb>thing but in Figure, they affirm, that they have with all perſpicuity <lb></lb>demonſtrated and ſenſibly manifeſted what they undertook; and <lb></lb>laſtly, that they have obtained their intent. </s><s>Nevertheleſs, I believe, <lb></lb>and thinke, I can demonſtrate, that that ſame Experiment proveth <lb></lb>nothing againſt my Concluſion.</s></p><p type="main"> <s>And firſt, it is falſe, that the Ball deſcends, and the Board not: <lb></lb><arrow.to.target n="marg1466"></arrow.to.target> <lb></lb>for the Board ſhall alſo deſcend, if you do to both the Figures, as <lb></lb>the words of our Queſtion requireth; that is, if you put them both <lb></lb>into the water. <lb></lb><arrow.to.target n="marg1467"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1466"></margin.target>In Experi <lb></lb>ments of Nata <lb></lb>tion, the Solid <lb></lb>is to be put into, <lb></lb>not upon the <lb></lb>water.</s></p><p type="margin"> <s><margin.target id="marg1467"></margin.target>The Queſtion <lb></lb>of Natation ſta <lb></lb>ted.</s></p><p type="main"> <s><emph type="italics"></emph>The words were theſe. </s><s>That the Antagoniſts having an opinion, that <lb></lb>the Figure would alter the Solid Bodies, in relation to the deſcending <lb></lb>or not deſcending, aſcending or not aſcending in the ſame<emph.end type="italics"></emph.end> Medium, <emph type="italics"></emph>as<emph.end type="italics"></emph.end> <lb></lb>v. </s><s>gr. <emph type="italics"></emph>in the ſame water, in ſuch ſort, that, for Example, a Solid that <lb></lb>being of a Sphericall Figure, ſhall deſcend to the Bottom, being reduced <lb></lb>into ſome other Figure, ſhall not deſcend: I holding the contrary, do <lb></lb>affirm, that a Corporeall Solid Body, which reduced into a Sphericall Fi <lb></lb>gure, or any other, ſhall go to the Bottom, ſhall do the like under whatſoever <lb></lb>other Figure, &c.<emph.end type="italics"></emph.end></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></lb><emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> own Definition of place, to be placed, importeth to be in <lb></lb>vironed by the Superficies of the Ambient Body, therefore, then <lb></lb>ſhall the two Figures be in the water, when the Superficies of the <lb></lb>water, ſhall imbrace and inviron them: but when the Adverſaries <lb></lb>ſhew the Board of Ebony not deſcending to the Bottom, they put it <lb></lb>not into the water, but upon the water, where being by a certain im <lb></lb>pediment (as by and by we will ſhew) retained, it is invironed, part <lb></lb>by water, and part by air, which thing is contrary to our agreement, <lb></lb>that was, that the Bodies ſhould be in the water, and not part in <lb></lb>water, and part in air.</s></p> <pb xlink:href="040/01/1126.jpg" pagenum="433"></pb><p type="margin"> <s><margin.target id="marg1468"></margin.target>Place defined <lb></lb>according to <lb></lb><emph type="italics"></emph>Ariſtotle.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>The which is again made manifest, by the queſtions being put as well <lb></lb>about the things which go to the Bottom, as thoſe which ariſe from the <lb></lb>Bottom to ſwimme, and who ſees not that things placed in the Bottom, <lb></lb>muſt have water about them.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>It is now to be noted, that the Board of Ebany and the Ball, put <lb></lb><arrow.to.target n="marg1469"></arrow.to.target> <lb></lb><emph type="italics"></emph>into<emph.end type="italics"></emph.end> the water, both ſink, but the Ball more ſwiftly, and the Board <lb></lb>more ſlowly; and ſlower and ſlower, according as it ſhall be more <lb></lb>broad and thin, and of this Tardity the breadth of the Figure is the <lb></lb>true Cauſe: But theſe broad Boards that ſlowly deſcend, are the <lb></lb>ſame, that being put lightly upon the water, do ſwimm: Therefore, <lb></lb>if that were true which the Adverſaries affirm, the ſame numerical <lb></lb>Figure, would in the ſame numericall water, cauſe one while Reſt, and <lb></lb>another while Tardity of Motion, which is impoſſible: for every per <lb></lb><arrow.to.target n="marg1470"></arrow.to.target> <lb></lb>ticular Figure which deſcends to the Bottom, hath of neceſſity its own <lb></lb>determinate Tardity and ſlowneſs, proper and naturall unto it, accor <lb></lb>ding to which it moveth, ſo that every other Tardity, greater or leſſer <lb></lb>is improper to its nature: if, therefore, a Board, as ſuppoſe of a foot <lb></lb>ſquare, deſcendeth naturally with ſix degrees of Tardity, it is impoſſi <lb></lb>ble, that it ſhould deſcend with ten or twenty, unleſs ſome new impe <lb></lb>diment do arreſt it. </s><s>Much leſs can it, by reaſon of the ſame Figure <lb></lb>reſt, and wholly ceaſe to move; but it is neceſſary, that when ever it <lb></lb>reſteth, there do ſome greater impediment intervene than the breadth <lb></lb>of the Figure. </s><s>Therefore, it muſt be ſomewhat elſe, and not the Fi <lb></lb>gure, that ſtayeth the Board of Ebany above water, of which Eigure <lb></lb>the only Effect is the retardment of the Motion, according to which <lb></lb>it deſcendeth more ſlowly than the Ball. </s><s>Let it be confeſſed, there <lb></lb>fore, rationally diſcourſing, that the true and ſole Cauſe of the Ebanys <lb></lb>going to the Bottom, is the exceſs of its Gravity above the Gravity of <lb></lb>the water: and the Cauſe of the greater or leſs Tardity, the breadth <lb></lb>of this Figure, or the contractedneſs of that: but of its Reſt, it can <lb></lb>by no means be allowed, that the quallity of the Figure, is the Cauſe <lb></lb>thereof: aſwell, becauſe, making the Tardity greater, according as <lb></lb>the Figure more dilateth, there cannot be ſo immenſe a Dilatation, to <lb></lb>which there may not be found a correſpondent immence Tardity. <lb></lb></s><s>without reduſing it to Nullity of Motion; as, becauſe the Figures <lb></lb>produced by the Antagoniſts for effecters of Reſt, are the ſelf ſame <lb></lb>that do alſo go to the Bottom. <lb></lb><arrow.to.target n="marg1471"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1469"></margin.target>The conſutati <lb></lb>on of the Expe <lb></lb>riment in the <lb></lb>Ebany.</s></p><p type="margin"> <s><margin.target id="marg1470"></margin.target>Every perticular <lb></lb>Figure hath its <lb></lb>own peculiat <lb></lb>Tardity.</s></p><p type="margin"> <s><margin.target id="marg1471"></margin.target>* The Figure & <lb></lb>Reſiſtance of <lb></lb>the Medium a <lb></lb>gainſt Diviſion, <lb></lb>have nothing to <lb></lb>do with the Ef <lb></lb>fect of Natation <lb></lb>or Submerſion, <lb></lb>by an Experi <lb></lb>ment in Wall <lb></lb>nut tree,</s></p><p type="main"> <s>I will not omit another reaſon, founded alſo upon Experience, and <lb></lb>if I deceive not my ſelf, manifeſtly concluding, how that the Intro <lb></lb>ducton of the breadth or amplitude of Figure, and the Reſiſtance of <lb></lb>the water againſt penetration, have nothing to do in the Effect of de <lb></lb>ſcending, or aſcending, or reſting in the water. ^{*}Take a piece of wood <lb></lb>or other Matter, of which a Ball aſcends from the Bottom of the water <pb xlink:href="040/01/1127.jpg" pagenum="434"></pb>to the Surface, more ſlowly than a Ball of Ebony of the ſame bigneſſe, <lb></lb>ſo that it is manifeſt, that the Ball of Ebony more readily divideth the <lb></lb>water in deſcending, than the other in aſcending; as for Example, let <lb></lb>the Wood be Walnut-tree. </s><s>Then take a Board of Walnut-tree, like <lb></lb>and equall to that of Ebony of the Antagoniſts, which ſwims; and if <lb></lb>it be true, that this floats above water, by reaſon of the Figure, unable <lb></lb>through its breadth, to pierce the Craſſitude of the ſame, the other of <lb></lb>Wallnut-tree, without all queſtion, being thruſt unto the Bottom, will <lb></lb>ſtay there, as leſs apt, through the ſame impediment of Figure, to di <lb></lb>vide the ſaid Reſiſtance of the water. </s><s>But if we ſhall find, and by <lb></lb>experience ſee, that not only the thin Board, but every other Figure <lb></lb>of the ſame Wallnut-tree will return to float, as undoubtedly we ſhall, <lb></lb>then I muſt deſier my oppoſers to forbear to attribute the floating of <lb></lb>the Ebony, unto the Figure of the Board, in regard that the Reſiſtance <lb></lb>of the water is the ſame, as well to the aſcent, as to the deſcent, and the <lb></lb>force of the Wallnut-trees aſcenſion, is leſſe than the Ebonys force in <lb></lb>going to the Bottom.</s></p><p type="main"> <s>Nay, I will ſay more, that if we ſhall conſider Gold in compariſon <lb></lb><arrow.to.target n="marg1472"></arrow.to.target> <lb></lb>of water, we ſhall find, that it exceeds it in Gravity almoſt twenty times, <lb></lb>ſo that the Force and Impetus, wherewith a Ball of Gold goes to the <lb></lb>Bottom, is very great. </s><s>On the contrary, there want not matters, as <lb></lb>Virgins Wax, and ſome Woods, which are not above a fiftieth part leſs <lb></lb>grave than water, whereupon their Aſcenſion therein is very ſlow, and <lb></lb>a thouſand times weaker than the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the Golds deſcent: yet <lb></lb>notwithſtanding, a plate of Gold ſwims without deſcending to the <lb></lb>Bottom, and, on the contrary, we cannot make a Cake of Wax, or thin <lb></lb>Board of Wood, which put in the Bottom of the Water, ſhall reſt there <lb></lb>without aſcending. </s><s>Now if the Figure can obſtruct the Penetration, <lb></lb>and impede the deſcent of Gold, that hath ſo great an <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> how <lb></lb>can it chooſe but ſuffice to reſiſt the ſame Penetration of the other mat <lb></lb>ter in aſcending, when as it hath ſcarce a thouſandth part of the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> <lb></lb>that the Gold hath in deſcending? </s><s>Its therefore, neceſſary, that that <lb></lb>which ſuſpends the thin Plate of Gold, or Board of Ebony, upon the <lb></lb>water, be ſome thing that is wanting to the other Cakes and Boards of <lb></lb>Matters leſs grave than the water; ſince that being put to the Bottom, <lb></lb>and left at liberty, they riſe up to the Surface, without any obſtruction: <lb></lb>But they want not for flatneſs and breadth of Figure: Therefore, the <lb></lb>ſpaciouſneſſe of the Figure, is not that which makes the Gold and Ebony <lb></lb>to ſwim.</s></p><p type="margin"> <s><margin.target id="marg1472"></margin.target>An Experi <lb></lb>ment in Gold, to <lb></lb>prove the non <lb></lb>operating of Fi <lb></lb>gure in Natation <lb></lb>and Submerſion.</s></p><p type="main"> <s>And, becauſe, that the exceſs of their Gravity above the Gravity of <lb></lb>the water, is queſtionleſs the Cauſe of the ſinking of the flat piece of <lb></lb>Ebony, and the thin Plate of Gold, when they go to the Bottom, there <lb></lb>fore, of neceſſity, when they float, the Cauſe of their ſtaying above <lb></lb>water, proceeds from Levity, which in that caſe, by ſome Accident, <pb xlink:href="040/01/1128.jpg" pagenum="435"></pb>peradventure not hitherto obſerved, cometh to meet with the ſaid <lb></lb>Board, rendering it no longer as it was before, whilſt it did fink more <lb></lb>ponderous than the water, but leſs.</s></p><p type="main"> <s>Now, let us return to take the thin Plate of Gold, or of Silver, or the <lb></lb>thin Board of Ebony, and let us lay it lightly upon the water, ſo that it <lb></lb>ſtay there without ſinking, and diligently obſerve its effect. </s><s>And <lb></lb>firſt, ſee how falſe the aſſertion of <emph type="italics"></emph>Aristotle,<emph.end type="italics"></emph.end> and our oponents is, to wit, <lb></lb>that it ſtayeth above water, through its unability to pierce and pene <lb></lb>trate the Reſiſtance of the waters Craſſitude: for it will manifeſtly <lb></lb>appear, not only that the ſaid Plates have penetrated the water, but <lb></lb>alſo that they are a conſiderable matter lower than the Surface of the <lb></lb>ſame, the which continueth eminent, and maketh as it were a Rampert <lb></lb>on all ſides, round about the ſaid Plates, the profundity of which they <lb></lb>ſtay ſwimming: and, according as the ſaid Plates ſhall be more grave <lb></lb>than the water, two, four, ten or twenty times, it is neceſſary, that <lb></lb>their Superficies do ſtay below the univerſall Surface of the water, ſo <lb></lb>much more, than the thickneſs of thoſe Plates, as we ſhal more diſtinctly <lb></lb>ſhew anon. </s><s>In the mean ſpace, for the more eaſie underſtanding of what <lb></lb>I ſay, obſerve with me a little the preſent <lb></lb><figure id="id.040.01.1128.1.jpg" xlink:href="040/01/1128/1.jpg"></figure> <lb></lb>Scheme: in which let us ſuppoſe the Surface <lb></lb>of the water to be diſtended, according to the <lb></lb>Lines F L D B, upon which if one ſhall put a <lb></lb>board of matter ſpecifically more grave than <lb></lb>water, but ſo lightly that it ſubmetge not, it <lb></lb>ſhall not reſt any thing above, but ſhall enter with its whole thickneſs <lb></lb>into the water: and, moreover, ſhall ſink alſo, as we ſee by the Board <lb></lb>A I, O I, whoſe breadth is wholly ſunk into the water, the little Ram <lb></lb>perts of water L A and D O incompaſſing it, whoſe Superficies is no <lb></lb>tably higher than the Superficies of the Board. </s><s>See now whether it be <lb></lb>true, that the ſaid Board goes not to the Bottom, as being of Figure <lb></lb>unapt to penetrate the Craſſitude of the water.</s></p><p type="main"> <s>But, if it hath already penetrated, and overcome the Continuity of <lb></lb><arrow.to.target n="marg1473"></arrow.to.target> <lb></lb>the water, & is of its own nature more grave than the ſaid water, why <lb></lb>doth it not proceed in its ſinking, but ſtop and ſuſpend its ſelf within <lb></lb>that little dimple or cavitie, which with its ponderoſity it hath made in <lb></lb>the water? </s><s>I anſwer; becauſe that in ſubmerging it ſelf, ſo far as till its <lb></lb>Superficies come to the Levell with that of the water, it loſeth a part <lb></lb>of its Gravity, and loſeth the reſt of it as it ſubmergeth & deſcends be <lb></lb>neath the Surface of the water, which maketh Ramperts and Banks <lb></lb>round about it, and it ſuſtaines this loſs by means of its drawing after it, <lb></lb>and carrying along with it, the Air that is above it, and by Contact ad <lb></lb>herent to it, which Air ſucceeds to fill the Cavity that is invironed by <lb></lb>the Ramperts of water: ſo that that which in this caſe deſcends and is <lb></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"></pb>but a compoſition of Ebony and Air, from which reſulteth a Solid <lb></lb>no longer ſuperiour in Gravity to the water, as was the ſimple Ebony, <lb></lb>or the ſimple Gold. </s><s>And, if we exactly conſider, what, and how <lb></lb>great the Solid is, that in this Experiment enters into the water, and <lb></lb>contraſts with the Gravity of the ſame, it will be found to be all that <lb></lb>which we find to be beneath the Surface of the water, the which is <lb></lb>an aggregate and Compound of a Board of Ebony, and of almoſt <lb></lb>the like quantity of Air, or a Maſs compounded of a Plate of Lead, <lb></lb>and ten or twelve times as much Air. </s><s>But, Genrlemen, you that <lb></lb>are my Antagoniſts in our Queſtion, we require the Identity of <lb></lb>Matter, and the alteration only of the Figure; therefore, you muſt <lb></lb>remove that Air, which being conjoyned with the Board, makes it <lb></lb>become another Body leſs grave than the Water, and put only the <lb></lb>Ebony into the Water, and you ſhall certainly ſee the Board deſcend <lb></lb>to the Bottom; and, if that do not happen, you have got the day. <lb></lb><arrow.to.target n="marg1474"></arrow.to.target> <lb></lb>And to ſeperate the Air from the Ebony, there needs no more but <lb></lb>only to bath the Superficies of the ſaid Board with the ſame Water: <lb></lb>for the Water being thus interpoſed between the Board and the Air, <lb></lb>the other circumfuſed Water ſhall run together without any impedi <lb></lb>ment, and ſhall receive into it the ſole and bare Ebony, as it was to do.</s></p><p type="margin"> <s><margin.target id="marg1473"></margin.target>Why ſolids <lb></lb>having penitra <lb></lb>ted the Water, <lb></lb>do not proceed <lb></lb>to a totail Sub <lb></lb>merſion.</s></p><p type="margin"> <s><margin.target id="marg1474"></margin.target>How to ſepe <lb></lb>rate the Air from <lb></lb>Solids in demit <lb></lb>ting them into <lb></lb>the water.</s></p><p type="main"> <s>But, me thinks I hear ſome of the Adverſaries cunningly oppoſing <lb></lb>this, and telling me, that they will not yield, by any means, that <lb></lb>their Board be wetted, becauſe the weight added thereto by the <lb></lb>Water, by making it heavier than it was before, draws it to the <lb></lb>Bottom, and that the addition of new weight is contrary to our a <lb></lb>greement, which was, that the Matter be the ſame.</s></p><p type="main"> <s>To this, I anſwer, firſt; that treating of the operation of Figure <lb></lb>in Bodies put into the Water, none can ſuppoſe them to be put into <lb></lb>the Water without being wet; nor do I deſire more to be done to <lb></lb>the Board, then I will give you leave to do to the Ball. </s><s>Moreover, <lb></lb>it is untrue, that the Board ſinks by vertue of the new Weight added <lb></lb>to it by the Water, in the ſingle and ſlight bathing of it: for I will <lb></lb>put ten or twenty drops of Water upon the ſame Board, whilſt it is <lb></lb>ſuſtained upon the water, which drops, becauſe not conjoyned with <lb></lb>the other Water circumfuſed, ſhall not ſo encreaſe the weight of it, as <lb></lb>to make it ſink: but if the Board being taken out, and all the water <lb></lb>wiped off that was added thereto, I ſhould bath all its Superficies <lb></lb>with one only very ſmall drop, and put it again upon the water, with <lb></lb>out doubt it ſhall ſink, the other Water running to cover it, not be <lb></lb>ing retained by the ſuperiour Air; which Air by the interpoſition of <lb></lb>the thin vail of water, that takes away its Contiguity unto the Ebony, <lb></lb>ſhall without Renitence be ſeperated, nor doth it in the leaſt oppoſe <lb></lb>the ſucceſſion of the other Water: but rather, to ſpeak better, it <lb></lb>ſhall deſcend freely; becauſe it ſhall be all invironed and covered <pb xlink:href="040/01/1130.jpg" pagenum="437"></pb>with water, as ſoon as its ſuperiour Superficies, before vailed with <lb></lb>water, doth arrive to the Levell of the univerſall Surface of the ſaid <lb></lb>water. </s><s>To ſay, in the next place, that water can encreaſe the weight <lb></lb><arrow.to.target n="marg1475"></arrow.to.target> <lb></lb>of things that are demitted into it, is moſt falſe, for water hath no <lb></lb>Gravity in water, ſince it deſcends not: yea, if we would well conſi <lb></lb>der what any immenſe Maſs of water doth put upon a grave Body; <lb></lb><arrow.to.target n="marg1476"></arrow.to.target> <lb></lb>that is placed in it, we ſhall find experimentally, that it, on the con <lb></lb>trary, will rather in a great part deminiſh the weight of it, and that <lb></lb>we may be able to lift an huge Stone from the Bottom of the water, <lb></lb>which the water being removed, we are not able to ſtir. </s><s>Nor let <lb></lb>them tell me by way of reply, that although the ſuperpoſed water <lb></lb>augment not the Gravity of things that are in it, yet it increaſeth the <lb></lb>ponderoſity of thoſe that ſwim, and are part in the water and part <lb></lb><arrow.to.target n="marg1477"></arrow.to.target> <lb></lb>in the Air, as is ſeen, for Example, in a Braſs Ketle, which whilſt it <lb></lb>is empty of water, and repleniſhed only with Air ſhall ſwim, but <lb></lb>pouring of Water therein, it ſhall become ſo grave, that it ſhall ſink <lb></lb>to the Bottom, and that by reaſon of the new weight added thereto. <lb></lb></s><s>To this I will return anſwer, as above, that the Gravity of the <lb></lb>Water, contained in the Veſſel is not that which ſinks it to the Bot <lb></lb>tom, but the proper Gravity of the Braſs, ſuperiour to the Specificall <lb></lb><arrow.to.target n="marg1478"></arrow.to.target> <lb></lb>Gravity of the Water: for if the Veſſel were leſs grave than <lb></lb>water, the Ocean would not ſuffice to ſubmerge it. </s><s>And, give me <lb></lb>leave to repeat it again, as the fundamentall and principall point in <lb></lb>this Caſe, that the Air contained in this Veſſel before the infuſion of <lb></lb>the Water, was that which kept it a-float, ſince that there was made <lb></lb><arrow.to.target n="marg1479"></arrow.to.target> <lb></lb>of it, and of the Braſs, a Compoſition leſs grave than an equall quanti <lb></lb>ty of Water: and the place that the Veſſel occupyeth in the <lb></lb>Water whilſt it floats, is not equall to the Braſs alone, but to the <lb></lb>Braſs and to the Air together, which filleth that part of the Veſſel <lb></lb>that is below the Levell of the water: Moreover, when the Water <lb></lb>is infuſed, the Air is removed, and there is a compoſition made of <lb></lb>Braſs and of water, more grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than the ſimple water, but <lb></lb>not by vertue of the water infuſed, as having greater Specifick <lb></lb>Gravity than the other water, but through the proper Gravity of <lb></lb>the Braſs, and through the alienation of the Air. </s><s>Now, as he that <lb></lb>ſhould ſay that Braſs, that by its nature goes to the Bottom, being <lb></lb><arrow.to.target n="marg1480"></arrow.to.target> <lb></lb>formed into the Figure of a Ketle, acquireth from that Figure a <lb></lb>vertue of lying in the Water without ſinking, would ſay that which <lb></lb>is falſe; becauſe that Braſs faſhioned into any whatever Figure, <lb></lb>goeth always to the Bottom, provided, that that which is put into the <lb></lb>water be ſimple Braſs; and it is not the Figure of the Veſſel that <lb></lb>makes the Braſs to float, but it is becauſe that that is not purely <lb></lb>Braſs which is put into the water, but an aggregate of Braſs and of <lb></lb>Air: ſo is it neither more nor leſs falſe, that a thin Plate of Braſs <pb xlink:href="040/01/1131.jpg" pagenum="438"></pb>or of Ebony, ſwims by vertue of its dilated & broad Figure: for the <lb></lb>truth is, that it bares up without ſubmerging, becauſe that that which <lb></lb>is put in the water, is not pure Braſs or ſimple Ebony, but an ag <lb></lb>gregate of Braſs and Air, or of Ebony and Air. </s><s>And, this is not <lb></lb>contrary unto my Concluſion, the which, (having many a time ſeen <lb></lb>Veſſels of Mettall, and thin pieces of diverſe grave Matters float, by <lb></lb>vertue of the Air conjoyned with them) did affirm, That Figure <lb></lb>was not the Cauſe of the Natation or Submerſion of ſuch Solids as <lb></lb>were placed in the water. </s><s>Nay more, I cannot omit, but muſt tell <lb></lb>my Antagoniſts, that this new conceit of denying that the Superfi <lb></lb>cies of the Board ſhould be bathed, may beget in a third perſon an <lb></lb>opinion of a poverty of Arguments of defence on their part, ſince <lb></lb>that ſuch bathing was never inſiſted upon by them in the beginning <lb></lb>of our Diſpute, and was not queſtioned in the leaſt, being that the <lb></lb>Originall of the diſcourſe aroſe upon the ſwiming of Flakes of Ice, <lb></lb>wherein it would be ſimplicity to require that their Superficies might <lb></lb>bedry: beſides, that whether theſe pieces of Ice be wet or dry they <lb></lb>alwayes ſwim, and as the Adverſaries ſay, by reaſon of the Figure. </s></p><p type="margin"> <s><margin.target id="marg1475"></margin.target>Water hath <lb></lb>no Gravity in <lb></lb>Water.</s></p><p type="margin"> <s><margin.target id="marg1476"></margin.target>Water de <lb></lb>miniſheth the <lb></lb>Gravity of So <lb></lb>lids immerged <lb></lb>therein.</s></p><p type="margin"> <s><margin.target id="marg1477"></margin.target>The Experi <lb></lb>ment of a Braſs <lb></lb>Ketle ſwiming <lb></lb>when empty, & <lb></lb>ſinking when <lb></lb>full, alledged to <lb></lb>prove that water <lb></lb>gravitates in <lb></lb>water, anſwered.</s></p><p type="margin"> <s><margin.target id="marg1478"></margin.target>An Ocean ſuf <lb></lb>ficeth not to <lb></lb>ſink a Veſſel ſpe <lb></lb>cifically leſs <lb></lb>grave than wa <lb></lb>ter.</s></p><p type="margin"> <s><margin.target id="marg1479"></margin.target>Air, the Cauſe <lb></lb>of the Natation <lb></lb>of empty Veſſels <lb></lb>of Matters gra <lb></lb>ver <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than <lb></lb>the water.</s></p><p type="margin"> <s><margin.target id="marg1480"></margin.target>Neither Figure, <lb></lb>nor the breadth <lb></lb>of Figure, is the <lb></lb>Cauſe of Nata <lb></lb>tion.</s></p><p type="main"> <s>Some peradventure, by way of defence, may ſay, that wetting the <lb></lb>Board of Ebony, and that in the ſuperiour Superficies, it would, <lb></lb>though of it ſelf unable to pierce and penetrate the water, be born <lb></lb>downwards, if not by the weight of the additionall water, at leaſt <lb></lb>by that deſire and propenſion that the ſuperiour parts of the water <lb></lb>have to re-unite and rejoyn themſelves: by the Motion of which <lb></lb>parts, the ſaid Board cometh in a certain manner, to be depreſſed <lb></lb>downwards. <lb></lb><arrow.to.target n="marg1481"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1481"></margin.target>The Bathed <lb></lb>Solid deſcends <lb></lb>not out of any <lb></lb>affectation of u <lb></lb>nion in the upper <lb></lb>parts of the wa <lb></lb>ter.</s></p><p type="main"> <s>This weak Refuge will be removed, if we do but conſider, that <lb></lb>the repugnancy of the inferiour parts of the water, is as great against <lb></lb>Diſ-union, as the Inclination of its ſuperiour parts is to union: nor can <lb></lb>the uper unite themſelves without depreſſing the board, nor can it <lb></lb>deſcend without diſuniting the parts of the nether Water: ſo that <lb></lb>it doth follow, by neceſſary conſequence, that for thoſe reſpects, it ſhall <lb></lb>not deſcend. </s><s>Moreover, the ſame that may be ſaid of the upper <lb></lb>parts of the water, may with equall reaſon be ſaid of the nethe, <lb></lb>namely, that deſiring to unite, they ſhall force the ſaid Board <lb></lb>upwards.</s></p><p type="main"> <s>Happily, ſome of theſe Gentlemen that diſſent from me, will won <lb></lb>der, that I affirm, that the contiguous ſuperiour Air is able to ſuſtain <lb></lb>that Plate of <emph type="italics"></emph>B<emph.end type="italics"></emph.end>raſs or of Silver, that ſtayeth above water; as if I <lb></lb><arrow.to.target n="marg1482"></arrow.to.target> <lb></lb>would in a certain ſence allow the Air, a kind of Magnetick vertue <lb></lb>of ſuſtaining the grave <emph type="italics"></emph>B<emph.end type="italics"></emph.end>odies, with which it is contiguous. </s><s>To ſa <lb></lb>tisſie all I may, to all doubts, I have been conſidering how by ſome <lb></lb>other ſenſible Experiment I might demonſtrate, how truly that little <lb></lb>contiguous and ſuperiour Air ſuſtaines thoſe Solids, which being by <pb xlink:href="040/01/1132.jpg" pagenum="439"></pb>nature apt to deſcend to the Bottom, being placed lightly on the water <lb></lb>ſubmerge not, unleſs they be firſt thorowly bathed; and have found, <lb></lb>that one of theſe Bodies having deſcended to the Bottom, by conveigh <lb></lb>ing to it (without touching it in the leaſt) a little Air, which conjoyneth <lb></lb>with the top of the ſame; it becometh ſufficient, not only, as before to <lb></lb>ſuſtain it, but alſo to raiſe it, and to carry it back to the top, where it <lb></lb>ſtays and abideth in the ſame manner, till ſuch time, as the aſſiſtance <lb></lb>of the conjoyned Air is taken away. </s><s>And to this effect, I have taken a <lb></lb>Ball of Wax, and made it with a little Lead, ſo grave, that it leaſurely <lb></lb>deſcends to the Bottom, making with all its Superficies very ſmooth and <lb></lb>pollite: and this being put gently into the water, almoſt wholly ſub <lb></lb><arrow.to.target n="marg1483"></arrow.to.target> <lb></lb>mergeth, there remaining viſſible only a little of the very top, the which <lb></lb>solong as it is conjoyned with the Air, ſhall retain the Ball a-top, but <lb></lb>the Contiguity of the Air taken away by wetting it, it ſhall deſcend to <lb></lb>the Bottom and there remain. </s><s>Now to make it by vertue of the Air, that <lb></lb>before ſuſtained it to return again to the top, and ſtay there, thruſt into <lb></lb>the water a Glaſs reverſed with the mouth downwards, the which ſhall <lb></lb>carry with it the Air it contains, and move this towards the Ball, abaſing <lb></lb>it till ſuch time that you ſee, by the tranſparency of the Glaſs, that the <lb></lb><arrow.to.target n="marg1484"></arrow.to.target> <lb></lb>contained Air do arrive to the ſummity of the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>all: then gently with <lb></lb>draw the Glaſs upwards, and you ſhall ſee the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>all to riſe, and afterwards <lb></lb><arrow.to.target n="marg1485"></arrow.to.target> <lb></lb>stay on the top of the water, if you carefully part the Glaſs and the water <lb></lb>without overmuch commoving and diſturbing it. </s><s>There is, therefore, a <lb></lb>certain affinity between the Air and other <emph type="italics"></emph>B<emph.end type="italics"></emph.end>odies, which holds them uni <lb></lb>ed, ſo, that they ſeperate not without a kind of violence. </s><s>The ſame <lb></lb><arrow.to.target n="marg1486"></arrow.to.target> <lb></lb>likewiſe is ſeen in the water; for if we ſhall wholly ſubmerge ſome <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ody <lb></lb>in it, ſo that it be thorowly bathed, in the drawing of it afterwards gent <lb></lb>ly out again, we ſhall ſee the water follow it, and riſe notably above its <lb></lb>Surface, before it ſeperates from it. </s><s>Solid <emph type="italics"></emph>B<emph.end type="italics"></emph.end>odies, alſo, if they be equall <lb></lb><arrow.to.target n="marg1487"></arrow.to.target> <lb></lb>and alike in Superficies, ſo, that they make an exact Contact without <lb></lb>the interpoſition of the leaſt Air, that may part them in the ſeperation <lb></lb>and yield untill that the ambient <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> ſucceeds to repleniſh the place, <lb></lb>do hold very firmly conjoyned, and are not to be ſeperated without great <lb></lb>force but, becauſe, the Air, Water, and other Liquids, very expedi <lb></lb>tiouſly ſhape themſelves to contact with any Solid <emph type="italics"></emph>B<emph.end type="italics"></emph.end>odies, ſo that their <lb></lb>Superficies do exquiſitely adopt themſelves to that of the Solids, without <lb></lb>any thing remaining between them, therefore, the effect of this Con <lb></lb>junction and Adherence is more manifeſtly and frequently obſerved in <lb></lb>them, than in hard and inflexible <emph type="italics"></emph>B<emph.end type="italics"></emph.end>odies, whoſe Superficies do very rate <lb></lb>ly conjoyn with exactneſs of Contact. </s><s>This is therefore that Magne <lb></lb><arrow.to.target n="marg1488"></arrow.to.target> <lb></lb>tick vertue, which with firm Connection conjoyneth all Bodies, that do <lb></lb>touch without the interpoſition of flexible fluids; and, who knows, but <lb></lb>that that a Contact, when it is very exact, may be a ſufficient Cauſe of <lb></lb>the Union and Continuity of the parts of a naturall <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ody?</s></p> <pb xlink:href="040/01/1133.jpg" pagenum="440"></pb><p type="margin"> <s><margin.target id="marg1482"></margin.target><emph type="italics"></emph>A<emph.end type="italics"></emph.end> Magnetiſme in <lb></lb>the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ir, by which <lb></lb>it bears up thoſe <lb></lb>Solids in the wa <lb></lb>ter, that are con <lb></lb>tiguous with it.</s></p><p type="margin"> <s><margin.target id="marg1483"></margin.target>The Effect of <lb></lb>the Airs Conti <lb></lb>guity in the Na <lb></lb>tation of Solids.</s></p><p type="margin"> <s><margin.target id="marg1484"></margin.target>The force of <lb></lb>Contact.</s></p><p type="margin"> <s><margin.target id="marg1485"></margin.target><emph type="italics"></emph>A<emph.end type="italics"></emph.end>n affectati <lb></lb>on of Conjunct <lb></lb>ion betwixt So <lb></lb>lids and the Air <lb></lb>contiguous to <lb></lb>them.</s></p><p type="margin"> <s><margin.target id="marg1486"></margin.target>The like affect <lb></lb>ation of Con <lb></lb>junction be <lb></lb>twixt Solids & <lb></lb>the water.</s></p><p type="margin"> <s><margin.target id="marg1487"></margin.target>Alſo the like <lb></lb>affectation and <lb></lb>Conjunction be <lb></lb>twixt Solids <lb></lb>themſeives.</s></p><p type="margin"> <s><margin.target id="marg1488"></margin.target>Contact may <lb></lb>be the Cauſe of <lb></lb>the Continuity <lb></lb>of Naturall Bo <lb></lb>dies.</s></p><p type="main"> <s>Now, purſuing my purpoſe, I ſay; that it needs not, that we have <lb></lb>recourſe to the Tenacity, that the parts of the water have amongſt them <lb></lb>ſelves, by which they reſiſt and oppoſe Diviſion, Diſtraction, and Seper <lb></lb>ration, becauſe there is no ſuch Coherence and Reſiſtance of Diviſion <lb></lb>for if there were, it would be no leſs in the internall parts than in thoſe <lb></lb>nearer the ſuperiour or externall Surface, ſo that the ſame Board, find <lb></lb>ing alwayes the ſame Reſiſtance and Renitence, would no leſs ſtop in <lb></lb>the middle of the water than about the Surface, which is falſe. More <lb></lb></s><s>over, what Reſiſtance can we place in the Continuity of the water <lb></lb>if we ſee that it is impoſſible to ſind any Body of whatſoever Matter <lb></lb>Figure or Magnitude, which being put into the water, ſhall be obſtructed <lb></lb>and impeded by the Tenacity of the parts of the water to one another <lb></lb>ſo, but that it is moved upwards or downwards, according as the Cauſe <lb></lb>of their Motion tranſports it? </s><s>And, what greater proof of it can we de <lb></lb>ſier, than that which we daily ſee in Muddy waters, which being put into <lb></lb>Veſſels to be drunk, and being, after ſome hours ſetling, ſtill, as we ſay <lb></lb><arrow.to.target n="marg1489"></arrow.to.target> <lb></lb>thick in the end, after four or ſix dayes they are wholly ſetled, and be <lb></lb>come pure and clear? </s><s>Nor can their Reſiſtance of Penetration ſtay thoſe <lb></lb>impalpable and inſenſible Atomes of Sand, which by reaſon of their <lb></lb>exceeding ſmall force, ſpend ſix dayes in deſcending the ſpace of half <lb></lb>a yard.</s></p><p type="margin"> <s><margin.target id="marg1489"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he ſettlement <lb></lb>of <emph type="italics"></emph>M<emph.end type="italics"></emph.end>uddy Wa <lb></lb>ter, proveth that <lb></lb>that Element <lb></lb>hath no averſi <lb></lb>on to Diviſion.</s></p><p type="main"> <s><emph type="italics"></emph>Nor let them ſay, that the ſeeing of ſuch ſmall Bodies, conſume ſix dayes in <lb></lb>deſcending ſo little a way, is a ſufficient Argument of the Waters Reſiſtance <lb></lb>of Diviſion; becauſe that is no reſiſting of Diviſion, but a retarding of<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1490"></arrow.to.target> <lb></lb><emph type="italics"></emph>Motion; and it would be ſimplicity to ſay, that a thing oppoſeth Diviſion <lb></lb>and that in the ſame inſtant, it permits it ſelf to be divided: nor doth the <lb></lb>Retardation of Motion at all favour the Adverſaries cauſe, for that they are <lb></lb>to inſtance in a thing that wholly prohibiteth Motion, and procureth Reſt; <lb></lb>it is neceſſary, therefore, to find out Bodies that ſtay in the water, if one would <lb></lb>ſhew its repugnancy to Diviſion, and not ſuch as move in it, howbeit <lb></lb>ſlowly.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1490"></margin.target>Water cannot <lb></lb>oppoſe diviſion, <lb></lb>and at the ſame <lb></lb>time permit it <lb></lb>ſelf to be divi <lb></lb>ded.</s></p><p type="main"> <s>What then is this Craſſitude of the water, with which it reſiſteth Di <lb></lb>viſion? </s><s>What, I beſeech you, ſhould it be, if we (as we have ſaid above) <lb></lb>with all diligence attempting the reduction of a Matter into ſo like a <lb></lb>Gravity with the water, that forming it into a dilated Plate it reſts ſuſ <lb></lb>pended as we have ſaid, between the two waters, it be impoſſible to <lb></lb>effect it, though we bring them to ſuch an Equiponderance, that as <lb></lb>much Lead as the fourth part of a Grain of Muſterd-ſeed, added to the <lb></lb>ſame expanded Plate, that in Air [<emph type="italics"></emph>i. </s><s>e. </s><s>out of the water<emph.end type="italics"></emph.end>] ſhall weigh four <lb></lb>or fix pounds, ſinketh it to the Bottom, and being ſubſtracted, it aſcends <lb></lb>to the Surface of the water? </s><s>I cannot ſee, (if what I ſay be true, as it is <lb></lb>moſt certain) what minute vertue and force we can poſſibly find or ima <lb></lb>gine, to which the Reſiſtance of the water againſt Diviſion and Penetra <pb xlink:href="040/01/1134.jpg" pagenum="441"></pb>tion is not inferiour; whereupon, we muſt of neceſſity conclude <lb></lb>that it is nothing: becanſe, if it were of any ſenſible power, ſome <lb></lb>large Plate might be found or compounded of a Matter alike in Gra <lb></lb>vity to the water, which not only would ſtay between the two wa <lb></lb>ters; but, moreover, ſhould not be able to deſcend or aſcend with <lb></lb>out notable force. </s><s>We may likewiſe collect the ſame from an o <lb></lb><arrow.to.target n="marg1491"></arrow.to.target> <lb></lb>ther Experiment, ſhewing that the Water gives way alſo in the ſame <lb></lb>manner to tranſverſall Diviſion; for if in a ſetled and ſtanding water <lb></lb>we ſhould place any great Maſs that goeth not to the bottom, draw <lb></lb>ing it with a ſingle (Womans) Hair, we might carry it from place to <lb></lb>place without any oppoſition, and this whatever Figure it hath, <lb></lb>though that it poſſeſs a great ſpace of water, as for inſtance, a great <lb></lb>Beam would do moved ſide-ways. </s><s>Perhaps ſome might oppoſe me <lb></lb>and ſay, that if the Reſiſtance of water againſt Diviſion, as I affirm, <lb></lb>were nothing; Ships ſhould not need ſuch a force of Oars and Sayles <lb></lb>for the moving of them from place to place in a tranquile Sea, or <lb></lb>ſtanding Lake. </s><s>To him that ſhould make ſuch an objection, I would <lb></lb><arrow.to.target n="marg1492"></arrow.to.target> <lb></lb>reply, that the water contraſteth not againſt, nor ſimply reſiſteth <lb></lb>Diviſion, but a ſudden Diviſion, and with ſo much greater Reni <lb></lb>tence, by how much greater the Velocity is: and the Cauſe of this <lb></lb>Reſiſtance depends not on Craſſitude, or any other thing that abſo <lb></lb>lutely oppoſeth Diviſion, but becauſe that the parts of the water <lb></lb>divided, in giving way to that Solid that is moved in it, are them <lb></lb>ſelves alſo neceſſitated locally to move, ſome to the one ſide, and ſome <lb></lb>to the other, and ſome downwards: and this muſt no leſs be done <lb></lb>by the waves before the Ship, or other Body ſwimming through the <lb></lb>water, than by the poſteriour and ſubſequent; becauſe, the Ship <lb></lb>proceeding forwards, to make it ſelf a way to receive its Bulk, it is <lb></lb>requiſite, that with the Prow it repulſe the adjacent parts of the <lb></lb>water, as well on one hand as on the other, and that it move them <lb></lb>as much tranſverſly, as is the half of the breadth of the Hull: and <lb></lb>the like removall muſt thoſe waves make, that ſucceeding the Poump <lb></lb>do run from the remoter parts of the Ship towards thoſe of the <lb></lb>middle, ſucceſſively to repleniſh the places, which the Ship in ad <lb></lb>vancing forwards, goeth, leaving vacant. </s><s>Now, becauſe, all Moti <lb></lb><arrow.to.target n="marg1493"></arrow.to.target> <lb></lb>tions are made in Time, and the longer in greater time: and it being <lb></lb>moreover true, that thoſe Bodies that in a certain time are moved <lb></lb>by a certain power ſuch a certain ſpace, ſhall not be moved the ſame <lb></lb>ſpace, and in a ſhorter Time, unleſs by a greater Power: therefore, <lb></lb>the broader Ships move ſlower than the narrower, being put on by <lb></lb>an equall Force: and the ſame Veſſel requires ſo much greater <lb></lb>force of Wind, or Oars, the faſter it is to move.</s></p> <pb xlink:href="040/01/1135.jpg" pagenum="442"></pb><p type="margin"> <s><margin.target id="marg1491"></margin.target>An hair will <lb></lb>draw a great <lb></lb>Maſs thorow the <lb></lb>Water; which <lb></lb>proveth, that it <lb></lb>hath no Reſiſt <lb></lb>ance againſt <lb></lb>tranſverſall Di <lb></lb>viſion.</s></p><p type="margin"> <s><margin.target id="marg1492"></margin.target>How ſhips are <lb></lb>moved in the <lb></lb>water.</s></p><p type="margin"> <s><margin.target id="marg1493"></margin.target>Bodies moved <lb></lb>a certain ſpace in <lb></lb>a certain Time, <lb></lb>by a certain <lb></lb>power, cannot be <lb></lb>moved the <lb></lb>ſame ſpace, and <lb></lb>in a ſhorter time, <lb></lb>but by a greater <lb></lb>power.</s></p><p type="main"> <s><emph type="italics"></emph>But yet for all this, any great Maſs ſwimming in a ſtanding Lake, may <lb></lb>be moved by any petit force; only it is true, that a leſſer force more <lb></lb>ſlowly moves it: but if the waters Reſiſtance of Diviſion, were in any <lb></lb>manner ſenſible, it would follow, that the ſaid Maſs, ſhould, notwith <lb></lb>ſtanding the percuſſion of ſome ſenſible force, continue immoveable, which is<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1494"></arrow.to.target> <lb></lb><emph type="italics"></emph>not ſo. </s><s>Yea, I will ſay farther, that ſhould we retire our ſelves into the <lb></lb>more internall contemplation of the Nature of water and other Fluids, <lb></lb>perhaps we ſhould diſcover the Conſtitution of their parts to be ſuch, that <lb></lb>they not only do not oppoſe Diviſion, but that they have not any thing in <lb></lb>them to be divided: ſo that the Reſiſtance that is obſerved in moving<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1495"></arrow.to.target> <lb></lb><emph type="italics"></emph>through the water, is like to that which we meet with in paſſing through <lb></lb>a great Throng of People, wherein we find impediment, and not by any <lb></lb>difficulty in the Diviſion, for that none of thoſe perſons are divided <lb></lb>whereof the Croud is compoſed, but only in moving of thoſe perſons ſide <lb></lb>ways which were before divided and disjoyned: and thus we find <lb></lb>Reſiſtance in thruſting a Stick into an heap of Sand, not becauſe any part <lb></lb>of the Sand is to be cut in pieces, but only to be moved and raiſed. two <emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1496"></arrow.to.target> <lb></lb><emph type="italics"></emph>manners of Penetration, therefore, offer themſelves to us, one in Bodies, <lb></lb>whoſe parts were continuall, and here Diviſion ſeemeth neceſſary; the <emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1497"></arrow.to.target> <lb></lb><emph type="italics"></emph>other in the aggregates of parts not continuall, but contiguous only, and <lb></lb>here there is no neceſſity of dividing but of moving only. </s><s>Now, I am <lb></lb>not well reſolved, whether water and other Fluids may be eſteemed to <lb></lb>be of parts continuall or contiguous only; yet I find my ſelf indeed incli<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1498"></arrow.to.target> <lb></lb><emph type="italics"></emph>ned to think that they are rather contiguous (if there be in Naturno <lb></lb>other manner of aggregating, than by the union, or by the touching of the <lb></lb>extreams:) and I am induced thereto by the great difference that I ſee > <lb></lb>between the Conjunction of the parts of an hard or Solid Body, and the<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1499"></arrow.to.target> <lb></lb><emph type="italics"></emph>Conjunction of the ſame parts when the ſame Body ſhall be made Liquid <lb></lb>and Fluid: for if, for example, I take a Maſs of Silver or other Solid <lb></lb>and hard Mettall, I ſhall in dividing it into two parts, find not only the <emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1500"></arrow.to.target> <lb></lb><emph type="italics"></emph>reſiſtance that is found in the moving of it only, but an other incomparably <lb></lb>greater, dependent on that vertue, whatever it be, which holds the parts <lb></lb>united: and ſo if we would divide again thoſe two parts into other two <lb></lb>and ſucceſſively into others and others, we ſhould ſtill find a like Reſiſt <lb></lb>ance, but ever leſs by how much ſmaller the parts to be divided ſhall be; <lb></lb>but if, laſtly, employing moſt ſubtile and acute Inſtruments, ſuch as are <lb></lb>the moſt tenuous parts of the Fire, we ſhall reſolve it (perhaps) into its <lb></lb>laſt and leaſt Particles, there ſhall not be left in them any longer either <lb></lb>Reſiſtance of Diviſion, or ſo much as a capacity of being farther divi <lb></lb>ded, eſpecially by Inſtruments more groſſe than the acuities of Fire: and <lb></lb>what Knife or Raſor put into well melted Silver can we finde, that will <lb></lb>divide a thing which ſurpaſſeth the ſeparating power of Fire? </s><s>Certainly <lb></lb>none: becauſe either the whole ſhall be reduced to the moſt minute and <lb></lb>ultimate Diviſions, or if there remain parts capable ſtill of other Suddi<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1136.jpg" pagenum="443"></pb><emph type="italics"></emph>diviſions, they cannot receive them, but only from acuter Diviſors than <lb></lb>Fire; but a Stick or Rod of Iron, moved in the melted Met all, is not <lb></lb>ſuch a one. </s><s>Of a like Conſtitution and Conſiſtence, I account the parts<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1501"></arrow.to.target> <lb></lb><emph type="italics"></emph>of Water, and other Liquids to be, namely, incapable of Diviſion by <lb></lb>reaſon of their Temtity; or if not abſolutely indiviſible, yet at leaſt <lb></lb>not to be divided by a Board, or other Solid Body, palpable unto the <lb></lb>band, the Sector being alwayes required to be more ſharp than the Solid <lb></lb>to be cut. </s><s>Solid Bodies, therefore, do only move, and not divide the<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1502"></arrow.to.target> <lb></lb><emph type="italics"></emph>Water, when put into it; whoſe parts being before divided to the ex <lb></lb>treameſt minuity, and therefore capable of being moved, either many of <lb></lb>them at once, or few, or very few, they ſoon give place to every ſmall Cor <lb></lb>puſcle, that deſcends in the ſame: for that, it being little and light, de <lb></lb>ſcending in the Air, and arriving to the Surface of the Water, it meets <lb></lb>with Particles of Water more ſmall, and of leſs Reſiſtance againſt <lb></lb>Motion and Extruſion, than is its own prement and extruſive force, <lb></lb>whereupon it ſubmergeth, and moveth ſuch a portion of them, as is pro <lb></lb>portionate to its Power. </s><s>There is not, therefore, any Reſiſtance in <lb></lb>Water againſt Diviſion, nay, there is not in it any diviſible parts. </s><s>I <lb></lb>adde, moreover, that in caſe yet there ſbould be any ſmall Reſiſtance<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1503"></arrow.to.target> <lb></lb><emph type="italics"></emph>found (which is abſolutely falſe) haply in attempting with an Hair to <lb></lb>move a very great natant Machine, or in eſſaying by the addition of one <lb></lb>ſmall Grain of Lead to ſink, or by removall of it to raiſe a very broad <lb></lb>Plate of Matter, equall in Gravity with Water, (which likewiſe will <lb></lb>not happen, in caſe we proceed with dexterity) we may obſerve that that <lb></lb>Reſiſtance is a very different thing from that which the Adverſaries pro <lb></lb>duce for the Cauſe of the Natation of the Plate of Lead or Board of Ebo <lb></lb>ny, for that one may make a Board of Ebony, which being put upon the <lb></lb>Water ſwimmeth, and cannot be ſubmerged, no not by the addition of an <lb></lb>bundred Grains of Lead put upon the ſame, and afterwards being ba <lb></lb>thed, not only ſinks, though the ſaid Lead be taken away, but though <lb></lb>moreover a quantity of Cork, or of ſome other light Body faſtened to it, <lb></lb>ſufficeth not to hinder it from ſinking unto the bottome: ſo that you <lb></lb>ſee, that although it were granted that there is a certain ſmall Reſiſt <lb></lb>ance of Diviſion found in the ſubstance of the Water, yet this hath no <lb></lb>thing to do with that Cauſe which ſupports the Board above the Water, <lb></lb>with a Reſiſtance an hundred times greater than that which men can <lb></lb>find in the parts of the Water: nor let them tell me, that only the Sur-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1504"></arrow.to.target> <lb></lb><emph type="italics"></emph>face of the Water hath ſuch Reſiſtance, and not the internall parts, or <lb></lb>that ſuch Reſiſtance is found greateſt in the beginning of the Submerſion, <lb></lb>as it alſo ſeems that in the beginning, Motion meets with greater oppoſiti <lb></lb>on, than in the continuance of it; becauſe, firſt, I will permit, that the<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1505"></arrow.to.target> <lb></lb><emph type="italics"></emph>Water be ſtirred, and that the ſuperiour parts be mingled with the mid <lb></lb>dle, and inferiour parts, or that thoſe above be wholly removed, and <lb></lb>thoſe in the middle only made uſe off, and yet you ſhall ſee the effect for<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1137.jpg" pagenum="444"></pb><emph type="italics"></emph>all that, to be still the ſame: Moreover, that Hair which draws a <lb></lb>Beam through the Water, is likewiſe to divide the upperparts, and is <lb></lb>alſo to begin the Motion, and yet it begins it, and yet it divides it: and <lb></lb>finally, let the Board of Ebony be put in the midway, betwixt the bottome <lb></lb>and the top of the Water, and let it there for a while be ſuſpended and <lb></lb>ſetled, and afterwards let it be left at liberty, and it will instantly begin <lb></lb>its Motion, and will continue it unto the bottome. </s><s>Nay, more, the Board <lb></lb>ſo ſoon as it is dimitted upon the Water, hath not only begun to move <lb></lb>and divide it, but is for a good ſpace dimerged into it.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1494"></margin.target>The parts of <lb></lb>Liquids, ſo farte <lb></lb>from reſiſting <lb></lb>Diviſion, that <lb></lb>they contain not <lb></lb>any thing that <lb></lb>may be divided.</s></p><p type="margin"> <s><margin.target id="marg1495"></margin.target>The Reſiſt <lb></lb>ance a Solid <lb></lb>findeth in mo <lb></lb>ving through <lb></lb>the water, like <lb></lb>to that we meet <lb></lb>with in paſſing <lb></lb>through a <lb></lb>throng of peo <lb></lb>ple;</s></p><p type="margin"> <s><margin.target id="marg1496"></margin.target>Or in thruſt <lb></lb>ing a Stick into <lb></lb>an heap of Sand.</s></p><p type="margin"> <s><margin.target id="marg1497"></margin.target>Two kinds of <lb></lb>Penetration, one <lb></lb>in Bodies conti <lb></lb>nuall, the other <lb></lb>in Bodies only <lb></lb>contiguous.</s></p><p type="margin"> <s><margin.target id="marg1498"></margin.target>Water conſiſts <lb></lb>not of continu <lb></lb>all, but only <lb></lb>of contiguous <lb></lb>parts.</s></p><p type="margin"> <s><margin.target id="marg1499"></margin.target><emph type="italics"></emph>Set what ſatis <lb></lb>faction he hath <lb></lb>given, as to this <lb></lb>point, in Lib. de <lb></lb>Motu. </s><s>Dial.<emph.end type="italics"></emph.end> 2.</s></p><p type="margin"> <s><margin.target id="marg1500"></margin.target>Great differ <lb></lb>ence betwixt the <lb></lb>Conjunction of <lb></lb>the parts of a Bo <lb></lb>dy when Solid, <lb></lb>and when fluid.</s></p><p type="margin"> <s><margin.target id="marg1501"></margin.target>Water conſiſts <lb></lb>of parts that ad <lb></lb>mit of no fat <lb></lb>ther diviſion.</s></p><p type="margin"> <s><margin.target id="marg1502"></margin.target>Solids dimit <lb></lb>ted into the wa <lb></lb>ter, do onely <lb></lb>move, and not <lb></lb>divide it.</s></p><p type="margin"> <s><margin.target id="marg1503"></margin.target>If there were <lb></lb>any Reſiſtance <lb></lb>of Diviſion in <lb></lb>water, it muſt <lb></lb>needs be ſmall, <lb></lb>in that it is over <lb></lb>come by an <lb></lb>Hair, a Grain of <lb></lb>Lead, or a ſlight <lb></lb>bathing of the <lb></lb>Solid.</s></p><p type="margin"> <s><margin.target id="marg1504"></margin.target>The uper parts <lb></lb>of the Water, do <lb></lb>no more reſiſt <lb></lb>Diviſion, than <lb></lb>the middle or <lb></lb>loweſt parts.</s></p><p type="margin"> <s><margin.target id="marg1505"></margin.target>Waters Re <lb></lb>ſiſtance of divi <lb></lb>ſion, not greater <lb></lb>in the begin <lb></lb>ning of the Sub <lb></lb>merſion.</s></p><p type="main"> <s>Let us receive it, therefore, for a true and undoubted Concluſi <lb></lb>on, That the Water hath not any Renitence againſt ſimple Diviſi <lb></lb>on, and that it is not poſſible to find any Solid Body, be it of what <lb></lb>Figure it will, which being put into the Water, its Motion upwards <lb></lb>or downwards, according as it exceedeth, or ſhall be exceeded by <lb></lb>the Water in Gravity (although ſuch exceſſe and difference be in <lb></lb>ſenſible) ſhall be prohibited, and taken away, by the Craſſitude of <lb></lb>the ſaid Water. </s><s>When, therefore, we ſee the Board of Ebony, or <lb></lb>of other Matter, more grave than the Water, to ſtay in the Con <lb></lb>fines of the Water and Air, without ſubmerging, we muſt have re <lb></lb>courſe to ſome other Originall, for the inveſting the Cauſe of that <lb></lb>Effect, than to the breadth of the Figure, unable to overcome the <lb></lb>Renitence with which the Water oppoſeth Diviſion, ſince there is <lb></lb>no Reſiſtance; and from that which is not in being, we can expect <lb></lb>no Action. </s><s>It remains moſt true, therefore, as we have ſaid before, that <lb></lb>this ſo ſucceds, for that that which in ſuch manner put upon the wa <lb></lb>ter, not the ſame Body with that which is put <emph type="italics"></emph>into<emph.end type="italics"></emph.end> the Water: becauſe <lb></lb>this which is put <emph type="italics"></emph>into<emph.end type="italics"></emph.end> the Water, is the pure Board of Ebony, which <lb></lb>for that it is more grave than the Water, ſinketh, and that which is <lb></lb>put <emph type="italics"></emph>upon<emph.end type="italics"></emph.end> the Water, is a Compoſition of Ebony, and of ſo much <lb></lb>Air, that both together are ſpecifically leſs grave than the Water, <lb></lb>and therefore they do not deſcend.</s></p><p type="main"> <s>I will farther confirm this which I ſay. </s><s>Gentlemen, my Antago <lb></lb>niſts, we are agreed, that the exceſs or defect of the Gravity of the <lb></lb>Solid, unto the Gravity of the Water, is the true and proper Cauſe <lb></lb>of Natation or Submerſion. <lb></lb><arrow.to.target n="marg1506"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1506"></margin.target>Great Caution <lb></lb>to be had in ex <lb></lb>perimenting the <lb></lb>operation of Fi <lb></lb>gure in Natati <lb></lb>on.</s></p><p type="main"> <s>Now, if you will ſhew that beſides the former Cauſe, there is ano <lb></lb>ther which is ſo powerfull, that it can hinder and remove the Sub <lb></lb>merſion of thoſe very Solids, that by their Gravity ſink, and if you <lb></lb>will ſay, that this is the breadth or ampleneſs of Figure, you are ob <lb></lb>lieged, when ever you would ſhew ſuch an Experiment, firſt to make <lb></lb>the circumſtances certain, that that Solid which you put into the <lb></lb>Water, be not leſs grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than it, for if you ſhould not do ſo <lb></lb>any one might with reaſon ſay, that not the Figure, but the Levity <lb></lb>was the cauſe of that Natation. </s><s>But I ſay, that when you ſhall di <pb xlink:href="040/01/1138.jpg" pagenum="445"></pb>mit a Board of Ebony into the Water, you do not put therein a Solid <lb></lb>more grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than the Water, but one lighter, for be ſides the <lb></lb>Ebony, there is in the Water a Maſs of Air, united with the Ebony, <lb></lb>and ſuch, and ſo light, that of both there reſults a Compoſition leſs <lb></lb>grave than the Water: See, therefore, that you remove the Air, and <lb></lb>put the Ebony alone into the Water, for ſo you ſhall immerge a So <lb></lb>lid more grave then the Water, and if this ſhall not go to the Bottom, <lb></lb>you have well Philoſophized, and I ill.</s></p><p type="main"> <s>Now, ſince we have found the true Cauſe of the Natation of thoſe <lb></lb>Bodies, which otherwiſe as being graver than the Water, would de <lb></lb>ſcend to the bottom, I think, that for the perfect and diſtinct know <lb></lb>ledge of this buſineſs, it would be good to proceed in a way of diſ <lb></lb>covering demonſtratively thoſe particular Accidents that do attend <lb></lb>theſe effects, and,</s></p><p type="head"> <s>PROBL. I.</s></p><p type="main"> <s><emph type="italics"></emph>To finde what proportion ſeverall Figures of different<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1507"></arrow.to.target> <lb></lb><emph type="italics"></emph>Matters ought to have, unto the Gravity of the <lb></lb>Water, that ſo they may be able by vertue of the <lb></lb>Contigucus Air to ſtay afloat.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1507"></margin.target>To finde the <lb></lb>proportion Fi <lb></lb>gures ought to <lb></lb>have to the wa <lb></lb>ters Gravity, <lb></lb>that by help of <lb></lb>the contiguous <lb></lb>Air, they may <lb></lb>ſwim.</s></p><p type="main"> <s>Let, therefore, for better illuſtration, D F N E be a Veſſell, <lb></lb>wherein the water is contained, and ſuppoſe a Plate or Board, <lb></lb>whoſe thickneſs is comprehended between the Lines I C and <lb></lb>O S, and let it be of Matter exceeding the water in Gravity, ſo that <lb></lb>being put upon the water, it dimergeth and abaſeth below the Levell <lb></lb>of the ſaid water, leaving the little Banks A I and B C, which are at <lb></lb>the greateſt height they can be, ſo that if the Plate I S ſhould but <lb></lb>deſcend any little ſpace farther, the little Banks or Ramparts would <lb></lb>no longer conſiſt, but expulſing the Air A I C B, they would dif <lb></lb>fuſe themſelves over the Superficies I C, and <lb></lb>would ſubmerge the Plate. </s><s>The height AIBC <lb></lb>is therefore the greateſt profundity that the <lb></lb><figure id="id.040.01.1138.1.jpg" xlink:href="040/01/1138/1.jpg"></figure> <lb></lb>little <emph type="italics"></emph>B<emph.end type="italics"></emph.end>anks of water admit of. </s><s>Now I ſay, <lb></lb>that from this, and from the proportion in Gra <lb></lb>vity, that the Matter of the Plate hath to the <lb></lb>water, we may eaſily ſinde of what thickneſs, at moſt, we may make <lb></lb>the ſaid Plates, to the end, they may be able to bear up above water: <lb></lb>for if the Matter of the Plate or <emph type="italics"></emph>B<emph.end type="italics"></emph.end>oard I S were, for Example, as <lb></lb>heavy again as the water, a <emph type="italics"></emph>B<emph.end type="italics"></emph.end>oard of that Matter ſhall be, at the moſt <lb></lb>of a thickneſs equall to the greateſt height of the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>anks, that is, as <lb></lb>thick as A I is high: which we will thus demonſtrate. </s><s>Lot the So <lb></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"></pb>Priſme, or Cylinder, to wit, that hath its two flat Superficies, ſuperi <lb></lb>our and inferiour, alike and equall, and at Right Angles with the o <lb></lb>ther laterall Superficies, and let its thickneſs I O be equall to the <lb></lb>greateſt Altitude of the Banks of water: I ſay, that if it be put upon <lb></lb>the water, it will not ſubmerge: for the Altitude <lb></lb>A I being equall to the Altitude I O, the Maſs <lb></lb>of the Air A B C I ſhall be equall to the Maſs of <lb></lb><figure id="id.040.01.1139.1.jpg" xlink:href="040/01/1139/1.jpg"></figure> <lb></lb>the Solid C I O S: and the whole Maſs A O S B <lb></lb>double to the Maſs I S; And ſince the Maſs <lb></lb>of the Air A C, neither encreaſeth nor dimi <lb></lb>niſheth the Gravity of the Maſs I S, and the Solid I S was ſuppoſed <lb></lb>double in Gravity to the water; Therefore as much water as the <lb></lb>Maſs ſubmerged A O S B, compounded of the Air A I C B, and of <lb></lb>the Solid I O S C, weighs juſt as much as the ſame ſubmerged Maſs <lb></lb>A O S B: but when ſuch a Maſs of water, as is the ſubmerged part of <lb></lb>the Solid, weighs as much as the ſaid Solid, it deſcends not farther, <lb></lb><arrow.to.target n="marg1508"></arrow.to.target> <lb></lb>but reſteth, as by <emph type="italics"></emph>(a) Archimedes,<emph.end type="italics"></emph.end> and above by us, hath been de> <lb></lb>monſtrated: Therefore, I S ſhall deſcend no farther, but ſhall reſt. <lb></lb>And if the Solid I S ſhall be Seſquialter in Gravity to the water, it <lb></lb>ſhall float, as long as its thickneſs be not above twice as much as the <lb></lb>greateſt Altitude of the Ramparts of water, that is, of A I. </s><s>For I S <lb></lb>being Seſquialter in Gravity to the water, and the Altitude O I <lb></lb>being double to I A, the Solid ſubmerged A O S B, ſhall be alſo <lb></lb>Seſquialter in Maſs to the Solid I S. </s><s>And becauſe the Air A C, <lb></lb>neither increaſeth nor diminiſheth the ponderoſity of the Solid I S: <lb></lb>Therefore, as much water in quantity as the ſubmerged Maſs AOSB, <lb></lb>weighs as much as the ſaid Maſs ſubmerged: And, therefore, that <lb></lb>Maſs ſhall reſt. </s><s>And briefly in generall.</s></p><p type="margin"> <s><margin.target id="marg1508"></margin.target>Of Natation <lb></lb>Lib. 1. Prop. </s><s>3.</s></p><p type="head"> <s>THEOREME. VI.</s></p><p type="main"> <s><emph type="italics"></emph>When ever the exceſs of the Gravity of the Solid above<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1509"></arrow.to.target> <lb></lb><emph type="italics"></emph>the Gravity of the Water, ſhall have the ſame pro <lb></lb>portion to the Gravity of the Water, that the Alti <lb></lb>tude of the Rampart, hath to the thickneſs of the <lb></lb>Solid, that Solid ſhall not ſink, but being never ſo lit <lb></lb>tle thicker it ſhall.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1509"></margin.target>The proporti <lb></lb>on of the great <lb></lb>eſt thickneſs of <lb></lb>Solids, beyond <lb></lb>which encrea <lb></lb>ſed they ſink.</s></p><p type="main"> <s>Let the Solid I S be ſuperior in Gravity to the water, and of ſuch <lb></lb>thickneſs, that the Altitude of the Rampart A I, be in proporti <lb></lb>on to the thickneſs of the Solid I O, as the exceſs of the Gravi <lb></lb>ty of the ſaid Solid I S, above the Gravity of a Maſs of water equall <lb></lb>to the Maſs I S, is to the Gravity of the Maſs of water equall to the <pb xlink:href="040/01/1140.jpg" pagenum="447"></pb>Maſs I S. </s><s>I ſay, that the Solid I S ſhall not <lb></lb>ſinke, but being never ſo little thicker it ſhall <lb></lb>go to the bottom: For being that as A I is <lb></lb><figure id="id.040.01.1140.1.jpg" xlink:href="040/01/1140/1.jpg"></figure> <lb></lb>to I O, ſo is the Exceſs of the Gravity of the <lb></lb>Solid I S, above the Gravity of a Maſs of water <lb></lb>equall to the Maſs I S, to the Gravity of the <lb></lb>ſaid Maſs of water: Therefore, compounding, as A O is to O I, ſo <lb></lb>ſhall the Gravity of the Solid I S, be to the Gravity of a Maſs of water <lb></lb>equall to the Maſs I S: And, converting, as I O is to O A, ſo ſhall the <lb></lb>Gravity of a Maſs of water equall to the Maſs I S, be to the Gravity <lb></lb>of the Solid I S: But as I O is to O A, ſo is a Maſs of water I S, to a <lb></lb>Maſs of water equall to the Maſs A B S O: and ſo is the Gravity of <lb></lb>a Maſs of water I S, to the Gravity of a Maſs of water A S: Therefore <lb></lb>as the Gravity of a Maſs of water, equall to the Maſs I S, is to the <lb></lb>Gravity of the Solid I S, ſo is the ſame Gravity of a Maſs of water <lb></lb>I S, to the Gravity of a Maſs of Water A S: Therefore the Gra <lb></lb>vity of the Solid I S, is equall to the Gravity of a Maſs of water e <lb></lb>quall to the Maſs A S: But the Gravity of the Solid I S, is the ſame <lb></lb>with the Gravity of the Solid A S, compounded of the Solid I S, <lb></lb>and of the Air A B C I. </s><s>Therefore the whole compounded Solid <lb></lb>A O S B, weighs as much as the water that would be compriſed in the <lb></lb>place of the ſaid Compound A O S B: And, therefore, it ſhall make <lb></lb>an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> and reſt, and that ſame Solid I O S C ſhall ſinke no <lb></lb>farther. </s><s>But if its thickneſs I O ſhould be increaſed, it would be ne <lb></lb>ceſſary alſo to encreaſe the Altitude of the Rampart A I, to main <lb></lb>tain the due proportion: But by what hath been ſuppoſed, the Alti <lb></lb>tude of the Rampart A I, is the greateſt that the Nature of the <lb></lb>Water and Air do admit, without the waters repulſing the Air ad <lb></lb>herent to the Superficies of the Solid I C, and poſſeſſing the ſpace <lb></lb>A I C B: Therefore, a Solid of greater thickneſs than I O, and of the <lb></lb>ſame Matter with the Solid I S, ſhall not reſt without ſubmerging, <lb></lb>but ſhall deſcend to the bottome: which was to be demonſtrated. <lb></lb></s><s>In conſequence of this that hath been demonſtrated, ſundry and va <lb></lb>rious Concluſions may be gathered, by which the truth of my prin <lb></lb>cipall Propoſition comes to be more and more confirmed, and the <lb></lb>imperfection of all former Argumentations touching the preſent <lb></lb>Queſtion cometh to be diſcovered.</s></p><p type="main"> <s><emph type="italics"></emph>And firſt we gather from the things demonstrated, that,<emph.end type="italics"></emph.end></s></p> <pb xlink:href="040/01/1141.jpg" pagenum="448"></pb><p type="head"> <s>THEOREME VII. <lb></lb><arrow.to.target n="marg1510"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1510"></margin.target>The heavieſt <lb></lb>Bodies may <lb></lb>ſwimme.</s></p><p type="main"> <s><emph type="italics"></emph>All Matters, how heavy ſoever, even to Gold it ſelf, the <lb></lb>heavieſt of all Bodies, known by us, may float upon <lb></lb>the Water.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Becauſe its Gravity being conſidered to be almoſt twenty times <lb></lb>greater than that of the water, and, moreover, the greateſt Alti <lb></lb>tude that the Rampart of water can be extended to, without break <lb></lb>ing the Contiguity of the Air, adherent to the Surface of the Solid, <lb></lb>that is put upon the water being predetermined, if we ſhould make <lb></lb>a Plate of Gold ſo thin, that it exceeds not the nineteenth part ofthe <lb></lb>Altitude of the ſaid Rampart, this put lightly upon the water ſhall <lb></lb>reſt, without going to the bottom: and if Ebony ſhall chance to be <lb></lb>in ſeſquiſeptimall proportion more grave than the water, the greateſt <lb></lb>thickneſs that can be allowed to a Board of Ebony, ſo that it may be <lb></lb>able to ſtay above water without ſinking, would be ſeaven times <lb></lb>more than the height of the Rampart Tinn, <emph type="italics"></emph>v. </s><s>gr.<emph.end type="italics"></emph.end> eight times more <lb></lb>grave than water, ſhall ſwimm as oft as the thickneſs of its Plate,</s></p><p type="main"> <s><arrow.to.target n="marg1511"></arrow.to.target> <lb></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"></emph>He elſewhere <lb></lb>cites this as a <lb></lb>Propoſition, there <lb></lb>fore I make it of <lb></lb>that number.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And here I will not omit to note, as a ſecond Corrollary dependent <lb></lb>upon the things demonſtrated, that,</s></p><p type="head"> <s>THEOREME VIII. <lb></lb><arrow.to.target n="marg1512"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1512"></margin.target>Natation and <lb></lb>Submerſion, col <lb></lb>lected from the <lb></lb>thickneſs, exclu <lb></lb>ding the length <lb></lb>and breadth of <lb></lb>Plates.</s></p><p type="main"> <s><emph type="italics"></emph>The Expanſion of Figure not only is not the Cauſe of the <lb></lb>Natation of thoſe grave Bodies, which otherwiſe <lb></lb>do ſubmerge, but alſo the determining what be thoſe <lb></lb>Boards of Ebony, or Plates of Iron or Gold that will <lb></lb>ſwimme, depends not on it, rather that ſame determina <lb></lb>tion is to be collected from the only thickneſs of thoſe <lb></lb>Figures of Ebony or Gold, wholly excluding the con <lb></lb>ſideration of length and breadth, as having no way <lb></lb>any ſhare in this Effect.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>It hath already been manifeſted, that the only cauſe of the Nata <lb></lb>tion of the ſaid Plates, is the reduction of them to be leſs grave <lb></lb>than the water, by means of the connexion of that Air, which de <lb></lb>ſcendeth together with them, and poſſeſſeth place in the water; <lb></lb>which place ſo occupyed, if before the circumfuſed water diffuſeth <lb></lb>it ſelf to fill it, it be capable of as much water, as ſhall weigh equall <lb></lb>with the Plate, the Plate ſhall remain ſuſpended, and ſinke no <lb></lb>farther.</s></p> <pb xlink:href="040/01/1142.jpg" pagenum="449"></pb><p type="main"> <s>Now let us ſee on which of theſe three dimenſions of the Solid <lb></lb>depends the terminating, what and how much the Maſs of that ought <lb></lb>to be, that ſo the aſſiſtance of the Air contiguous unto it, may ſuffice <lb></lb>to render it ſpecifically leſs grave than the water, whereupon it may <lb></lb>reſt without Submerſion. </s><s>It ſhall undoubtedly be found, that the <lb></lb>length and breadth have not any thing to do in the ſaid determina <lb></lb>tion, but only the height, or if you will the thickneſs: for, if we take <lb></lb>a Plate or Board, as for Example, of Ebony, whoſe Altitude hath <lb></lb>unto the greateſt poſſible Altitude of the Rampart, the proportion <lb></lb>above declared, for which cauſe it ſwims indeed, but yet not if we <lb></lb>never ſo little increaſe its thickneſs; I ſay, that retaining its thick <lb></lb>neſs, and encreaſing its Superficies to twice, four times, or ten times <lb></lb>its bigneſs, or dminiſning it by dividing it into four, or ſix, or <lb></lb>twenty, or a hundred parts, it ſhall ſtill in the ſame manner continue <lb></lb>to float: but encreaſing its thickneſs only a Hairs breadth, it will <lb></lb>alwaies ſubmerge, although we ſhould multiply the Superficies a <lb></lb>hundred and a hundred times. </s><s>Now foraſmuch as that this is a <lb></lb>Cauſe, which being added, we adde alſo the Effect, and being remo <lb></lb>ved, it is removed; and by augmenting or leſſening the length or <lb></lb>breadth in any manner, the effect of going, or not going to the bot <lb></lb>tom, is not added or removed: I conclude, that the greatneſs and <lb></lb>ſmalneſs of the Superficies hath no influence upon the Natation or <lb></lb>Submerſion. </s><s>And that the proportion of the Altitude of the Ram <lb></lb>parts of Water, to the Altitude of the Solid, being conſtituted in <lb></lb>the manner aforeſaid, the greatneſs or ſmalneſs of the Superficies, <lb></lb>makes not any variation, is manifeſt from that which hath been above <lb></lb>demonſtrated, and from this, that, <emph type="italics"></emph>The Priſms and Cylinders which<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1513"></arrow.to.target> <lb></lb><emph type="italics"></emph>have the ſame Baſe, are in proportion to one another as their heights:<emph.end type="italics"></emph.end> <lb></lb>Whence Cylinders or Prifmes, namely, the Board, be they great or <lb></lb>little, ſo that they be all of equall thickneſs, have the ſame proportion <lb></lb>to their Conterminall Air, which hath for Baſe the ſaid Superficies of <lb></lb>the Board, and for height the Ramparts of water; ſo that alwayes <lb></lb>of that Air, and of the Board, Solids are compounded, that in Gravity <lb></lb>equall a Maſs of water equall to the Maſs of the Solids, compounded <lb></lb>of Air, and of the Board: whereupon all the ſaid Solids do in the <lb></lb>ſame manner continue afloat. </s><s>We will conclude in the third place, <lb></lb>that,</s></p> <pb xlink:href="040/01/1143.jpg" pagenum="450"></pb><p type="margin"> <s><margin.target id="marg1513"></margin.target>Priſmes and <lb></lb>Cylinders ha <lb></lb>ving the ſame <lb></lb>Baſe, are to one <lb></lb>another as their <lb></lb>heights.</s></p><p type="head"> <s>THEOREME. IX. <lb></lb><arrow.to.target n="marg1514"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1514"></margin.target>All Figures <lb></lb>of all Matters, <lb></lb>float by hep of <lb></lb>the Rampart re <lb></lb>pleniſhed with <lb></lb>Air, and ſome <lb></lb>but only touch <lb></lb>the water.</s></p><p type="main"> <s><emph type="italics"></emph>All ſorts of Figures of whatſoever Matter, albeit more <lb></lb>grave than the Water, do by Benefit of the ſaid Ram <lb></lb>part, not only float, but ſome Figures, though of the <lb></lb>graveſt Matter, do ſtay wholly above Water, wetting <lb></lb>only the inferiour Surface that toucheth the Water.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And theſe ſhall be all Figures, which from the inferiour Baſe up <lb></lb>wards, grow leſſer and leſſer; the which we ſhall exemplifie for <lb></lb>this time in Piramides or Cones, of which Figures the paſſions sre <lb></lb>common. </s><s>We will demonſtrate therefore, that,</s></p><p type="main"> <s><emph type="italics"></emph>It is poſſible to form a Piramide, of any whatſoever Matter propoſed, <lb></lb>which being put with its Baſe upon the Water, reſts not only without <lb></lb>ſubmerging, but without wetting it more then its Baſe.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>For the explication of which it is requiſite, that we firſt demonſtrate <lb></lb>the ſubſequent Lemma, namely, that,</s></p><p type="head"> <s>LEMMA II.</s></p><p type="main"> <s><emph type="italics"></emph>Solids whoſe Maſſes anſwer in proportion contrarily to<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1515"></arrow.to.target> <lb></lb><emph type="italics"></emph>their Specificall Gravities, are equall in Abſolute <lb></lb>Gravities.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1515"></margin.target>Solids whoſe <lb></lb>Maſſes are in <lb></lb>contrary pro <lb></lb>portion to their <lb></lb>Specifick Gra <lb></lb>vities, are equall <lb></lb>in abſolute Gra <lb></lb>vity.</s></p><p type="main"> <s>Let A C and B be two Solids, and let the Maſs A C be to the <lb></lb>Maſs B, as the Specificall Gravity of the Solid B, is to the Speci <lb></lb>ficall Gravity of the Solid A C: I ſay, the Solids A C and B are <lb></lb>equall in abſolute weight, that is, equally grave. For <lb></lb><figure id="id.040.01.1143.1.jpg" xlink:href="040/01/1143/1.jpg"></figure> <lb></lb>if the Maſs A C be equall to the Maſs B, then, by the <lb></lb>Aſſumption, the Specificall Gravity of B, ſhall be e <lb></lb>quall to the Specificall Gravity of A C, and being e <lb></lb>quall in Maſs, and of the ſame Specificall Gravity they <lb></lb>ſhall abſolutely weigh one as much as another. </s><s>But <lb></lb>if their Maſſes ſhall be unequall, let the Maſs A C be greater, and in it <lb></lb>take the part C, equall to the Maſs B. And, becauſe the Maſſes B <lb></lb>and C are equall; the Abſolute weight of B, ſhall have the ſame pro <lb></lb>portion to the Abſolute weight of C, that the Specificall Gravity of <lb></lb>B, hath to the Specificall Gravity of C; or of C A, which is the <lb></lb>ſame <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end>: But look what proportion the Specificall Gravity of <lb></lb>B, hath to the Specificall Gravity of C A, the like proportion, by the <lb></lb>Aſſumption, hath the Maſs C A, to the Maſs B; that is, to the Maſs C: <pb xlink:href="040/01/1144.jpg" pagenum="451"></pb>Therefore, the abſolute weight of B, to the abſolute weight of C, is <lb></lb>as the Maſs A C to the Maſs <emph type="italics"></emph>C<emph.end type="italics"></emph.end>: But as the Maſs AC, is to the Maſs C, <lb></lb>ſo is the abſolute weight of A C, to the abſolute weight of C: There <lb></lb>fore the abſolute weight of B, hath the ſame proportion to the abſo <lb></lb>lute weight of C, that the abſolute weight of A C, hath to the ab <lb></lb>ſolute weight of C: Therefore, the two Solids A C and B are equall <lb></lb>in abſolute Gravity: which was to be demonſtrated. </s><s>Having de <lb></lb>monſtrated this, I ſay,</s></p><p type="head"> <s>THEOREME X.</s></p><p type="main"> <s><emph type="italics"></emph>That it is poſſible of any aſſigned Matter, to form a Pi-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1516"></arrow.to.target> <lb></lb><emph type="italics"></emph>ramide or Cone upon any Baſe, which being put upon <lb></lb>the Water ſhall not ſubmerge, nor wet any more than <lb></lb>its Baſe.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1516"></margin.target>There may be <lb></lb>Cones and Pira <lb></lb>mides of any <lb></lb><emph type="italics"></emph>M<emph.end type="italics"></emph.end>atter, which <lb></lb>demittedinto the <lb></lb>water, reſt only <lb></lb>their Baſes.</s></p><p type="main"> <s>Let the greateſt poſſible Altitude of the Rampart be the Line D B, <lb></lb>and the Diameter of the Baſe of the Cone to be made of any Mat <lb></lb>ter aſſigned B C, at right angles to D B: And as the Specificall Gravity <lb></lb>of the Matter of the Piramide or Cone to be made, is to the Specificall <lb></lb>Gravity of the water, ſo let the Altitude of the <lb></lb><figure id="id.040.01.1144.1.jpg" xlink:href="040/01/1144/1.jpg"></figure> <lb></lb>Rampart D B, be to the third part of the Piramide <lb></lb>or Cone A B C, deſcribed upon the Baſe, whoſe <lb></lb>Diameter is B C: I ſay, that the ſaid Cone A B C, <lb></lb>and any other Cone, lower then the ſame, ſhall reſt <lb></lb>upon the Surface of the water B C without ſinking. <lb></lb></s><s>Draw D F parallel to B C, and ſuppoſe the Priſme <lb></lb>or Cylinder E C, which ſhall be tripple to the Cone <lb></lb>A B C. And, becauſe the Cylinder D C hath the ſame proportion <lb></lb>to the Cylinder C E, that the Altitude D B, hath to the Altitude B E: <lb></lb>But the Cylinder C E, is to the Cone A B C, as the Altitude E B is to <lb></lb>the third part of the Altitude of the Cone: Therefore, by Equality of <lb></lb>proportion, the Cylinder D C is to the Cone A B C, as D B is to the <lb></lb>third part of the Altitude B E: But as D B is to the third part of B E, <lb></lb>ſo is the Specificall Gravity of the Cone A B C, to the Specificall Gra <lb></lb>vity of the water: Therefore, as the Maſs of the Solid D C, is to the <lb></lb>Maſs of the Cone A <emph type="italics"></emph>B<emph.end type="italics"></emph.end> C, ſo is the Specificall Gravity of the ſaid Cone, <lb></lb>to the Specificall Gravity of the water: Therefore, by the precedent <lb></lb>Lemma, the Cone A B C weighs in abſolute Gravity as much as a <lb></lb>Maſs of Water equall to the Maſs D C: But the water which by the <lb></lb>impoſition of the Cone A B C, is driven out of its place, is as much <lb></lb>as would preciſely lie in the place D C, and is equall in weight to the <lb></lb>Cone that diſplaceth it: Therefore, there ſhall be an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> <lb></lb>and the Cone ſhall reſt without farther ſubmerging. </s><s>And its ma <lb></lb>nifeſt,</s></p> <pb xlink:href="040/01/1145.jpg" pagenum="452"></pb><p type="head"> <s>COROLARY I. <lb></lb><arrow.to.target n="marg1517"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1517"></margin.target>Amongſt Cones <lb></lb>of the ſame Baſe, <lb></lb>thoſe of leaſt Al <lb></lb>titude ſhall ſink <lb></lb>the leaſt.</s></p><p type="main"> <s><emph type="italics"></emph>That making upon the ſame Baſis, a Cone of a leſs Altitude, it ſhall be <lb></lb>alſo leſs grave, and ſhall ſo much the more reſt without Submerſion.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>COROLARY II.</s></p><p type="main"> <s><emph type="italics"></emph>It is manifeſt, alſo, that one may make Cones and Piramids of any Matter <emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1518"></arrow.to.target> <lb></lb><emph type="italics"></emph>whatſoever, more grave than the water, which being put into the <lb></lb>water, with the Apix or Point downwards, reſt without Submerſion. <emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1518"></margin.target>There may be <lb></lb>Cones and Pira <lb></lb>mides of any <lb></lb>Matter, which <lb></lb>demitted with <lb></lb>the Point down <lb></lb>wards do float a <lb></lb>top.</s></p><p type="main"> <s>Becauſe if we reaſſume what hath been above demonſtrated, of <lb></lb>Priſms and Cylinders, and that on Baſes equall to thoſe of the <lb></lb>ſaid Cylinders, we make Cones of the ſame Matter, and thrree <lb></lb>times as high as the Cylinders, they ſhall reſt afloat, for that in Maſs <lb></lb>and Gravity they ſhall be equall to thoſe Cylinders, and by having <lb></lb>their Baſes equall to thoſe of the Cylinders, they ſhall leave equall <lb></lb>Maſſes of Air included within the Ramparts. </s><s>This, which for Exam <lb></lb>ple ſake hath been demonſtrated, in Priſms, Cylinders, Cones and <lb></lb>Piramids, might be proved in all other Solid Figures, but it would <lb></lb>require a whole Volume (ſuch is the multitude and variety of their <lb></lb>Symptoms and Accidents) to comprehend the particuler demonſtration <lb></lb>of them all, and of their ſeverall Segments: but I will to avoid prolixity <lb></lb>in the preſent Diſcourſe, content my ſelf, that by what I have declared <lb></lb>every one of ordinary Capacity may comprehend, that there is not <lb></lb>any Matter ſo grave, no not Gold it ſelf, of which one may not form <lb></lb>all ſorts of Figures, which by vertue of the ſuperiour Air adherent to <lb></lb>them, and not by the Waters Reſiſtance of Penetration, do remain <lb></lb>afloat, ſo that they ſink not. </s><s>Nay, farther, I will ſhew, for removing <lb></lb>that Error, that,</s></p><p type="head"> <s>THEOREME XI. <lb></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></lb>Cone, demitted <lb></lb>with the Point <lb></lb>downwards ſhal <lb></lb>ſwim, with its <lb></lb>Baſe downward <lb></lb>ſhall ſink.</s></p><p type="main"> <s><emph type="italics"></emph>A Piramide or Cone put into the Water, with the Point <lb></lb>downward ſhall ſwimme, and the ſame put with the <lb></lb>Baſe downwards ſhall ſinke, and it ſhall be impoſſible <lb></lb>to make it float.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Now the quite contrary would happen, if the difficulty of Pene <lb></lb>trating the water, were that which had hindred the deſcent, for <lb></lb>that the ſaid Cone is far apter to pierce and penetrate with its ſharp <lb></lb>Point, than with its broad and ſpacious Baſe.</s></p><p type="main"> <s>And, to demonſtrate this, let the Cone be <emph type="italics"></emph>A B C,<emph.end type="italics"></emph.end> twice as grave <lb></lb>as the water, and let its height be tripple to the height of the Rampart <lb></lb><emph type="italics"></emph>D A E C<emph.end type="italics"></emph.end>: I ſay, firſt, that being put lightly into the water with the <pb xlink:href="040/01/1146.jpg" pagenum="453"></pb>Point downwards, it ſhall not deſcend to the bot <lb></lb>tom: for the Aeriall Cylinder contained betwixt <lb></lb><figure id="id.040.01.1146.1.jpg" xlink:href="040/01/1146/1.jpg"></figure> <lb></lb>the Ramparts <emph type="italics"></emph>D A C E,<emph.end type="italics"></emph.end> is equall in Maſs to the <lb></lb>Cone <emph type="italics"></emph>A B C<emph.end type="italics"></emph.end>; ſo that the whole Maſs of the Solid <lb></lb>compounded of the Air <emph type="italics"></emph>D A C E,<emph.end type="italics"></emph.end> and of the Cone <lb></lb><emph type="italics"></emph>A B C,<emph.end type="italics"></emph.end> ſhall be double to the Cone <emph type="italics"></emph>A C B:<emph.end type="italics"></emph.end> And, <lb></lb>becauſe the Cone <emph type="italics"></emph>A B C<emph.end type="italics"></emph.end> is ſuppoſed to be of Matter double in Gra <lb></lb>vity to the water, therefore as much water as the whole Maſſe <lb></lb><emph type="italics"></emph>D A B C E,<emph.end type="italics"></emph.end> placed beneath the Levell of the water, weighs as much <lb></lb>as the Cone <emph type="italics"></emph>A B C<emph.end type="italics"></emph.end>: and, therefore, there ſhall be an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> <lb></lb>and the Cone <emph type="italics"></emph>A B C<emph.end type="italics"></emph.end> ſhall deſcend no lower. </s><s>Now, I ſay farther, <lb></lb>that the ſame Cone placed with the Baſe downwards, ſhall ſink to <lb></lb>the bottom, without any poſſibility of returning again, by any means <lb></lb>to ſwimme.</s></p><p type="main"> <s>Let, therefore, the Cone be <emph type="italics"></emph>A B D,<emph.end type="italics"></emph.end> double in Gravity to the <lb></lb>water, and let its height be tripple the height <lb></lb><figure id="id.040.01.1146.2.jpg" xlink:href="040/01/1146/2.jpg"></figure> <lb></lb>of the Rampart of water L B: It is already <lb></lb>manifeſt, that it ſhall not ſtay wholly out of <lb></lb>the water, becauſe the Cylinder being com <lb></lb>prehended betwixt the Ramparts <emph type="italics"></emph>L B D P,<emph.end type="italics"></emph.end> <lb></lb>equall to the Cone <emph type="italics"></emph>A B D,<emph.end type="italics"></emph.end> and the Matter of <lb></lb>the Cone, beig double in Gravity to the <lb></lb>water, it is evident that the weight of the ſaid <lb></lb>Cone ſhall be double to the weight of the Maſs of water equall to the <lb></lb>Cylinder <emph type="italics"></emph>L B D P<emph.end type="italics"></emph.end>: Therefore it ſhall not reſt in this ſtate, but <lb></lb>ſhall deſcend.</s></p><p type="head"> <s>COROLARY I.</s></p><p type="main"> <s><emph type="italics"></emph>I ſay farther; that much leſſe ſhall the ſaid Cone stay afloat, if one<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1520"></arrow.to.target> <lb></lb><emph type="italics"></emph>immerge a part thereof.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1520"></margin.target>Much leſs ſhall <lb></lb>the ſaid Cone <lb></lb>ſwim, if one im <lb></lb>merge a part <lb></lb>thereof.</s></p><p type="main"> <s>Which you may ſee, comparing with the water as well the part <lb></lb>that ſhall immerge as the other above water. </s><s>Let us therefore <lb></lb>of the Cone A B D, ſubmergeth part N T O S, and advance the <lb></lb>Point N S F above water. </s><s>The Altitude of the Cone F N S, ſhall <lb></lb>either be more than half the whole Altitude of the Cone F T O, or <lb></lb>it ſhall not be more: if it ſhall be more than half, the Cone F N S <lb></lb>ſhall be more than half of the Cylinder E N S C: for the Altitude <lb></lb>of the Cone F N S, ſhall be more than Seſquialter of the Altitude <lb></lb>of the Cylinder E N S C: And, becauſe the Matter of the Cone is <lb></lb>ſuppoſed to be double in Specificall Gravity to the water, the water <lb></lb>which would be contained within the Rampart E N S C, would be <lb></lb>leſs grave abſolutely than the Cone F N S; ſo that the whole Cone <lb></lb>F N S cannot be ſuſtained by the Rampart: But the part immerged <lb></lb>N T O S, by being double in Specificall Gravity to the water, ſhall <pb xlink:href="040/01/1147.jpg" pagenum="454"></pb>tend to the bottom: Therefore, the whole <emph type="italics"></emph>C<emph.end type="italics"></emph.end>one F T O, as well in <lb></lb>reſpect of the part ſubmerged, as the part above water ſhall de <lb></lb>ſcend to the bottom. </s><s>But if the Altitude of the Point F N S, ſhall <lb></lb>be half the Altitude of the whole Cone F T O, the ſame Altitude of <lb></lb>the ſaid <emph type="italics"></emph>C<emph.end type="italics"></emph.end>one F N S ſhall be Seſquialter to the Altitude E N: and, <lb></lb>therefore, E N S C ſhall be double to the Cone F N S; and as much <lb></lb>water in Maſs as the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>ylinder E N S C, would weigh as much as the <lb></lb>part of the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>one F N S. But, becauſe the other immerged part <lb></lb>N T O S, is double in Gravity to the water, a Maſs of water equall <lb></lb>to that compounded of the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>ylinder E N S C, and of the Solid N T O S, <lb></lb>ſhall weigh leſs than the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>one F T O, by as much as the weight of <lb></lb>a Maſs of water equall to the Solid N T O S: Therefore, the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>one <lb></lb>ſha l alſo deſcend. </s><s>Again, becauſe the Solid N T O S, is ſeptuple <lb></lb>to the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>one F N S, to which the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>ylinder E S is double, the propor <lb></lb>tion of the Solid N T O S, ſhall be to the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>ylinder E N S C, as ſeaven <lb></lb>to two: Therefore, the whole Solid compounded of the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>ylinder <lb></lb>E N S C, and of the Solid N T O S, is much leſs than double the <lb></lb>Solid N T O S: Therefore, the ſingle Solid N T O S, is much graver <lb></lb>than a Maſs of water equall to the Maſs, compounded of the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>y <lb></lb>linder E N S C, and of N T O S.</s></p><p type="head"> <s>COROLARY II. <lb></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></lb>Cones towards <lb></lb>the Cuſpis remo <lb></lb>ved, it ſhall ſtill <lb></lb>ſink.</s></p><p type="main"> <s><emph type="italics"></emph>From whence it followeth, that though one ſhould remove and take a <lb></lb>way the part of the Cone F N S, the ſole remainder N T O S would <lb></lb>go to the bottom.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>COROLARY III.</s></p><p type="main"> <s><emph type="italics"></emph>And if we ſhould more depreſs the Cone F T O, it would be ſo much the<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1522"></arrow.to.target> <lb></lb><emph type="italics"></emph>more impoſſible that it ſhould ſuſtain it ſelf afloat, the part ſubmerged <lb></lb>N T O S ſtill encreaſing, and the Maſs of Air contained in the Rampart <lb></lb>diminiſhing, which ever grows leſs, the more the Cone ſubmergeth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1522"></margin.target>The more the <lb></lb>Cone is immer <lb></lb>ged, the more <lb></lb>impoſſible is its <lb></lb>floating.</s></p><p type="main"> <s>That Cone, therefore, that with its Baſe upwards, and its <lb></lb><emph type="italics"></emph>Cuſpis<emph.end type="italics"></emph.end> downwards doth ſwimme, being dimitted with its Baſe <lb></lb>downward muſt of neceſſity ſinke. </s><s>They have argued farre <lb></lb>from the truth, therefore, who have aſcribed the cauſe of Natation <lb></lb>to waters reſiſtance of Diviſion, as to a paſſive principle, and to the <lb></lb>breadth of the Figure, with which the diviſion is to be made, as the <lb></lb>Efficient.</s></p><p type="main"> <s>I come in the fourth place, to collect and conclude the reaſon of <lb></lb>that which I have propoſed to the Adverſaries, namely,</s></p> <pb xlink:href="040/01/1148.jpg" pagenum="455"></pb><p type="head"> <s>THE OREME XII.</s></p><p type="main"> <s><emph type="italics"></emph>That it is poſſible to fo m Solid Bodies, of what Figure<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1523"></arrow.to.target> <lb></lb><emph type="italics"></emph>and greatneſs ſoever, that of their own Nature goe <lb></lb>to the Bottome; But by the help of the Air con <lb></lb>tained in the Rampart, reſt without ſubmerging.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1523"></margin.target>Solids of any <lb></lb>Figure & great <lb></lb>neſſe, that natu <lb></lb>rally ſink, may <lb></lb>by help of the <lb></lb>Air in the Ram <lb></lb>part ſwimme.</s></p><p type="main"> <s>The truth of this Propoſition is ſufficiently manifeſt in all thoſe <lb></lb>Solid Figures, that determine in their uppermoſt part in a plane <lb></lb>Superficies: for making ſuch Figures of ſome Matter ſpecifi <lb></lb>cally as grave as the water, putting them into the water, ſo that the <lb></lb>whole Maſs be covered, it is manifeſt, that they ſhall reſt in all <lb></lb>places, provided, that ſuch a Matter equall in weight to the water, <lb></lb>may be exactly adjuſted: and they ſhall by conſequence, reſt or <lb></lb>lie even with the Levell of the water, without making any Rampart. <lb></lb></s><s>If, therefore, in reſpect of the Matter, ſuch Figures are apt to reſt <lb></lb>without ſubmerging, though deprived of the help of the Rampart, <lb></lb>it is manifeſt, that they may admit ſo much encreaſe of Gravity, <lb></lb>(without encreaſing their Maſſes) as is the weight of as much water <lb></lb>as would be contained within the Rampart, that is made about their <lb></lb>upper plane Surface: by the help of which being ſuſtained, they <lb></lb>ſhall reſt afloat, but being bathed, they ſhall deſcend, having been <lb></lb>made graver than the water. </s><s>In Figures, therefore, that determine <lb></lb>above in a plane, we may cleerly comprehend, that the Rampart <lb></lb>added or removed, may prohibit or permit the deſcent: but in thoſe <lb></lb>Figures that go leſſening upwards towards the top, ſome Perſons <lb></lb>may, and that not without much ſeeming Reaſon, doubt whether <lb></lb>the ſame may be done, and eſpecially by thoſe which terminate in a <lb></lb>very acute Point, ſuch as are your Cones and ſmall Piramids. </s><s>Touch <lb></lb>ing theſe, therefore, as more dubious than the reſt, I will endeavour <lb></lb>to demonſtrate, that they alſo lie under the ſame Accident of going, <lb></lb>or not going to the Bottom, be they of any whatever bigneſs. </s><s>Let <lb></lb>therefore the Cone be A B D, made of a matter <lb></lb>ſpecifically as grave as the water; it is manifeſt <lb></lb><figure id="id.040.01.1148.1.jpg" xlink:href="040/01/1148/1.jpg"></figure> <lb></lb>that being put all under water, it ſhall reſt in <lb></lb>all places (alwayes provided, that it ſhall weigh <lb></lb>exactly as much as the water, which is almoſt <lb></lb>impoſſible to effect) and that any ſmall weight <lb></lb>being added to it, it ſhall ſink to the bottom: <lb></lb>but if it ſhall deſcend downwards gently, I ſay, <lb></lb>that it ſhall make the Rampart E S T O, and <lb></lb>that there ſhall ſtay out of the water the point A S T, tripple in <lb></lb>height to the Rampart E S: which is manifeſt, for the Matter of the <pb xlink:href="040/01/1149.jpg" pagenum="456"></pb>Cone weighing equally with the water, the part ſubmerged S B D T, <lb></lb>becomes indifferent to move downwards or upwards; and the Cone <lb></lb><emph type="italics"></emph>A S T,<emph.end type="italics"></emph.end> being equall in Maſs to the water that would be contained in <lb></lb>the concave of the Rampart <emph type="italics"></emph>E S T O,<emph.end type="italics"></emph.end> ſhall be alſo equall unto it in <lb></lb>Gravity: and, therefore, there ſhall be a perfect <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> and, <lb></lb>conſequently, a Reſt. </s><s>Now here ariſeth a doubt, whether the <lb></lb>Cone <emph type="italics"></emph>A B D<emph.end type="italics"></emph.end> may be made heavier, in ſuch ſort, that when it is put <lb></lb>wholly under water, it goes to the bottom, but yet not in ſuch ſort, <lb></lb>as to take from the Rampart the vertue of ſuſtaining it that it ſink not, <lb></lb>and, the reaſon of the doubt is this: that although at ſuch time as <lb></lb>the Cone <emph type="italics"></emph>A B D<emph.end type="italics"></emph.end> is ſpecifically as grave as the water, the Rampart <lb></lb><emph type="italics"></emph>E S T O<emph.end type="italics"></emph.end> ſuſtaines it, not only when the point <emph type="italics"></emph>A S T<emph.end type="italics"></emph.end> is tripple in <lb></lb>height to the Altitude of the Rampart <emph type="italics"></emph>E S,<emph.end type="italics"></emph.end> but alſo when a leſſer <lb></lb>part is above water; [for although in the Deſcent of the Cone the <lb></lb>Point <emph type="italics"></emph>A S T<emph.end type="italics"></emph.end> by little and little diminiſheth, and ſo likewiſe the <lb></lb>Rampart <emph type="italics"></emph>E S T O,<emph.end type="italics"></emph.end> yet the Point diminiſheth in <lb></lb><figure id="id.040.01.1149.1.jpg" xlink:href="040/01/1149/1.jpg"></figure> <lb></lb>greater proportion than the Rampart, in that <lb></lb>it diminiſheth according to all the three Di <lb></lb>menſions, but the Rampart according to two <lb></lb>only, the Altitude ſtill remaining the ſame; <lb></lb>or, if you will, becauſe the Cone <emph type="italics"></emph>S T<emph.end type="italics"></emph.end> goes di <lb></lb>miniſhing, according to the proportion of the <lb></lb>cubes of the Lines that do ſucceſſively become <lb></lb>the Diameters of the Baſes of emergent Cones, <lb></lb>and the Ramparts diminiſh according to the proportion of the <lb></lb>Squares of the ſame Lines; whereupon the proportions of the Points <lb></lb>are alwayes Seſquialter of the proportions of the Cylinders, con <lb></lb>tained within the Rampart; ſo that if, for Example, the height of <lb></lb>the emergent Point were double, or equall to the height of the <lb></lb>Rampart, in theſe caſes, the Cylinder contained within the Ram <lb></lb>part, would be much greater than the ſaid Point, becauſe it would be <lb></lb>either ſeſquialter or tripple, by reaſon of which it would perhaps <lb></lb>ſerve over and above to fuſtain the whole Cone, ſince the part ſub <lb></lb>merged would no longer weigh any thing;] yet, nevertheleſs, when <lb></lb>any Gravity is added to the whole Maſs of the Cone, ſo that alſo the <lb></lb>part ſubmerged is not without ſome exceſſe of Gravity above the <lb></lb>Gravity of the water, it is not manifeſt, whether the Cylinder con <lb></lb>tained within the Rampart, in the deſcent that the Cone ſhall make, <lb></lb>can be reduced to ſuch a proportion unto the emergent Point, and to <lb></lb>ſuch an exceſſe of Maſs above the Maſs of it, as to compenſate the <lb></lb>exceſſe of the Cones Specificall Gravity above the Gravity of the wa <lb></lb>ter: and the Scruple ariſeth, becauſe that howbeit in the deſcent <lb></lb>made by the Cone, the emergent Point <emph type="italics"></emph>A S T<emph.end type="italics"></emph.end> diminiſheth, whereby <lb></lb>there is alſo a diminution of the exceſs of the Cones Gravity above <pb xlink:href="040/01/1150.jpg" pagenum="459"></pb>the Gravity of the water, yet the caſe ſtands ſo, that the Rampart <lb></lb>doth alſo contract it ſelf, and the Cylinder contained in it doth de <lb></lb>miniſh. </s><s>Nevertheleſs it ſhall be demonſtrated, how that the Cone <lb></lb><emph type="italics"></emph>A B D<emph.end type="italics"></emph.end> being of any ſuppoſed bigneſſe, and made at the firſt of a <lb></lb>Matter exactly equall in Gravity to the Water, if there may <lb></lb>be affixed to it ſome Weight, by means of which it may deſcend to <lb></lb>the bottom, when ſubmerged under water, it may alſo by vertue of <lb></lb>the Rampart ſtay above without ſinking.</s></p><p type="main"> <s>Let, therefore, the Cone <emph type="italics"></emph>A B D<emph.end type="italics"></emph.end> be of any ſuppoſed greatneſſe, <lb></lb>and alike in ſpecificall Gravity to the water. </s><s>It is manifeſt, that <lb></lb>being put lightly into the water, it ſhall reſt without deſcending; <lb></lb>and it ſhall advance above water, the Point <lb></lb><figure id="id.040.01.1150.1.jpg" xlink:href="040/01/1150/1.jpg"></figure> <lb></lb><emph type="italics"></emph>AS T,<emph.end type="italics"></emph.end> tripple in height to the height of the <lb></lb>Rampart <emph type="italics"></emph>E S<emph.end type="italics"></emph.end>: Now, ſuppoſe the Cone <emph type="italics"></emph>A B D<emph.end type="italics"></emph.end> <lb></lb>more depreſſed, ſo that it advance above wa <lb></lb>ter, only the Point <emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> higher by half than <lb></lb>the Point <emph type="italics"></emph>A S T,<emph.end type="italics"></emph.end> with the Rampart about it <lb></lb><emph type="italics"></emph>C I R N.<emph.end type="italics"></emph.end> And, becauſe, the Cone <emph type="italics"></emph>A B D<emph.end type="italics"></emph.end> is <lb></lb>to the Cone <emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> as the cube of the Line <emph type="italics"></emph>S T<emph.end type="italics"></emph.end> <lb></lb>is to the cube of the Line <emph type="italics"></emph>I R,<emph.end type="italics"></emph.end> but the Cylin <lb></lb>der <emph type="italics"></emph>E S T O,<emph.end type="italics"></emph.end> is to the Cylinder <emph type="italics"></emph>C I R N,<emph.end type="italics"></emph.end> as the Square of <emph type="italics"></emph>S T<emph.end type="italics"></emph.end> to <lb></lb>the Square of <emph type="italics"></emph>I R,<emph.end type="italics"></emph.end> the Cone <emph type="italics"></emph>A S T<emph.end type="italics"></emph.end> ſhall be Octuple to the Cone <lb></lb><emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> and the Cylinder <emph type="italics"></emph>E S T O,<emph.end type="italics"></emph.end> quadruple to the Cylinder <emph type="italics"></emph>C I R N<emph.end type="italics"></emph.end>: <lb></lb>But the Cone <emph type="italics"></emph>A S T,<emph.end type="italics"></emph.end> is equall to the Cylinder E <emph type="italics"></emph>S T O<emph.end type="italics"></emph.end>: Therefore, <lb></lb>the Cylinder <emph type="italics"></emph>C I R N,<emph.end type="italics"></emph.end> ſhall be double to the Cone <emph type="italics"></emph>A I R:<emph.end type="italics"></emph.end> and the <lb></lb>water which might be contained in the Rampart <emph type="italics"></emph>C I R N,<emph.end type="italics"></emph.end> would be <lb></lb>double in Maſs and in Weight to the Cone <emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> and, therefore, <lb></lb>would be able to ſuſtain the double of the Weight of the Cone <emph type="italics"></emph>AIR<emph.end type="italics"></emph.end>: <lb></lb>Therefore, if to the whole Cone <emph type="italics"></emph>A B D,<emph.end type="italics"></emph.end> there be added as much <lb></lb>Weight as the Gravity of the Cone <emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> that is to ſay, the eighth <lb></lb>part of the weight of the Cone <emph type="italics"></emph>A S T,<emph.end type="italics"></emph.end> it alſo ſhall be ſuſtained by <lb></lb>the Rampart <emph type="italics"></emph>C I R N,<emph.end type="italics"></emph.end> but without that it ſhall go to the bottome: <lb></lb>the Cone <emph type="italics"></emph>A B D,<emph.end type="italics"></emph.end> being, by the addition of the eighth part of the <lb></lb>weight of the Cone <emph type="italics"></emph>A S T,<emph.end type="italics"></emph.end> made ſpecifically more grave than the <lb></lb>water. </s><s>But if the Altitude of the Cone <emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> were two thirds <lb></lb>of the Altitude of the Cone <emph type="italics"></emph>A S T,<emph.end type="italics"></emph.end> the Cone <emph type="italics"></emph>A S T<emph.end type="italics"></emph.end> would be to the <lb></lb>Cone <emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> as twenty ſeven to eight; and the Cylinder <emph type="italics"></emph>E S T O,<emph.end type="italics"></emph.end> to <lb></lb>the Cylinder <emph type="italics"></emph>C I R N,<emph.end type="italics"></emph.end> as nine to four, that is, as twenty ſeven to <lb></lb>twelve; and, therefore, the Cylinder <emph type="italics"></emph>C I R N,<emph.end type="italics"></emph.end> to the Cone <emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> <lb></lb>as twelve to eight; and the exceſs of the Cylinder <emph type="italics"></emph>C I R N,<emph.end type="italics"></emph.end> above <lb></lb>the Cone <emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> to the Cone <emph type="italics"></emph>A S T,<emph.end type="italics"></emph.end> as four to twenty ſeven: there <lb></lb>fore if to the Cone <emph type="italics"></emph>A B D<emph.end type="italics"></emph.end> be added ſo much weight as is the four <lb></lb>twenty ſevenths of the weight of the Cone <emph type="italics"></emph>A S T,<emph.end type="italics"></emph.end> which is a little <lb></lb>more then its ſeventh part, it alſo ſhall continue to ſwimme, and <pb xlink:href="040/01/1151.jpg" pagenum="460"></pb>the height of the emergent Point ſhall be double to the height of the <lb></lb>Rampart. </s><s>This that hath been demonſtrated in Cones, exactly holds <lb></lb>in Piramides, although the one or the other ſhould be very ſharp in <lb></lb><arrow.to.target n="marg1524"></arrow.to.target> <lb></lb>their Point or Cuſpis: From whence we conclude, that the ſame <lb></lb>Accident ſhall ſo much the more eaſily happen in all other Figures, <lb></lb>by how much the leſs ſharp the Tops ſhall be, in which they deter <lb></lb>mine, being aſſiſted by more ſpacious Ramparts.</s></p><p type="margin"> <s><margin.target id="marg1524"></margin.target>Natatiou eaſi <lb></lb>eſt effected in <lb></lb>Figures broad <lb></lb>toward the top.</s></p><p type="head"> <s>THEOREME XIII. <lb></lb><arrow.to.target n="marg1525"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1525"></margin.target>All Figures ſink <lb></lb>or ſwim, upon <lb></lb>bathing or not <lb></lb>bathing of their <lb></lb>tops.</s></p><p type="main"> <s><emph type="italics"></emph>All Figures, therefore, of whatever greatneſſe, may <lb></lb>go, and not go, to the Bottom, according as their Sumi <lb></lb>ties or Tops ſhall be bathed or not bathed.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And this Accident being common to all ſorts of Figures, without <lb></lb>exception of ſo much as one. </s><s>Figure hath, therefore, no part <lb></lb>in the production of this Effect, of ſometimes ſinking, and ſome <lb></lb>times again not ſinking, but only the being ſometimes conjoyned <lb></lb>to, and ſometimes ſeperated from, the ſupereminent Air: which <lb></lb>cauſe, in fine, who ſo ſhall rightly, and, as we ſay, with both his <lb></lb>Eyes, conſider this buſineſs, will find that it is reduced to, yea, that <lb></lb>it really is the ſame with, the true, Naturall and primary cauſe of <lb></lb>Natation or Submerſion; to wit, the exceſs or deficiency of the <lb></lb>Gravity of the water, in relation to the Gravity of that Solid Mag <lb></lb>nitude, that is demitted into the water. </s><s>For like as a Plate of Lead, <lb></lb>as thick as the back of a Knife, which being put into the water by it <lb></lb>ſelf alone goes to the bottom, if upon it you faſten a piece of Cork <lb></lb>four fingers thick, doth continue afloat, for that now the Solid that <lb></lb>is demitted in the water, is not, as before, more grave than the water, <lb></lb>but leſs, ſo the Board of Ebony, of its own nature more grave than <lb></lb>water; and, therefore, deſcending to the bottom, when it is demit <lb></lb>ted by it ſelf alone into the water, if it ſhall be put upon the water, <lb></lb>conjoyned with an Expanded vail of Air, that together with the <lb></lb>Ebony doth deſcend, and that it be ſuch, as that it doth make with <lb></lb>it a compound leſs grave than ſo much water in Maſs, as equalleth <lb></lb>the Maſs already ſubmerged and depreſſed beneath the Levell of the <lb></lb>waters Surface, it ſhall not deſcend any farther, but ſhall reſt, for <lb></lb>no other than the univerſall and moſt common cauſe, which is that <lb></lb>Solid Magnitudes, leſs grave <emph type="italics"></emph>inſpecie<emph.end type="italics"></emph.end> than the water, go not to the <lb></lb>bottom.</s></p><p type="main"> <s>So that if one ſhould take a Plate of Lead, as for Example, a finger <lb></lb>thick, and an handfull broad every way, and ſhould attempt to make <lb></lb>it ſwimme, with putting it lightly on the water, he would loſe his <lb></lb>Labour, becauſe that if it ſhould be depreſſed an Hairs breadth be <pb xlink:href="040/01/1152.jpg" pagenum="461"></pb>yond the poſſible Altitude of the Ramparts of water, it would dive <lb></lb>and ſink; but if whilſt it is going downwards, one ſhould make <lb></lb>certain Banks or Ramparts about it, that ſhould hinder the do fuſion <lb></lb>of the water upon the ſaid Plate, the which Banks ſhould riſe ſo <lb></lb>high, as that they might be able to contain as much water, as ſhould <lb></lb>weigh equally with the ſaid Plate, it would, without all Queſtion, <lb></lb>deſcend no lower, but would reſt, as being ſuſtained by vertue of <lb></lb>the Air contained within the aforeſaid Ramparts: and, in ſhort, <lb></lb>there would be a Veſſell by this means formed with the bottom of <lb></lb>Lead. </s><s>But if the thinneſs of the Lead ſhall be ſuch, that a very <lb></lb>ſmall height of Rampart would ſuffice to contain ſo much Air, as might <lb></lb>keep it afloat, it ſhall alſo reſt without the Artificiall Banks or Ram <lb></lb>parts, but yet not without the Air, becauſe the Air by it ſelf makes <lb></lb>Banks ſufficient for a ſmall height, to reſiſt the Superfuſion of the <lb></lb>water: ſo that that which in this caſe ſwimmes, is as it were a <lb></lb>Veſſell filled with Air, by vertue of which it continueth afloat.</s></p><p type="main"> <s>I will, in the laſt place, with an other Experimeut, attempt to <lb></lb>remove all difficulties, if ſo be there ſhould yet be any doubt leſt in <lb></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></lb>the thin Plate which ſwims, and afterwards put an end to this part of <lb></lb>my diſcourſe.</s></p><p type="margin"> <s><margin.target id="marg1526"></margin.target>*Or rather Cor <lb></lb>tiguity,</s></p><p type="main"> <s>I ſuppoſe my ſelf to be queſtioning with ſome of my Oponents.</s></p><p type="main"> <s>Whether Figure have any influence upon the encreaſe or diminu <lb></lb><arrow.to.target n="marg1527"></arrow.to.target> <lb></lb>tion of the Reſiſtance in any Weight againſt its being raiſed in the <lb></lb>Air, and I ſuppoſe, that I am to maintain the Affirmative, aſſert <lb></lb>ing that a Maſs of Lead, reduced to the Figure of a Ball, ſhall be <lb></lb>raiſed with leſs force, then if the ſame had been made into a thinne <lb></lb>and broad Plate, becauſe that it in this ſpacious Figure, hath a great <lb></lb>quantity of Air to penetrate, and in that other, more compacted and <lb></lb>contracted very little: and to demonſtrate the truth of ſuch my O <lb></lb>pinion, I will hang in a ſmall thred firſt the Ball or Bullet, and put <lb></lb>that into the water, tying the thred that upholds it to one end of <lb></lb>the Ballance that I hold in the Air, and to the other end I by degrees <lb></lb>adde ſo much Weight, till that at laſt it brings up the Ball of Lead <lb></lb>out of the water: to do which, ſuppoſe a Gravity of thirty Ounces <lb></lb>ſufficeth; I afcerwards reduce the ſaid Lead into a flat and thinne <lb></lb>Plate, the which I likewiſe put into the water, ſuſpended by three <lb></lb>threds, which hold it parallel to the Surface of the water, and put <lb></lb>ting in the ſame manner, Weights to the other end, till ſuch time as <lb></lb>the Place comes to be raiſed and drawn out of the water: I finde <lb></lb>that thirty ſix ounces will not ſuffice to ſeperate it from the water, <lb></lb>and raiſe it thorow the Air: and arguing from this Experiment, I af <lb></lb>firm, that I have fully demonſtrated the truth of my Propoſition. <lb></lb></s><s>He re my Oponents deſires me to look down, ſhewing me a thing <pb xlink:href="040/01/1153.jpg" pagenum="462"></pb>which I had not before obſerved, to wit, that in the Aſcent of the <lb></lb>Plate out of the water, it draws after it another Plate <emph type="italics"></emph>(if I may ſo <lb></lb>call it)<emph.end type="italics"></emph.end> of water, which before it divides and parts from the inferiour <lb></lb>Surface of the Plate of Lead, is raiſed above the Levell of the other <lb></lb>water, more than the thickneſs of the back of a Knife: Then he <lb></lb>goeth to repeat the Experiment with the Ball, and makes me ſee, <lb></lb>that it is but a very ſmall quantity of water, which cleaves to its <lb></lb>compacted and contracted Figure: and then he ſubjoynes, that its <lb></lb>no wonder, if in ſeperating the thinne and broad Plate from the <lb></lb>water, we meet with much greater Reſiſtance, than in ſeperating the <lb></lb>Ball, ſince together with the Plate, we are to raiſe a great quantity of <lb></lb>water, which occurreth not in the Ball: He telleth me moreover, <lb></lb>how that our Queſtion is, whether the Reſiſtance of Elevation be <lb></lb>greater in a dilated Plate of Lead, than in a Ball, and not whether <lb></lb>more reſiſteth a Plate of Lead with a great quantity of water, or a <lb></lb>Ball with a very little water: He ſheweth me in the cloſe, that the <lb></lb>putting the Plate and the Ball firſt into the water, to make proofe <lb></lb>thereby of their Reſiſtance in the Air, is beſides our caſe, which <lb></lb>treats of Elivating in the Air, and of things placed in the Air, and <lb></lb>not of the Reſiſtance that is made in the Confines of the Air and <lb></lb>water, and by things which are part in Air and part in water: and <lb></lb>laſtly, they make me feel with my hand, that when the thinne Plate <lb></lb>is in the Air, and free from the weight of the water, it is raiſed with <lb></lb>the very ſame Force that raiſeth the Ball. </s><s>Seeing, and underſtand <lb></lb>ing theſe things, I know not what to do, unleſs to grant my ſelf con <lb></lb>vinced, and to thank ſuch a Friend, for having made me to ſee that <lb></lb>which I never till then obſerved: and, being advertiſed by this ſame <lb></lb>Accident, to tell my Adverſaries, that our Queſtion is, whether a <lb></lb>Board and a Ball of Ebony, equally go to the bottom in water, and <lb></lb>not a Ball of Ebony and a Board of Ebony, joyned with another <lb></lb>flat Body of Air: and, farthermore, that we ſpeak of ſinking, and <lb></lb>not ſinking to the bottom, in water, and not of that which happeneth <lb></lb>in the Confines of the water and Air to Bodies that be part in the <lb></lb>Air, and part in the water; nor much leſs do we treat of the greater <lb></lb>or leſſer Force requiſite in ſeperating this or that Body from the Air; <lb></lb>not omitting to tell them, in the laſt place, that the Air doth reſiſt, <lb></lb>and gravitate downwards in the water, juſt ſo much as the water (if <lb></lb>I may ſo ſpeak) gravitates and reſiſts upwards in the Air, and that the <lb></lb>ſame force is required to ſinke a Bladder under water, that is full of <lb></lb>Air, as to raiſe it in the Air, being full of water, removing the con <lb></lb>ſideration of the weight of that Filme or Skinne, and confidering the <lb></lb>water and the Air only. </s><s>And it is likewiſe true, that the ſame Force <lb></lb>is required to ſink a Cup or ſuch like Veſſell under water, whilſt it is <lb></lb>full of Air, as to raiſe it above the Superficies of the water, keeping <pb xlink:href="040/01/1154.jpg" pagenum="463"></pb>it with the mouth downwards; whilſt it is full of water, which is <lb></lb>conſtrained in the ſame manner to follow the Cup which contains it, <lb></lb>and to riſe above the other water into the Region of the Air, as the <lb></lb>Air is forced to follow the ſame Veſſell under the Surface of the wa <lb></lb>ter, till that in this caſe the water, ſurmounting the brimme of the <lb></lb>Cup, breaks in, driving thence the Air, and in that caſe, the ſaid <lb></lb>brimme coming out of the water, and arriving to the Confines of the <lb></lb>Air, the water falls down, and the Air ſub-enters to fill the cavity of <lb></lb>the Cup: upon which enſues, that he no leſs tranſgreſſes the Arti <lb></lb>cles of the <emph type="italics"></emph>Convention,<emph.end type="italics"></emph.end> who produceth a Plate conjoyned with much <lb></lb>Air, to ſee if it de ſeend to the bottom in water, then he that makes <lb></lb>proof of the Reſiſtance againſt Elevation in Air with a Plate of Lead, <lb></lb>joyned with a like quantity of water.</s></p><p type="margin"> <s><margin.target id="marg1527"></margin.target>An Experi <lb></lb>ment of the op <lb></lb>peration of Fi <lb></lb>gures, in en <lb></lb>creaſing or leſ <lb></lb>ſening of the <lb></lb>Airs Reſiſtance <lb></lb>of Diviſion.</s></p><p type="main"> <s>I have ſaid all that I could at preſent think of, to maintain the <lb></lb><arrow.to.target n="marg1528"></arrow.to.target> <lb></lb>Aſſertion I have undertook. </s><s>It remains, that I examine that which <lb></lb><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> hath writ of this matter towards the end of his Book <emph type="italics"></emph>De Cælo<emph.end type="italics"></emph.end>; <lb></lb>wherein I ſhall note two things: the one that it being true as hath <lb></lb><arrow.to.target n="marg1529"></arrow.to.target> <lb></lb>been demonſtrated, that Figure hath nothing to do about the moving <lb></lb>or not moving it ſelf upwards or downwards, it ſeemes that <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> <lb></lb>at his firſt falling upon this Sp. </s><s>culation, was of the ſame opinion, as <lb></lb>in my opinion may be collected from the examination of his words. <lb></lb></s><s>Tis true, indeed, that in eſſaying afterwards to render a reaſon of <lb></lb>ſuch effect, as not having in my conceit hit upon the right, (which <lb></lb>in the ſecond place I will examine) it ſeems that he is brought to <lb></lb>admit the largeneſſe of Figure, to be intereſſed in this operation. <lb></lb></s><s>As to the firſt particuler, hear the preciſe words of <emph type="italics"></emph>Aristotle.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1528"></margin.target><emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> opi <lb></lb>nion touching <lb></lb>the Operation <lb></lb>of Figure ex <lb></lb>amined.</s></p><p type="margin"> <s><margin.target id="marg1529"></margin.target><emph type="italics"></emph>Ariſtot de Cælo,<emph.end type="italics"></emph.end> <lb></lb>Lib. 4. Cap. 66.</s></p><p type="main"> <s><emph type="italics"></emph>Figures are not the Cauſes of moving ſimply upwards or downwards,<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1530"></arrow.to.target> <lb></lb><emph type="italics"></emph>but of moving more ſlowly or ſwiftly, and by what means this comes to <lb></lb>paſs, it is not difficult to ſee.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1530"></margin.target><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> makes <lb></lb>not Figure the <lb></lb>cauſe of Motion <lb></lb>abſolutely, but <lb></lb>of ſwiſt or ſlow <lb></lb>motion,</s></p><p type="main"> <s>Here firſt I note, that the terms being four, which fall under the <lb></lb>preſent conſideration, namely, Motion, Reſt, Slowly and Swiftly: <lb></lb><arrow.to.target n="marg1531"></arrow.to.target> <lb></lb>And <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> naming Figures as Cauſes of Tardity and Velocity, ex <lb></lb>cluding them from being the Cauſe of abſolute and ſimple Motion, <lb></lb>it ſeems neceſſary, that he exclude them on the other ſide, from being <lb></lb>the Cauſe of Reſt, ſo that his meaning is this. </s><s>Figures are not the <lb></lb>Cauſes of moving or not moving abſolutely, but of moving quickly <lb></lb>or ſlowly: and, here, if any ſhould ſay the mind of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> is to <lb></lb>exclude Figures from being Cauſes of Motion, but yet not from <lb></lb>being Cauſes of Reſt, ſo that the ſence would be to remove from <lb></lb>Figures, there being the Cauſes of moving ſimply, but yet not there <lb></lb>being Cauſes of Reſt, I would demand, whether we ought with <lb></lb><emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> to underſtand, that all Figures univerſally, are, in ſome <lb></lb>manner, the cauſes of Reſt in thoſe Bodies, which otherwiſe would <lb></lb>move, or elſe ſome particular Figures only, as for Example, broad <pb xlink:href="040/01/1155.jpg" pagenum="464"></pb>and thinne Figures: If all indifferently, then every Body ſhall reſt: <lb></lb>becauſe every Body hath ſome Figure, which is falſe: but if ſome <lb></lb>particular Figures only may be in ſome manner a Cauſe of Reſt, as, <lb></lb>for Example, the broad, then the others would be in ſome manner <lb></lb>the Cauſes of Motion: for if from ſeeing ſome Bodies of a contracted <lb></lb>Figure move, which after dilated into Plates reſt, may be inferred, <lb></lb>that the Amplitude of Figure hath a part in the Cauſe of that Reſt; <lb></lb>ſo from ſeeing ſuch like Figures reſt, which afterwards contracted <lb></lb>move, it may with the ſame reaſon be affirmed, that the united and <lb></lb>contracted Figure, hath a part in cauſing Motion, as the remover of <lb></lb>that which impeded it: The which again is directly oppoſite to what <lb></lb><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſaith, namely, that Figures are not the Cauſes of Motion. <lb></lb></s><s>Beſides, if <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> had admitted and not excluded Figures from be <lb></lb>ing Cauſes of not moving in ſome Bodies, which moulded into ano <lb></lb>ther Figure would move, he would have impertinently propounded <lb></lb>in a dubitative manner, in the words immediately following, whence <lb></lb>it is, that the large and thinne Plates of Lead or Iron, reſt upon the <lb></lb>water, ſince the Cauſe was apparent, namely, the Amplitude of <lb></lb>Figure. </s><s>Let us conclude, therefore, that the meaning of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> <lb></lb>in this place is to affirm, that Figures are not the Cauſes of abſolutely <lb></lb>moving or not moving, but only of moving ſwiftly or ſlowly: which <lb></lb>we ought the rather to believe, in regard it is indeed a meſt true con <lb></lb>ceipt and opinion. </s><s>Now the mird of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> being ſuch, and ap <lb></lb>pearing by conſequence, rather contrary at the firſt ſight, then fa <lb></lb>vourable to the aſſertion of the Oponents, it is neceſſary, that their <lb></lb>Interpretation be not exactly the ſame with that, but ſuch, as being <lb></lb>in part underſtood by ſome of them, and in part by others, was ſet <lb></lb>down: and it may eaſily be indeed ſo, being an Interpretation <lb></lb>conſonent to the ſence of the more famous Interpretors, which is, <lb></lb>that the Adverbe <emph type="italics"></emph>Simply<emph.end type="italics"></emph.end> or <emph type="italics"></emph>Abſolutely,<emph.end type="italics"></emph.end> put in the Text, orght not to <lb></lb>be joyned to the Verbe to <emph type="italics"></emph>Move,<emph.end type="italics"></emph.end> but with the Noun <emph type="italics"></emph>Cauſes<emph.end type="italics"></emph.end>: ſo that <lb></lb>the purport of <emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> words, is to affirm, That Figures are not the <lb></lb>Cauſes abſolutely of moving or not moving, but yet are Cauſes <emph type="italics"></emph>Se <lb></lb>cundum quid, viz<emph.end type="italics"></emph.end> in ſome ſort; by which means, they are called <lb></lb>Auxiliary and Concomitant Cauſes: and this Propoſition is received <lb></lb>and aſſerted as true by <emph type="italics"></emph>Signor Buonamico Lib.<emph.end type="italics"></emph.end> 5. <emph type="italics"></emph>Cap.<emph.end type="italics"></emph.end> 28. where he <lb></lb>thus writes. <emph type="italics"></emph>There are other Cauſes concomitant, by which ſome <lb></lb>things float, and others ſink, among which the Figures of Bodies hath <lb></lb>the firſt place,<emph.end type="italics"></emph.end> &c.</s></p><p type="margin"> <s><margin.target id="marg1531"></margin.target>Lib. 4. Cap. 61 <lb></lb>Text. </s><s>42.</s></p><p type="main"> <s>Concerning this Propoſition, I meet with many doubts and diffi <lb></lb>culties, for which me thinks the words of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> are not capable of <lb></lb>ſuch a conſtruction and ſence, and the difficulties are theſe.</s></p><p type="main"> <s>Firſt in the order and diſpoſure of the words of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> the par <lb></lb>ticle <emph type="italics"></emph>Simpliciter,<emph.end type="italics"></emph.end> or if you will <emph type="italics"></emph>abſoluté,<emph.end type="italics"></emph.end> is conjoyned with the Verb <pb xlink:href="040/01/1156.jpg" pagenum="465"></pb><emph type="italics"></emph>to move,<emph.end type="italics"></emph.end> and ſeperated from the Noun <emph type="italics"></emph>Cauſes,<emph.end type="italics"></emph.end> the which is a great <lb></lb>preſumption in my favour, ſeeing that the writing and the Text <lb></lb>ſaith, Figures are not the Cauſe of moving ſimply upwards or <lb></lb>downwards, but of quicker or ſlower Motion: and, ſaith not, <lb></lb>Figures are not ſimply the Cauſes of moving upwards or down <lb></lb>wards, and when the words of a Text receive, tranſpoſed, a ſence <lb></lb>different from that which they found, taken in the order wherein <lb></lb>the Author diſpoſeth them, it is not convenient to inverte them. <lb></lb></s><s>And who will affirm that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> deſiring to write a Propoſition, <lb></lb>would diſpoſe the words in ſuch ſort, that they ſhould import a <lb></lb>different, nay, a contrary ſence? </s><s>contrary, I ſay, becauſe under <lb></lb>ſtood as they are written; they ſay, that Figures are not the <lb></lb>Cauſes of Motion, but inverted, they ſay, that Figures are the <lb></lb>Cauſes of Motion, &c.</s></p><p type="main"> <s>Moreover, if the intent of <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> had been to ſay, that Figures <lb></lb>are not ſimply the Cauſes of moving upwards or downwards, but <lb></lb>only Cauſes <emph type="italics"></emph>Secundum quid,<emph.end type="italics"></emph.end> he would not have adjoyned thoſe <lb></lb>words, <emph type="italics"></emph>but they are Cauſes of the more ſwift or ſlow Motion<emph.end type="italics"></emph.end>; yea, the <lb></lb>ſubjoining this would have been not only ſuperfluous but falſe, for <lb></lb>that the whole tenour of the Propoſition would import thus much. <lb></lb></s><s>Figures are not the abſolute Cauſes of moving upwards or down <lb></lb>wards, but are the abſolute Cauſe of the ſwift or ſlow Motion; <lb></lb>which is not true: becauſe the primary Cauſes of greater or leſſer <lb></lb>Velocity, are by <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in the 4th of his <emph type="italics"></emph>Phyſicks, Text.<emph.end type="italics"></emph.end> 71. attri <lb></lb>buted to the greater or leſſer Gravity of Moveables, compared a <lb></lb>mong themſelves, and to the greater or leſſer Reſiſtance of the <lb></lb><emph type="italics"></emph>Medium's,<emph.end type="italics"></emph.end> depending on their greater or leſs Craſſitude: and theſe <lb></lb>are inſerted by <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> as the primary Cauſes; and theſe two only <lb></lb>are in that place nominated: and Figure comes afterwards to be <lb></lb>conſidered, <emph type="italics"></emph>Text.<emph.end type="italics"></emph.end> 74. rather as an Inſtrumentall Cauſe of the force <lb></lb>of the Gravity, the which divides either with the Figure, or with <lb></lb>the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end>; and, indeed, Figure by it ſelf without the force of <lb></lb>Gravity or Levity, would opperate nothing.</s></p><p type="main"> <s>Iadde, that if <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> had an opinion that Figure had been in <lb></lb>ſome ſort the Cauſe of moving or not moving, the inquiſition <lb></lb>which he makes immediately in a doubtfull manner, whence it <lb></lb>comes, that a Plate of Lead flotes, would have been impertinent; <lb></lb>for if but juſt before he had ſaid, that Figure was in a certain ſort <lb></lb>the Cauſe of moving or not moving, he needed not to call in <lb></lb>Queſtion, by what Cauſe the Plate of Lead ſwims, and then aſcri <lb></lb>bing the Cauſe to its Figure; and framing a diſcourſe in this manner. <lb></lb></s><s>Figure is a Cauſe <emph type="italics"></emph>Secundum quid<emph.end type="italics"></emph.end> of not ſinking: but, now, if it be <lb></lb>doubted, for what Cauſe a thin Plate of Lead goes not to the bottom; <lb></lb>it ſhall be anſwered, that that proceeds from its Figure: a diſcourſe <pb xlink:href="040/01/1157.jpg" pagenum="466"></pb>which would be indecent in a Child, much more in <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end>; For <lb></lb>where is the occaſion of doubting? </s><s>And who ſees not, that if <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> <lb></lb>had held, that Figure was in ſome ſort a Cauſe of Natation, he <lb></lb>would without the leaſt Heſitation have writ; That Figure is in a <lb></lb>certain ſort the Cauſe of Natation, and therefore the Plate of Lead <lb></lb>in reſpect of its large and expatiated Figure ſwims; but if we take <lb></lb>the propoſition of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> as I ſay, and as it is writte n, and as in <lb></lb>deed it is true, the enſuing words come in very oppoſitely, as well in <lb></lb>the introduction of ſwift and ſlow, as in the queſtion, which very <lb></lb>pertinently offers it ſelf, and would ſay thus much.</s></p><p type="main"> <s>Figures are not the Cauſe of moving or not moving ſimply up <lb></lb>wards or downwards, but of moving more quickly or ſlowly: But if <lb></lb>it be ſo, the Cauſe is doubtfull, whence it proceeds, that a Plate of <lb></lb>Lead or of Iron broad and thin doth ſwim, &c. </s><s>And the occaſion of <lb></lb>the doubt is obvious, becauſe it ſeems at the firſt glance, that the <lb></lb>Figure is the Cauſe of this Natation, ſince the ſame Lead, or a leſs <lb></lb>quantity, but in another Figure, goes to the bottom, and we have <lb></lb>already affirmed, that the Figure hath no ſhare in this effect.</s></p><p type="main"> <s>Laſtly, if the intent of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in this place had been to ſay, <lb></lb>that Figures, although not abſolutely, are at leaſt in ſome meaſure <lb></lb>the Cauſe of moving or not moving: I would have it conſidered, <lb></lb>that he names no leſs the Motion upwards, than the other down <lb></lb>wards: and becauſe in exemplifying it afterwards, he produceth <lb></lb>no other Experiments than of a Plate of Lead, and Board of Ebony, <lb></lb>Matters that of their own Nature go to the bottom, but by vertue <lb></lb>(as our Adverſaries ſay) of their Figure, reſt afloat; it is ſit that <lb></lb>they ſhould produce ſome other Experiment of thoſe Matters, which <lb></lb>by their Nature ſwims, but retained by their Figure reſt at the <lb></lb>bottom. </s><s>But ſince this is impoſſible to be done, we conclude, that <lb></lb><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in this place, hath not attributed any action to the Figure <lb></lb>of ſimply moving or not moving.</s></p><p type="main"> <s>But though he hath exquiſitely Philoſophiz'd, in inveſtigating <lb></lb>the ſolution of the doubts he propoſeth, yet will I not undertake <lb></lb>to maintain, rather various difficulties, that preſent themſelves <lb></lb>unto me, give me occaſion of ſuſpecting that he hath not entirely <lb></lb>diſplaid unto us, the true Cauſe of the preſent Concluſion: which <lb></lb>difficulties I will propound one by one, ready to change opinion, <lb></lb>when ever I am ſhewed, that the Truth is different from what I ſay; <lb></lb>to the confeſſion whereof I am much more inclinable than to contra <lb></lb>diction. <lb></lb><arrow.to.target n="marg1532"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1532"></margin.target><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> erred <lb></lb>in affirming a <lb></lb>Needle dimitted <lb></lb>long wayes to <lb></lb>ſink.</s></p><p type="main"> <s><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> having propounded the Queſtion, whence it proceeds, <lb></lb>that broad Plates of Iron or Lead, float or ſwim; he addeth (as <lb></lb>it were ſtrengthening the occaſion of doubting) foraſmuch as other <lb></lb>things, leſs, and leſs grave, be they round or long, as for inſtance a <pb xlink:href="040/01/1158.jpg" pagenum="467"></pb>Needle go to the bottom. </s><s>Now I here doubt, or rather am certain, <lb></lb>that a Needle put lightly upon the water, reſts afloat, no leſs than the <lb></lb>thin Plates of Iron or Lead. </s><s>I cannot believe, albeit it hath been <lb></lb>told me, that ſome to defend <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſhould ſay, that he intends a <lb></lb>Needle demitted not longwayes but endwayes, and with the Point <lb></lb>downwards; nevertheleſs, not to leave them ſo much as this, though <lb></lb>very weak refuge, and which in my judgement <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> himſelf <lb></lb>would refuſe, I ſay it ought to be underſtood, that the Needle muſt <lb></lb>be demitted, according to the Dimenſion named by <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> which <lb></lb>is the length: becauſe, if any other Dimenſion than that which is <lb></lb>named, might or ought to be taken, I would ſay, that even the Plates <lb></lb>of Iron and Lead, ſink to the bottom, if they be put into the water <lb></lb>edgewayes and not flatwayes. </s><s>But becauſe <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſaith, broad <lb></lb>Figures go not to the bottom, it is to be underſtood, being demitted <lb></lb>broadwayes: and, therefore, when he ſaith, long Figures as a <lb></lb>Needle, albeit light, reſt not afloat, it ought to be underſtood of <lb></lb>them when demitted longwayes.</s></p><p type="main"> <s><emph type="italics"></emph>Morcover, to ſay that<emph.end type="italics"></emph.end> Ariſtotle <emph type="italics"></emph>is to be underſtood of the Needle de <lb></lb>mitted with the Point downwards, is to father upon him a great imper <lb></lb>tinency; for in this place he ſaith, that little Particles of Lead or Iron, <lb></lb>if they be round or long as a Needle, do ſink to the bottome; ſo that by <lb></lb>his Opinion, a Particle or ſmall Grain of Iron cannot ſwim: and if he <lb></lb>thus believed, what a great folly would it be to ſubjoyn, that neither <lb></lb>would a Needle demitted endwayes ſwim? </s><s>And what other is ſuch a <lb></lb>Needle, but many ſuch like Graines accumulated one upon another? </s><s>It <lb></lb>was too unworthy of ſuch a man to ſay, that one ſingle Grain of Iron could <lb></lb>not ſwim, and that neither can it ſwim, though you put a hundred more <lb></lb>upon it.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Laſtly, either <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> believed, that a Needle demitted long <lb></lb>wayes upon the water, would ſwim, or he believed that it would <lb></lb>not ſwim: If he believed it would not ſwim, he might well ſpeak <lb></lb>as indeed he did; but if he believed and knew that it would ſloat, <lb></lb>why, together with the dubious Problem of the Natation of broad <lb></lb>Figure, though of ponderous Matter, hath he not alſo introduced <lb></lb>the Queſtion; whence it proceeds, that even long and ſlender Fi <lb></lb>gures, howbeit of Iron or Lead do ſwim? </s><s>And the rather, for that <lb></lb>the occaſion of doubting ſeems greater in long and narrow Figures, <lb></lb>than in broad and thin, as from <emph type="italics"></emph>Aristotles<emph.end type="italics"></emph.end> not having doubted of it, <lb></lb>is manifeſted.</s></p><p type="main"> <s>No leſſer an inconvenience would they faſten upon <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> who <lb></lb>in his defence ſhould ſay, that he means a Needle pretty thick, and <lb></lb>not a ſmall one; for take it for granted to be intended of a ſmall one <pb xlink:href="040/01/1159.jpg" pagenum="468"></pb>and it ſhall ſuffice to reply, that he believed that it would ſwim; <lb></lb>and I will again charge him with having avoided a more wonderfull <lb></lb>and intricate Probleme, and introduced the more facile and leſs <lb></lb>wonderfull.</s></p><p type="main"> <s>We ſay freely therefore; that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> did hold, that only the <lb></lb>broad Figure did ſwim, but the long and ſlender, ſuch as a Needle, <lb></lb>not. </s><s>The which nevertheleſs is falſe, as it is alſo falſe in round <lb></lb>Bodies: becauſe, as from what hath been predemonſtrated, may be ga <lb></lb>thered, little Balls of Lead and Iron, do in like manner ſwim.</s></p><p type="main"> <s>He propoſeth likewiſe another Concluſion, which likewiſe ſeems </s></p><p type="main"> <s><arrow.to.target n="marg1533"></arrow.to.target> <lb></lb>different from the truth, and it is, That ſome things, by reaſon of <lb></lb>their littleneſs fly in the Air, as the ſmall duſt of the Earth, and the <lb></lb>thin leaves of beaten Gold: but in my Opinion, Experience ſhews <lb></lb>us, that that happens not only in the Air, but alſo in the water, in <lb></lb>which do deſcend, even thoſe Particles or Atomes of Earth, that <lb></lb>diſtur be it, whoſe minuity is ſuch, that they are not deſervable, ſave <lb></lb>only when they are many hundreds together. </s><s>Therefore, the duſt <lb></lb>of the Earth, and beaten Gold, do not any way ſuſtain themſelves <lb></lb>in the Air, but deſcend downwards, and only fly to and again in <lb></lb>the ſame, when ſtrong Windes raiſe them, or other agitations of the <lb></lb>Air commove them: and this alſo happens in the commotion of the <lb></lb>water, which raiſeth its Sand from the bottom, and makes it muddy. <lb></lb></s><s>But <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> cannot mean this impediment of the commotion, of <lb></lb>which he makes no mention, nor names other than the lightneſs of <lb></lb>ſuch Minutiæ or Atomes, and the Reſiſtance of the Craſſitudes of the <lb></lb>Water and Air, by which we ſee, that he ſpeakes of a calme, and <lb></lb>not diſturbed and agitated Air: but in that caſe, neither Gold nor <lb></lb>Earth, be they never ſo ſmall, are ſuſtained, but ſpeedily deſcend. <lb></lb><arrow.to.target n="marg1534"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1533"></margin.target><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> af <lb></lb>fir meth ſome <lb></lb>Bodies volatile <lb></lb>for their Minu <lb></lb>ity, Text. </s><s>42.</s></p><p type="margin"> <s><margin.target id="marg1534"></margin.target><emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> pla <lb></lb>ced the Cauſe of <lb></lb>Natation in <lb></lb>certain ſiery A <lb></lb>tomes.</s></p><p type="main"> <s>He paſſeth next to confute <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> which, by his Teſtimony <lb></lb>would have it, that ſome Fiery Atomes, which continually aſcend <lb></lb>through the water, do ſpring upwards, and ſuſtain thoſe grave Bodies, <lb></lb>which are very broad, and that the narrow deſcend to the bottom, </s></p><p type="main"> <s><arrow.to.target n="marg1535"></arrow.to.target> <lb></lb>for that but a ſmall quantity of thoſe Atomes, encounter and reſiſt <lb></lb>them.</s></p><p type="margin"> <s><margin.target id="marg1535"></margin.target><emph type="italics"></emph>Ariſtot. </s><s>De Cœlo<emph.end type="italics"></emph.end> <lb></lb>lib. 4. cap. 6. <lb></lb>text. </s><s>43.</s></p><p type="main"> <s>I ſay, <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> confutes this poſition, ſaying, that that ſhould <lb></lb><arrow.to.target n="marg1536"></arrow.to.target> <lb></lb>much more occurre in the Air, as the ſame <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> inſtances a <lb></lb>gainſt himſelf, but after he had moved the objection, he ſlightly re <lb></lb>ſolves it, with ſaying, that thoſe Corpuſcles which aſcend in the Air, <lb></lb>make not their <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> conjunctly. </s><s>Here I will not ſay, that the <lb></lb><arrow.to.target n="marg1537"></arrow.to.target> <lb></lb>reaſon alledged by <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> is true, but I will only ſay, it ſeems <lb></lb>in my judgement, that it is not wholly confuted by <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> whilſt he <lb></lb>ſaith, that were it true, that the calid aſcending Atomes, ſhould <lb></lb>ſuſtain Bodies grave, but very broad, it would much more be done <lb></lb>in the Air, than in Water, for that haply in the Opinion of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1160.jpg" pagenum="469"></pb>the ſaid calid Atomes aſcend with much greater Force and Velocity <lb></lb>through the Air, than through the water. </s><s>And if this be ſo, as I veri <lb></lb>ly believe it is, the Objection of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in my judgement ſeems to <lb></lb>give occaſion of ſuſpecting, that he may poſſibly be deceived in more <lb></lb>than one particular: Firſt, becauſe thoſe calid Atomes, (whether <lb></lb>they be Fiery Corpuſcles, or whether they be Exhalations, or in <lb></lb>ſhort, whatever other matter they be, that aſcends upwards through <lb></lb>the Air) cannot be believed to mount faſter through Air, than <lb></lb>through water: but rather on the contrary, they peradventure move <lb></lb>more impetuouſly through the water, than through the Air, as hath <lb></lb>been in part demonſtrated above. </s><s>And here I cannot finde the rea <lb></lb>ſon, why <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſeeing, that the deſeending Motion of the ſame <lb></lb>Moveable, is more ſwift in Air, than in water, hath not advertiſed <lb></lb>us, that from the contrary Motion, the contrary ſhould neceſſarily <lb></lb>follow; to wit, that it is more ſwift in the water, than in the Air: for <lb></lb>ſince that the Moveable which deſcendeth, moves ſwifter through <lb></lb>the Air, than through the water, if we ſhould ſuppoſe its Gravity <lb></lb>gradually to diminiſh, it would firſt become ſuch, that deſcending <lb></lb>ſwiftly through the Air, it would deſcend but ſlowly through the <lb></lb>water: and then again, it might be ſuch, that deſcending in the <lb></lb>Air, it ſhould aſcend in the water: and being made yet leſs grave, <lb></lb>it ſhall aſcend ſwiftly through the water, and yet deſcend likewiſe <lb></lb>through the Air: and in ſhort, before it can begin to aſcend, though <lb></lb>but ſlowly through the Air, it ſhall aſcend ſwiftly through the water: <lb></lb>how then is it true, that aſcending Moveables move ſwifter through <lb></lb>the Air, than through the water?</s></p><p type="margin"> <s><margin.target id="marg1536"></margin.target><emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> con <lb></lb>futed by <emph type="italics"></emph>Ari <lb></lb>ſtotle,<emph.end type="italics"></emph.end> text 43.</s></p><p type="margin"> <s><margin.target id="marg1537"></margin.target><emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> con <lb></lb>futation of <emph type="italics"></emph>De <lb></lb>mocritus<emph.end type="italics"></emph.end> refuted <lb></lb>by the Author.</s></p><p type="main"> <s>That which hath made <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> believe, the Motion of Aſcent to be <lb></lb>ſwifter in Air, than in water, was firſt, the having referred the <lb></lb>Cauſes of ſlow and quick, as well in the Motion of Aſcent, as of <lb></lb>Deſcent, only to the diverſity of the Figures of the Moveable, and to <lb></lb>the more or leſs Reſiſtance of the greater or leſſer Craſſitude, or Ra <lb></lb>rity of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end>; not regarding the compariſon of the Exceſſes <lb></lb>of the Gravities of the Moveables, and of the <emph type="italics"></emph>Mediums<emph.end type="italics"></emph.end>: the which <lb></lb>notwithſtanding, is the moſt principal point in this affair: for if the <lb></lb>augmentation and diminution of the Tardity or Velocity, ſhould <lb></lb>have only reſpect to the Denſity or Rarity of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> every Body <lb></lb>that deſcends in Air, would deſcend in water: becauſe whatever <lb></lb>difference is found between the Craſſitude of the water, and that of <lb></lb>the Air, may well be found between the Velocity of the ſame Move <lb></lb>able in the Air, and ſome other Velocity: and this ſhould be its <lb></lb>proper Velocity in the water, which is abſolutely falſe. </s><s>The other <lb></lb>occaſion is, that he did believe, that like as there is a poſitive and in <lb></lb>trinſecall Quality, whereby Elementary Bodies have a propenſion <lb></lb>of moving towards the Centre of the Earth, ſo there is another like <pb xlink:href="040/01/1161.jpg" pagenum="470"></pb>wiſe intrinſecall, whereby ſome of thoſe Bodies have an <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of <lb></lb><arrow.to.target n="marg1538"></arrow.to.target> <lb></lb>flying the Centre, and moving upwards: by Vertue of which in <lb></lb>trinſe call Principle, called by him Levity, the Moveables which have <lb></lb>that ſame Motion more eaſily penetrate the more ſubtle <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> <lb></lb>than the more denſe: but ſuch a Propoſition appears likewiſe un <lb></lb>certain, as I have above hinted in part, and as with Reaſons and <lb></lb>Experiments, I could demonſtrate, did not the preſent Argument im <lb></lb>portune me, or could I diſpatch 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"></emph>Ariſtotle<emph.end type="italics"></emph.end> againſt <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> whilſt <lb></lb>he ſaith, that if the Fiery aſcending Atomes ſhould ſuſtain Bodies <lb></lb>grave, but of a diſtended Figure, it would be more obſervable in <lb></lb>the Air than in the water, becauſe ſuch Corpuſcles move ſwifter in <lb></lb>that, than in this, is not good; yea the contrary would evene, for <lb></lb>that they aſcend more ſlowly through the Air: and, beſides their <lb></lb>moving ſlowly, they aſcend, not united together, as in the water, <lb></lb>but diſcontinue, and, as we ſay, ſcatter: And, therefore, as <lb></lb><emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> well replyes, reſolving the inſtance they make not their <lb></lb>puſh or <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> conjunctly.</s></p><p type="main"> <s><emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> in the ſecond place, deceives himſelf, whilſt he will <lb></lb>have the ſaid grave Bodies to be more eaſily ſuſtained by the ſaid <lb></lb>Fiery aſcending Atomes in the Air than in the Water: not obſerv <lb></lb>ing, that the ſaid Bodies are much more grave in that, than in this, <lb></lb>and that ſuch a Body weighs ten pounds in the Air, which will not <lb></lb>in the water weigh 1/2 an ounce; how can it then be more eaſily <lb></lb>ſuſtained in the Air, than in the Water?</s></p><p type="main"> <s>Let us conclude, therefore, that <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> hath in this particular <lb></lb>better Philoſophated than <emph type="italics"></emph>Ariſtotle.<emph.end type="italics"></emph.end> But yet will not I affirm, that <emph type="italics"></emph>De-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1539"></arrow.to.target> <lb></lb><emph type="italics"></emph>mocritus<emph.end type="italics"></emph.end> hath reaſon'd rightly, but I rather ſay, that there is a ma <lb></lb>nifeſt Experiment that overthrows his Reaſon, and this it is, That <lb></lb>if it were true, that calid aſcending Atomes ſhould uphold a Body, <lb></lb>that if they did not hinder, would go to the bottom, it would follow, <lb></lb>that we may find a Matter very little ſuperiour in Gravity to the <lb></lb>water, the which being reduced into a Ball, or other contracted <lb></lb>Figure, ſhould go to the bottom, as encountring but few Fiery A <lb></lb>tomes; and which being diſtended afterwards into a dilated and <lb></lb>thin Plate, ſhould come to be thruſt upwards by the impulſion of a <lb></lb>great Multitude of thoſe Corpuſcles, and at laſt carried to the very <lb></lb>Surface of the water: which wee ſee not to happen; Experience <lb></lb>ſhewing us, that a Body <emph type="italics"></emph>v. </s><s>gra.<emph.end type="italics"></emph.end> of a Sphericall Figure, which very <lb></lb>hardly, and with very great leaſure goeth to the bottom, will reſt <lb></lb>there, and will alſo deſcend thither, being reduced into whatſoever <lb></lb>other diſtended Figure. </s><s>We muſt needs ſay then, either that in the <lb></lb>water, there are no ſuch aſcending Fiery Atoms, or if that ſuch there <lb></lb>be, that they are not able to raiſe and lift up any Plate of a Matter, <pb xlink:href="040/01/1162.jpg" pagenum="471"></pb>that without them would go to the bottom: Of which two Pofitions, <lb></lb>I eſteem the ſecond to be true, underſtanding it of water, conſtituted <lb></lb>in its naturall Coldneſs. </s><s>But if we take a Veſſel of Glaſs, or Braſs, <lb></lb>or any other hard matter, full of cold water, within which is put a <lb></lb>Solid of a flat or concave Figure, but that in Gravity exceeds the <lb></lb>water ſo little, that it goes ſlowly to the bottom; I ſay, that putting <lb></lb>ſome burning Coals under the ſaid Veſſel, as ſoon as the new Fiery <lb></lb>Atomes ſhall have penetrated the ſubſtance of the Veſſel, they ſhall <lb></lb>without doubt, aſcend through that of the water, and thruſting a <lb></lb>gainſt the foreſaid Solid, they ſhall drive it to the Superficies, and <lb></lb>there detain it, as long as the incurſions of the ſaid Corpuſcles ſhall <lb></lb>laſt, which ceaſing after the removall of the Fire, the Solid being a <lb></lb>bandoned by its ſupporters, ſhall return to the bottom.</s></p><p type="margin"> <s><margin.target id="marg1539"></margin.target><emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> con <lb></lb>futed by the <lb></lb>Authour.</s></p><p type="main"> <s>But <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> notes, that this Caufe only takes place when we <lb></lb>treat of raiſing and ſuſtaining of Plates of Matters, but very little <lb></lb>heavier than the water, or extreamly thin: but in Matters very <lb></lb>grave, and of ſome thickneſs, as Plates of Lead or other Mettal, that <lb></lb>ſame Effect wholly ceaſeth: In Teſtimony of which, let's obſerve <lb></lb>that ſuch Plates, being raiſed by the Fiery Atomes, aſcend through <lb></lb>all the depth of the water, and ſtop at the Confines of the Air, ſtill <lb></lb>ſtaying under water: but the Plates of the Opponents ſtay not, but <lb></lb>only when they have their upper Superficies dry, nor is there any <lb></lb>means to be uſed, that when they are within the water, they may <lb></lb>not ſink to the bottom. </s><s>The cauſe, therefore, of the Supernatation <lb></lb>of the things of which <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> ſpeaks is one, and that of the Super <lb></lb>natation of the things of which we ſpeak is another. </s><s>But, returning <lb></lb><arrow.to.target n="marg1540"></arrow.to.target> <lb></lb>to <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> methinks that he hath more weakly confuted <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> <lb></lb>than <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> himſelf hath done: For <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> having propounded <lb></lb>the Objection which he maketh againſt him, and oppoſed him with <lb></lb>ſaying, that if the calid aſcendent Corpuſcles were thoſe that raiſed <lb></lb>the thin Plate, much more then would ſuch a Solid be raiſed and <lb></lb>born upwards through the Air, it ſheweth that the deſire in <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> <lb></lb>to detect <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> was predominate over the exquiſiteneſs of Solid <lb></lb>Philoſophizing: which deſire of his he hath diſcovered in other oc <lb></lb>caſions, and that we may not digreſs too far from this place, in the <lb></lb>Text precedent to this Chapter which we have in hand; where he <lb></lb><arrow.to.target n="marg1541"></arrow.to.target> <lb></lb>attempts to confute the ſame <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> for that he, not content <lb></lb>ing himſelf with names only, had eſſayed more particularly to de <lb></lb>clare what things Gravity and Levity were; that is, the Cauſes of <lb></lb>deſcending and aſcending, (and had introduced Repletion and Va <lb></lb>cuity) aſcribing this to Fire, by which it moves upwards, and that to <lb></lb>the Earth, by which it deſcends; afterwards attributing to the <lb></lb>Air more of Fire, and to the water more of Earth. </s><s>But <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> <lb></lb>deſiring a poſitive Cauſe, even of aſcending Motion, and not as <emph type="italics"></emph>Plato,<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1163.jpg" pagenum="472"></pb>or theſe others, a ſimple negation, or privation, ſuch as Vacuity <lb></lb><arrow.to.target n="marg1542"></arrow.to.target> <lb></lb>would be in reference to Repletion, argueth againſt <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> and <lb></lb>ſaith: If it be true, as you ſuppoſe, then there ſhall be a great Maſs <lb></lb>of water, which ſhall have more of Fire, than a ſmall Maſs of Air, <lb></lb>and a great Maſs of Air, which ſhall have more of Earth than a lit <lb></lb>tle Maſs of water, whereby it would enſue, that a great Maſs of Air, <lb></lb>ſhould come more ſwiftly downwards, than a little quantity of <lb></lb>water: But that is never in any caſe ſoever: Therefore <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> <lb></lb>diſcourſeth erroneouſly.</s></p><p type="margin"> <s><margin.target id="marg1540"></margin.target><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſhews <lb></lb>his deſire of <lb></lb>finding <emph type="italics"></emph>Demo <lb></lb>critus<emph.end type="italics"></emph.end> in an Er <lb></lb>ror, to exceed <lb></lb>that of diſco <lb></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"></emph>Democritus,<emph.end type="italics"></emph.end> is not by this alle <lb></lb>gation overthrown, but if I erre not, the manner of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> deduction <lb></lb>either concludes not, or if it do conclude any thing, it may with e <lb></lb>quall force be reſtored againſt himſelf. <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> will grant to <lb></lb><emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> that there may be a great Maſs of Air taken, which con <lb></lb>tains more Earth, than a ſmall quantity of water, but yet will deny, <lb></lb>that ſuch a Maſs of Air, ſhall go faſter downwards than a little water, <lb></lb>and that for many reaſons. </s><s>Firſt, becauſe if the greater quantity <lb></lb>of Earth, contained in the great Maſs of Air, ought to cauſe a greater <lb></lb>Velocity than a leſs quantity of Earth, contained in a little quantity <lb></lb>of water, it would be neceſſary, firſt, that it were true, that a <lb></lb>greater Maſs of pure Earth, ſhould move more ſwiftly than a leſs: <lb></lb>But this is falſe, though <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in many places affirms it to be true: <lb></lb>becauſe not the greater abſolute, but the greater ſpecificall Gravity, <lb></lb><arrow.to.target n="marg1543"></arrow.to.target> <lb></lb>is the cauſe of greater Velocity: nor doth a Ball of Wood, weigh <lb></lb>ing ten pounds, deſcend more ſwiftly than one weighing ten Ounces, <lb></lb>and that is of the ſame Matter: but indeed a Bullet of Lead of four <lb></lb>Ounces, deſcendeth more ſwiftly than a Ball of Wood of twenty <lb></lb>Pounds: becauſe the Lead is more grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than the Wood. <lb></lb></s><s>Therefore, its not neceſſary, that a great Maſs of Air, by reaſon of <lb></lb>the much Earth contained in it, do deſcend more ſwiftly than a little <lb></lb><arrow.to.target n="marg1544"></arrow.to.target> <lb></lb>Maſs of water, but on the contrary, any whatſoever Maſs of water, <lb></lb>ſhall move more ſwiftly than any other of Air, by reaſon the partici <lb></lb>pation of the terrene parts <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> is greater in the water, than in the <lb></lb>Air. </s><s>Let us note, in the ſecond place, how that in multiplying the <lb></lb>Maſs of the Air, we not only multiply that which is therein of terrene, <lb></lb>but its Fire alſo: whence the Cauſe of aſcending, no leſs encreaſeth, <lb></lb>by vertue of the Fire, than that of deſcending on the account of its <lb></lb>multiplied Earth. </s><s>It was requiſite in increaſing the greatneſs of the <lb></lb>Air, to multiply that which it hath of terrene only, leaving its Fire <lb></lb>in its firſt ſtate, for then the terrene parts of the augmented Air, <lb></lb>overcoming the terrene parts of the ſmall quantity of water, it might <lb></lb>with more probability have been pretended, that the great quanti <lb></lb>ty of Air, ought to deſcend with a greater <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> than the little <lb></lb>quantity of water.</s></p> <pb xlink:href="040/01/1164.jpg" pagenum="467"></pb><p type="margin"> <s><margin.target id="marg1543"></margin.target>The greater <lb></lb>Specificall, not <lb></lb>the greater ab <lb></lb>ſolute Gravity, <lb></lb>is the Cauſe of <lb></lb>Velocity.</s></p><p type="margin"> <s><margin.target id="marg1544"></margin.target>Any Maſs of <lb></lb>water ſhal move <lb></lb>more ſwiftly, <lb></lb>than any of Air, <lb></lb>and why.</s></p><p type="main"> <s>Therefore, the Fallacy lyes more in the Diſcourſe of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> than <lb></lb>in that of <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> who with ſeverall other Reaſons might oppoſe <lb></lb><emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> and alledge; If it be true, that the extreame Elements be <lb></lb>one ſimply grave, and the other ſimply light, and that the mean <lb></lb>Elements participate of the one, and of the other Nature; but the <lb></lb>Air more of Levity, and the water more of Gravity, then there ſhall <lb></lb>be a great Maſs of Air, whoſe Gravity ſhall exceed the Gravity of a <lb></lb>little quantity of water; and therefore ſuch a Maſs of Air ſhall de <lb></lb>ſcend more ſwiftly than that little water: But that is never ſeen to <lb></lb>occurr: Therefore its not true, that the mean Elements do partici <lb></lb>pate of the one, and the other quality. </s><s>This argument is fallacious, <lb></lb>no leſs than the other againſt <emph type="italics"></emph>Democritus.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Laſtly, <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> having ſaid, that if the Poſition of <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> <lb></lb>were true, it would follow, that a great Maſs of Air ſhould move <lb></lb>more ſwiftly than a ſmall Maſs of water, and afterwards ſubjoyned, <lb></lb>that that is never ſeen in any Caſe: methinks others may become de <lb></lb>ſirous to know of him in what place this ſhould evene, which he de <lb></lb>duceth againſt <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> and what Experiment teacheth us, that <lb></lb>it never falls out ſo. </s><s>To ſuppoſe to ſee it in the Element of water, <lb></lb>or in that of the Air is vain, becauſe neither doth water through <lb></lb>water, nor Air through Air move, nor would they ever by any <lb></lb>whatever participation others aſſign them, of Earth or of Fire: the <lb></lb>Earth, in that it is not a Body fluid, and yielding to the mobility of <lb></lb>other Bodies, is a moſt improper place and <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> for ſuch an Ex <lb></lb>periment: <emph type="italics"></emph>Vacuum,<emph.end type="italics"></emph.end> according to the ſame <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> himſelf, there <lb></lb>is none, and were there, nothing would move in it: there remaine <lb></lb>the Region of Fire, but being ſo far diſtant from us, what Experi <lb></lb>ment can aſſure us, or hath aſſertained <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in ſuch ſort, that he <lb></lb>ſhould as of a thing moſt obvious to ſence, affirm what he produ <lb></lb>ceth in confutation of <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> to wit, that a great Maſs of Air, <lb></lb>is moved no ſwifter than a little one of water? </s><s>But I will dwell no <lb></lb>longer upon this matter, whereon I have ſpoke ſufficiently: but <lb></lb>leaving <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> I return to the Text of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> wherein he <lb></lb>goes about to render the true reaſon, how it comes to paſs, that the <lb></lb>thin Plates of Iron or Lead do ſwim on the water; and, moreover, <lb></lb>that Gold it ſelf being beaten into thin Leaves, not only ſwims in <lb></lb>water, but flyeth too and again in the Air. </s><s>He ſuppoſeth that of <lb></lb><arrow.to.target n="marg1545"></arrow.to.target> <lb></lb>Continualls, ſome are eaſily diviſible, others not: and that of the <lb></lb>eaſily diviſible, ſome are more ſo, and ſome leſs: and theſe he <lb></lb>affirms we ſhould eſteem the Cauſes. </s><s>He addes that that is eaſily <lb></lb>diviſible, which is well terminated, and the more the more diviſible, <lb></lb>and that the Air is more ſo, than the water, and the water than the <lb></lb>Earth. </s><s>And, laſtly, he ſuppoſeth that in each kind, the leſſe quan <lb></lb>tity is eaſlyer divided and broken than the greater.</s></p> <pb xlink:href="040/01/1165.jpg" pagenum="474"></pb><p type="margin"> <s><margin.target id="marg1545"></margin.target><emph type="italics"></emph>De Cœlo<emph.end type="italics"></emph.end> l. </s><s>4. c. <lb></lb></s><s>6. t. </s><s>44.</s></p><p type="main"> <s>Here I note, that the Concluſions of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in generall are all <lb></lb>true, but methinks, that he applyeth them to particulars, in which <lb></lb>they have no place, as indeed they have in others, as for Example, <lb></lb>Wax is more eaſily diviſible than Lead, and Lead than Silver, in <lb></lb>aſmuch as Wax receives all the terms more eaſiler than Lead, and <lb></lb>Lead than Silver. </s><s>Its true, moreover, that a little quantity of Sil <lb></lb>ver is eaſlier divided than a great Maſs: and all theſe Propoſitions <lb></lb>are true, becauſe true it is, that in Silver, Lead and Wax, there <lb></lb>is ſimply a Reſiſtance againſt Diviſion, and where there is the abſo <lb></lb>lute, there is alſo the reſpective. </s><s>But if as well in water as in Air, <lb></lb>there be no Renitence againſt ſimple Diviſion, how can we ſay, that <lb></lb>the water is eaſlier divided than the Air? </s><s>We know not how to ex <lb></lb>tricate our ſelves from the Equivocation: whereupon I return to <lb></lb>anſwer, that Reſiſtance of abſolute Diviſion is one thing, and Re <lb></lb>ſiſtance of Diviſion made with ſuch and ſuch Velocity is another. <lb></lb></s><s>But to produce Reſt, and to abate the Motion, the Reſiſtance of <lb></lb>abſolute Diviſion is neceſſary; and the Reſiſtance of ſpeedy Di <lb></lb>viſion, cauſeth not Reſt, but ſlowneſs of Motion. </s><s>But that as well <lb></lb>in the Air, as in water, there is no Reſiſtance of ſimple Diviſion, is <lb></lb>manifeſt, for that there is not found any Solid Body which divides <lb></lb>not the Air, and alſo the water: and that beaten Gold, or ſmall <lb></lb>duſt, are not able to ſuperate the Reſiſtance of the Air, is contrary <lb></lb>to that which Experience ſhews us, for we ſee Gold and Duſt to go <lb></lb>waving to and again in the Air, and at laſt to deſcend down <lb></lb>wards, and to do the ſame in the water, if it be put therein, and ſe <lb></lb>parated from the Air. </s><s>And, becauſe, as I ſay, neither the water, <lb></lb>nor the Air do reſiſt ſimple Diviſion, it cannot be ſaid, that the water <lb></lb>reſiſts more than the Air. </s><s>Nor let any object unto me, the Exam <lb></lb>ple of moſt light Bodies, as a Feather, or a little of the pith of El <lb></lb>der, or water-reed that divides the Air and not the water, and from <lb></lb>this infer, that the Ait is eaſlier diviſible than the water; for I ſay <lb></lb>unto them, that if they do well obſerve, they ſhall ſee the ſame <lb></lb><arrow.to.target n="marg1546"></arrow.to.target> <lb></lb>Body likewiſe divide the Continuity of the water, and ſubmerge in <lb></lb>part, and in ſuch a part, as that ſo much water in Maſs would weigh <lb></lb>as much as the whole Solid. </s><s>And if they ſhal yet perſiſt in their doubt, <lb></lb>that ſuch a Solid ſinks not through inability to divide the water, I will <lb></lb>return them this reply, that if they put it under water, and then let it <lb></lb>go, they ſhall ſee it divide the water, and preſently aſcend with no leſs <lb></lb>celerity, than that with which it divided the Air in deſcending: ſo that <lb></lb>to ſay that this Solid aſcends in the Air, but that coming to the water, <lb></lb>it ceaſeth its Motion, and therefore the water is more difficult to be <lb></lb>divided, concludes nothing: for I, on the contrary, will propoſe them <lb></lb>a piece of Wood, or of Wax, which riſeth from the bottom of the <lb></lb>water, and eaſily divides its Reſiſtance, which afterwards being arri <pb xlink:href="040/01/1166.jpg" pagenum="475"></pb>ved at the Air, ſtayeth there, and hardly toucheth it; whence I may <lb></lb>aswell ſay, that the water is more eaſier divided than the Air</s></p><p type="margin"> <s><margin.target id="marg1546"></margin.target><emph type="italics"></emph>Archimed. </s><s>De <lb></lb>Inſident, humi<emph.end type="italics"></emph.end> lib. <lb></lb></s><s>2. prop. 1.</s></p><p type="main"> <s>I will not on this occaſion forbear to give warning of another fal <lb></lb>lacy of theſe perſons, who attribute the reaſon of ſinking or ſwimming <lb></lb>to the greater or leſſe Reſiſtance of the Craſſitude of the water againſt <lb></lb>Diviſion, making uſe of the example of an Egg, which in ſweet water <lb></lb>goeth to the bottom, but in ſalt water ſwims; and alledging for the <lb></lb>cauſe thereof, the faint Reſiſtance of freſh water againſt Diviſion, and <lb></lb>the ſtrong Reſiſtance of ſalt water But if I miſtake not, from the ſame <lb></lb>Experiment, we may aswell deduce the quite contrary; namely, that <lb></lb>the freſh water is more denſe, and the ſalt more tenuous and ſubtle, <lb></lb>ſince an Egg from the bottom of ſalt water ſpeedily aſcends to the <lb></lb>top, and divides its Reſiſtance, which it cannot do in the freſh, in whoſe <lb></lb>bottom it ſtays, being unable to riſe upwards. </s><s>Into ſuch like perplex <lb></lb>ities, do falſe Principles Lead men: but he that rightly Philoſophating, <lb></lb>ſhall acknowledge the exceſſes of the Gravities of the Moveables and <lb></lb>of the Mediums, to be the Cauſes of thoſe effects, will ſay, that the <lb></lb>Egg ſinks to the bottom in freſh water, for that it is more grave than <lb></lb>it, and ſwimeth in the ſalt, for that its leſs grave than it: and ſhall <lb></lb>without any abſurdity, very ſolidly eſtabliſh his Concluſions.</s></p><p type="main"> <s>Therefore the reaſon totally ceaſeth, that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſubjoyns in the <lb></lb><arrow.to.target n="marg1547"></arrow.to.target> <lb></lb>Text ſaying; The things, therefore, which have great breadth remain <lb></lb>above, becauſe they comprehend much, and that which is greater, <lb></lb>is not eaſily divided. </s><s>Such diſcourſing ceaſeth, I ſay, becauſe its not <lb></lb>true, that there is in water or in Air any Reſiſtance of Diviſion; be <lb></lb>ſides that the Plate of Lead when it ſtays, hath already divided and <lb></lb>penetrated the Craſſitude of the water, and profounded it ſelf ten or <lb></lb>twelve times more than its own thickneſs: beſides that ſuch Reſiſtance <lb></lb>of Diviſion, were it ſuppoſed to be in the water, could not rationally <lb></lb>be affirmed to be more in its ſuperiour parts than in the middle, and <lb></lb>lower: but if there were any difference, the inferiour ſhould be the <lb></lb>more denſe, ſo that the Plate would be no leſs unable to penetrate <lb></lb>the lower, than the ſuperiour parts of the water; nevertheleſs we ſee <lb></lb>that no ſooner do we wet the ſuperious Superficies of the Board or <lb></lb>thin Piece of Wood, but it precipitatly, and without any retenſion, <lb></lb>deſcends 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></lb>defend <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end>) will ſay, that it being true, that the much water re <lb></lb>ſiſts more than the little, the ſaid Board being put lower deſcendeth, <lb></lb>becauſe there remaineth a leſs Maſs of water to be divided by it: be <lb></lb>cauſe if after the having ſeen the ſame Board ſwim in four Inches of <lb></lb>water, and alſo after that in the ſame to ſink, he ſhall try the ſame <lb></lb>Experiment upon a profundity of ten or twenty fathom water, he <lb></lb>ſhall ſee the very ſelf ſame effect. </s><s>And here I will take occaſion to <pb xlink:href="040/01/1167.jpg" pagenum="476"></pb>remember, for the removall of an Error that is too common; That <lb></lb>that Ship or other whatſoever Body, that on the depth of an hundred <lb></lb>or a thouſand fathom, ſwims with ſubmerging only ſix fathom of its <lb></lb>own height, [<emph type="italics"></emph>or in the Sea dialect, that draws ſix fathom water<emph.end type="italics"></emph.end>] ſhall <lb></lb>ſwim in the ſame manner in water, that hath but ſix fathom and half <lb></lb><arrow.to.target n="marg1548"></arrow.to.target> <lb></lb>an Inch of depth. </s><s>Nor do I on the other ſide, think that it can be <lb></lb>ſaid, that the ſuperiour parts of the water are the more denſe, al <lb></lb>though a moſt grave Authour hath eſteemed the ſuperiour water in <lb></lb>the Sea to be ſo, grounding his opinion upon its being more ſalt, than <lb></lb>that at the bottom: but I doubt the Experiment, whether hitherto <lb></lb>in taking the water from the bottom, the Obſervatour did not light <lb></lb>upon ſome ſpring of freſh water there ſpouting up: but we plainly <lb></lb>ſee on the contrary, the freſh Waters of Rivers to dilate themſelves <lb></lb>for ſome miles beyond their place of meeting with the ſalt water of <lb></lb>the Sea, without deſcending in it, or mixing with it, unleſs by the <lb></lb>intervention of ſome commotion or turbulency of the Windes.</s></p><p type="margin"> <s><margin.target id="marg1548"></margin.target>A Ship that <lb></lb>in 100 Fathome <lb></lb>water draweth <lb></lb>6 Fathome, ſhall <lb></lb>float in 6 Fa <lb></lb>thome and 1/2 an <lb></lb>Inch of depth.</s></p><p type="main"> <s>But returning to <emph type="italics"></emph>Aristotle,<emph.end type="italics"></emph.end> I ſay, that the breadth of Figure hath <lb></lb>nothing to do in this buſineſs more or leſs, becauſe the ſaid Plate of <lb></lb><arrow.to.target n="marg1549"></arrow.to.target> <lb></lb>Lead, or other Matter, cut into long Slices, ſwim neither more nor <lb></lb>leſs; and the ſame ſhall the Slices do, being cut anew into little <lb></lb>pieces, becauſe its not the breadth but the thickneſs that operates in <lb></lb>this buſineſs. </s><s>I ſay farther, that in caſe it were really true, that the <lb></lb><arrow.to.target n="marg1550"></arrow.to.target> <lb></lb>Renitence to Diviſion were the proper Cauſe of ſwimming, the Fi <lb></lb>gures more narrow and ſhort, would much better ſwim than the more <lb></lb>ſpacious and broad, ſo that augmenting the breadth of the Figure, <lb></lb>the facility of ſupernatation will be deminiſhed, and decreaſing, that <lb></lb>this will encreaſe.</s></p><p type="margin"> <s><margin.target id="marg1549"></margin.target>Thickneſs not <lb></lb>breadth of Fi <lb></lb>gure to be re <lb></lb>ſpected in Na <lb></lb>tation.</s></p><p type="margin"> <s><margin.target id="marg1550"></margin.target>Were Reni <lb></lb>tence the cauſe <lb></lb>of Natation, <lb></lb>breadth of Fi <lb></lb>gure would <lb></lb>hinder the <lb></lb>ſwiming of Bo <lb></lb>dies.</s></p><p type="main"> <s>And for declaration of what I ſay, conſider that when a thin Plate <lb></lb>of Lead deſcends, dividing the water, the Diviſion and diſcontinu <lb></lb>ation is made between the parts of the water, invironing the perime <lb></lb>ter or Circumference of the ſaid Plate, and according to the big <lb></lb>neſs greater or leſſer of that circuit, it hath to divide a greater or <lb></lb>leſſer quantity of water, ſo that if the circuit, ſuppoſe of a Board, <lb></lb>be ten Feet in ſinking it flatways, it is to make the ſeperation and <lb></lb>diviſion, and to ſo ſpeak, an inciſſion upon ten Feet of water; and <lb></lb>likewiſe a leſſer Board that is four Feet in Perimeter, muſt make an <lb></lb>inceſſion of four Feet. </s><s>This granted, he that hath any knowledge <lb></lb>in Geometry, will comprehend, not only that a Board ſawed in many <lb></lb>long thin pieces, will much better float than when it was entire, but <lb></lb>that all Figures, the more ſhort and narrow they be, ſhall ſo much the <lb></lb>better ſwim. </s><s>Let the Board ABCD be, for Example, eight <lb></lb>Palmes long, and five broad, its circuit ſhall be twenty ſix Palmes; <lb></lb>and ſo many muſt the inceſſion be, which it ſhall make in the water to <lb></lb>deſcend therein: but if we do ſaw ir, as ſuppoſe into eight little <pb xlink:href="040/01/1168.jpg" pagenum="469"></pb>pieces, according to the Lines E F, G H, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> making ſeven Segments, <lb></lb>we muſt adde to the twenty ſix Palmes of the circuit of the whole <lb></lb>Board, ſeventy others; whereupon the eight little pieces ſo cut and <lb></lb>ſeperated, have to cut ninty ſix Palmes of water. </s><s>And, if moreover, <lb></lb>we cur each of the ſaid pieces into five parts, re <lb></lb><figure id="id.040.01.1168.1.jpg" xlink:href="040/01/1168/1.jpg"></figure> <lb></lb>ducing them into Squares, to the circuit of ninty <lb></lb>ſix Palmes, with four cuts of eight Palmes apiece; <lb></lb>we ſhall adde alſo ſixty four Palmes, whereupon <lb></lb>the ſaid Squares to deſcend in the water, muſt <lb></lb>divide one hundred and ſixty Palmes of water, <lb></lb>but the Reſiſtance is much greater than that of <lb></lb>twenty ſix; therefore to the leſſer Superficies, <lb></lb>we ſhall reduce them, ſo much the more eaſily <lb></lb>will they float: and the ſame will happen in all <lb></lb>other Figures, whoſe Superficies are ſimular amongſt themſelves, but <lb></lb>different in bigneſs: becauſe the ſaid Superficies, being either demini <lb></lb>ſhed or encreaſed, always diminiſh or encreaſe their Perimeters in <lb></lb>ſubduple proportion; to wit, the Reſiſtance that they find in pene <lb></lb>trating the water; therefore the little pieces gradually ſwim, with more <lb></lb>and more facility as their breadth is leſſened.</s></p><p type="main"> <s><emph type="italics"></emph>This is manifeſt; for keeping ſtill the ſame height of the Solid, with <lb></lb>the ſame proportion as the Baſe encreaſeth or deminiſheth, doth the ſaid <lb></lb>Solid alſo encreaſe or diminiſh; whereupon the Solid more diminiſhing <lb></lb>than the Circuit, the Cauſe of Submerſion more diminiſheth than the Cauſe <lb></lb>of Natation: And on the contrary, the Solid more encreaſing than the <lb></lb>Circuit, the Cauſe of Submerſion encreaſeth more, that of Natation <lb></lb>leſs.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And this may all be dedueed out of the Doctrine of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> a <lb></lb>gainſt his own Doctrine.</s></p><p type="main"> <s>Laſtly, to that which we read in the latter part of the Text, that <lb></lb><arrow.to.target n="marg1551"></arrow.to.target> <lb></lb>is to ſay, that we muſt compare the Gravity of the Moveable with <lb></lb>the Reſiſtance of the Medium againſt Diviſion, becauſe if the force of <lb></lb>the Gravity exceed the Reſiſtance of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> the Moveable will <lb></lb>deſcend, if not it will float. </s><s>I need not make any other anſwer, <lb></lb>but that which hath been already delivered; namely, that its not <lb></lb>the Reſiſtance of abſolute Diviſion, (which neither is in Water nor <lb></lb>Air) but the Gravity of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> that muſt be compared with the <lb></lb>Gravity of the Moveables; and if that of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> be greater, the <lb></lb>Moveable ſhall not deſcend, nor ſo much as make a totall Submerſion, <lb></lb>but a partiall only: becauſe in the place which it would occupy in <lb></lb>the water, there muſt not remain a Body that weighs leſs than a like <lb></lb>quantity of water: but if the Moveable be more grave, it ſhall deſ <lb></lb>cend to the bottom, and poſſeſs a place where it is more conformable <pb xlink:href="040/01/1169.jpg"></pb> for it to remain, than another Body that is leſs grave. </s><s>And this <lb></lb>is the only true proper and abſolute Cauſe of Natation and Sub <lb></lb>merſion, ſo that nothing elſe hath part therein: and the Board of the <lb></lb>Adverſaries ſwimmeth, when it is conjoyned with as much Air, <lb></lb>as, together with it, doth form a Body leſs grave than ſo much water <lb></lb>as would fill the place that the ſaid Compound occupyes in the <lb></lb>water; but when they ſhall demit the ſimple Ebony into <lb></lb>the water, according to the Tenour of our Que <lb></lb>ſtion, it ſhall alwayes go to the bottom, <lb></lb>though it were as thin as a <lb></lb>Paper.</s></p><p type="margin"> <s><margin.target id="marg1551"></margin.target>Lib. 4. c. </s><s>6. <lb></lb>Text 45.</s></p><p type="head"> <s><emph type="italics"></emph>FINIS.<emph.end type="italics"></emph.end></s></p> </chap> <pb xlink:href="040/01/1170.jpg"></pb> <chap> <p type="head"> <s>THE <lb></lb>TROUBLESOME <lb></lb>INVENTION <lb></lb><emph type="italics"></emph>OF<emph.end type="italics"></emph.end><lb></lb>Nicolas Tartalea:</s></p><p type="head"> <s>BEING <lb></lb>A Generall way to recover from the bottome of the <emph type="italics"></emph>Water,<emph.end type="italics"></emph.end><lb></lb>any <emph type="italics"></emph>SHIP<emph.end type="italics"></emph.end> that's <emph type="italics"></emph>Sunke,<emph.end type="italics"></emph.end> Or any other <emph type="italics"></emph>Ponderous Maſſe,<emph.end type="italics"></emph.end> though <lb></lb>it were a <emph type="italics"></emph>Solid TOWER of Metal.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>TOGETHER WITH<emph.end type="italics"></emph.end><lb></lb>An Artificiall way of DIVING, and ſtaying a long <lb></lb>time under <emph type="italics"></emph>Water,<emph.end type="italics"></emph.end> to ſeeke any thing <emph type="italics"></emph>Sunke<emph.end type="italics"></emph.end> in the <lb></lb>greateſt <emph type="italics"></emph>DEPTHS.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>AS ALSO, <lb></lb>A SVPPLEMENT,<emph.end type="italics"></emph.end> Shewing a <lb></lb>Generall and Secure Way to <emph type="italics"></emph>Grapple, &c.<emph.end type="italics"></emph.end> any <lb></lb><emph type="italics"></emph>Submerged SHIP.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>Engliſhed, By <emph type="italics"></emph>THO. SALUSBURY,<emph.end type="italics"></emph.end> <expan abbr="Eſq;">Eſque</expan></s></p><figure id="id.040.01.1170.1.jpg" xlink:href="040/01/1170/1.jpg"></figure><p type="head"> <s><emph type="italics"></emph>LONDON,<emph.end type="italics"></emph.end><lb></lb>Printed by WILLIAM LEYBOURN, <emph type="italics"></emph>Anno Dom.<emph.end type="italics"></emph.end><lb></lb><emph type="italics"></emph>MDC LXIV.<emph.end type="italics"></emph.end></s></p><pb xlink:href="040/01/1171.jpg"></pb></chap><chap><p type="main"> <s>To the moſt <emph type="italics"></emph>Serene,<emph.end type="italics"></emph.end> and moſt <emph type="italics"></emph>Illustrious<emph.end type="italics"></emph.end><lb></lb>Prince, FRANCESCO DONATO <lb></lb>Duke of VENICE.</s></p><p type="main"> <s><emph type="italics"></emph>It having been told me here at<emph.end type="italics"></emph.end><lb></lb>Breſcia, <emph type="italics"></emph>Moſt Serene and Moſt <lb></lb>Illuſtrious Prince, that about ten <lb></lb>years ſince, that a Ship full-laden <lb></lb>did ſinke near to<emph.end type="italics"></emph.end> Malamoccho, <emph type="italics"></emph>in <lb></lb>about<emph.end type="italics"></emph.end> 5 <emph type="italics"></emph>Fathome of Water, and <lb></lb>that to endeavour the recovering and getting it from <lb></lb>thence, there had been uſed all thoſe Means, and boun <lb></lb>tifull Offers and Tenders that could be imagined, aſwel <lb></lb>by the Illuſtrious Signory, for the Preſervation of the <lb></lb>Port, as by the chief Owners of the Ship and its Cargo: <lb></lb>and that although there were many that had tried, and <lb></lb>attempted the ſame, by ſundry and divers wayes, of no <lb></lb>ſmall expence, and that it had been ſever all times well <lb></lb>grappled and begirt, yet nevertheleſs as far as I could <lb></lb>hear, none of them were able to raiſe her from that ſmall <lb></lb>depth: And it being alſo told me, that of late there was <lb></lb>another ſunk again in leſs than four Fathome of Water, <lb></lb>ſo that all its Poope and Prow, and a greate part of its <lb></lb>Hull, was above Water, and that yet not with ſtanding this <lb></lb>alſo was judged by the fruitleſs Experiments and Ex <lb></lb>penſes made about the former, to be irrecoverable, ſo<emph.end type="italics"></emph.end><pb xlink:href="040/01/1172.jpg"></pb><emph type="italics"></emph>that for the clearing of the Port, it is preſently reſolved, <lb></lb>that the ſaid Ship ſhould be broken up, & taken to pieces <lb></lb>at low Water: and ſo, for ought that I hear, it hath been. <lb></lb></s><s>Now I having conſidered of how great prejudice the <lb></lb>breaking up of ſuch a Veſſel was, beſides the loſs of the <lb></lb>Cargo, I deliberated about the finding of a way or Rule, <lb></lb>that might remedy ſuch detriment all Occurrences: And <lb></lb>having found out one thats generall and unquestionable, I <lb></lb>thought fit, for the common benefit of this renowned City, <lb></lb>to declare, and by Figures to dilucidate the ſame in the <lb></lb>preſent Tractate, and to offer and dedicate the ſame to <lb></lb>your Highneſs; not as a preſent worthy of yon (for indeed <lb></lb>theſe Mechanicall Matters are exceeding diſproporti <lb></lb>onate to your Highneſs Merits) but only with an Ambi <lb></lb>tion to Enoble and Dignifie my Book with your Glorious <lb></lb>Name; In confidence that like as the Sun doth not diſ <lb></lb>dain that all ſorts of Perſons ſhould make uſe of its light <lb></lb>and heat, ſoneither will Your accuſtomed Humanity be <lb></lb>offended with this my Preſumption; and therefore I <lb></lb>humbly lay my ſelf at your Highneſs Feet,<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Nicolas Tartalea.</s></p><pb xlink:href="040/01/1173.jpg" pagenum="483"></pb><p type="head"> <s>THE <lb></lb>Induſtrious or Troubleſome <lb></lb>INVENTION <lb></lb>OF <lb></lb>Nicolas Tartalea:</s></p> </chap> <chap> <p type="head"> <s><emph type="italics"></emph>BOOKEI.<emph.end type="italics"></emph.end></s></p><p type="caption"> <s><emph type="italics"></emph>The Figure of a Ship ſunke according to the Relation made of that <lb></lb>which was cauſed to be broken up neere<emph.end type="italics"></emph.end> Malamoccho, <emph type="italics"></emph>as being <lb></lb>judged irrecoverable.<emph.end type="italics"></emph.end></s></p><figure id="id.040.01.1173.1.jpg" xlink:href="040/01/1173/1.jpg"></figure><p type="head"> <s><emph type="italics"></emph>EXPLANATION I.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Before I come to declare the promiſed way <lb></lb>to recover any laden or empty Ship when <lb></lb>it is ſunke; I thinke it convenient (<emph type="italics"></emph>Moſt <lb></lb>Serene and Illuſtrious Prince,<emph.end type="italics"></emph.end>) firſt to de <lb></lb>clare the reall cauſe of its ſinking.<pb xlink:href="040/01/1174.jpg" pagenum="484"></pb><arrow.to.target n="marg1552"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1552"></margin.target><emph type="italics"></emph>Archimed.<emph.end type="italics"></emph.end> of <lb></lb>Natation, Lib. 2. <lb></lb>Prop. </s><s>1.</s></p><p type="main"> <s>I ſay then; That its impoſſible that the water ſhould wholly <lb></lb>ſwallow or receive into it any materiall Body lighter than it ſelf (as <lb></lb>to ſpecies;) but it will leave or cauſe one part thereof to lie above <lb></lb>the Superficies of the ſaid water, that is uncovered by it. </s><s>And as <lb></lb>the whole Body demitted into the water, is to the part thereof, <lb></lb>which ſhall be received or admitted by the water, ſo ſhall the Spe <lb></lb>cificall Gravity of the water, be unto the Specificall Gravity of the <lb></lb>ſaid 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"></emph>Archimed.<emph.end type="italics"></emph.end> of <lb></lb>Natation, Lib. 1. <lb></lb>Prop. </s><s>7.</s></p><p type="main"> <s>But thoſe Solid Bodies which are more grave than the water; be <lb></lb>ing demitted into the ſaid water, ſuddenly make the water to give <lb></lb>place; and not only enter wholly into the ſame, but they do go <lb></lb>continually deſcending, till they arrive at the bottom: And they <lb></lb>deſcend with ſo much greater Velocity, by how much they exceed <lb></lb>the water in ſpecificall 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"></emph>A chimed.<emph.end type="italics"></emph.end> of <lb></lb>Natation, Lib. 1. <lb></lb>Prop. </s><s>111.</s></p><p type="main"> <s>And thoſe again which happen to be of the ſame Gravity with the <lb></lb>water, of neceſſary conſequence being put into it, are admitted <lb></lb>and received totally into the ſame, but yet they ſtay in the Surface <lb></lb>of the ſaid water; that is, they ſuffer not any part to lie above the <lb></lb>Superficies of the ſaid water, nor much leſs doth the water conſent <lb></lb>to their deſcent to the bottom.</s></p><p type="main"> <s>And all this is demonſtrated by <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> of <emph type="italics"></emph>Syracuſa,<emph.end type="italics"></emph.end> in that <lb></lb>his Tract <emph type="italics"></emph>De inſidentibus aquæ,<emph.end type="italics"></emph.end> by us tranſlated. </s><s>And becauſe the <lb></lb>greateſt part of woods are lighter, or leſs grave than the water; he <lb></lb>therefore that ſhall build a Ship or other Veſſel meerly of wood, <lb></lb>lighter than water, its manifeſt that he cannot (though he ſhould <lb></lb>fill the ſame with water, as full as it would hold) make the ſame <lb></lb>totally to ſink, but that neceſſarily ſome one part or other of the <lb></lb>ſaid Ship or Veſſel ſhall ſtand above the Surface of the water: For <lb></lb>its a thing very clear, that all that ſame Body, compounded of wood <lb></lb>and of water, would be much lighter than if it were all only of water <lb></lb>without wood: Such a compound Body therefore being leſs grave <lb></lb>than the water, its neceſſary (for the reaſons above produced) that <lb></lb>a part of the ſame remain above the Surface of the water.</s></p><p type="main"> <s>And if the ſaid Ship or Bark ſhall be built (as it is uſual) with <lb></lb>Bolts, Nailes, and other Materials of Iron, and that ſuch Iron <lb></lb>works be not of ſuch quantity, as to make that Body compounded <lb></lb>of wood and Iron, graver than the water, but that it continue ſtill <lb></lb>leſs grave than the water (as I judge all Ships and Barks to be;) The <lb></lb>ſame will follow as did before, namely, that filling the ſaid Ship <lb></lb>with water, as full as is poſible, it cannot by any means go to the <lb></lb>bottom If then a Ship or other Veſſel being wholly fill'd with <lb></lb>water, cannot be thereby ſunk to the bottom; It is a thing evident, <lb></lb>that if ſuch a Ship or Veſſel ſhall be totally fill'd with a Matter <lb></lb>lighter than the water; not only its totall ſinking under that weight <pb xlink:href="040/01/1175.jpg" pagenum="485"></pb>will be impoſſible, but alſo its floating in ſome part above the Sur <lb></lb>face of the water will be neceſſary: And ſo much the greater part <lb></lb>ſhall be viſible above the water, by how much the Matter of the <lb></lb>Lading, is lighter than the water.</s></p><p type="main"> <s>Therefore, if all the Cargo of a Ship (for inſtance) Buts of Oyl, <lb></lb>and that no other Matters of a graver Nature than water were intro <lb></lb>duced, and that the ſaid Ship ſhould by ſome Accident be filled <lb></lb>up with water, it is not only manifeſt that the Ship cannot be there <lb></lb>by ſunk to the bottom, but that a part thereof muſt neceſſarily float <lb></lb>above the Surface of the water: Becauſe all that Compoſition of <lb></lb>Wood, Water and Oyl, would be lighter than if it had been all <lb></lb>ſimply of water. </s><s>The very ſame would follow, if the Cargo had <lb></lb>been ſoley of Wine, Wax, Camphor, Spices, or the like Matters, <lb></lb>lighter than the water. </s><s>But becauſe the Merchandizes that fraight <lb></lb>Ships, or other Veſſels, are ſome (ſpecifically) graver, and ſome <lb></lb>(ſpecifically) lighter than the water: (The graver are all forts of <lb></lb>Mettals, as Iron, Tinn, Lead, Braſs, Copper, Silver, Gold, and infi <lb></lb>nite other Species of Commodities; likewiſe the perſons of Men, <lb></lb>Stones, Ballaſts, and the like:) And that alſo there are ſome ſorts of <lb></lb>Commodities that chance to differ very little in Gravity from the <lb></lb>water: Therefore I conclude, that as oft as any Ship accidentally <lb></lb>is fill'd with water, and ſo ſinks by degrees to the bottom, it is ne <lb></lb>ceſſary to grant that all the Compoſition, namely, of the Fraight, <lb></lb>of the Veſſel, and of the water that entered into it, is more grave, <lb></lb>than if the compoſition had been all ſimply of water, by the reaſons <lb></lb>before alledg'd.</s></p><p type="main"> <s>And therefore in ſuch a caſe things graver than the water, muſt <lb></lb>of neceſſity exceed in force thoſe that be lighter: and by how much <lb></lb>things graver than the water, exceed the lighter, ſo much the more <lb></lb>Force will be required to recover ſuch a Ship or other Veſſel being <lb></lb>ſunk, and on the contrary, ſo much leſs Force will be required, <lb></lb>when the Maſs of the Materials more grave than the water, ſhall <lb></lb>not differ much from the Maſs of the leſs grave: provided the Re <lb></lb>covery be undertaken in ſome ſhort time after the Ship ſhall be ſunk, <lb></lb>For if the Ship lie many dayes under water, the delay will intro. <lb></lb></s><s>duce many difficulties: One will be, that it will conſolidate with <lb></lb>and dock or work it ſelf farther into the Mudd or Sand, which will <lb></lb>not a little hinder its Recovery; and again, the water will continu <lb></lb>ally carry into the ſaid Ship, Ouze, Mudd, and Sand, which Mat <lb></lb>ter is much graver than the water, whereby the Ship is continually <lb></lb>made graver as to the water, than it was at the beginning when it <lb></lb>was firſt ſubmerg'd. </s><s>And moreover the corruptible Matters, which <lb></lb>are by nature lighter than the water, will corrupt, and corrupting <lb></lb>will change into other earthy ſubſtances much graver than the <pb xlink:href="040/01/1176.jpg" pagenum="486"></pb>water: inſomuch that at the length, it ought to be preſuppoſed in <lb></lb>order to the recovery of the ſaid Ship, as if it were ſolely laden <lb></lb>with Mire, Dirt, and Sand: which doing, you will not be deceived <lb></lb>in the operation, that is to ſay, preparing and working with a Force <lb></lb>equivalent to that its Gravity. </s><s>The way to know how to prepare <lb></lb>Forces equivalent to the Gravity ſhall be ſhewn in the eight Expla <lb></lb>nation of this.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> II.</s></p><p type="main"> <s>Now to give beginning to the buſineſs propoſed, I ſay, that <lb></lb>in the Recovery of a Foundred Ship laden, or any other la <lb></lb>den Veſſel that is foundered or ſunk, there interveneth more <lb></lb>eſpecially theſe three great Obſtructions. </s><s>The firſt difficulty is, how <lb></lb>to imbreech and grapple it with ſuch, and ſo many Ropes, as may <lb></lb>ſuffice to bear it up; for if this either by ill chance cannot be done <lb></lb>(whether through its being in a place two deep, or too far dockt in <lb></lb>the Mudd or Sand) all our other labour will be fruſtrate and vain.</s></p><p type="main"> <s>The ſecond difficulty, when once it is grappled, is how with dex <lb></lb>terity to ſeperate it from the bottom of the Sea; and this difficulty <lb></lb>will be much greater, the Ship being in a Miry or Sandy bottom, <lb></lb>than if it ſhall be in a Stony place; and it ſhall be alſo a greater <lb></lb>difficulty to ſeperate it from a very deep bottom, than from a Shal <lb></lb>low; (alwayes ſuppoſing that the two bottoms be both alike, name <lb></lb>ly, either both Stony or both Sandy;) and alſo far greater ſhall the <lb></lb>ſaid difficulty be in a Ship long ſunk, than in one newly four dered; <lb></lb>(as we have already ſaid in the precedent Explanation:) But when <lb></lb>ſhe is once water-born, or ſeperated from the bottom, its an caſie <lb></lb>matter to raiſe her up to the Surface of the water; for then ſhe ſhall <lb></lb>not be a little aleviated in her Gravity: But the truth is, the draw <lb></lb>ing of it after wards above the Superficies of the water, is no very ca <lb></lb>ſie matter, but is extream hard to be done; and this is the third <lb></lb>difficulty; the principal cauſe of which two laſt difficulties ſhall be <lb></lb>aſſigned by and by.</s></p><p type="main"> <s>But becauſe the means to obviate and ſuperate the firſt difficulties <lb></lb><arrow.to.target n="marg1555"></arrow.to.target> <lb></lb>as more ^{*} common, we ſhall forbear to ſpeak of them untill the <lb></lb>next Book. </s><s>To provide, and that briefly, to the ſecond and third <lb></lb>impediments (which are the leaſt known) that is, not only to ſe <lb></lb>perate the Ship from the bottom, but to raiſe it alſo ſomewhat above <lb></lb>the Surface of the water.</s></p> <pb xlink:href="040/01/1177.jpg" pagenum="487"></pb><p type="margin"> <s><margin.target id="marg1555"></margin.target>* <emph type="italics"></emph>The Author be <lb></lb>lieved (as he de <lb></lb>clareth in the E <lb></lb>piſtle to the enſu <lb></lb>ing Suppliment of <lb></lb>this his<emph.end type="italics"></emph.end> Inventi <lb></lb>on) <emph type="italics"></emph>that the Ma <lb></lb>riners converſant in theſe affairs, had many wayes to imbreech a Veſſel uuder water; and for that reaſon he <lb></lb>over paſſeth it here, and is very curſive upon the ſame Point, in the ſecond Book, but giveth a generall Rule <lb></lb>for it in the ſaid Suppliment: to which the Reader is referred for fuller Satisfaction.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And this is the Rule that you muſt obſerve; If the Ship be newly <lb></lb>ſunk, you muſt immediately, if it be poſſible, find two other Ships, <lb></lb>that be each of them rather of greater bulk than the foundered Ship <lb></lb>than leſs: and when you have found theſe two Ships, you muſt <lb></lb>free them of all the inward and outward lading, and rigging, eſpe <lb></lb>cially of thoſe things which are by nature more grave than the water, <lb></lb>as are the Guns, the Shot, and any kind of Ballaſt, which is preſup <lb></lb>poſed to be in the Hold, and of other things of impediment; and <lb></lb>when theſe Ships are thus cleared, you muſt ſtop all the Loop-holes, <lb></lb>Cat-holes, Skuppers and Hauſes, which you ſhall finde between or <lb></lb>above Decks, graving and calking them ſo with Okum, and paying <lb></lb>them with Pitch, that the water can neither get in nor out thereat. <lb></lb></s><s>And next you muſt join or grapple theſe two Ships together with five <lb></lb>or more Tires or Orders of thick and ſtrong Beames tripplicated; <lb></lb>that is, that each of the ſaid Orders conſiſt of three Beams, joyned <lb></lb>lengthways; and that each of the three Beams be ſomewhat longer <lb></lb>than the bredth of the Deck or Hull of each Ship; and that theybe <lb></lb>thick and ſtrong, as being to ſupport the Foundered Ship, as you <lb></lb>ſhall ſee it made to appear preſently: and couple the ſaid Ships to <lb></lb>gether, at ſuch a diſtance from each other, that you give berth, or <lb></lb>leave room enough betwixt for the foundered Ship to play; and <lb></lb>you muſt make this couppling in ſuch ſort, that the length or ſide <lb></lb>of the one Ship, look towards the length or ſide of the other; and <lb></lb>albeit this conjunction or grappling may be made with many Orders <lb></lb>or Tires of thoſe Bcams tripplicated lengthways, as was ſaid above, </s></p><p type="caption"> <s><emph type="italics"></emph>The Figurall repreſentation of the two empty Ships, conjoyned with <lb></lb>five Orders of Beams, and towed juſt over the place where the <lb></lb>Foundered Ship is.<emph.end type="italics"></emph.end> <lb></lb><figure id="id.040.01.1177.1.jpg" xlink:href="040/01/1177/1.jpg"></figure> <lb></lb>yet that we may not cauſe confuſion in the Figure, we would have <lb></lb>this colligation to be made only of five Rows, as appeareth in the <pb xlink:href="040/01/1178.jpg" pagenum="488"></pb>Scheme: and although the ſaid Rows of Beames cannot be all <lb></lb>placed equidiſtant from the Surface of the water, for that the <lb></lb>Wailes or Rifings of the two Ships are not fluſh, but cuved, it is <lb></lb>not of any importance, ſo that they be well faſtened and ſtrength <lb></lb>ened in thoſe places where they reſt upon the ſaid Rifings: upon <lb></lb>which Riſings, you ſhall conjoyn the ſaid Beams, namely, the two <lb></lb>ends of them, which two ends ſhall be the ſtrongeſt place, able to <lb></lb>ſupport any great weight. </s><s>Yet the truth is, that to fit theſe Tires <lb></lb>of Beams, you need not have regard to make them paſs through from <lb></lb>ſide to ſide, in that weak part of the Ships Poop and Prow, to reſt <lb></lb>them on the Rifings or Gun-wales of the Deck of thoſe Ships, and <lb></lb>to go croſs the Hull in thoſe places. </s><s>And next you are to make upon <lb></lb>theſe Beams, that is upon the mouths of both the Ships, a Plat-form <lb></lb>of Planks for to ſtand upon whilſt you are about the work; leaving <lb></lb>diverſe Scuttles or Spaces open, whereby to deſcend, aud for other <lb></lb>uſes: And all this being done, you are to tow or hall theſe Veſſels <lb></lb>to the place where the Ship is that did ſink, and to lay them Board <lb></lb>and Board in ſuch faſhion, that the one may lie on one ſide of it, and <lb></lb>the other upon the other, as in the Scheme is apparent.</s></p><p type="main"> <s>This being done, fill thoſe two Ships as full of water as they can <lb></lb>hold or ſwim, (the way to free them with great facility and expe <lb></lb>dition, ſhall be ſhewn in the twelfth Explanation;) and being full, <lb></lb>wait the time of low water; that is, when the Tide returning, the <lb></lb>Sea doth low as much as it can do; and at that inſtant of time, <lb></lb>make the Ship very faſt with thoſe ends of Cords or Cables (with <lb></lb>which it was Swite or bound) to thoſe five, or more Tires of Beams, <lb></lb>wherewith the foreſaid two Ships were imbreecht or grappled: And <lb></lb>having well belayd or faſtned thoſe Cables, you muſt bale or take <lb></lb>out a ſmall part of the water out of one of the two Ships, and then <lb></lb>let it reſt ſo, till ſuch time as you have baled or taken a little more <lb></lb>than that quantity out of the other Ship; and then again take a <lb></lb>little more out of the firſt Ship, and leave it ſo till you have taken <lb></lb>another ſuch a quantity from the other Ship, and thus proceed gra <lb></lb>dually, till you find the Foundered Ship, water-born or looſned <lb></lb>from the bottom: but being water-born (if it be in a Showle bot <lb></lb>tom, as was that at <emph type="italics"></emph>Malamoccho)<emph.end type="italics"></emph.end> you are to take out the ſaid water, <lb></lb>equally from both the Ships, at one and the ſaid time, to the end <lb></lb>the Ship may riſe evenly without ſwagging or ſhaking; and thus you <lb></lb>are to proceed till you have taken all the water from the one & the <lb></lb>other of the two Ships: In ſo doing, you ſhall ſee the two Shpis lea <lb></lb>ſurely and gently raiſe the Ship that was ſunk, ſo high above the <lb></lb>Surface of the water, that you may commodiouſly free it, and <lb></lb>diſcharge it of its lading, as appeareth in the following Figures. <lb></lb></s><s>And if you would not keep the two Ships ſo long imploy'd, you may <pb xlink:href="040/01/1179.jpg" pagenum="489"></pb>warpe or towe the Foundered Ship at high-water to ſome place <lb></lb>where it may lie a-ground: and by that means upon the Ebbe or <lb></lb>Receſſion of the Tide, it will lie much more above water; and then <lb></lb>you may ſafely unfaſten it from thoſe five or more Tires of Beames, <lb></lb>to which it was at firſt tyed, to hall it to a place of ſafety, as it was <lb></lb>our purpoſe to do; and this ſhall ſucceed as well in an ouzie bot <lb></lb>tom, as in a Stony, This though you may take notice of, that if <lb></lb>the Cargo of this new Foundred Ship was ſuch, that the things more <lb></lb>grave than the water, did not much exceed the leſs grave, it would <lb></lb>be eaſie to effect the recovery with two Ships, very much leſs than <lb></lb>thoſe which we have ſpoken of above; yet nevertheleſs it will be <lb></lb>good prudence to take them rather bigger than leſſer, that ſo they <lb></lb>may exceed 200000 pounds in Power, rather than want one only <lb></lb>ounce in Act; eſpecially in caſe you would in a deep place at the <lb></lb>firſt motion hoiſt it by meer Force ſomewhat above the Surface of <lb></lb>the water, for in that point alone it will require incomparably much <lb></lb>more force, than in all the other operations.</s></p><p type="main"> <s>How you are to preceed, in caſe the Ship ſhould be ſunk in a <lb></lb>place very deep, ſhall be declared in the ſeaventh Explanation. </s><s>The <lb></lb>Figures of this Explanation are theſe two that folllow.</s></p><p type="caption"> <s><emph type="italics"></emph>The Figure of the two Ships filled with water, to raiſe the Ship that <lb></lb>is ſunk<emph.end type="italics"></emph.end> <lb></lb><figure id="id.040.01.1179.1.jpg" xlink:href="040/01/1179/1.jpg"></figure></s></p> <pb xlink:href="040/01/1180.jpg" pagenum="490"></pb><p type="caption"> <s><emph type="italics"></emph>The Figure of the two Ships emptied as they lie, with the other Ship <lb></lb>raiſed up above water.<emph.end type="italics"></emph.end></s></p><figure id="id.040.01.1180.1.jpg" xlink:href="040/01/1180/1.jpg"></figure><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> III.</s></p><p type="main"> <s>But if it ſo fall out, that you cannot on ſnch an inſtant, finde <lb></lb>two Ships of the ſame Bulk with the Ship ſunk, you may take <lb></lb>four ſmaller; provided, that all the four together hold twice <lb></lb>as much burden as the Ship ſunk, and rather more than leſs. </s><s>Which <lb></lb>four ſmall Ships being all firſt cleer'd of their lading, and well ſtopt <lb></lb>in all their Skuppers and Portholes (as was ſaid in the two) you muſt <lb></lb>couple them with Beams and good Planks, by two and two, as you <lb></lb>uſe to do with two Lighters, when you would make a Bridge of <lb></lb>them: and theſe two pair of Hoys or Barkes thus coupled together, <lb></lb>you muſt afterwards faſten one pair to another, with ſeven of thoſe <lb></lb>Tires or Rows of thick and ſtrong Beams tripplicated, as was ſaid in <lb></lb>the precedent Explanation; and place them at ſuch a diſtance one <lb></lb>pair from another, as that you may leave berth or ſpace enough for <lb></lb>the ſunk or foundered Ship to riſe between them, and ſome what <lb></lb>more, (as was ſaid of the two.) And though this conjunction of the <lb></lb>two pair of Ships, may be made three ſeverall wayes, yet I will have <lb></lb>you make the two Poops or Hin decks of the one couple, to lie op <lb></lb>poſite to the two Poops of the other couple. </s><s>And to make this <lb></lb>conjunction, you are to place two Tires of thoſe great Beams along <lb></lb>the upper parts of the ſaid Poops, ſo, that they may reſt in the in <lb></lb>ſide on thoſe leſſer Beams and Planks, where with each of thoſe two <lb></lb>pair of Ships were coupled: and each of theſe Orders or Tires of <pb xlink:href="040/01/1181.jpg" pagenum="491"></pb>Beames ought to be compoſed of three Beams conjoyned length <lb></lb>wayes, as was ſaid in the precedent Explanation; and make two of <lb></lb>the Tires lie upon the Ships; and to thoſe Tires, let that ſunk Ship <lb></lb>be grappled: and another Tire of the ſaid Beams is to be placed in <lb></lb>the midſt between the one and the other couple; and two other <lb></lb>Tires of the ſaid Beams ought to be faſtened upon the one and other <lb></lb>ſide, that is, upon the Rifings or Bends of thoſe two couples of <lb></lb>Ships; and that being done, there will be in all ſeven Tires or Or <lb></lb>ders of Beams; which ſeaven Orders of Beams ought conjunctly to <lb></lb>be prolonged, on the one and on the other ſide. </s><s>almoſt to the <lb></lb>length of the Hull of each Ship, as in the Figure is represented: and </s></p><p type="caption"> <s><emph type="italics"></emph>The Figurall example how to recover a Foundered Ship with four <lb></lb>ſmall Ships<emph.end type="italics"></emph.end> <lb></lb><figure id="id.040.01.1181.1.jpg" xlink:href="040/01/1181/1.jpg"></figure> <lb></lb>this being done, you are to proceed, as hath been ſhewn in the two, <lb></lb>that is, fill them top full of water, and at low water, imbreech the <lb></lb>Ship ſunk very well, withall thoſe ends of Ropes or Cables, that <lb></lb>you did belay to thoſe ſeven Tires of Beams: and when thoſe <lb></lb>Grapplings ſhall be well made faſt; you ſhall at high water bale or <lb></lb>free the water by little and little out of the Ships, one pair after a <lb></lb>nother, till you feel the foundered Ship is diſengaged from the bot <lb></lb>tom, and water-born, as was ſaid in the two. </s><s>And having ſepera <lb></lb>ted it from the bottom (if it be in a ſhallow place, as was that where <lb></lb>the Ship was foundered neer <emph type="italics"></emph>Malamoccho<emph.end type="italics"></emph.end>) you are to proceed to let <lb></lb>out the reſt of the ſaid water, but take it equally and gradually from <lb></lb>the one and the other pair, that they may deſcend evenly, and with <lb></lb>out heeling, as was ſaid of the two; and in ſo doing, the ſaid Ship <lb></lb>ſhall not only be hoiſted up to the Surface of the water, but much <pb xlink:href="040/01/1182.jpg" pagenum="492"></pb>above the ſame; ſo that you may in that poſture free or drain it <lb></lb>and diſcharge it of the Cargo. </s><s>But if you cannot ſo long ſpare <lb></lb>thoſe four Ships from other uſes, then you may at high water tow <lb></lb>it to ſome place, where running it on ground, you may at the ebbe <lb></lb>of the Tide (for that then there will lie much more of it above wa <lb></lb>ter) ſafely looſe it from thoſe Beames, as was alſo ſaid in the prece <lb></lb>dent Explanation of the two Ships.</s></p><p type="main"> <s>But in caſe the Foundered Ship ſhould chance to be in a very deep <lb></lb>Sea, in the ſeventh Explanation (to be the briefer in this place) <lb></lb>ſhall be ſhewn how you are to proceed.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> IV.</s></p><p type="main"> <s>And if it happen that it ſhould be in a place where there are <lb></lb>no Ships to be got, either great cr little; you may take of <lb></lb>other kind of Pinaces, Barks or Barges, but endeavour to <lb></lb>get ſuch as are floaty, and higheſt built in there Rifings, that ſo they <lb></lb>may, at ſuch time as they are full of water, deſcend very far under <lb></lb>water, (or according to the Mariners phraſe, may draw much wa <lb></lb>ter) and of theſe you muſt ſtop all the Skuppers, Hawſes, Cat-holes <lb></lb>and Port holes, that you finde, as in the Ships, that they may hold <lb></lb>the more water, and conſequently draw the more water, or be de <lb></lb>preſſed deeper into the ſame; and take ſo many couple of theſe <lb></lb>Botes, that they may all together contain double the burden of <lb></lb>the Ship to be recovered, and rather much more, than any thing <lb></lb>leſs. </s><s>And of all theſe Boats or Barks, make two Squadrons, conjoyning <lb></lb>each Squadron with good ſmall Timbers & Planks, as you uſe to do, <lb></lb>when you would make a Bridge of Boats: And theſe ſame Veſſels of <lb></lb>the one and other diviſion, ſhould be placed board and board, that ſo <lb></lb>the great Beams, which are to conjoyn one Squadron to the other, <lb></lb>may bear upon the Rifings, Bends or Wales, of the ſaid Veſſels. </s><s>And <lb></lb>this being done, you are to couple theſe two Squadrons, to each other <lb></lb>with thoſe thick and ſtrong Tires of Beams, mentioned in the former <lb></lb>Explanations, which Orders of Beams ſhould be fixed between two & <lb></lb>two of thoſe Botes, as is ſaid above, to the end, that they may bear or <lb></lb>reſt upon the Bends of thoſe Boats; and place another Tire upon the <lb></lb>outſides of both the Diviſions, upon the ends of the croſs ſmall Beams <lb></lb>which hold the ſeverall Veſſels together: So that if the Squadrons con <lb></lb>ſiſted each of four Barks, the Tires of the ſaid Beams would come to <lb></lb>be five,; and if there ſhould be five in a Squadron, the Tires of <lb></lb>Beams would be ſix, and ſo forwards; that is, the Orders of Beams, by <lb></lb>this means, ſhall be alwayes one more than the number of Botes in <lb></lb>each Squadron. </s><s>But in the Ships you muſt obſerve another method, <lb></lb>becauſe of thoſe two Orders, which are placed in each Poop; by </s></p> <pb xlink:href="040/01/1183.jpg" pagenum="493"></pb><p type="caption"> <s><emph type="italics"></emph>The way to recover a Foundered Ship with many Barks or Wherryes.<emph.end type="italics"></emph.end> <lb></lb><figure id="id.040.01.1183.1.jpg" xlink:href="040/01/1183/1.jpg"></figure> <lb></lb>which means in every two Ships to a Diviſion (which in all make <lb></lb>four Ships) there muſt be ſeven Orders of Beams, and in three Ships <lb></lb>to a Squadron, there muſt be ten Orders of Beams, and in four <lb></lb>Ships to a Squadron thirteen; and thus proceeding forwards to a <lb></lb>greater number of Ships in a Squadron. </s><s>And having underſtood the <lb></lb>way of coupling many Barks or Wherryes in Squadrons; as alſo the <lb></lb>manner how to joyn or faſten them to each other, and with how <lb></lb>many Orders of Beams; you are to proceed in the reſt, as in the <lb></lb>precedent Explanations hath been demonſtrated in ſhowle bottoms, <lb></lb>but the directions how to manage this affair in deep places, ſhall be <lb></lb>declared in the ſeventh Explanation.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> V.</s></p><p type="main"> <s>To remove this inconvenience of taking Ships or other Veſſels; <lb></lb>and of ſtanding to lighten them of their Guns & lading, and of <lb></lb>ſtopping their Loop-holes; you may inſuch a misfortune cauſe <lb></lb>to be made two great Veſſels, almoſt in form of ^{*} Cheſts without co <lb></lb><arrow.to.target n="marg1556"></arrow.to.target> <lb></lb>vers, the length of each to be equal to the Hull of a middle rate Ship, <lb></lb>and the breadth equall to that of the ſame Ship at the Main-maſt, <lb></lb>and the height alſo the ſame with that of the Ship in the Bow, ſo <lb></lb>that each of theſe Plat forms or Cheſts, ſhall hold much more than <lb></lb>a common Ship, and thus both will contain more than the double <lb></lb>burden of ſuch a Ship. </s><s>And for the making of theſe Veſſels, you <lb></lb>muſt firſt make the Models in Carvel-manner of thick and ſtrong <lb></lb>Timber, with their Eutertaces, Tranſomes and Knees, to hold their <lb></lb>ſides and ends together: and this done, ſpike down to them certain <pb xlink:href="040/01/1184.jpg" pagenum="494"></pb>thick and ſtrong Planks; and then cauſe them to be well graved and <lb></lb>calked in the Seames or Strakes by a Calker, with Okum, and paid <lb></lb>with Pitch, as you uſe to do Ships or Gallyes, and then apply them <lb></lb>to your purpoſe. </s><s>And when you would uſe them, you need only <lb></lb>faſten them together with thoſe five or more Orders of thick and <lb></lb>luſty Beams, trippled lengthwayes, that is, prolonged both wayes, <lb></lb>ſo as that they may lie athwart the Decks of the ſaid two Veſſels, <lb></lb>and place the ſaid Ships ſo far diſtant from each other, as you gueſſe <lb></lb>the bredth of the Foundered Ship to be, and ſomething more: And <lb></lb>then make upon the Deck of each of them, that is, upon thoſe <lb></lb>Beams, a Plat-form of Planks, as was ſaid in the two Ships of the <lb></lb>ſecond Explanation, and afterwards proceed as in thoſe two Ships.</s></p><p type="margin"> <s><margin.target id="marg1556"></margin.target>* Of theſe Veſ <lb></lb>ſels Cardinall <lb></lb><emph type="italics"></emph>Richleiu<emph.end type="italics"></emph.end> made <lb></lb>uſe at the Siege <lb></lb>of <emph type="italics"></emph>Rochell<emph.end type="italics"></emph.end> to ſhut <lb></lb>up the Haven.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> VI.</s></p><p type="main"> <s>And incaſe you think the making of a couple of ſuch great <lb></lb>Modles or Veſſels, as we mentioned in the foregoing Ex <lb></lb>planation, would be too great a trouble or expence; you <lb></lb>may make two pair of ſuch Cheſts, each of them but of halſ the <lb></lb>bulk of one of the former: but if you judge theſe two pair too <lb></lb>troubleſome, you may make three, four, or more pairs; alwayes <lb></lb>provided, that amongſt them all they hold about twiſe the burden <lb></lb>of the Ship ſunk; and theſe Frames when you would uſe them, muſt <lb></lb>be joyned together in two Ranks, with leſſer Beams and Planks, <lb></lb>as was ſaid of the four Boats or Wherryes; and then faſten theſe <lb></lb>two Ranks to each other at the requiſite diſtance, with great and <lb></lb>ſtrong tripplicated Beams, as was ſaid of the Ships, Barks and Boats; <lb></lb>and then operate as you was to do with thoſe: alwayes remembring <lb></lb>in the freeing or emptying the ſaid Veſſels, to bale out the water by <lb></lb>little and little firſt from one Rank, and then from the other; and <lb></lb>ſo proceed interchangeably till you percieve that the Ship is clear of <lb></lb>the bottom: and being diſengaged, if it be in a ſhallow place, <lb></lb>continue taking the water equally out of the one and other Diviſi <lb></lb>on of Veſſels, till all the water be drained out of them, as was requi <lb></lb>red upon the former Explanations: but if it be ſunk in a deep Sea, <lb></lb>the next Explanation ſhall ſhew how you are to proceed; and that <lb></lb>briefly.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> VII.</s></p><p type="main"> <s>And in caſe the ſaid Ship newly ſunk, chance to be in a very <lb></lb>deep bottom; It will be neceſſary firſt to fix upon thoſe <lb></lb>two or four Ships, or upon thoſe two Squadrons of Barks, <lb></lb>Fly-boats or Wherryes, at leaſt ſix or eight Capſtains, Ship-Cranes <pb xlink:href="040/01/1185.jpg" pagenum="495"></pb>or Windlaſſes, with their neceſſary Garnets or Pullies, requiſite to <lb></lb>ſnch a weight: and you may eaſily accomodate theſe Pullies, to thoſe <lb></lb>Orders of great Beams, wherewith the ſaid Veſſels were conjoyned. <lb></lb></s><s>And having prepared theſe Capſtains, you are to proceed in all <lb></lb>things, as hath been directed you in the precedent Explanations, <lb></lb>excepting only in this, that whilſt you are freeing the water alter <lb></lb>nately by degrees out of the two or more Ships, or from the two <lb></lb>Squadrons of Barks, Fly-boats or Wherryes, as ſoon as you finde <lb></lb>the Foundered Ship to be water-born or got clear of the bottom of <lb></lb>the Sea, I would have you ceaſe to take any more water forth of <lb></lb>the ſaid Ships, or leſſer Veſſels before filled; and I would have you <lb></lb>with thoſe Capſtains, attempt to draw the ſaid Ship that was funk <lb></lb>unto the Levell or Surtace of the water, or to lie Horizontal unto it, <lb></lb>which may be eaſily done, for that its ponderoſity will be much di <lb></lb>miniſhed. </s><s>And when you have drawn it to the Surface of the water, <lb></lb>then I would have you diſcharge all the other water out of the two <lb></lb>Ships, or the two Squadrons of ſmall Veſſels. </s><s>And this ſecond wa <lb></lb>ter, I would have raken equally, and at the ſame time, from the one <lb></lb>and the other Ship, or from each Rank of Barks or Boats, as hath <lb></lb>been ſaid of the other. </s><s>And thus thoſe Ships or Squadrons of Boats <lb></lb>ſhall hoiſt the ſaid Foundered Ship, ſo high above the Superficies of <lb></lb>the water, that you may free it of the water which was got into it, <lb></lb>and unlade its Cargo, which was our purpoſe.</s></p><p type="main"> <s>You muſt note, that all that hath been hitherto ſaid of a Ship <lb></lb>newly ſunk, ought to be underſtood of all other kind of Foundered <lb></lb>Ships, proceeding alwayes proportionately as was directed in that <lb></lb>Ship. </s><s>And again, I give you no Figure how you are to fit and fix <lb></lb>the Capſtains and Pullies, as being a thing common and manifeſt.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> VIII.</s></p><p type="main"> <s>But if it ſo fall out, that the ſaid Ship or other Veſſel hath been <lb></lb>ſunk many Months; albeit that there might have been many <lb></lb>matters in the Cargo of a lighter nature than water, yet you <lb></lb>muſt ſuppoſe the caſe as if the Ship were as heavy as if it had been <lb></lb>fil'd with Sand or Gravel; yea and much heavier, for many Reaſons, <lb></lb>as hath been alledg'd in the firſt Explanation. </s><s>Therefore that you <lb></lb>may not deceive your ſelves in the deſigned recovering of it, you <lb></lb>would do well to double the Forces required to the recovery of a <lb></lb>new ſunk Ship; that is, you muſt take four Ships, each as big as <lb></lb>the Foundered <emph type="italics"></emph>S<emph.end type="italics"></emph.end>hip, and combine theſe four <emph type="italics"></emph>S<emph.end type="italics"></emph.end>hips, as you were re <lb></lb>quired to joyn the four ſmall <emph type="italics"></emph>S<emph.end type="italics"></emph.end>hips in the third Explanation. </s><s>And <lb></lb>if you cannot procure them of that burthen, take eight leſſer, pro <lb></lb>vided that altogether they be quadruple in contence to the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>hip to <pb xlink:href="040/01/1186.jpg" pagenum="496"></pb>to be recovered: and divide theſe eight leſſer <emph type="italics"></emph>S<emph.end type="italics"></emph.end>hips or Barks into <lb></lb>two <emph type="italics"></emph>S<emph.end type="italics"></emph.end>quadrons, of four in a <emph type="italics"></emph>S<emph.end type="italics"></emph.end>quadron, according as you was di <lb></lb>rected in the four Ships in the third direction. </s><s>And if you cannot pro <lb></lb>cure <emph type="italics"></emph>S<emph.end type="italics"></emph.end>hips great or ſmal, take ſo many pair of other Veſſels, Fly boats <lb></lb>or Wherryes, that in all they may at leaſt contain four times the bur <lb></lb>then of the Foundered <emph type="italics"></emph>S<emph.end type="italics"></emph.end>hip: And reduce theſe Barks, Boats or <lb></lb>Wherryes into two Diviſions, as you are taught in the fourth Ex <lb></lb>planation: and in all other particulars, proceed according to the <lb></lb>method preſcribed in the recovery of the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>hip newly ſunk; and <lb></lb>that as well in deep, as ſhallow places; that is, placing in a deep <lb></lb><emph type="italics"></emph>S<emph.end type="italics"></emph.end>ea upon the ſaid Ships, or <emph type="italics"></emph>S<emph.end type="italics"></emph.end>quadrons of Boats, at leaſt twelve or <lb></lb>ſixteen Capſtains, which it will be eaſie to do, for that you will have <lb></lb>a large ſpace upon thoſe <emph type="italics"></emph>S<emph.end type="italics"></emph.end>hips or ranks of Boats, as alſo there will <lb></lb>not want room to faſten their Pullies to thoſe Tires of Beams, which <lb></lb>combine the ſaid <emph type="italics"></emph>S<emph.end type="italics"></emph.end>hips or ranks of Boats. </s><s>In all things elſe proceed <lb></lb>preciſely according as you have been directed in the ſecond, third, <lb></lb>fourth, fifth, ſixth and ſeventh Explanations.</s></p><p type="main"> <s>This indeed muſt be granted, that incaſe the ſaid <emph type="italics"></emph>S<emph.end type="italics"></emph.end>hip long ſunk, <lb></lb>ſhould be in a <emph type="italics"></emph>S<emph.end type="italics"></emph.end>tony bottom, or where ſhe hath a great current, the <lb></lb>which current ſuffereth not any great bed or ſhelves of Mudd to <lb></lb>gather about the ſaid <emph type="italics"></emph>S<emph.end type="italics"></emph.end>hip, it may then eaſily be got clear of the bot <lb></lb>tom, with the ſame Forces as were imploy'd in that newly ſunk, to <lb></lb>recover it; and alſo may as eaſily be drawn to the Surface of the <lb></lb>water: But whether you can raiſe it with part of its Hull above <lb></lb>the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>uperficies of the water, is a thing much to be doubted; <lb></lb>yet if it ſhould prove ſo upon the Experiment, namely, that you <lb></lb>cannot elevate its Hull above the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>urface of the water, you may in <lb></lb>ſuch a caſe hall it at high water to ſhore, or to ſome place where it <lb></lb>may lie a ground, whereby at the retreat of the Tide, it will lye with <lb></lb>part of its Hull above water, ſo that you may commodiouſly clear <lb></lb>it of the imbibed water and Cargo.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> IX.</s></p><p type="main"> <s>And to the end that this invention may be of generall uſe <lb></lb>for the re covery or raiſing any kind of Colloſſus, that may <lb></lb>happen to be ſunk, to wit, of all <emph type="italics"></emph>S<emph.end type="italics"></emph.end>pecies of <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid Bodies, <lb></lb>whether of <emph type="italics"></emph>S<emph.end type="italics"></emph.end>tone, Iron, Pewter, Braſs, Lead, <emph type="italics"></emph>S<emph.end type="italics"></emph.end>ilver or Gold (as you <lb></lb>may have many occaſions voluntarily to ſink them in time of war, to <lb></lb>preſerve them) and then that you may know how to get them up <lb></lb>again, you muſt obſerve this Rule: If the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid long time ſubmer <lb></lb>ged were of Brick; ſo ſoon as it is imbreecht, you muſt take ſo ma <lb></lb>ny couple of <emph type="italics"></emph>S<emph.end type="italics"></emph.end>hips, Barks, Hoyes or Wherryes, that the ſum of their <lb></lb>contents put together, may exceed the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>quare of the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid Area <lb></lb>of the ſubmerged <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid: and if the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid ſo long ſunk were of Mar <pb xlink:href="040/01/1187.jpg" pagenum="497"></pb>ble, the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid Content of all the <emph type="italics"></emph>Vacua<emph.end type="italics"></emph.end> of thoſe <emph type="italics"></emph>S<emph.end type="italics"></emph.end>hips or Veſſels ad <lb></lb>ded together, muſt not be leſs than Septuple to the Solid Content <lb></lb>of the ſubmerged Body; namely, ſeven times as much. </s><s>And if <lb></lb>that long ſunk Solid chance to be of Iron; you muſt make the Solid <lb></lb>Content of all the <emph type="italics"></emph>Vacuum's<emph.end type="italics"></emph.end> of thoſe Veſſels to be no leſſe in the <lb></lb>Aggregate than 12 3/2 times as much as the Solid Content of that ſub <lb></lb>merged Solid: and the like muſt be done, if the ſubmerged Solid <lb></lb>be of Pewter, for that Iron and Pewter differ not much in Gravity. <lb></lb></s><s>But and if the drowned <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid be of Copper, it is requiſite that the <lb></lb><emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid Content of all the Veſſels Cavities in ſum, be no leſs than <lb></lb>thirteen times as much as the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid Content of the ſaid <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid ſunk. <lb></lb></s><s>And if the ſubmerged <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid were of Lead, the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid Content of all <lb></lb>the <emph type="italics"></emph>Vacua<emph.end type="italics"></emph.end> of thoſe <emph type="italics"></emph>S<emph.end type="italics"></emph.end>hips, wherewith you would recover it, ſhould <lb></lb>be no leſs than twenty times as much as the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid content of the <lb></lb>drowned <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid, and rather more than leſs; and almoſt the ſame <lb></lb>proportion ought to be obſerved, if the ſubmerged Solid were of fine <lb></lb>Silver, for that Lead and pure Silver differ not much in Gravity: <lb></lb>truth is, that Lead is ſomewhat more weighty than Silver, but not <lb></lb>much.</s></p><p type="main"> <s>But if the Solid which was ſunk, ſhould chance to be of pure <lb></lb>Gold, you muſt for its recovery take ſo many couple of Barks or <lb></lb>Boats, that the Solid Content of their <emph type="italics"></emph>Vacua,<emph.end type="italics"></emph.end> taken in aggregate, <lb></lb>may be no leſs than 34 times as much as the Solid content of the <lb></lb>ſaid Golden Solid ſubmerged. </s><s>And that you may the better under <lb></lb>ſtand me, I will put an Example, that you were to recover or raiſe <lb></lb>out of the water, a Solid Body reſembling a great Tower, which I <lb></lb>imagine to be in length an 100 Paces, and in breadth 10, and in <lb></lb>thickneſs alſo ten: and I ſuppoſe that it is all one <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid, that is to <lb></lb>ſay, not hollow within. </s><s>And firſt we put the caſe that this Tower <lb></lb>were made of Brick. </s><s>Now becauſe the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid Content of this ſup <lb></lb>poſed <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid would be 10000 cubical Paces: therefore in this caſe, <lb></lb>if you would recover this ſame Body, that is, not only looſen it from <lb></lb>the bottom of the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>ea, but alſo raiſe it a good height above water, <lb></lb>it will be requiſite, as is ſaid above, to take ſo many pair of Ships, <lb></lb>Barks, Boats, or other Veſſels, (as hath been ſhewn in the 5 and 6 <lb></lb>Explanation) that the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid Content of all the <emph type="italics"></emph>Vacua<emph.end type="italics"></emph.end> of them put <lb></lb>together, be not leſs than four times the ſaid ſum of 10000 cubick <lb></lb>Paces; that is, it muſt not be under 40000 cubicall Paces, as was <lb></lb>above determined. </s><s>And ſo ìf it happen that the ſaid ſubmerged So <lb></lb>lid ſhould be all of Marble, the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid Content of all the Vacuities <lb></lb>of the ſaid <emph type="italics"></emph>S<emph.end type="italics"></emph.end>hips, ought not to be leſs than 70000 cubicall Paces, <lb></lb>namely Septuple, as was before concluded. </s><s>And thus if the ſunk. <lb></lb><emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid were all of Iron or Pewter, the aggregate of all the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid Con <lb></lb>tent of all thoſe <emph type="italics"></emph>Vacuums<emph.end type="italics"></emph.end> put together, muſt be rather more than <pb xlink:href="040/01/1188.jpg" pagenum="498"></pb>leſs then 126666 2/3 cubical Paces. </s><s>And in caſe the Solid were all of <lb></lb>Copper, the Solid Content of the ſaid <emph type="italics"></emph>Vacua<emph.end type="italics"></emph.end> ought to be about <lb></lb>130000 cubick Paces. </s><s>And likewiſe if the Solid were all of Lead <lb></lb>or Silver, the Solid Content of all the ſaid <emph type="italics"></emph>Vacua<emph.end type="italics"></emph.end> is to be no leſs than <lb></lb>200000 Paces cubical. </s><s>Laſtly, if ſuch ſubmerged Solid be pro <lb></lb>pounded all of fine Gold, the ſum of thoſe Cavities ought to be no <lb></lb>leſs than 340000 cubick Paces.</s></p><p type="main"> <s>The manner how to proceed in the recovery of thoſe ſeverall <lb></lb>kinds of Solids, is to be underſtood to be like to that which was <lb></lb>preſcribed in the recovery of the Ship: and that as well in deep, as <lb></lb>ſhallow waters. </s><s>And the greater number of Ships or Boats are re <lb></lb>quired to opperate in the recovery of the ſaid ſubmerged Solid in a <lb></lb>deep Channell, ſo much the more room muſt yon take upon the <lb></lb>one and the other Squadron, for to be able to pitch ſuch a number <lb></lb>of Capſtens as ſhall be needfull, and more if occaſion be. </s><s>Yet you <lb></lb>muſt obſerve, that in the taking the water alternately from the one <lb></lb>and other Squadron, when you perceive the ſaid Solid to be diſ <lb></lb>engaged from the bottom, you are to forbear taking out any more <lb></lb>from either of them; as was appointed touching the Ship, in the <lb></lb>ſeventh Explanation. </s><s>And make uſe of as many Pullies as you ſhall <lb></lb>ſee cauſe for, not only to lift it to, but alſo to draw it above the <lb></lb>waters Surface: and that if notwholly, yet for the greater part: <lb></lb>and when it is lifted as high as is poſible, then take the remaining <lb></lb>water by equall meaſures, out of the one and other Squadron, or <lb></lb>Rank of Ships; which being done, it ſhall be hoiſted ſo high out of <lb></lb>the water, that you may put under it as many Lighters or Flat-boats, <lb></lb>as ſhall be ſufficient to bear it up, and to carry it to any place, as <lb></lb>occaſion ſhall require.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION X.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Albeit <emph type="italics"></emph>Vitruvius, Vegetius<emph.end type="italics"></emph.end> and <emph type="italics"></emph>Valturius<emph.end type="italics"></emph.end> do teach diverſe and ſun <lb></lb>dry wayes to carry water up on high, many whereof may <lb></lb>ſtand us in much ſtead in this our Invention, for the commo <lb></lb>dious filling and emptying all the ſeverall kinds of Veſſels ſpoken of <lb></lb>above; of which alſo, many are very well known and familiar to <lb></lb>every one; to wit, with Bur-pumps, Chain pumps, common-pumps, <lb></lb>and many others: yet nevertheleſs to fill the ſaid Ships or other <lb></lb>Veſſels with water, with great facility and dexterity; I judge this <lb></lb>more expedient than any of them; namely, to make a Hole in the <lb></lb>bottom of each of thoſe Ships or other Veſſels, of two or three inches <lb></lb>Diameter at leaſt, and for every Ship to appoint a Boome or long <lb></lb>tapered Pole like a Plugg or Tapp, ſo that being thruſt into the ſaid <lb></lb>Hole, it will ſtop it ſo cloſe, that unleſs you conſent thereto, no <pb xlink:href="040/01/1189.jpg" pagenum="499"></pb>water can enter in thereat, and this Pole is to be ſomewhat longer <lb></lb>than to reach from the Keel to the upper deck of the ſaid Ship; and <lb></lb>near the other end, put another piece of a Pole croſs wayes; that <lb></lb>you may be able by means of that to rule it; namely, to pull it up, <lb></lb>when you would unſtop the Hole, to let in the water that ſhould <lb></lb>fill the Ship, and to thruſt it down when you would ſtop the Hole <lb></lb>that no more water may enter; and this ſame Pole ſhould paſs <lb></lb>through two Rings, fixed in the Hold of the Ship, which are to <lb></lb>keep the ſaid Pole directly over the Hole, that if you would ſtop it, <lb></lb>the Plugg or Spiggot may not go beſides the Hole, when you thruſt <lb></lb>the Pole downwards. </s><s>And that I may be the better underſtood, I <lb></lb>have here below drawn the ſame Pole, with its Tapp or Plugg at the <lb></lb>end. </s><s>And when you go about to recover any Ship, you muſt ſtop <lb></lb>the ſaid Holes, till ſuch time as the ſaid Ships are carried <lb></lb><figure id="id.040.01.1189.1.jpg" xlink:href="040/01/1189/1.jpg"></figure> <lb></lb>and fitted upon the place, as is ſhewn above. </s><s>And <lb></lb>when you would fill them with water, it is but with <lb></lb>drawing the ſaid Poles, and opening the Holes; and <lb></lb>faſten them at that ſtay, till you have a mind to ſtop <lb></lb>the Holes; and then look downwards, and obſerve <lb></lb>when the Ships are as full as they can ſwim, or when <lb></lb>they are full enough, which will be in a very ſhort <lb></lb>time: and then let down thoſe Poles, and ſtop the <lb></lb>Holes very cloſe. </s><s>And when they are as full as they <lb></lb>need, in the ebb of the Tide, combine the Ship with the Pullies, to <lb></lb>thoſe five or more Orders of Beams often mentioned: and then draw <lb></lb>out the water with Pumps by little and little, and one while out of <lb></lb>one, and another while out of the other Ship, as was appointed in <lb></lb>the ſecond Explication: and in all other particulars proceed, as was <lb></lb>alſo there directed But if the Gravity of thoſe Veſſels, cauſeth <lb></lb>them not to fill faſt enough, you muſt fill them at the top, that is <lb></lb>by baling in water by the Deck (I mean the ſaid Poles being firſt <lb></lb>thruſt down) to make the ſaid Veſſels to deſcend faſter, and to raiſe <lb></lb>the Matter ſubmerged with more Force; many other new wayes <lb></lb>might be ſhewn, as well to empty, as to fill theſe Veſſels; but for <lb></lb>the preſent this ſhall ſuffice.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> XI.</s></p><p type="main"> <s>If you would attempt to recover a Ship or other Veſſel by the <lb></lb>wayes here preſcribed: you muſt go about the ſame, when the <lb></lb><arrow.to.target n="marg1557"></arrow.to.target> <lb></lb>Moon is in the Auge of the Excentrick, for at that time the Sea <lb></lb>ebbeth and floweth more than at any other time in the Moneth; <lb></lb>and this happens in her Coujunction and Oppoſition, which is a <lb></lb>matter of great avail in theſe operations: and herewith we conclude <lb></lb>this our firſt Book.</s></p> <pb xlink:href="040/01/1190.jpg" pagenum="500"></pb><p type="margin"> <s><margin.target id="marg1557"></margin.target><emph type="italics"></emph>i.e.<emph.end type="italics"></emph.end> At a ſpring, <lb></lb>tide, which is <lb></lb>greateſt the third <lb></lb>day after the fuil <lb></lb>and change.</s></p><p type="head"> <s>THE <lb></lb>Induſtrious or Troubleſome <lb></lb>INVENTION <lb></lb>OF <lb></lb>Nicholaus Tartalea:</s></p><p type="head"> <s><emph type="italics"></emph>BOOKE<emph.end type="italics"></emph.end> II.</s></p><p type="main"> <s>In which are taught, ſome artificial wayes of <emph type="italics"></emph>Diving<emph.end type="italics"></emph.end> <lb></lb>and ſtaying long under Water: whereby one may <lb></lb>eaſily deſcend to the Bottom, to finde out, not on <lb></lb>ly a Ship ſunke, but alſo, any other ſmall thing of <lb></lb>Value: And the place being darke, many wayes <lb></lb>are ſhewn how to enlighten it: And the thing <lb></lb>ſunk being found, ſeverall wayes and means are <lb></lb>preſcribed how to imbreach them, as well in a <lb></lb>Deepe, as Shallow Channel.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> I.</s></p><p type="main"> <s>Having underſtood, <emph type="italics"></emph>Moſt Serene Prince,<emph.end type="italics"></emph.end> from ſun <lb></lb>dry Sea men, that there are many now adayes, <lb></lb>who without any particular Artifice or help, do <lb></lb>upon occaſion dive and continue a long time <lb></lb>under Water, and in places very deep; I had <lb></lb>thought to have added nothing touching the <lb></lb>way of Artificiall Diving, and ſtaying under <lb></lb>water, to ſeeke and finde out a Ship, Boare, <lb></lb>or other thing of Value ſubmerged, and that for two Reaſons. </s><s>Firſt, <lb></lb>Fearing that I ſhould be derided by thoſe kinde of men, it being to <lb></lb>them a ſuperfluous thing to go about to do thoſe things by Art, <lb></lb>which they know how to execute without any arrificiall help. <pb xlink:href="040/01/1191.jpg" pagenum="501"></pb>Secondly, doubting, by reaſon of my ſmall experience in Maratine <lb></lb>Affairs, to incurre ſome Soleciſme: but there coming into my mind <lb></lb>an excellent expreſſion of a famous Philoſopher of this Renowned <lb></lb>City; who upon a time perſwading me to write ſomething that <lb></lb>was new, and I having anſwered (it being incident for humanly to <lb></lb>erre) that I was afraid leaſt my ſo great deſire to publiſh my fund y <lb></lb>new Conjectures, might run me into ſome fantaſtical conceits, that <lb></lb>might make me become the ſubject of vulgar diſcourſe, this excel <lb></lb>lent perſon replied: That if Nature ſhould forbear her operations for <lb></lb>fear of producing ſometimes ſome monſtrous things, the worlds de <lb></lb>ſtruction would enſue, for that they onely are free from erring who <lb></lb>do nothing, whoſe ſpeech hath emboldened me to ſpeak of a point, <lb></lb>which I never thought to have medled with; namely, To declare <lb></lb>ſome of my conjectural wayes of artificial diving, and continuing <lb></lb>under water, to ſeek out any thing that was ſunk in the ſame, though <lb></lb>in places very deep. </s><s>And I judge theſe the moſt expedient that can <lb></lb>be deviſed: and becauſe theſe and the like wayes may be varied <lb></lb>into ſeveral forms, and ſorts, one more ingenious, and artificial than <lb></lb>another; the prettieſt, and moſt ingenious is this, I would have you <lb></lb><arrow.to.target n="marg1558"></arrow.to.target> <lb></lb>get, made at <emph type="italics"></emph>Murano,<emph.end type="italics"></emph.end> a hollow Globe of Tranſparent Glaſſe, the di <lb></lb>ameter of which I would have to be at leaſt two foot, with a round <lb></lb>mouth, that the Diameter of the ſaid mouth may be at leaſt one <lb></lb>foot, or wrather more; that is, ſo much as one may eaſily put his <lb></lb>head therein, and at pleaſure draw it forth; and next you muſt <lb></lb>make two round Boards of a Diameter ſomething bigger then that <lb></lb>of the ſaid Globe, and with theſe two round Boards, and four ſlen <lb></lb>der pieces of Wood, as long as a man is high, and a little more, you <lb></lb>muſt make a little Modell for a man to ſtand betwixt theſe four pie <lb></lb><arrow.to.target n="marg1559"></arrow.to.target> <lb></lb>ces of Wood; and with one of the round Boards above, and the o <lb></lb>ther beneath; and theſe round Boards are to be very faſt nailed or <lb></lb>otherwiſe faſtened to the four pieces of the Frame, and in the top of <lb></lb>this Machine, you muſt fit and fix the ſaid Sphere of Glaſſe with the <lb></lb>mouth downwards, ſo, that if a man ſtand upright in the ſaid Frame, <lb></lb>he may hold his head in the ſaid glaſſe without ſtooping. </s><s>And this <lb></lb>being done, take neer upon as much Lead as all this Machine weighs, <lb></lb>and make it into a round figure, of the compaſſe of the round <lb></lb>Boards, and then faſten and nail it to the bottome of the ſaid Mo <lb></lb>dell, namely, underneath the lowermoſt Board on which your feet <lb></lb>ſtand when you put it into the Water: And then, (or before) <lb></lb>make an hole as big as a Shilling in the Centre of this Lead and <lb></lb>Board, paſſing through them both; and this ſame Lead will be able <lb></lb>to draw almoſt all the Machine together with him that ſhall be <lb></lb>therein under Water. </s><s>Truth is, that the Experiment requireth that <lb></lb>the ſaid Lead be ſo limitted that it may be able to draw the Ma <pb xlink:href="040/01/1192.jpg" pagenum="502"></pb>chine and perſon in it under Water, but ſo, that the ſupreme or up <lb></lb>per part of the ſame, that is the uppermoſt round Board, may ſtay at <lb></lb>the Superficies of the Water; that is, if the Lead chance to be ſo <lb></lb>ponderous, that it cauſe the Engine to ſink leiſurely to the bottome, <lb></lb>you muſt take away ſome of the ſaid Lead; and on the contrary, <lb></lb>if it chance that the Lead be not able to draw it all in that manner <lb></lb>under Water, ſo as to make the ſaid upper round Board to lye and <lb></lb>ſtay exactly level with the Surface of the Water, but that a part of it <lb></lb>reſts viſible above the Water, you muſt encreaſe the ſaid Lead ſo, <lb></lb>that the upper Board may lye and abide preciſely, as was ſaid be <lb></lb>fore, in the Surface of the Water: and when you have thus adju <lb></lb>ſted the ſaid Lead, I would have you take a Ball or Bullet of Lead <lb></lb>weighing two or three pounds, (that is to ſay of ſuch a weight, that <lb></lb>it may be ſufficient to make the Machine and perſon diving to de <lb></lb>ſcend to the bottome as oft as it is interpoſed, or added,) with an <lb></lb>Iron Ring in the ſaid Ball, to which bend or faſten a Rope as long as <lb></lb>the ſaid Water is deep, in which the Diver is to deſcend, and ſome <lb></lb>what more; and reeve or paſſe the other end of the ſaid <lb></lb>Cord through the hole <lb></lb>made in the Board and <lb></lb>Lead through the bot <lb></lb><figure id="id.040.01.1192.1.jpg" xlink:href="040/01/1192/1.jpg"></figure> <lb></lb>tom of the Model; and <lb></lb>faſten that ſame end <lb></lb>of the Cord in a place <lb></lb>of the Machine, ſo, that <lb></lb>the Diver may take it, <lb></lb>and draw it, or ſlack <lb></lb>it as he pleaſeth: and <lb></lb>this being done, the <lb></lb>ſaid Machine will be <lb></lb>finiſhed. </s><s>And that you <lb></lb>may better under <lb></lb>ſtand it, I have here in <lb></lb>ſerted it graphically: <lb></lb>yet I ſhould have told <lb></lb>you, that for many rea <lb></lb>ons you ſhould in the beginning have faſtened a Ring in the Cen <lb></lb>tre of the upper Board, on the outſide, to tye a Cord to the ſame as <lb></lb>occaſion ſerveth.</s></p> <pb xlink:href="040/01/1193.jpg" pagenum="503"></pb><p type="margin"> <s><margin.target id="marg1558"></margin.target>A Place near to <lb></lb><emph type="italics"></emph>Venice,<emph.end type="italics"></emph.end> where the <lb></lb>famous Glahes <lb></lb>are made.</s></p><p type="margin"> <s><margin.target id="marg1559"></margin.target>Like the Frame <lb></lb>of an Houre <lb></lb>glaſſe.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> II.</s></p><p type="main"> <s>Having underſtood the manner how to make this ſame En <lb></lb>gine, it remains to ſhew how it is to be uſed; And for your <lb></lb>direction therein, I ſay, That he that would dive or go under <lb></lb>Water to ſeek any thing that was ſunk, ſhould carry the ſaid Ma <lb></lb>chine to the place where he reſolves to deſcend, and firſt to let that <lb></lb>Ball of Lead with the Line go to the bottome, and then to put in <lb></lb>the Machine it ſelf, which by means of its heavy bottome of Lead <lb></lb>will reſt upright in the Water, with almoſt all the Globe of Glaſſe <lb></lb>above Water, in ſuch ſort, that he that would may eaſily enter into <lb></lb>the ſame: yet you muſt be dexterous in going into it, that you do <lb></lb>not much ſway the Machine ſidewayes, for that, if it lye too oblique <lb></lb>the Water will enter into the Globe of Glaſſe, and drive the Aire <lb></lb>thence that was in the ſame, or at leaſt in part, but holding it up <lb></lb>right when you enter the ſame, the Water ſhall keep in the Aire on <lb></lb>all ſides, whereby the water will be kept from entring. </s><s>And therefore <lb></lb>if he that ſhall enter into the ſaid Machine, do nimbly thruſt his head <lb></lb>into the ſaid Globe by the hole thereof, he ſhall finde it quite fil <lb></lb>led with Ayre; in which place he may breath for verry many Re <lb></lb>ſpirations, without the leaſt obſtruction from the Water: And be <lb></lb>cauſe this Machine will ſtay with its upper end level with the Wa <lb></lb>ters ſurface (the affixed Lead having been ſo limited) therefore <lb></lb>deſiring to deſcend to the bottom, the Diver ſhould hale the Ball <lb></lb>and Line upwards, which was ſent before to the Bottom, in haling <lb></lb>of which the ſaid Machine will deſcend as much under Water as he <lb></lb>hales the Corde; and if he continue haling it, till there be none of <lb></lb>it left, he ſhall deſcend to the Bottome; and in the deſcent, and after <lb></lb>that he ſhall be got to the bottom, he muſt look round about him <lb></lb>through that tranſparent Globe for to finde out the thing he ſeeks, <lb></lb>and ſeeing it, he may many wayes with caſe transferre himſelf <lb></lb>thither without riſing again to the top; And when he would re <lb></lb>turn upwards to the toppe of the Water, he needs do no more but <lb></lb>ſlacken that corde faſtned to the Ball of Lead, for thereupon the <lb></lb>Machine ſhall begin to riſe upwards, and letting the ſaid Corde goe, <lb></lb>it ſhall not ſtay till the Machines upper parte arrive at the ſurface of <lb></lb>the Water; and being aſcended thither, the Diver may come out <lb></lb>thereof, and ſwim to the top, and provide himſelf afterwards of <lb></lb>ſuch things as are neceſſary for embreching the ſaid Ship or other <lb></lb>matter ſunke: And in caſe the Diver cannot ſwim, it will be neceſſa <lb></lb>ry to faſten a Corde to the Ring placed in the Centre of the upper <lb></lb>Board, and thereby to draw the Modell above the Surface of the <pb xlink:href="040/01/1194.jpg" pagenum="504"></pb>Water; but knowing how to ſwim, he may enter, aſcend, and <lb></lb>deſcend of himſelf, without any help.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> III.</s></p><p type="main"> <s>But if you chance to be in a place where you cannot procure <lb></lb>the ſaid Globe to be made of Glaſſe, it may be made of Wood; <lb></lb>but then you muſt make therein great Sights, or Eyeholes of <lb></lb>clear Glaſſe of each ſide to look four ſeverall wayes; and pay it <lb></lb>without, and alſo within if you ſee cauſe with Pitch. </s><s>And if you <lb></lb>cannot get ſuch a Ball of Wood, you may make ſhift with a little <lb></lb>Cubicall Cheſt or Boxe, like one of thoſe Cheſts wherein they plant <lb></lb>Ceaders, which muſt be well joyned graved and pitch't, with four <lb></lb>ſuch Sights of Glaſſe as before, namely one upon every lateral flat <lb></lb>or plain, ſo placed, that the Diver may ſee through them every way, <lb></lb>and be able to look downwards, it would be good to make the <lb></lb>Box ſomewhat narrower towards the mouth, that ſo the four late <lb></lb>rall Planes may look ſomewhat ſloping: and in the entrance, de <lb></lb>ſcent, aſcent, and coming forth, you are to uſe the ſame Rules as be <lb></lb>fore; aud if you have a deſire to deſcend faſter, you muſt make the <lb></lb>Ball of Lead ſomewhat heavier, that was tyed to the end of the <lb></lb>Corde, and this done the Machine ſhall deſcend faſter to the bottom <lb></lb>upon halling the ſaid Corde and Ball; and when you vere or let <lb></lb>looſe the Cord, the Engine will re-aſcend but according to its former <lb></lb>ſpeed: But if you would alſo make it ſwifter in its aſcent you are <lb></lb>to proceed quite contrary, that is, you muſt ſomewhat diminiſh the <lb></lb>Lead, which is under the Baſe of the fiame; and the more you di <lb></lb>miniſh the ſaid Lead, the ſwifter ſhall it be in aſcending. </s><s>But you <lb></lb>muſt remember withall to encreaſe the Ball of Lead, ſo that it may <lb></lb>be able to draw the ſaid Machine to the bottome ſpeedily or leiſure <lb></lb>ly according as occaſion requires.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> IV.</s></p><p type="main"> <s>But if there be any likelihood of any obnoxious Fiſh in the place <lb></lb>where the Diver is to deſcend, that may hurt him, being quite na <lb></lb>ked; though that in the former kind of Machine with four pillars you <lb></lb>may ſe u e him with a wire Grate, made in the manner of doors to the <lb></lb>ſame, yet to the end that you may know that this Invention may be <lb></lb>varied ſundry ways; you may in this caſe have a Globe of tranſparent <lb></lb>glaſs made at <emph type="italics"></emph>Murano,<emph.end type="italics"></emph.end> of ſuch a bigneſs, that a man ſtanding on his feet, <lb></lb>or elſe ſitting, may be contain'd therein, having amouth or round hole <lb></lb>of capacity ſufficient for a man, commodiouſly to enter and goe out <lb></lb>thereby, and ſomewhat larger: & then coffin or encloſe the ſaid Globe <pb xlink:href="040/01/1195.jpg" pagenum="505"></pb>between two round Boards of ſomewhat a greater Diameter than <lb></lb>the Globe, with four pillars, as in the enſuing figure doth graphically <lb></lb>appear. </s><s>But in the round Board which is put over the hole or mouth <lb></lb>of the ſaid Globe, you muſt alſo make a round hole ſomewhat nar <lb></lb>rower than that of the Globe, but yet big enough for a man to paſſe <lb></lb>in and out thereat. </s><s>Afterwards under this round Board ſo bored, <lb></lb>you muſt place and fix another round bored piece of Lead of ſuch <lb></lb>thickneſſe, as that it may be able to draw the ſaid Ball or Globe of <lb></lb>Glaſſe, together with the Diver in ſuch manner under Water, that <lb></lb>the upper round Board do reſt in the Surface of the Water, namely, <lb></lb>that it may not be ſo heavy as to ſink the Globe and Diver to the <lb></lb>bottome, but only to retain it beneath the Surface of the Water, <lb></lb>which by tryal may be eaſily proportioned, namely, by adding or <lb></lb>taking away Lead from the Baſe, according as occaſion ſhall require. <lb></lb></s><s>Next you are to frame a ſeat for the Diver to ſit commodiouſly in <lb></lb>the ſaid Ball or Globe, and next faſten a Ball of Lead to the end of <lb></lb>a Rope, as many fathom long as the water is deep into which you <lb></lb>would deſcend, and ſomewhat more, as was ſaid in the preceding <lb></lb>Explanation. </s><s>And that Ball of Lead ſhould be of ſuch bigneſſe, that <lb></lb>applied to the ſaid Model, it may be ſufficient to make it deſcend to <lb></lb>the bottome leiſurely, or ſwiftly, as he ſeeth cauſe who is to dive. <lb></lb></s><s>And make an handle or peg in the ſaid Globe whereat to faſten or <lb></lb>belay the other end of <lb></lb>the ſaid Rope, and to <lb></lb>draw it eaſily upwards, <lb></lb><figure id="id.040.01.1195.1.jpg" xlink:href="040/01/1195/1.jpg"></figure> <lb></lb>or let it looſe at the <lb></lb>pleaſure of him that is <lb></lb>within, and this may be <lb></lb>eaſily done by joyning <lb></lb>and faſtening four <lb></lb>pieces of wood upright <lb></lb>in the mouth or hole of <lb></lb>that bored Board and <lb></lb>Lead, which ſhall be <lb></lb>about the mouth of the <lb></lb>ſaid Globe; and that <lb></lb>I may be the better <lb></lb>underſtood, I will give <lb></lb>it you in figure with the <lb></lb>Diver ſitting therein. <lb></lb></s><s>If you would deſcend to the bottome of ſome deep water by help <lb></lb>of this Machine, you are to proceed according to the directions gi <lb></lb>ven in the precedent Explanation.</s></p> <pb xlink:href="040/01/1196.jpg" pagenum="506"></pb><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> V.</s></p><p type="main"> <s>In caſe you ſhould be in a place where you could not have ſuch <lb></lb>a Globe made of Glaſſe, you may procure one of Copper or <lb></lb><arrow.to.target n="marg1560"></arrow.to.target> <lb></lb>Lead, round in faſhion of a greater ^{*} Churne, wide in the bot <lb></lb>tome and narrow in the mouth, and at leaſt five foot high, and four <lb></lb>foot broad. </s><s>It may indeed be made quadrangular, that is, ſo that <lb></lb>the mouth be at leaſt three foot ſquare every way, and the bottome <lb></lb>at leaſt four foot every ſide, and not under five foot high, and this <lb></lb>ſame veſſel, making it of Lead, muſt be ſo contrived, or proportio <lb></lb>ned, that the corporeal or ſolid <emph type="italics"></emph>Area,<emph.end type="italics"></emph.end> or Content of its interiour va <lb></lb>cuity, or ſpace, be about <gap></gap>oruple to the ſolid <emph type="italics"></emph>Area<emph.end type="italics"></emph.end> of the Lead, <lb></lb>which is imployed in making the ſaid Veſſel; that is, make the Lead <lb></lb>of ſuch a thickneſſe, that the Veſſels vacuity may be nine tenths of <lb></lb>the ſolid Area of all the whole Frame, which may be eaſily done by <lb></lb>any one that is not ignorant of practical Geometry: and this Veſſel <lb></lb>being made, you ſhould place or ſet therein four great Fye holes or <lb></lb>Sights of tranſparent or criſtaline Glaſſe, ſo placed as to ſee any way <lb></lb>as you ſhall need or deſire: and furthermore, in the framing of this <lb></lb>ſame Veſſel, you muſt make ſome proviſion for the ſetling or ſtay <lb></lb>ing your feet, and to ſit down, and likewiſe you muſt make a <lb></lb>Pulley to hall the Ball of Lead up, or let it down, which is faſtened <lb></lb>to the end of the long cord, as was ſaid in the two precedent caſes. <lb></lb></s><s>And moreover, in the making of this Veſſel, you are to faſten four <lb></lb>Rings of Iron to the bottome without, namely, to the four Angles, <lb></lb>it being Quadrangular; (and being round, let them divide the Cir <lb></lb>cumference into four equal parts) and betwixt theſe four Rings, <lb></lb>you muſt place a ſquare or round Deal Board. </s><s>And this Veſſel thus <lb></lb>modellized ſhall be ſo contrived, that putting it into the water with <lb></lb>the mouth downwards, with him in it who is to Dive, it ſhall but juſt <lb></lb>ſtay in the Surface of the water with that bottome of wood; but if <lb></lb>it chance that it ſhall not ſtay at the Surface of the water by helpof <lb></lb>that bottome of Board, but that it will deſcend, you muſt upon that <lb></lb>bottome faſten another, or two, or more ſquare or round Boards to <lb></lb>the four Rings, in ſuch wiſe, that by means of the ſaid Boaids it may <lb></lb>be reduced to ſuch a quality, that it may reſt with the ſaid round <lb></lb>Boards in the Surface of the water, and deſcend no farther. </s><s>Having <lb></lb>with judgement and experience provided all theſe things, and the <lb></lb>Diver being deſirous to deſcend of himſelf, and likewiſe to return <lb></lb>to the top when he pleaſeth, this may be performed with that Ball <lb></lb>of Lead tied to the end of that long Rope, as hath been ſaid in the <lb></lb>precedent Explanations, that is, to ſend the Ball firſt to the bottom in <lb></lb>he place where the Diver would deſcend, and then to enter into the <pb xlink:href="040/01/1197.jpg" pagenum="507"></pb>Machine, and to ſettle himſelf therein; and then to pull the Ball <lb></lb>upwards, which ſhould be of that Gravity, that it may be apt to <lb></lb>make ſuch a Veſſel or Machine deſcend together with the Diver; and <lb></lb>if the Machine chance to be juſtly contrived, as hath been ſaid a <lb></lb>bove, I hold that a Ball of ſive or ſix pounds may be ſufficient to <lb></lb>make it deſcend nimbly upon the pulling of the Cord, and lifting <lb></lb>the Ball from the bottome, and continuing to draw the ſaid Cord, <lb></lb>as long as there is any remaining, he ſhall arrive at the bottome; and <lb></lb>whenever he would return upwards, he need but only vere or ſlack <lb></lb>en that Cord, and letting it all go he will not ceaſe aſcending till the <lb></lb>Machine attains with its top (covered with thoſe ſquare or round <lb></lb>Boards) unto the Surface of the Water, as hath been ſaid of the o <lb></lb>thers. </s><s>I will not ſtand to ſhew you the many particularities which <lb></lb>might be inſerted for the tranſporting your ſelves from one place to <lb></lb>another, keeping at the bottome, that is, without returning to the <lb></lb>top, for that they are almoſt infinite, but it ſhall ſuffice to let you <lb></lb>know, that he may eaſily do it, carrying with him a long Hitcher, or <lb></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"></emph>Brenta,<emph.end type="italics"></emph.end> a Veſſel <lb></lb>in which they <lb></lb>in Italy carry <lb></lb>Grapes to the <lb></lb>Preſs.</s></p><p type="main"> <s>Many other particulars there might be inſiſted on, and eſpecially <lb></lb>how many may ſimply (that is, without any of the forsaid Ma <lb></lb>chines) go to the bottome, and ſtay for many hours under Water, <lb></lb>which, beſides the many profitable concluſions that might from <lb></lb>thence be inferred for Diving in indifferent depths, being accompa <lb></lb>nied with the helps preſcribed in the foregoing Explanations, they <lb></lb>would be much to the purpoſe, for that the Liver being once condu <lb></lb>cted with the Machine near unto the thing ſunk, he might come out <lb></lb>of the ſaid Machine, and go and ſtay for a long time about the ſame, <lb></lb>to faſten, or prepare thoſe things that are neceſſary for the raiſing <lb></lb>it: And farthermore, there is ſomething to be ſaid, when the thing <lb></lb>ſunk is in a muddy or dark Water, how the Diver may in ſundry <lb></lb>wayes, kindle there a great and flaming light, which flaming fire, <lb></lb>beſides that it would make him diſcern the thing ſunk, it would alſo <lb></lb>ſecure him in his going forth of the Machine from any devouring <lb></lb>Fiſhes, for that all ſuch as ſhould chance to be near that place would <lb></lb>be affrighted at ſuch an unuſual ſpectacle, and would make far <lb></lb>from it. </s><s>I might alſo ſhew many wayes to embreech and grapple a <lb></lb>Ship when it is found, as well in deep as ſhallow Channels, which <lb></lb>particulars I ſhall reſerve for another time.</s></p><p type="main"> <s>I will not ſtand to ſhew how this kind of Diving Machine might <lb></lb>be made of Boards, and that in ſundry faſhions, well calked and <lb></lb>pitcht, with four Lights or Sights, faſtening about the mouth of the <lb></lb>ſame as much Lead as ſhould be neceſſary, oraſinuch as by what <lb></lb>hath been ſpoken in the third Explanation, it is ſufficiently manifeſt. </s></p> <pb xlink:href="040/01/1198.jpg" pagenum="508"></pb><p type="head"> <s>A <lb></lb>SUPPLEMENT <lb></lb>OF THE <lb></lb>Induſtrious or Troubleſome <lb></lb>INVENTION <lb></lb>OF <lb></lb>Nicholaus Tartalea:</s></p><p type="main"> <s>In which is ſhewn a general and ſafe way to im <lb></lb>breech Cables, and hitch Grappling irons to any <lb></lb>Ship that's ſunk, aſwell in a deep as ſhallow Bot <lb></lb>tome, provided you know the exact place where <lb></lb>the ſaid Ship is. </s><s>Together with another new way <lb></lb>of raiſing or recovering the ſame.</s></p><p type="main"> <s><emph type="italics"></emph>Whereunto is, laſt of all, added ſome new ways to conduct a Light, or <lb></lb>Flaming Matter, unto the Bottome of the Water, to enlighten, upon oc <lb></lb>caſion, any dark Bottome, for the diſcovery, not onely, of a Ship or Bark, <lb></lb>but alſo any ſmall thing of value that is ſunk, and that in the night as <lb></lb>well as in the day.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>To the Moſt <lb></lb>Illuſtrious and moſt Serene</s></p><p type="head"> <s>PRINCE <lb></lb>Franceſco Donato, <lb></lb>Duke of <lb></lb>VENICE.</s></p><p type="main"> <s><emph type="italics"></emph>Having not long ſince, Most Serene, and Moſt <lb></lb>Illuſtrious Prince, publiſhed under the Glorious <lb></lb>Name of your Highneſſe, ſundry and diverſe <lb></lb>way storaiſe a Ship ſunk, with its Cargo in it (when once<emph.end type="italics"></emph.end> <pb xlink:href="040/01/1199.jpg" pagenum="509"></pb><emph type="italics"></emph>it is Grappled) I muſt confeſſe I was not then ſollicitous to <lb></lb>find a way to imbreach or grapple the ſaid Ship (though <lb></lb>it is neceſſary to be known) and the cauſe thereof was, for <lb></lb>that I concluded that amongſt Mariners there were a <lb></lb>thouſand means to effect it, and I was loath to enquire af <lb></lb>ter ſuch things as are commonly known to many, although <lb></lb>I be ignorant of them; but delight to ſearch into thoſe <lb></lb>things which none elſe can do. </s><s>Now, having been ſince <lb></lb>told and aſſured by many, that Mariners, and all other <lb></lb>perſons of ingenuity find far greater difficulty in imbrea <lb></lb>ching and Grappling ſuch a Ship, than they do, (when <lb></lb>once they have hold of it) to raiſe the ſame: I underſtan <lb></lb>ding the ſame, preſently deliberated upon ſome way that <lb></lb>ſhould be general and ſecure, and to adde it in the end of <lb></lb>my Treatiſe, that ſo it might not, for want thereof, be vain <lb></lb>and uſeleſs. </s><s>And thus; of many that I have found, that <lb></lb>which to me hath ſeemed moſt univerſal and eaſy to be <lb></lb>explained by writing; I have here ſubjoined, together <lb></lb>with another new way to recover the ſaid Ship: and the <lb></lb>manner how to illuminate the bottome of a dark Water, <lb></lb>but still under the Illustrious Name of your Serene <lb></lb>Highneſſe, at whoſe feet I once more humbly throw my <lb></lb>ſelf<emph.end type="italics"></emph.end></s></p><p type="main"> <s>NICOLO TARTAGLIA.</s></p> <pb xlink:href="040/01/1200.jpg" pagenum="510"></pb><p type="head"> <s>A Supplement.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> I.</s></p><p type="main"> <s>To hitch therefore, and ſling, or grapple faſt a laden Ship <lb></lb>that is ſunk, being in a ſhowle bottome, as was that broken <lb></lb>up near to <emph type="italics"></emph>Malamoccho,<emph.end type="italics"></emph.end> you are to take a very ſtrong <lb></lb>Sheat-anchor Cable, of ſuch a length as is ſufficient for <lb></lb>the Uſes hereafter to be underſtood, and at one end of <lb></lb>ſuch a Cable you are to ſeiz or faſten very well a thick and ſtrong Iron <lb></lb>Ring, big enough for the other end of the Cable to paſſe through with <lb></lb>eaſe, and make thereof a running Parbunckle: and then, near to this <lb></lb>Ring (that is under this Cable at the place where it ſhall be bent to <lb></lb>the Ring) you muſt ſeiz or faſten one of the Flooks of a thick and <lb></lb>ſtrong Anchor, and about three fathoms ſpace from that firſt An <lb></lb>chor hitch the Flook of another ſecond Anchor into the ſaid Cable, <lb></lb>ſeizing or faſtening it that it ſtir not: and about two fathoms di <lb></lb>ſtance from this ſecond Anchor, ſeiz, as before the Flook of a third <lb></lb>Anchor, and ſo two fathom from that a fourth Anchor; and ſo pro <lb></lb>ceed, placing in that manner as many Anchors as ſuffice to go round <lb></lb>the Hull of the ſaid Ship under its Wails, and rather leſſe than more, <lb></lb>to the end the laſt Anchor may be no hinderance to the running of <lb></lb>the Parbunckle at the Ring at ſuch time as it is to be rouſed or vered, <lb></lb>that is, to be drawn or let ſlip. </s><s>The truth is, that in the part of the <lb></lb>Cable marked E, in the Figure following, and in the oppoſite <lb></lb>part marked G (which parts you are to place ſo that they may fall <lb></lb>one at the Stem, the other at the Stern) no Anchor is to be placed, <lb></lb>but you muſt leave at leaſt three fathom interval betwixt thoſe An <lb></lb>chors at G, as was required to be done betwixt the firſt and ſecond <lb></lb>at E. </s><s>And then form the ſaid Running Parbunckle, that is, reeve the <lb></lb>other end of the Cable through the Ring of Iron; and, that being <lb></lb>made, you are to place many perſons upon Flat-bottome Boats fa <lb></lb>ſtened in an Oval Figure round the place where the Ship lyeth: and <lb></lb>then vere or ſlacken the Parbunckle, but in an Oval Form, to that <lb></lb>wideneſſe, that it may at four or five foot diſtance, inviron the foun <lb></lb>dered Ship: and this done, you muſt let all the Anchors, together <lb></lb>with this Girdle or Parbunckle, (being kept at that wideneſſe) gent <lb></lb>ly and equally fall to the bottome of the Sea, keeping the Ship in <lb></lb>the midſt of the Ovall: and when you perceive all the Anchors de <lb></lb>ſcended to the bottome, you muſt vere there ſeveral Cables, that <lb></lb>they may ſink deep into the ſand or Ouze; and then after this you <pb xlink:href="040/01/1201.jpg" pagenum="511"></pb>muſt draw, and bring them by degrees cloſe underneath the Hull of <lb></lb>the Veſſel, and then hall or ſtrain hard the end of the Sheat Anchor <lb></lb>Cable which was reeved through the Ring; and begirt the Hull <lb></lb>of the Ship therewith, as with a Girdle (and to ſtrain it very taught, it <lb></lb>would not be amiſſe to make uſe of a Capſtan) and when this <lb></lb>Girdle is drawn to its due exactneſſe, to the end it may not ſlip (in <lb></lb>the elevation of the Ship) faſten to that part which you hold above <lb></lb>Water another Ring of Iron, and paſſe through this Ring one of <lb></lb>the Anchor-Cables that is on the ſame ſide as the firſt Ring is on, <lb></lb>and almoſt as far from the ſaid Ring, as the ſecond Ring is diſtant <lb></lb>from the firſt; whereupon making this ſecond Ring to ſlip along <lb></lb>the ſaid Anchor Cable, and then in the Elevation halling the ſame, <lb></lb>it ſhall make the ſaid Girdle taught under the ſaid Ship: and that I <lb></lb>may be the better underſtood, I have here underneath repreſented <lb></lb>the ſaid Girdle pul'd together in an Oval Figure as it is to lye under <lb></lb>the Rake of the Ships Hull with fourteen Flooks of fourteen An <lb></lb>chors under the ſame (except in the part inked E, and in its oppo <lb></lb>ſite part G,) well ſeaſ <lb></lb>ed; of which Girdle, or <lb></lb>Parbunckle, the firſt <lb></lb><figure id="id.040.01.1201.1.jpg" xlink:href="040/01/1201/1.jpg"></figure> <lb></lb>Ring ſhall be A, <lb></lb>through which the <lb></lb>Sheat-Anchor Cable <lb></lb>paſſeth, namely, the <lb></lb>Cable A B, to which <lb></lb>Cable was faſtened a <lb></lb>ſecond Ring in the <lb></lb>point B, through which <lb></lb>ſecond Ring, (to the <lb></lb>end the Girdle might <lb></lb>not ſlio) we will reeve <lb></lb>the Cable of the An <lb></lb>chor C; which Anchor <lb></lb>C we ſuppoſe to be <lb></lb>ſomewhat farther from <lb></lb>the Ring A, than the ſecond Ring B is from the firſt Ring A, and <lb></lb>then make the ſaid Ring B to ſlip along the Cable of the ſaid <emph type="italics"></emph>A<emph.end type="italics"></emph.end>nchot <lb></lb>C, till it come to the point C. <emph type="italics"></emph>A<emph.end type="italics"></emph.end>nd thus the Ship ſhall be ſecurely <lb></lb>and ſtrongly grappled and begirt. <emph type="italics"></emph>W<emph.end type="italics"></emph.end>hich done, proceeding as we <lb></lb>directed in the firſt Book of our <emph type="italics"></emph>Indnſtrious Invention,<emph.end type="italics"></emph.end> you will exe <lb></lb>cute your purpoſe; That is, when the two or more coupled Ships <lb></lb>ſhall be full of water, at the ebbing of the Tide you are to faſten <lb></lb>and belay to thoſe Tires of Beams that couple the ſaid Ships, all <lb></lb>thoſe fourteen Cables, taking a little more care in tying, and belay <pb xlink:href="040/01/1202.jpg" pagenum="512"></pb>ing that of the Anchor C, which will keep the Girdle from ſlipping <lb></lb>in the Elevation.</s></p><p type="main"> <s>But if you doubt that that ſingle Cable, to which the Anchors <lb></lb>are faſtened, is not ſufficient for ſo great a weight, you may above <lb></lb>that, place another with a Ring alſo, through which (as before) the <lb></lb>end of it may paſſe, by that means begirting the Ship with two of <lb></lb>thoſe Girdles, and obſerving the ſame Rules you may take three or <lb></lb>four of thoſe ſlipping ſheat-anchor Cables, each with its Ring <lb></lb>wherein to run in the manner of a Nooſe. <emph type="italics"></emph>A<emph.end type="italics"></emph.end>nd when the ſaid new <lb></lb>Girdle is pulled ſtrait and cloſe to the Ship, faſten to the ſaid Cable, <lb></lb>(or to each of them if you uſe more) another ſecond Ring, to gird <lb></lb>and hold the ſaid Nooſe faſt, that it ſlip not with the Cable of the <lb></lb><emph type="italics"></emph>A<emph.end type="italics"></emph.end>nchor C, or with more of thoſe <emph type="italics"></emph>A<emph.end type="italics"></emph.end>nchor-Cables if there be occa <lb></lb>ſion.</s></p><p type="main"> <s><emph type="italics"></emph>A<emph.end type="italics"></emph.end>nd in caſe that thoſe fourteen Cables be thought inſufficient <lb></lb>to bear ſo great a burden, you may take twenty or thirty of them, or <lb></lb>as many as you pleaſe, tying them cloſer to one the other, under <lb></lb>the running Cable, and make half of them to be placed on one ſide, <lb></lb>and the other half on the other ſide of the ſaid Ship.</s></p><p type="main"> <s><emph type="italics"></emph>A<emph.end type="italics"></emph.end>nd if again it be doubted that the ſingle Cable of the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>nchor <lb></lb>C s not able to hold the Nooſe faſt, you may take two or three of <lb></lb>them, for you may judge what the ſtreſs of that anchor is by means of <lb></lb>the height of the water. </s><s>Truth is, this office might be diſtributed <lb></lb>amongſt more <emph type="italics"></emph>A<emph.end type="italics"></emph.end>nchors, by adding a third Ring to the main Cable, <lb></lb>as far from the ſecond, as the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>nchor D is diſtant from the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>nchor <lb></lb>C, ſo that the Cable of the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>nchor D, paſſing through that third <lb></lb>Ring, and ſlipping the ſaid Ring along till it come to D, it will fol <lb></lb>low that thoſe two Cables of thoſe two Anchors C and D, will keep <lb></lb>the Parbunckle ſtraight; aud in this manner you may proceed by ad <lb></lb>ding new Rings, and imploying more Anchor-Cables, for the great <lb></lb>er ſecurity.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> II.</s></p><p type="main"> <s>The ſame method may alſo be obſerved when the Ship is in a <lb></lb>deep place, provided that the depth exceed not the length of the <lb></lb>Hull of the Ship, becauſe then there may be alwaies found ſome one <lb></lb>or more Cables ſufficient to reeve through the ſecond and follow <lb></lb>ing Rings of the Main Cable to ſecure the Nooſe from ſlipping, or <lb></lb>growing ſlack, as in the preceding declaration hath been ſaid. </s><s>But if <lb></lb>it chance that the depth of the place be far greater than the length <lb></lb>of the Ship, you can no longer ſecure the Nooſe with that ſecond <lb></lb>Ring, but muſt find out ſome other way, and though there might be <lb></lb>many found out, I ſhall inſtance but in this one.</s></p> <pb xlink:href="040/01/1203.jpg" pagenum="513"></pb><p type="main"> <s>After you have ſtrained, drawn the ſaid Girdle as taught as you <lb></lb>can, you may take the Cable thereof, and the Cable of the anchor <lb></lb>next adjoyning on the ſame ſide that the firſt Ring is on (namely, <lb></lb>the Cable marked F,) and twiſt and wind them together, and then <lb></lb>reeve the ſingle Cable of the Girdle <emph type="italics"></emph>A B,<emph.end type="italics"></emph.end> through the Ring of a <lb></lb>Sheat-anchor, (without its Cable) and let the anchor ſlide down <lb></lb>wards along the ſaid Main Cable, which by reaſon of its weight will <lb></lb>run almoſt cloſe to the Ring <emph type="italics"></emph>A,<emph.end type="italics"></emph.end> of the Main Cable, preſſing the twiſt <lb></lb>of the two Cables cloſe at <emph type="italics"></emph>A<emph.end type="italics"></emph.end>; and this done, once more twine or <lb></lb>twiſt a little the two former Cables, namely the Sheat anchor-cable <lb></lb>B, and the leſſer Cable F, and then ſeaſe thoſe two Cables ſeverally <lb></lb>to the Orders of Beams, that is, one to one Order, and the other to <lb></lb>another at ſome diſtance from the former, to the end they drive <lb></lb>down the twiſting near to the Ring of the anchor: which twiſting <lb></lb>will keep the Nooſe from ſlipping or opening in elevating the Ship. <lb></lb><emph type="italics"></emph>A<emph.end type="italics"></emph.end>nd if there be any occaſion to uſe a Capſtain (as was ſaid in the <lb></lb>ſeventh Explanation of the firſt Book) you muſt always take care <lb></lb>to ſtrain theſe two Cables equally, and much aſunder, which doing, <lb></lb>the Girdle ſhall be kept ſtrait. </s><s>Many other ways might be ſhewen <lb></lb>for to keep the ſaid Grand Cable from ſlipping, but eſteeming them <lb></lb>ſuperfluous, I omit them.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> III.</s></p><p type="main"> <s>He that is deſirous to recover a foundered Ship laden with <lb></lb>Fraight, by other ways than thoſe preſcribed in the firſt Book, <lb></lb>namely, without ſtanding to fill thoſe two or more Ships, or other <lb></lb>Veſſels with water, and then to empty them, may only by force of <lb></lb>Capſtains or Cranes eaſily effect the ſame in the manner following, <lb></lb>(ſtill making uſe of the Parbunckle and flooks of anchors explained <lb></lb>in the firſt Explanation of this) namely: By taking from their an <lb></lb>chors Rings all their Cables, except that which is to make faſt the <lb></lb>Main-Cable Nooſe that begirts the Ship, and in their places make <lb></lb>faſt to each Ring a ſtrong Pulley or Block, in ſuch ſort, that all the <lb></lb>ſaid Pulleys or Blocks have equal number of Shivers, or wheels, and <lb></lb>thoſe as many as you can make them: and through theſe Shivers or <lb></lb>wheels reeve their proper and convenient Cables or Ropes, incatena <lb></lb>ting each Pulley with its ſuperiour; and this done, make two ſqua <lb></lb>drons of Barks, or Lighters, or Flat-boats, according to the method <lb></lb>laid down in the fourth Explanation of the firſt Book, collated and <lb></lb>bound together with thoſe Tires of thick and ſtrong Beams tripled, <lb></lb>and with a great and ſpacious platform of thick Planks upon each <lb></lb>ſquadron, and upon thoſe two ſpacious platforms place as many <lb></lb>Capſters or Ship-cranes as you ſhall judge neceſſary for ſuch a <pb xlink:href="040/01/1204.jpg" pagenum="514"></pb>weight, and rather much more, then ever ſo little leſs, and then let <lb></lb>fall the ſaid Anchors leiſurely, with the Girdle opened in an Oval <lb></lb>Figure, untill they come to the bottome of the Sea, ſo that the Girdle <lb></lb>do encircle or ſurround the foundered Ship. </s><s>And having once be <lb></lb>girt it carefully, approximate all the Anchors with the Girdle to the <lb></lb>Hull of the Ship, and then ſharpen or make taught the Girdle-cable <lb></lb>by halling it hard and ſtreight to the Ships hull, and when it is <lb></lb>drawn cloſe, belay it that it may not ſlacken, with that ſingle An <lb></lb>chor-cable, or more, according to that ſecure way ſpoken of but <lb></lb>now, or by ſome other than ſhall ſeem more expedient, (for many <lb></lb>more, if one think thereon may be found:) and this being done, <lb></lb>ſeek to looſen the Ship by degrees from its bed of Ouze, a little on <lb></lb>one ſide, and a little on the other with the aforeſaid Capſters, and, <lb></lb>being once water born, then draw it upwards equally on both ſides, <lb></lb>and proceed in this manner till ſuch time as you have hoiſted it ſuf <lb></lb>ficiently above the Waters ſurface, and then pump out the Water, <lb></lb>and unlade its Cargo.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> IV.</s></p><p type="main"> <s>Having in the ſecond Book ſhewn ſeveral ways of Diving under <lb></lb>Water in ſearch of things ſunk, in this place I have thought <lb></lb>fit to add, in caſe that ſome little thing of value ſhould fall <lb></lb>into a Water in ſome ſhady place, and where its bottome is obſcure <lb></lb>and dark, a way how to conveigh a Light thither that may give light <lb></lb>enough for the diſcerning of that little thing, provided that it be not <lb></lb>buried in, or covered with the old Ouze. </s><s>Now to perform this, and <lb></lb>that with expedition, we may in ſmall depths take one of thoſe braſs <lb></lb>Buckets or Pails, which are uſed in carrying and keeping of Water <lb></lb>for houſehold uſes: and thoſe of them that are ſhaped long and <lb></lb>deep, with feet ſhall be better then thoſe that are made round and <lb></lb>ſhallow, without feet; and the bigger and higher it is, ſo much the <lb></lb>better it ſhall be. </s><s>And having made choice of ſuch a Bucket, you <lb></lb>are to faſten to the Ears of it two ſmall Ropes of about two yardes <lb></lb>apiece, in ſuch a faſhion, as that they may one croſs the other at the <lb></lb>mouth of the Bucket, making upon it a perfect croſs, and that the <lb></lb>Knot of the Ropes may be in the midſt of the Buckets bottom with <lb></lb>out, making of the ropes a Hoop over the bottome whereat to faſten <lb></lb>another Rope of greater length; ſo that the Bucket being held by <lb></lb>that laſt Rope may come to hang with its mouth perpendicularly <lb></lb>downwards. </s><s>And this done, faſten as much Lead to the two Eares of <lb></lb>the Bucket as may juſt make it ſink to the Bottome, and then ſet <lb></lb>and faſten a little Wax candle lighted in the interſection that thoſe <lb></lb>two Ropes make over the mouth of the Bucket, that is, in the centre <pb xlink:href="040/01/1205.jpg" pagenum="515"></pb>of that perfect croſs; ſo that the candle with its light may be with <lb></lb>in, and near the bottome of the ſaid Bucket. </s><s>This being done, let <lb></lb>down the Bucket, with the candle in it gently unto the bottome, <lb></lb>which doing, you ſhall ſee the burning candle clearly enlighten the <lb></lb>bottome of the Water. </s><s>And this Bucket you may remove from <lb></lb>place to place, without drawing it upwards. </s><s>The truth is, that this <lb></lb>candle will not long continue burning, but will ſerve for a little <lb></lb>while, and when it ſhall go out of it ſelf, it may be drawn up, re <lb></lb>lighted, and let down, as occaſion requires: but the greater that the <lb></lb>Bucket, and the leſſer that the candle ſhall be, ſo much the longer <lb></lb>time ſhall it keep its light under Water: and therefore if the ſaid <lb></lb>bottome were very deep, it would be requiſite to perform that eſſect <lb></lb>with ſo much a greater Veſſel, as a great Caldron, but yet of Brals, <lb></lb>or by that means the candle ſhall continue longer lighted.</s></p><p type="head"> <s><emph type="italics"></emph>EXPLANATION<emph.end type="italics"></emph.end> V.</s></p><p type="main"> <s>But in caſe that a Ship or Bark were foundered in ſome ſpacious <lb></lb>and profound Gulph, and that the exact place where it ſunk <lb></lb>were unknown, and that the bottome of the ſaid ſpacious Gulph <lb></lb>were very obſcure, it is manifeſt that ſo little a light as that ſpoke <lb></lb>of in the precedent Explanation would hardly ſerve. </s><s>And therefore <lb></lb>if you would convey thither one much bigger, you may do it ſeve <lb></lb>rall wayes, of which one is this. </s><s>Take nine ounces of refined Salt <lb></lb>peter, ſix ounces (Greek weight) of Brimſtone that is clear and <lb></lb>tranſparent, three ounces of Camphire refined, and one ounce of <lb></lb>Maſtick; and beat all theſe things ſeverally, not very ſmall; and <lb></lb>when you have beaten them, mix them all together in an Earthen <lb></lb>Pan; and when they are well mingled, put thereto three pounds of <lb></lb>common Gunpowder, and then remingle them very well together; <lb></lb>and afterwards put therein four ounces of oyl of Stone, and mix all <lb></lb>very well; and this done, take a Cartredge thereof, and give fire to <lb></lb>it; and if it burn too ſlowly, put a little more Gunpowder to it, <lb></lb>but if it burn too vehemently and ſuddenly, add thereto more oyl. <lb></lb></s><s>Put this Compoſition, after this, into a little Bag of double Canvis, <lb></lb>of ſuch a wideneſſe, that when all the mixture is out, therein it may <lb></lb>be as broad, as high, and cram the Compoſition hard down into the <lb></lb>Bag; and then with very good Pack thread ſew up the mouth of the <lb></lb>Sack, cutting away the ſuperfluous Canvas. </s><s>Then winde a good <lb></lb>hempen cord round about it very hard every way, reducing it to the <lb></lb>form of a round Ball, and after it is very well bound and ſwathed a <lb></lb>bout many ſeverall times, you muſt melt Brimſtone into a great Veſ <lb></lb>ſel, and when it is melted, roll the ſaid Ball therein ſo, as that it may <lb></lb>be covered all over with a cruſt of Brimſtone. </s><s>And this being done <pb xlink:href="040/01/1206.jpg" pagenum="516"></pb>affix a piece of Lead unto the Ball by an iron Wire, and make it ve <lb></lb>ry faſt, and frame in the top of the Ball a Bow or Nooſe with the <lb></lb>ſaid Wire, and to that faſten a long Rope, and then in the oppoſite <lb></lb>place where the Lead is fixed, make an hole with an iron rod into <lb></lb>the middle of the Ball, and ſtop that hole with a little fine Gunpow <lb></lb>der, holding it ſuſpended by the Rope: and when you would have <lb></lb>that Light deſcend into the bottome of the Sea or Gulph, goe to the <lb></lb>place, and give fire to the little hole, and when it is inkindled, let <lb></lb>down the Ball and Lead, lengthwayes, almoſt to the bottome, where <lb></lb>he ſhall be that would find the thing ſunk, and you ſhall find that <lb></lb>the ſaid fire will illuminate very much round about the ſaid bottom, <lb></lb>and ſhall laſt a long time, and more or leſs, according to the hole <lb></lb>made in the Ball. 'Tis to be noted, that the Ball is to be held over <lb></lb>the head of him that diveth, for that the ſmoke proceeding from it <lb></lb>will much obſcure the Waters above it, ſo as that it will give Light <lb></lb>only downwards; and this fire will be a dreadful ſight unto the Fiſh, <lb></lb>ſo that they will fly from ſo new a ſpectacle.</s></p><p type="head"> <s><emph type="italics"></emph>The END of the firſt part <lb></lb>of the Second TOME.<emph.end type="italics"></emph.end></s></p> </chap> </body> <back></back> </text></archimedes>