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version 1.6, 2002/07/09 23:38:54

version 1.9, 2002/08/05 20:41:02

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<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes> <info> <author>Gassendi, Pierre</author> <title>De proportione qua gravia decidentia accelerantur</title> <date>1646</date>

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]><archimedes> <info> <author>Gassendi, Pierre</author> <title>De proportione qua gravia decidentia accelerantur</title> <date>1646</date>

<place>Paris</place> <editor></editor> <publisher></publisher> <translator></translator> <lang>la</lang> <chunk unit="page*">page</chunk><locator>0000000028</locator> </info> <text> <front> </front> <body> <chap> <pb/>

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<s><emph type="center"/>PETRVS GASSENDVS S.<emph.end type="center"/></s>

<s>PELLEGI, optime Cazræe, quam dig<lb/>natus es ad me dare, ac publici iuris &longs;imul <lb/>facere <emph type="italics"/>Demon&longs;trationem Phy&longs;icam,<emph.end type="italics"/> qua <lb/><emph type="italics"/>Ratio accelerationis in motu rerum grauium <lb/>naturali determinatur.<emph.end type="italics"/> Agnoui verò imprimis illam &longs;in<lb/>gularem beneuolentiam, qua perrexi&longs;ti ob&longs;tringere <lb/>me, quæque e&longs;t &longs;anè tota ad tuam bonitatis eximiæ <lb/>indolem accepta ferenda. </s>

<s>PELLEGI, optime Cazræe, quam dig<lb/>natus es ad me dare, ac publici iuris &longs;imul <lb/>facere <emph type="italics"/>Demon&longs;trationem Phy&longs;icam,<emph.end type="italics"/> qua <lb/><emph type="italics"/>Ratio accelerationis in motu rerum grauium <lb/>naturali determinatur.<emph.end type="italics"/></s><s> Agnoui verò imprimis illam &longs;in<lb/>gularem beneuolentiam, qua perrexi&longs;ti ob&longs;tringere <lb/>me, quæque e&longs;t &longs;anè tota ad tuam bonitatis eximiæ <lb/>indolem accepta ferenda. </s>

<s>Promptum deinde fuit <lb/>memini&longs;&longs;e eruditæ Epi&longs;tolæ, qua ante duos annos ea <lb/>&longs;igni&longs;ica&longs;ti, quæ in meis illis, <emph type="italics"/>de Motu impre&longs;&longs;o à motore <lb/>tran&longs;lato,<emph.end type="italics"/> minimè probares; ac illud inter cætera, quòd <pb pagenum="2"/>&longs;en&longs;i&longs;&longs;em cum Galileo, <emph type="italics"/>Motum naturalem rerum deci<lb/>dentium ea ratione accelerari, vt &longs;uperata &longs;patia temporibus <lb/>æqualibus, numerorum imparium progreßionem imitarentur.<emph.end type="italics"/><lb/>Commemini etiam, cùm fui&longs;&longs;em conatus facere &longs;atis <lb/>in cæteris, expetii&longs;&longs;e me, vt quia neque Paralogi&longs;mum, <lb/>quem in Galileo cau&longs;abaris, animaduerti&longs;&longs;em, neque <lb/>experientia, aut ratio mon&longs;tra&longs;&longs;et quidpiam oppo&longs;i<lb/>tum; <gap/>ig<gap/>areris ip&longs;e tum mihi fallaciam Galilei rete<lb/>gere, tum inuentam illam à te progre&longs;&longs;ionem me edo<lb/>cere. </s>

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<s>V. Iam, Tu initio argumentum Di&longs;&longs;ertationis ita <lb/>partiris, vt duo præ&longs;tanda tibi proponas. </s>

<s>Vnum, <lb/><emph type="italics"/>vt Galilei hac inre errores, eorumque fonteis aperias; claré<lb/>que demon&longs;tres ea, quæ ab ip&longs;o de acceleratione Motus in na<lb/>turali de&longs;cen&longs;u grauium Libro &longs;ecundo nouæ &longs;cientiæ, & <lb/>toto Dialogo tertio dicta &longs;unt, non modò &longs;u&longs;picionibus meris, <lb/>vixque probabilibus coniecturis niti, &longs;ed ex principijs etiam <lb/>apertè fal&longs;is, euidentibu&longs;que paralogi&longs;mis omnia concludi; ex <lb/>quo con&longs;equens &longs;it, nouam illam &longs;cientiam euane&longs;cere, quam <lb/>ingenio&longs;o quidem, & plau&longs;ibili, &longs;ed inani tamen, & ca&longs;&longs;o <lb/>apparatu nobis<emph.end type="italics"/> G<emph type="italics"/>alileus exhibuerit.<emph.end type="italics"/> Alterum, <emph type="italics"/>vt reiecta<emph.end type="italics"/><lb/>G<emph type="italics"/>alilei p&longs;eudo-&longs;cientia, veram tu, ac certam in eius locum <lb/>&longs;ubstituas, rationemque, modum, ac men&longs;uram acceleratio<lb/>nis eiu&longs;dem in naturali de&longs;cen&longs;u grauium ex euidentibus, at<lb/>que indubitatis experientiis demonstres.<emph.end type="italics"/> Circa priùs de<lb/>inde caput, duo &longs;unt, in quibus occuparis; nam impe<lb/>tis <emph type="italics"/>primò<emph.end type="italics"/> definitionem Motus æquabiliter accelerati à <lb/>Galileo traditam: & <emph type="italics"/>&longs;ecundò<emph.end type="italics"/> quod idem ait de gradi<lb/>bus velocitatis, qui acquiruntur à mobili, dùm &longs;uper <pb pagenum="9"/>planis inclinatis mouetur. </s>

<s>Vnum, <lb/><emph type="italics"/>vt Galilei hac inre errores, eorumque fonteis aperias; claré<lb/>que demon&longs;tres ea, quæ ab ip&longs;o de acceleratione Motus in na<lb/>turali de&longs;cen&longs;u grauium Libro &longs;ecundo nouæ &longs;cientiæ, & <lb/>toto Dialogo tertio dicta &longs;unt, non modò &longs;u&longs;picionibus meris, <lb/>vixque probabilibus coniecturis niti, &longs;ed ex principijs etiam <lb/>apertè fal&longs;is, euidentibu&longs;que paralogi&longs;mis omnia concludi; ex <lb/>quo con&longs;equens &longs;it, nouam illam &longs;cientiam euane&longs;cere, quam <lb/>ingenio&longs;o quidem, & plau&longs;ibili, &longs;ed inani tamen, & ca&longs;&longs;o <lb/>apparatu nobis<emph.end type="italics"/> G<emph type="italics"/>alileus exhibuerit.<emph.end type="italics"/></s><s> Alterum, <emph type="italics"/>vt reiecta<emph.end type="italics"/><lb/>G<emph type="italics"/>alilei p&longs;eudo-&longs;cientia, veram tu, ac certam in eius locum <lb/>&longs;ubstituas, rationemque, modum, ac men&longs;uram acceleratio<lb/>nis eiu&longs;dem in naturali de&longs;cen&longs;u grauium ex euidentibus, at<lb/>que indubitatis experientiis demonstres.<emph.end type="italics"/></s><s> Circa priùs de<lb/>inde caput, duo &longs;unt, in quibus occuparis; nam impe<lb/>tis <emph type="italics"/>primò<emph.end type="italics"/> definitionem Motus æquabiliter accelerati à <lb/>Galileo traditam: & <emph type="italics"/>&longs;ecundò<emph.end type="italics"/> quod idem ait de gradi<lb/>bus velocitatis, qui acquiruntur à mobili, dùm &longs;uper <pb pagenum="9"/>planis inclinatis mouetur. </s>

<s>Circa po&longs;terius ex&longs;equeris <lb/>tria: Nam <emph type="italics"/>primò<emph.end type="italics"/> declaras quod experimentum, circa <lb/>Bilancem excogita&longs;ti; <emph type="italics"/>&longs;ecundò<emph.end type="italics"/> deducis quam putas ex<lb/>inde accelerationis <expan abbr="ration&etilde;">rationem</expan> haberi; ac <emph type="italics"/>tertiò<emph.end type="italics"/> infers pro<lb/>gre&longs;&longs;ionem, qua &longs;uperantur &longs;patia temporibus æqua<lb/>libus, imitari progre&longs;&longs;ionem non numerorum impa<lb/>rium, &longs;ed rationis continuò duplæ, quam & exprimis <lb/>in de&longs;cen&longs;u globi à Luna v&longs;que in centrum terræ. </s>

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<s>Vt ordine autem de &longs;ingulis dicam, & à <lb/>Priore capite incipiam, <emph type="italics"/>Primum errorem, & tanquam <lb/>originem cæterorum<emph.end type="italics"/> dicis, quòd <emph type="italics"/>Galileus fal&longs;am hanc ac<lb/>celerati Motus definitionem in&longs;tituerit, Motum æquabiliter <lb/>acceleratum dico eum, qui à quiete recedens temporibus æqua<lb/>libus æqualia celeritatis momenta acquirat.<emph.end type="italics"/> Rem autem <lb/>putas eius momenti, vt dicas <emph type="italics"/>te contendere huiu&longs;modi <lb/>definitionem adulterinam e&longs;&longs;e, ac fal&longs;am; & quicquid <lb/>toto illo Libro de eodem motu accelerato, &longs;atis alioquin <lb/>ingeniosè<emph.end type="italics"/> G<emph type="italics"/>alileus commentus e&longs;t, nibil veritatis habere.<emph.end type="italics"/><lb/>Improbas &longs;ubinde, quòd <emph type="italics"/>definitionem non experientia <lb/>certa, ac euidenti confirmauerit, &longs;ed ab eius tantum &longs;im<lb/>plicitate motibus naturalibus maximè congruente; à per<lb/>fecta cum demon&longs;tratis à &longs;e theorematibus con&longs;en&longs;ione; & <lb/>ab aperta, vt ip&longs;e quidem fidenter a&longs;&longs;erat, receptæ vulgò <lb/>definitionis ab&longs;urditate.<emph.end type="italics"/> Tum verò circa &longs;implicitatem <lb/>perpendere &longs;olùm me iubes, an non &longs;implicior &longs;it <lb/>definitio, quæ à cæteris vulgò v&longs;urpatur, dum Mo<lb/>tum æquabiliter acceleratum eum potiùs e&longs;&longs;e a&longs;&longs;e-<pb pagenum="10"/>runt, <emph type="italics"/>Qui æqualibus &longs;patijs æqualia celeritatis augmenta <lb/>acquirit.<emph.end type="italics"/> Circa con&longs;en&longs;ionem autem &longs;olùm, bucis, <lb/><emph type="italics"/>nouum non e&longs;&longs;e, &longs;i fal&longs;a fal&longs;is ap<gap/>è quandó que, & con<lb/>cinnè cohæreant;<emph.end type="italics"/> ac po&longs;tremò in eo in&longs;iltis, vt probes <lb/>e&longs;&longs;e paralogi&longs;mum, quo ille vulgarem, moxque re<lb/>latam definitionem ab&longs;urditatis apertæ damna<lb/>uit. </s>

<s>Vt ordine autem de &longs;ingulis dicam, & à <lb/>Priore capite incipiam, <emph type="italics"/>Primum errorem, & tanquam <lb/>originem cæterorum<emph.end type="italics"/> dicis, quòd <emph type="italics"/>Galileus fal&longs;am hanc ac<lb/>celerati Motus definitionem in&longs;tituerit, Motum æquabiliter <lb/>acceleratum dico eum, qui à quiete recedens temporibus æqua<lb/>libus æqualia celeritatis momenta acquirat.<emph.end type="italics"/></s><s> Rem autem <lb/>putas eius momenti, vt dicas <emph type="italics"/>te contendere huiu&longs;modi <lb/>definitionem adulterinam e&longs;&longs;e, ac fal&longs;am; & quicquid <lb/>toto illo Libro de eodem motu accelerato, &longs;atis alioquin <lb/>ingeniosè<emph.end type="italics"/> G<emph type="italics"/>alileus commentus e&longs;t, nibil veritatis habere.<emph.end type="italics"/><lb/>Improbas &longs;ubinde, quòd <emph type="italics"/>definitionem non experientia <lb/>certa, ac euidenti confirmauerit, &longs;ed ab eius tantum &longs;im<lb/>plicitate motibus naturalibus maximè congruente; à per<lb/>fecta cum demon&longs;tratis à &longs;e theorematibus con&longs;en&longs;ione; & <lb/>ab aperta, vt ip&longs;e quidem fidenter a&longs;&longs;erat, receptæ vulgò <lb/>definitionis ab&longs;urditate.<emph.end type="italics"/></s><s> Tum verò circa &longs;implicitatem <lb/>perpendere &longs;olùm me iubes, an non &longs;implicior &longs;it <lb/>definitio, quæ à cæteris vulgò v&longs;urpatur, dum Mo<lb/>tum æquabiliter acceleratum eum potiùs e&longs;&longs;e a&longs;&longs;e-<pb pagenum="10"/>runt, <emph type="italics"/>Qui æqualibus &longs;patijs æqualia celeritatis augmenta <lb/>acquirit.<emph.end type="italics"/></s><s> Circa con&longs;en&longs;ionem autem &longs;olùm, bucis, <lb/><emph type="italics"/>nouum non e&longs;&longs;e, &longs;i fal&longs;a fal&longs;is ap<gap/>è quandó que, & con<lb/>cinnè cohæreant;<emph.end type="italics"/> ac po&longs;tremò in eo in&longs;iltis, vt probes <lb/>e&longs;&longs;e paralogi&longs;mum, quo ille vulgarem, moxque re<lb/>latam definitionem ab&longs;urditatis apertæ damna<lb/>uit. </s>

<s>VII Ego intereà, optime Vir, neque video De<lb/>&longs;initionem a Galileo in&longs;titutam à te directè impu<lb/>gnari, fal&longs;itati&longs;ve vllius conuinci; neque agno&longs;co quî <lb/>magis vera, congruaque potuerit in&longs;titui. </s>

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<s>Ac tu id quidem non fers; fed ais, <emph type="italics"/>Mirari to <lb/>&longs;atis non po&longs;&longs;e, quomodo<emph.end type="italics"/> G<emph type="italics"/>alileus vir alioquin perspicacis <lb/>ingenij receptam communi con&longs;en&longs;u motus accelerati defini<lb/>tionem non modò fal&longs;am, atque impoßibilem exi&longs;timauerit; <lb/>&longs;ed patenti quoque, ip&longs;i&longs;que tyronibus obuio paralogi&longs;mo <lb/>eiu&longs;dem fal&longs;itatem palam, atque euidenter demon&longs;tra&longs;&longs;e adeò <lb/>prafidenter a&longs;&longs;eruerit; & quod ampliùs e&longs;t, etiam viru non <lb/>ineruditis per&longs;ua&longs;erit.<emph.end type="italics"/> Tum autem pergis, <emph type="italics"/>Audi igitur; <lb/>mi<emph.end type="italics"/> G<emph type="italics"/>a&longs;&longs;ende, & mecum mirare tanti viri demon&longs;trationem. <lb/></s>

<s>Ac tu id quidem non fers; fed ais, <emph type="italics"/>Mirari to <lb/>&longs;atis non po&longs;&longs;e, quomodo<emph.end type="italics"/> G<emph type="italics"/>alileus vir alioquin perspicacis <lb/>ingenij receptam communi con&longs;en&longs;u motus accelerati defini<lb/>tionem non modò fal&longs;am, atque impoßibilem exi&longs;timauerit; <lb/>&longs;ed patenti quoque, ip&longs;i&longs;que tyronibus obuio paralogi&longs;mo <lb/>eiu&longs;dem fal&longs;itatem palam, atque euidenter demon&longs;tra&longs;&longs;e adeò <lb/>prafidenter a&longs;&longs;eruerit; & quod ampliùs e&longs;t, etiam viru non <lb/>ineruditis per&longs;ua&longs;erit.<emph.end type="italics"/></s><s> Tum autem pergis, <emph type="italics"/>Audi igitur; <lb/>mi<emph.end type="italics"/> G<emph type="italics"/>a&longs;&longs;ende, & mecum mirare tanti viri demon&longs;trationem. <lb/></s>

<s>Si acceleratio motus,<emph.end type="italics"/> inquit, <emph type="italics"/>in de&longs;cen&longs;u grauium æquali<lb/>bus &longs;patiis æqualia &longs;umeret velocitatu ineremema, e&longs;&longs;ent <lb/>&longs;ine dubio velocitates inter &longs;e, vt emen&longs;a spatia: At quoite&longs;. <lb/></s>

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<s>Jmpoßibile est au<lb/>tem, vt corpus graue de&longs;cendens per AC eodem, <lb/>aut æquali tempore percurrat totam AC, quo per<lb/>currit partem eius AB, ni&longs;i motus fiat in instanti. <lb/></s>

<s>Tam impoßibile e&longs;t igitur, vt velocitates in de&longs;cen&longs;u <lb/>grauium inter &longs;e &longs;int, vt emen&longs;a &longs;patia (ac proinde, <lb/>vt etiam æqualibus &longs;patiis cre&longs;cant æqualiter) quàm <lb/>impoßibile e&longs;t motum illum fieri in instanti.<emph.end type="italics"/> Pergis &longs;ub<lb/>inde, <emph type="italics"/>Proh tuam, mi<emph.end type="italics"/> G<emph type="italics"/>a&longs;&longs;ende, Philo&longs;ophorumque omnium, <lb/>ac Mathematicorum fidem! istud<gap/>ne demon&longs;trare e&longs;t? </s>

<s>Tam impoßibile e&longs;t igitur, vt velocitates in de&longs;cen&longs;u <lb/>grauium inter &longs;e &longs;int, vt emen&longs;a &longs;patia (ac proinde, <lb/>vt etiam æqualibus &longs;patiis cre&longs;cant æqualiter) quàm <lb/>impoßibile e&longs;t motum illum fieri in instanti.<emph.end type="italics"/></s><s> Pergis &longs;ub<lb/>inde, <emph type="italics"/>Proh tuam, mi<emph.end type="italics"/> G<emph type="italics"/>a&longs;&longs;ende, Philo&longs;ophorumque omnium, <lb/>ac Mathematicorum fidem! istud<gap/>ne demon&longs;trare e&longs;t? </s>

<s>Et <lb/>tamen mirum quantum Galileus de hac, vt putat, &longs;ubtili, <lb/>clara, euidenti, ac Mathematica demon&longs;tratione &longs;ibi applau<lb/><gap/>at, quam integra pagina mirificis laudibus exaggerat. </s>

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<s>Atque ego quidem rem itaconcipio. </s>

<s>XI Verum tu &longs;i m&longs;tas, <emph type="italics"/>Vt prima illius Paralo<lb/>gi&longs;mi a&longs;&longs;umptio in motu vniformi, ac perpetuò &longs;ibi æquali<emph.end type="italics"/><pb pagenum="18"/><emph type="italics"/>vera, & nece&longs;&longs;aria &longs;it; in motu tamen accelerato min<gap/>me <lb/>nece&longs;&longs;aria e&longs;t, & non vno modo tantum, &longs;ed pluribus in<lb/>telligi potest, quo modo velocitates &longs;int inter &longs;e, vt emen&longs;a <lb/>&longs;patia: licet eadem &longs;patia neque eodem, neque æquali tem<lb/>pore percurrantur.<emph.end type="italics"/> Pergis autem, <emph type="italics"/>Vt, &longs;i graue de&longs;cen-<emph.end type="italics"/><lb/><emph type="italics"/>dens per AB tempus quodcumque in&longs;umat, putà qua<lb/><figure id="fig8"></figure><lb/>drantem; ac deinde BC ip&longs;i AB æquale, dimidio <lb/>quadrante percurrat; quis neget in<emph.end type="italics"/> C <emph type="italics"/>duplam ha<lb/>beri velocitatem eius, quæ fuit in B? & tamen <lb/>idem graue totam AC, & dimidium eius AB <lb/>non percurreret.<emph.end type="italics"/> Et hæc e&longs;t quidem tota tua ad <lb/>conuincendum paralogi&longs;mi Galileum proba<lb/>tio, ob quam continenter hæc verba &longs;ubiun<lb/>gis: <emph type="italics"/>A&longs;&longs;umptio igitur Galilei fal&longs;a e&longs;t, & tota eius <lb/>ratiocinatio merus Paralogi&longs;mus id óque nullo modo, vt ip&longs;e <lb/>gloriatur communem, &longs;anioremque aliorum &longs;en&longs;um erroris <lb/>reuincit, qui in naturali grauium de&longs;cen&longs;u volunt æqualibus <lb/>spatijs æqualia velocitatis momenta acquiri.<emph.end type="italics"/> An verò pa<lb/>tietur tua bonitas, &longs;i dicam po&longs;&longs;e cuipiam videri, e&longs;&longs;e <lb/>te potiùs, qui hoc loco incidas in paralogi&longs;mum? </s>

<s>XI Verum tu &longs;i m&longs;tas, <emph type="italics"/>Vt prima illius Paralo<lb/>gi&longs;mi a&longs;&longs;umptio in motu vniformi, ac perpetuò &longs;ibi æquali<emph.end type="italics"/><pb pagenum="18"/><emph type="italics"/>vera, & nece&longs;&longs;aria &longs;it; in motu tamen accelerato min<gap/>me <lb/>nece&longs;&longs;aria e&longs;t, & non vno modo tantum, &longs;ed pluribus in<lb/>telligi potest, quo modo velocitates &longs;int inter &longs;e, vt emen&longs;a <lb/>&longs;patia: licet eadem &longs;patia neque eodem, neque æquali tem<lb/>pore percurrantur.<emph.end type="italics"/></s><s> Pergis autem, <emph type="italics"/>Vt, &longs;i graue de&longs;cen-<emph.end type="italics"/><lb/><emph type="italics"/>dens per AB tempus quodcumque in&longs;umat, putà qua<lb/><figure id="fig8"></figure><lb/>drantem; ac deinde BC ip&longs;i AB æquale, dimidio <lb/>quadrante percurrat; quis neget in<emph.end type="italics"/> C <emph type="italics"/>duplam ha<lb/>beri velocitatem eius, quæ fuit in B? & tamen <lb/>idem graue totam AC, & dimidium eius AB <lb/>non percurreret.<emph.end type="italics"/></s><s> Et hæc e&longs;t quidem tota tua ad <lb/>conuincendum paralogi&longs;mi Galileum proba<lb/>tio, ob quam continenter hæc verba &longs;ubiun<lb/>gis: <emph type="italics"/>A&longs;&longs;umptio igitur Galilei fal&longs;a e&longs;t, & tota eius <lb/>ratiocinatio merus Paralogi&longs;mus id óque nullo modo, vt ip&longs;e <lb/>gloriatur communem, &longs;anioremque aliorum &longs;en&longs;um erroris <lb/>reuincit, qui in naturali grauium de&longs;cen&longs;u volunt æqualibus <lb/>spatijs æqualia velocitatis momenta acquiri.<emph.end type="italics"/></s><s> An verò pa<lb/>tietur tua bonitas, &longs;i dicam po&longs;&longs;e cuipiam videri, e&longs;&longs;e <lb/>te potiùs, qui hoc loco incidas in paralogi&longs;mum? </s>

<s>Ni<lb/>mirum videris &longs;ic argumentari, vt id, quod contro<lb/>uertitur, a&longs;&longs;umas pro principio, dum nihil aliud, quàm <lb/>&longs;upponis &longs;patium AB, percurri duplo temporis, quo <lb/>&longs;patium BC; & velocitatem in C, e&longs;&longs;e duplam eius, <lb/>quæ fuit in B; quæ ip&longs;a tamen e&longs;t controuer&longs;ia. </s>

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<s>Ad hæc, addam-ne fui&longs;&longs;e rem mihi <lb/>quodammodò &longs;tupendam, acce&longs;&longs;i&longs;&longs;e ca&longs;u ad me i&longs;ta <lb/>con&longs;cribentem, nobili&longs;&longs;imum Senatorem Petrum <lb/>Calcauium virum omninò promouendis bonis arti<lb/>bus comparatum, puræque cum-primis Mathe&longs;eos <lb/>&longs;tudio&longs;i&longs;&longs;imum; ac vi&longs;a mihi præ manibus tua Di&longs;&longs;er<lb/>tatione, argumentóque cognito, innui&longs;&longs;e tran&longs;mi&longs;<lb/>&longs;um in hanc vrbem exemplum editi nuperrimè Libri <lb/>ab Euangeli&longs;ta Torricellio, qui Galilei &longs;ucce&longs;&longs;or exi<lb/>mius demon&longs;trauerit in eo i&longs;tud Po&longs;tulatum? </s>

<s>Præ<lb/>tereo autem, vt copiâ illius videndi &longs;tatim impetratâ, <lb/>deprehenderim rem confectam quinque propo&longs;itio<lb/>nibus, ac Præmi&longs;&longs;o illo, <emph type="italics"/>Non po&longs;&longs;e duo<emph.end type="italics"/> G<emph type="italics"/>rauia &longs;imul <lb/>iuncta ex &longs;e moueri, ni&longs;i centrum commune grauitatis ip&longs;o<lb/>rum de&longs;cendat.<emph.end type="italics"/> Videlicet prima Propo&longs;itio e&longs;t, <lb/>G<emph type="italics"/>rauia in planis inæqualiter inclinatis, ac eandem tamen <lb/>eleuationem habentibus, con&longs;tituta: &longs;i eandem inter &longs;e ratio<lb/>nem homologè habeant, quam habent planorum longitudi<lb/>nes, habere æqualia momenta.<emph.end type="italics"/> Secunda, <emph type="italics"/>Eadem grauia &longs;i <lb/>æqualia fuerint, habere momenta in ratione reciproca longi<lb/>tud num eorumdem planorum.<emph.end type="italics"/> Tertia, <emph type="italics"/>Illa <expan abbr="æquali&utilde;">æqualium</expan> grauium <lb/>momenta e&longs;&longs;e in ratione homologa cum perpendiculis par<lb/>tium æqualium eorumdem planorum.<emph.end type="italics"/> Quarta, <emph type="italics"/>Tempora <lb/>la<gap/>i<gap/>um ex quiete e&longs;&longs;e homologè vt longitudines eorum<lb/>dem planorum.<emph.end type="italics"/> Quinta autem e&longs;t ip&longs;um Po&longs;tulatum <pb pagenum="24"/>ex &longs;uperioribus deductum, G<emph type="italics"/>radus velocitatis eiu&longs;dem <lb/>mobilis &longs;uper diuer&longs;as planorum inclinationes acqui&longs;itos tunc <lb/>e&longs;&longs;e æqualeis, cùm eorumdem planorum eleuationes &ecedil;quales <lb/>&longs;unt.<emph.end type="italics"/></s>

<s>Præ<lb/>tereo autem, vt copiâ illius videndi &longs;tatim impetratâ, <lb/>deprehenderim rem confectam quinque propo&longs;itio<lb/>nibus, ac Præmi&longs;&longs;o illo, <emph type="italics"/>Non po&longs;&longs;e duo<emph.end type="italics"/> G<emph type="italics"/>rauia &longs;imul <lb/>iuncta ex &longs;e moueri, ni&longs;i centrum commune grauitatis ip&longs;o<lb/>rum de&longs;cendat.<emph.end type="italics"/></s><s> Videlicet prima Propo&longs;itio e&longs;t, <lb/>G<emph type="italics"/>rauia in planis inæqualiter inclinatis, ac eandem tamen <lb/>eleuationem habentibus, con&longs;tituta: &longs;i eandem inter &longs;e ratio<lb/>nem homologè habeant, quam habent planorum longitudi<lb/>nes, habere æqualia momenta.<emph.end type="italics"/></s><s> Secunda, <emph type="italics"/>Eadem grauia &longs;i <lb/>æqualia fuerint, habere momenta in ratione reciproca longi<lb/>tud num eorumdem planorum.<emph.end type="italics"/></s><s> Tertia, <emph type="italics"/>Illa <expan abbr="æquali&utilde;">æqualium</expan> grauium <lb/>momenta e&longs;&longs;e in ratione homologa cum perpendiculis par<lb/>tium æqualium eorumdem planorum.<emph.end type="italics"/></s><s> Quarta, <emph type="italics"/>Tempora <lb/>la<gap/>i<gap/>um ex quiete e&longs;&longs;e homologè vt longitudines eorum<lb/>dem planorum.<emph.end type="italics"/></s><s> Quinta autem e&longs;t ip&longs;um Po&longs;tulatum <pb pagenum="24"/>ex &longs;uperioribus deductum, G<emph type="italics"/>radus velocitatis eiu&longs;dem <lb/>mobilis &longs;uper diuer&longs;as planorum inclinationes acqui&longs;itos tunc <lb/>e&longs;&longs;e æqualeis, cùm eorumdem planorum eleuationes &ecedil;quales <lb/>&longs;unt.<emph.end type="italics"/></s>

<s>XV. Verùm, ne ad alia excurram, quàm quæ <lb/>ip&longs;emet ex Galileo commemoras, improbas ec<gap/>e ex<lb/>perimentum, quo ille e&longs;t conatus h<gap/>em Po&longs;tulato <lb/>a&longs;&longs;erere, quodque ad&longs;cripta figura &longs;ic refers E <emph type="italics"/>clauo A<emph.end type="italics"/><lb/><figure id="fig11"></figure><lb/><emph type="italics"/>parieti infixo, globus plumbeus, aut alius quilibet tenui filo, <lb/>tribus, aut quatuor digitis à pariete remoto &longs;u&longs;pendatur, &longs;it<lb/>que AB, De&longs;criptaque in pariete recta CD horizonti <lb/>parallela, globus B à perpendiculari eductus v&longs;que ad alti<lb/>tudinem rectæ CD manu altollatur, nempe ad C; indeque <lb/>liberè dimittatur. </s>

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<s>Ergo è quolibet de&longs;cen&longs;u æqualem acquirit impetum; ni&longs;i <lb/>enim e&longs;&longs;et impetus æqualis, globum ad æqualem altitudinem <lb/>non attolleret. </s>

<s>Quid ni igitur idem quoque faciat globus, <lb/>&longs;i per plana CB, GB, IB de&longs;cendat?<emph.end type="italics"/> C<emph type="italics"/>redibile igitur <lb/>etiam e&longs;t globum per illa, aut &longs;imilia plana decidentem, æqua<lb/>lem tali de&longs;cen&longs;u impetum, ac proinde æqualem quoque ve<lb/>locitatis gradum acquirere.<emph.end type="italics"/> Subinde autem, vt o&longs;ten<lb/>das quàm hæc &longs;int incerta, incohæcentia, &c. <emph type="italics"/>Impri<lb/>mis quidem ne&longs;cio,<emph.end type="italics"/> inquis, <emph type="italics"/>an globi ea, qua vult<emph.end type="italics"/> G<emph type="italics"/>alileus <lb/>ratione &longs;u&longs;pen&longs;i, ac librati alitùs in Etruria, quàm in Gal<lb/>lia a&longs;&longs;urgant; at heic neque tam propè ad horizontalem li<lb/>neam, neque per diuer&longs;os arcus ad eam æqualiter accedunt. <lb/></s>

<s>Quid ni igitur idem quoque faciat globus, <lb/>&longs;i per plana CB, GB, IB de&longs;cendat?<emph.end type="italics"/> C<emph type="italics"/>redibile igitur <lb/>etiam e&longs;t globum per illa, aut &longs;imilia plana decidentem, æqua<lb/>lem tali de&longs;cen&longs;u impetum, ac proinde æqualem quoque ve<lb/>locitatis gradum acquirere.<emph.end type="italics"/></s><s> Subinde autem, vt o&longs;ten<lb/>das quàm hæc &longs;int incerta, incohæcentia, &c. <emph type="italics"/>Impri<lb/>mis quidem ne&longs;cio,<emph.end type="italics"/> inquis, <emph type="italics"/>an globi ea, qua vult<emph.end type="italics"/> G<emph type="italics"/>alileus <lb/>ratione &longs;u&longs;pen&longs;i, ac librati alitùs in Etruria, quàm in Gal<lb/>lia a&longs;&longs;urgant; at heic neque tam propè ad horizontalem li<lb/>neam, neque per diuer&longs;os arcus ad eam æqualiter accedunt. <lb/></s>

<s>Nempe filo pedum quatuor cum dimidio &longs;u&longs;pen&longs;us globus ad <lb/>lineam horizontalem tribus infra centum pedibus <expan abbr="de&longs;criptã">de&longs;criptam</expan>, <lb/>propiùs quàm duobus digitis nunquam acceßit. </s>

<s>At centro <lb/>nouem tantum digitis &longs;upra lineam horizontalem accepto, <lb/>filóque duorum pedum con&longs;tituto, iam globus ad lineam ho<lb/>rizontalem vno digito, quàm anteà propiùs acceßit. </s>

<s>Vbi <lb/>verò centrum &longs;eptem infra lineam horizontalem digitis a&longs;<lb/>&longs;umptum est, vix ad quatuor à linea horizontali digitos <lb/>globus a&longs;cendit.<emph.end type="italics"/> Concludis idcircò his verbis, <emph type="italics"/>Qua <lb/>igitur fide<emph.end type="italics"/> G<emph type="italics"/>alileus tam a&longs;&longs;eueranter ait globum ita &longs;u&longs;pen<lb/>&longs;um, ac per quo&longs;cumque arcus librarum, ad æqualem &longs;em<lb/>per altitudinem a&longs;&longs;urgere? </s>

<s>Vbi <lb/>verò centrum &longs;eptem infra lineam horizontalem digitis a&longs;<lb/>&longs;umptum est, vix ad quatuor à linea horizontali digitos <lb/>globus a&longs;cendit.<emph.end type="italics"/></s><s> Concludis idcircò his verbis, <emph type="italics"/>Qua <lb/>igitur fide<emph.end type="italics"/> G<emph type="italics"/>alileus tam a&longs;&longs;eueranter ait globum ita &longs;u&longs;pen<lb/>&longs;um, ac per quo&longs;cumque arcus librarum, ad æqualem &longs;em<lb/>per altitudinem a&longs;&longs;urgere? </s>

<s>aut quomodo ex re adeò euiden<lb/>ter fal&longs;a petere au&longs;us e&longs;t testim<gap/>nium veritatis?<emph.end type="italics"/></s><pb pagenum="26"/>

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<s>Quod attinet autem ad comparationem <lb/>arcuum CB, GB, IB, cum ip&longs;is planis punctim <lb/>notatis inter extrema eadem; tu &longs;ic in&longs;tas, vt licet <lb/>totum id e&longs;&longs;e verum concederetur, quod dicitur de <lb/>impetu globi per diuer&longs;os arcus librati, vrgeas <emph type="italics"/>aliam <lb/>e&longs;&longs;e rationem, aut meritò &longs;altem videri po&longs;&longs;e aliam,<emph.end type="italics"/> de&longs;<lb/>cendentis globi per diuer&longs;a plana. </s>

<s>G<emph type="italics"/>lobus enim,<emph.end type="italics"/> in<lb/>quis, <emph type="italics"/>per aërem &longs;emper toto &longs;uo pondere deorsùm nititur, <lb/>& eatenus &longs;olum eius de&longs;cen&longs;us interturbatur, quatenus à <lb/>recto, & perpendiculari cur&longs;u ad circularem cogitur, at<lb/>que adducitur: at præter impedimentum ex varia plano<lb/>rum inclinatione, adhûc maius, dum globus etiam magis <lb/>à perpendiculari de&longs;cen&longs;u di&longs;trahitur; tantò minoribus in<lb/>&longs;uper momentis globus per planum de&longs;cendit, quan ò mi<lb/>nùs accliue fuerit, vt facilè omnibus notum e&longs;t.<emph.end type="italics"/> Verùm <lb/>non video quî id concludas; quatenùs non a&longs;&longs;umis <lb/>planum, quantò minùs decliue e&longs;t, tantò e&longs;&longs;e quo<lb/>que prolixius. </s>

<s>G<emph type="italics"/>lobus enim,<emph.end type="italics"/> in<lb/>quis, <emph type="italics"/>per aërem &longs;emper toto &longs;uo pondere deorsùm nititur, <lb/>& eatenus &longs;olum eius de&longs;cen&longs;us interturbatur, quatenus à <lb/>recto, & perpendiculari cur&longs;u ad circularem cogitur, at<lb/>que adducitur: at præter impedimentum ex varia plano<lb/>rum inclinatione, adhûc maius, dum globus etiam magis <lb/>à perpendiculari de&longs;cen&longs;u di&longs;trahitur; tantò minoribus in<lb/>&longs;uper momentis globus per planum de&longs;cendit, quan ò mi<lb/>nùs accliue fuerit, vt facilè omnibus notum e&longs;t.<emph.end type="italics"/></s><s> Verùm <lb/>non video quî id concludas; quatenùs non a&longs;&longs;umis <lb/>planum, quantò minùs decliue e&longs;t, tantò e&longs;&longs;e quo<lb/>que prolixius. </s>

<s>Etenim notum quidem e&longs;t acquiri <lb/>minores velocitatis gradus in minus decliui, quod <lb/>&longs;it decliuiori æquale, at, &longs;i vt minùs decliue, ita etiam <lb/>prolixius &longs;it, notum quoque e&longs;t velocitatem in fine <lb/>illius quæ&longs;itam e&longs;&longs;e po&longs;&longs;e æqualem velocitati in fine <lb/>decliuioris acqui&longs;itæ, prolixitate nempe de&longs;cen&longs;us par<lb/>uitatem incrementorum velocitatis compen&longs;ante. <lb/></s>

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<s>Id prætereo, quod &longs;ub<gap/>icis, ex a&longs;cen&longs;u <lb/>globi ad eandem altitudinem, non &longs;atis rectè colli<lb/>gi impetus æqualitatem; quoniam id aduer&longs;<gap/>tur <lb/>recitandæ tuæ rationi, atque experientiæ: vti & dum <lb/>cau&longs;&longs;am petis ex eo, <emph type="italics"/>quòd, quò circulus minor e&longs;t, <gap/><emph.end type="italics"/><pb pagenum="30"/><emph type="italics"/>de&longs;cen&longs;us procliuior, faciliorque, & a&longs;cen&longs;us difficilior vi<lb/>deatur:<emph.end type="italics"/> id repugnaret tum compen&longs;ationi, aduer&longs;us <lb/>quam nihil obiicis, inter breuitatem, & decliu<gap/>ta<lb/>tem &longs;patij; tum familiari experientiæ de rebus deor<lb/>sùm impactis, quæ impetu pari deicctæ tantò emer<lb/>gunt altiùs, quantò incidentia e&longs;t magis perpendi<lb/>cularis. </s>

<s>Attingo ergo potiùs id, quod &longs;upere&longs;t, <lb/>dum id &longs;ugillas, quod Galileus &longs;e e&longs;&longs;e &longs;æpiùs exper<lb/>tum ait, <emph type="italics"/>tum globum ferreum per aërem cadentem, tum <lb/>globum æneum per excauatum in longiore tigillo alueolum, <lb/>in quacumque tigilli &longs;upra horizontem eleuatione de&longs;cenden<lb/>tem, perpetuò tantum præcisè temporis in de&longs;cen&longs;u per pri<lb/>mum totius percurrendi spatij quadrantem, quantum in <lb/>trium reliquorum decur&longs;u in&longs;ump&longs;i&longs;&longs;e: ex quo &longs;ine dubio con<lb/>&longs;equens e&longs;&longs;et, &longs;patia æqualibus temporibus decur&longs;a in ea <lb/>e&longs;&longs;e ratione, quæ reperitur inter numeros impareis ab vnita<lb/>te procedenteis.<emph.end type="italics"/> Nimirùm, vt o&longs;tendas ea, quæ ex i&longs;tis <lb/>qua&longs;i principiis con&longs;equuntur, aut inferuntur, e&longs;&longs;e ip<lb/>&longs;is certiora, aut cuidentiora non po&longs;&longs;e: <emph type="italics"/>Id,<emph.end type="italics"/> inquis, <emph type="italics"/>tot <lb/>erroribus obnoxium e&longs;t, & exploratu adcò difficile, vt nihil <lb/>inde certi concludi po&longs;&longs;e videatur.<emph.end type="italics"/> Enimverò, vtcum<lb/>que experiundi modus difficilis &longs;it, obnoxiu&longs;que er<lb/>roribus; non idcircò tamen experimentum conuin<lb/>citur fal&longs;um. </s>

<s>Attingo ergo potiùs id, quod &longs;upere&longs;t, <lb/>dum id &longs;ugillas, quod Galileus &longs;e e&longs;&longs;e &longs;æpiùs exper<lb/>tum ait, <emph type="italics"/>tum globum ferreum per aërem cadentem, tum <lb/>globum æneum per excauatum in longiore tigillo alueolum, <lb/>in quacumque tigilli &longs;upra horizontem eleuatione de&longs;cenden<lb/>tem, perpetuò tantum præcisè temporis in de&longs;cen&longs;u per pri<lb/>mum totius percurrendi spatij quadrantem, quantum in <lb/>trium reliquorum decur&longs;u in&longs;ump&longs;i&longs;&longs;e: ex quo &longs;ine dubio con<lb/>&longs;equens e&longs;&longs;et, &longs;patia æqualibus temporibus decur&longs;a in ea <lb/>e&longs;&longs;e ratione, quæ reperitur inter numeros impareis ab vnita<lb/>te procedenteis.<emph.end type="italics"/></s><s> Nimirùm, vt o&longs;tendas ea, quæ ex i&longs;tis <lb/>qua&longs;i principiis con&longs;equuntur, aut inferuntur, e&longs;&longs;e ip<lb/>&longs;is certiora, aut cuidentiora non po&longs;&longs;e: <emph type="italics"/>Id,<emph.end type="italics"/> inquis, <emph type="italics"/>tot <lb/>erroribus obnoxium e&longs;t, & exploratu adcò difficile, vt nihil <lb/>inde certi concludi po&longs;&longs;e videatur.<emph.end type="italics"/></s><s> Enimverò, vtcum<lb/>que experiundi modus difficilis &longs;it, obnoxiu&longs;que er<lb/>roribus; non idcircò tamen experimentum conuin<lb/>citur fal&longs;um. </s>

<s>Tuum certè illud de Libra, cui totus <lb/>po&longs;teà inniteris, quot quæ&longs;o, vel te deducente, er<lb/>roribus obnoxium e&longs;t? </s>

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<s>Indubitatum enim e&longs;t,<emph.end type="italics"/><lb/>pergis, <emph type="italics"/>quod ip&longs;emet<emph.end type="italics"/> G<emph type="italics"/>alileus paßim agno&longs;cit, tantam præ<lb/>ci&longs;e percutientis corporis e&longs;&longs;e velocitatem, quantus impetus, <lb/>quantaque ip&longs;a percußio fuerit. </s>

<s>Impetus enim omnis, & <lb/>percußio ex velocitate est; imò impetus ip&longs;e velocitas est, <lb/>nulloque hæc abinuicem di&longs;crimine dirimuntur, vt meritò, pro<lb/>inde, qua ratione accre&longs;cit velocitas, eadem impetus, & per<lb/>cußio augeantur.<emph.end type="italics"/> Hactenus nihil e&longs;t, quod non probem. <lb/></s>

<s>Impetus enim omnis, & <lb/>percußio ex velocitate est; imò impetus ip&longs;e velocitas est, <lb/>nulloque hæc abinuicem di&longs;crimine dirimuntur, vt meritò, pro<lb/>inde, qua ratione accre&longs;cit velocitas, eadem impetus, & per<lb/>cußio augeantur.<emph.end type="italics"/></s><s> Hactenus nihil e&longs;t, quod non probem. <lb/></s>

<s>Pro&longs;equeris autem: <emph type="italics"/>At facilè experientiâ con&longs;tat corpus <lb/>graue quodcumque ex qualibet altitudine per aërem cadens, <lb/>& percutiens, vt libet, perpetuò ex altitudine dupla duplo<emph.end type="italics"/><pb pagenum="33"/><emph type="italics"/>præcisè ampliùs, & ex tripla, quadrupláue di&longs;tantia, triplo, <lb/>quadruplóue fortiùs percutere: velocitas igitur quoque ex <lb/>altitudine dupla, duplò maior e&longs;t, & tripla, aut quadrupla, <lb/>&longs;i tripla, quadrupláue altitudo &longs;uerit: ac proinde velocitas, <lb/>spatiis æqualibus, non autem æqualibus temporibus, æqualia <lb/>momenta acquirit.<emph.end type="italics"/> Quæ&longs;o verò heic patere, religio&longs;i&longs;<lb/>&longs;imè Vir, me meam te&longs;tari h<gap/> betudmem; neque enim <lb/>quod tu a&longs;&longs;umis, <emph type="italics"/>facilè experientiâ con&longs;tare,<emph.end type="italics"/> mihi vllà <lb/>prorsùs experientiâ con&longs;tat; neque tu vllam &longs;pecia<lb/>lem affers, ex qua res, vt tibi, ita mihi con&longs;tet. </s>

<s>Pro&longs;equeris autem: <emph type="italics"/>At facilè experientiâ con&longs;tat corpus <lb/>graue quodcumque ex qualibet altitudine per aërem cadens, <lb/>& percutiens, vt libet, perpetuò ex altitudine dupla duplo<emph.end type="italics"/><pb pagenum="33"/><emph type="italics"/>præcisè ampliùs, & ex tripla, quadrupláue di&longs;tantia, triplo, <lb/>quadruplóue fortiùs percutere: velocitas igitur quoque ex <lb/>altitudine dupla, duplò maior e&longs;t, & tripla, aut quadrupla, <lb/>&longs;i tripla, quadrupláue altitudo &longs;uerit: ac proinde velocitas, <lb/>spatiis æqualibus, non autem æqualibus temporibus, æqualia <lb/>momenta acquirit.<emph.end type="italics"/></s><s> Quæ&longs;o verò heic patere, religio&longs;i&longs;<lb/>&longs;imè Vir, me meam te&longs;tari h<gap/> betudmem; neque enim <lb/>quod tu a&longs;&longs;umis, <emph type="italics"/>facilè experientiâ con&longs;tare,<emph.end type="italics"/> mihi vllà <lb/>prorsùs experientiâ con&longs;tat; neque tu vllam &longs;pecia<lb/>lem affers, ex qua res, vt tibi, ita mihi con&longs;tet. </s>

<s>Ac <lb/>deducis quidem deinceps, qua&longs;i &longs;ecundam experien<lb/>tiam, id, quod in Libra expertus es: &longs;ed interim circa <lb/>hanc primam, cæcutio planè, neque agno&longs;co, qui <lb/>rem facilè exploraris. </s>

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<s><emph type="center"/><emph type="italics"/>De Experimento in Bilance facto ac aliud reuera probante, <lb/>quàm velocitates e&longs;&longs;e &longs;icut spatia.<emph.end type="italics"/><emph.end type="center"/></s>

<s>XXIII. Verumtamen, hi&longs;ce dimi&longs;&longs;is, acceden<lb/>dum e&longs;t ad &longs;ecundam, peculiaremve experientiam, <lb/>cui totam &longs;cientiam &longs;uper-ex&longs;truis, & de qua in hunc <lb/>modum præfaris. <emph type="italics"/>Atque, vt quam tibi promi&longs;i expe<lb/>rientiam, cum f&oelig;nore etiam exhibeam, adiungam & aliam, <lb/>à nullo mortalium hactenus ob&longs;eruatam, quæ & priorem <lb/>perfectißimè includat, & non rationem &longs;olùm, quâ celeritas <lb/>in naturali de&longs;cen&longs;u grauium augetur, &longs;ed eiu&longs;dem quoque <lb/>celeritatis pene incredibilem modum, ac men&longs;uram, exacti&longs;-<emph.end type="italics"/><pb pagenum="42"/><emph type="italics"/>&longs;imè determinet.<emph.end type="italics"/> Pergis declarando ecqua illa &longs;ie <lb/><emph type="italics"/>Aio igitur, ita e&longs;&longs;e à natura con&longs;titutum, vt globus quilibet, <lb/>tuiu&longs;cumque materiæ, ex vnius diametri altitudine cadens, <lb/>duplum &longs;ui ponderis, hoc e&longs;t, præter pondus quod &longs;ine im<lb/>petu in æquilibrio retineret, aliud &longs;ibi æquale attollat; & <lb/>ex altitudine duarum diametrorum, triplum; ex tribus dia<lb/>metris, quadruplum; & ita deinceps: adeo vt ex quauis <lb/>altitudine cadens, &longs;emper (vltra æquilibrium) toties pro<lb/>prium pondus multiplieatum attollat, quot in tota, vnde <lb/>cadit, altitudine diametri continentur.<emph.end type="italics"/> Subiicis, rem exag<lb/>gerando, <emph type="italics"/>Mirum &longs;anè quòd globus, cuius figuram, vt<lb/>pote &longs;implicißimam, capacißimàmque, natura &longs;ingulariter <lb/>amare videtur, men&longs;uram, ac modum, tam velocitatis <lb/>motus in de&longs;cen&longs;u grauium, quàm virtutis eius motricis, <lb/>quæ in eadem velocitate continetur, &longs;uâ nobis diametro exhi<lb/>beat: adeo vt ex decem, aut centum diametrorum altitudine <lb/>decidens, eum acquirat impetum, qui attollendis decem, aut <lb/>centum &longs;imilibus globis, in altera lance impo&longs;itis, &longs;ufficere <lb/>poßit, &longs;i materiæ conditio id patiatur.<emph.end type="italics"/> Addis & quid <lb/>ip&longs;e ob&longs;eruaueris. <emph type="italics"/>Expertus &longs;um ego,<emph.end type="italics"/> inquis, <emph type="italics"/>globum plum<lb/>beum vnius vnciæ, ex altitudine &longs;ex pedum, &longs;iue dia<lb/>metrorum centum quatuordecim cadentem, vncias toti<lb/>dem vltra æquilibrium, hoc est, libras &longs;eptem, & <lb/>vncias tres in altera lance impo&longs;itas, &longs;uo impetu eleua&longs;&longs;e, <lb/>non &longs;ine ingenti eorum qui præ&longs;entes aderant admiratione, <lb/>ac stupore.<emph.end type="italics"/> Tum & hæc habes. <emph type="italics"/>Porrò &longs;i id in paucis <lb/>diametris experiri placuerit, non admodùm magna opus <lb/>erit diligentia: at &longs;i è maiore altitudine idem tentare pla<lb/>cuerit, tum in hac, vt in cæteris Phy&longs;icis experientiis,<emph.end type="italics"/><pb pagenum="43"/><emph type="italics"/>accurata, ac &longs;olerti diligentia, atque industria, variis incom<lb/>modis occurrendum erit; vt ne fortè ex conditione materiæ <lb/>effectus impediatur, nó&longs;que ex errore, aut ex ignorantia, id <lb/>impoßibile arbitremur, quod &longs;olius materiæ vitio, ac defectu, <lb/>in certis circum&longs;tantiis minùs ex animi &longs;ententia &longs;uccedit.<emph.end type="italics"/><lb/><figure id="fig15"></figure><lb/>Paginas de<lb/>inceps ali<lb/>quot in&longs;umis, <lb/>vt ea incom<lb/>moda de&longs;cri<lb/>bas, & mo<lb/>dum, quo il<lb/>lis occurra<lb/>tur, tradas; <lb/>depicta &longs;cili<lb/>cet Bilanco, <lb/>quæ ip&longs;i&longs;&longs;i<lb/>ma heic ap<lb/>pingitur, agi<lb/>na putà im<lb/>mobili, & al<lb/>tera lancium <lb/>&longs;u&longs;pen&longs;a in <lb/>aëre, altera <lb/>&longs;upra men<lb/>&longs;am CD qui<lb/>e&longs;cente, cum <lb/>impo&longs;ito pondere, ac &longs;peculatore ad&longs;tante, qui ad <lb/>quamque vel minimam eius elationem attendat (id<lb/>que dum globus manu H dimi&longs;&longs;us incidit in alterius <pb pagenum="44"/>medium, directione circuli G, cui ob æquilibrium <lb/>re&longs;pondet con&longs;imilis F) ac in&longs;uper vtraque lance ca<lb/>tenulis ferreis à &longs;capo AB per intermedios circulos, <lb/>triangulo&longs;-ve, dependente. </s>

<s>XXIII. Verumtamen, hi&longs;ce dimi&longs;&longs;is, acceden<lb/>dum e&longs;t ad &longs;ecundam, peculiaremve experientiam, <lb/>cui totam &longs;cientiam &longs;uper-ex&longs;truis, & de qua in hunc <lb/>modum præfaris. <emph type="italics"/>Atque, vt quam tibi promi&longs;i expe<lb/>rientiam, cum f&oelig;nore etiam exhibeam, adiungam & aliam, <lb/>à nullo mortalium hactenus ob&longs;eruatam, quæ & priorem <lb/>perfectißimè includat, & non rationem &longs;olùm, quâ celeritas <lb/>in naturali de&longs;cen&longs;u grauium augetur, &longs;ed eiu&longs;dem quoque <lb/>celeritatis pene incredibilem modum, ac men&longs;uram, exacti&longs;-<emph.end type="italics"/><pb pagenum="42"/><emph type="italics"/>&longs;imè determinet.<emph.end type="italics"/></s><s> Pergis declarando ecqua illa &longs;ie <lb/><emph type="italics"/>Aio igitur, ita e&longs;&longs;e à natura con&longs;titutum, vt globus quilibet, <lb/>tuiu&longs;cumque materiæ, ex vnius diametri altitudine cadens, <lb/>duplum &longs;ui ponderis, hoc e&longs;t, præter pondus quod &longs;ine im<lb/>petu in æquilibrio retineret, aliud &longs;ibi æquale attollat; & <lb/>ex altitudine duarum diametrorum, triplum; ex tribus dia<lb/>metris, quadruplum; & ita deinceps: adeo vt ex quauis <lb/>altitudine cadens, &longs;emper (vltra æquilibrium) toties pro<lb/>prium pondus multiplieatum attollat, quot in tota, vnde <lb/>cadit, altitudine diametri continentur.<emph.end type="italics"/></s><s> Subiicis, rem exag<lb/>gerando, <emph type="italics"/>Mirum &longs;anè quòd globus, cuius figuram, vt<lb/>pote &longs;implicißimam, capacißimàmque, natura &longs;ingulariter <lb/>amare videtur, men&longs;uram, ac modum, tam velocitatis <lb/>motus in de&longs;cen&longs;u grauium, quàm virtutis eius motricis, <lb/>quæ in eadem velocitate continetur, &longs;uâ nobis diametro exhi<lb/>beat: adeo vt ex decem, aut centum diametrorum altitudine <lb/>decidens, eum acquirat impetum, qui attollendis decem, aut <lb/>centum &longs;imilibus globis, in altera lance impo&longs;itis, &longs;ufficere <lb/>poßit, &longs;i materiæ conditio id patiatur.<emph.end type="italics"/></s><s> Addis & quid <lb/>ip&longs;e ob&longs;eruaueris. <emph type="italics"/>Expertus &longs;um ego,<emph.end type="italics"/> inquis, <emph type="italics"/>globum plum<lb/>beum vnius vnciæ, ex altitudine &longs;ex pedum, &longs;iue dia<lb/>metrorum centum quatuordecim cadentem, vncias toti<lb/>dem vltra æquilibrium, hoc est, libras &longs;eptem, & <lb/>vncias tres in altera lance impo&longs;itas, &longs;uo impetu eleua&longs;&longs;e, <lb/>non &longs;ine ingenti eorum qui præ&longs;entes aderant admiratione, <lb/>ac stupore.<emph.end type="italics"/></s><s> Tum & hæc habes. <emph type="italics"/>Porrò &longs;i id in paucis <lb/>diametris experiri placuerit, non admodùm magna opus <lb/>erit diligentia: at &longs;i è maiore altitudine idem tentare pla<lb/>cuerit, tum in hac, vt in cæteris Phy&longs;icis experientiis,<emph.end type="italics"/><pb pagenum="43"/><emph type="italics"/>accurata, ac &longs;olerti diligentia, atque industria, variis incom<lb/>modis occurrendum erit; vt ne fortè ex conditione materiæ <lb/>effectus impediatur, nó&longs;que ex errore, aut ex ignorantia, id <lb/>impoßibile arbitremur, quod &longs;olius materiæ vitio, ac defectu, <lb/>in certis circum&longs;tantiis minùs ex animi &longs;ententia &longs;uccedit.<emph.end type="italics"/><lb/><figure id="fig15"></figure><lb/>Paginas de<lb/>inceps ali<lb/>quot in&longs;umis, <lb/>vt ea incom<lb/>moda de&longs;cri<lb/>bas, & mo<lb/>dum, quo il<lb/>lis occurra<lb/>tur, tradas; <lb/>depicta &longs;cili<lb/>cet Bilanco, <lb/>quæ ip&longs;i&longs;&longs;i<lb/>ma heic ap<lb/>pingitur, agi<lb/>na putà im<lb/>mobili, & al<lb/>tera lancium <lb/>&longs;u&longs;pen&longs;a in <lb/>aëre, altera <lb/>&longs;upra men<lb/>&longs;am CD qui<lb/>e&longs;cente, cum <lb/>impo&longs;ito pondere, ac &longs;peculatore ad&longs;tante, qui ad <lb/>quamque vel minimam eius elationem attendat (id<lb/>que dum globus manu H dimi&longs;&longs;us incidit in alterius <pb pagenum="44"/>medium, directione circuli G, cui ob æquilibrium <lb/>re&longs;pondet con&longs;imilis F) ac in&longs;uper vtraque lance ca<lb/>tenulis ferreis à &longs;capo AB per intermedios circulos, <lb/>triangulo&longs;-ve, dependente. </s>

<s>Denique autem &longs;ubiun<lb/>gis, <emph type="italics"/>Tam apertam e&longs;&longs;e eius rei demon&longs;trationem, vt nul<lb/>lus,<emph.end type="italics"/> inquis, <emph type="italics"/>intellectus refragari po&longs;&longs;e videatur; dum &longs;emel <lb/>con&longs;tet (quod quilibet &longs;ine tanto apparatu, tantáque diligen<lb/>tia facillimè experiri potest) globum quemcumque, ex vnius <lb/>diametri altitudine, po&longs;&longs;e (vltra æquilibrium) pondus &longs;ibi <lb/>æquale, & ex duabus diametris duplum pondus attollere.<emph.end type="italics"/><lb/>Prætereo autem demon&longs;trationem non alio nixam <lb/>fundamento, quàm ipsâ experientiâ à te &longs;uppo&longs;itâ; <lb/>prætereoque item, quod iterùm &longs;ubdis, <emph type="italics"/>Illud quoque <lb/>pari certitudine constare, quod antè dictum e&longs;t, nihil ad pro<lb/>po&longs;itionis veritatem, atque euidentiam opus e&longs;&longs;e, vt ex al<lb/>tiore di&longs;tantia, tantóque apparatu experientia inquiratur, <lb/>quæ ex aliquot diametrorum altitudine plu&longs;quam abundè; <lb/>ac facillimè habeatur.<emph.end type="italics"/></s>

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<s>Sed patietur &longs;anè <lb/>&longs;inceritas tua, vt, quod &longs;upere&longs;t, &longs;i quid erroneum <lb/>videbitur, culpam coniiciam aut in quidpiam non <lb/>&longs;atis fortè animaduer&longs;um, vt omnes &longs;umus homines; <lb/>aut, &longs;i malis, etiam in illos, quorum operâ v&longs;us fueris, <lb/>quibu&longs;ve referentibus cen&longs;ueris pro tua bonitate non <lb/>e&longs;&longs;e negandum a&longs;&longs;en&longs;um. </s>

<s>Itaque cùm tua verba <lb/>relegens, deprehendam te nihil aliud tibi, tanquam <lb/>ob&longs;eruatum à te vindicare; quàm illud, quod iam re<lb/>tuli, <emph type="italics"/>Expertus &longs;um ego globum plumbeum vnius vnciæ ex <lb/>altitudine &longs;ex pedum, &longs;iue diametrorum centum quatuorde<lb/>cim cadentem, vncias totidem vltra æquilibrium, hoc e&longs;t li<lb/>bras &longs;eptem, & vncias treis in altera lance impo&longs;itas &longs;uo <lb/>impetu eleua&longs;&longs;e.<emph.end type="italics"/> Itemque illud, quod po&longs;teà impedi<lb/>menta memorans, <emph type="italics"/>Propria,<emph.end type="italics"/> inquis, <emph type="italics"/>experientia ip&longs;e <lb/>edoctus &longs;um, qui adhibita omni indu&longs;tria globum vnius vn<lb/>ciæ ex altitudine &longs;ex pedum in lancem &longs;ubiectam, viginti <lb/>quinque, aut triginta vicibus dimittens, ter &longs;olùm centrum <lb/>attingere, & pondus perfectè attollere potui.<emph.end type="italics"/> Cùm, in<lb/>quam, ita deprehendam, non cau&longs;or tuam fidem, <lb/>quam cum per&longs;ua&longs;ione aliqua non vera (re familiari <pb pagenum="46"/>hominibus, etiam optimis) &longs;tare nihil vetat. </s>

<s>Itaque cùm tua verba <lb/>relegens, deprehendam te nihil aliud tibi, tanquam <lb/>ob&longs;eruatum à te vindicare; quàm illud, quod iam re<lb/>tuli, <emph type="italics"/>Expertus &longs;um ego globum plumbeum vnius vnciæ ex <lb/>altitudine &longs;ex pedum, &longs;iue diametrorum centum quatuorde<lb/>cim cadentem, vncias totidem vltra æquilibrium, hoc e&longs;t li<lb/>bras &longs;eptem, & vncias treis in altera lance impo&longs;itas &longs;uo <lb/>impetu eleua&longs;&longs;e.<emph.end type="italics"/></s><s> Itemque illud, quod po&longs;teà impedi<lb/>menta memorans, <emph type="italics"/>Propria,<emph.end type="italics"/> inquis, <emph type="italics"/>experientia ip&longs;e <lb/>edoctus &longs;um, qui adhibita omni indu&longs;tria globum vnius vn<lb/>ciæ ex altitudine &longs;ex pedum in lancem &longs;ubiectam, viginti <lb/>quinque, aut triginta vicibus dimittens, ter &longs;olùm centrum <lb/>attingere, & pondus perfectè attollere potui.<emph.end type="italics"/> Cùm, in<lb/>quam, ita deprehendam, non cau&longs;or tuam fidem, <lb/>quam cum per&longs;ua&longs;ione aliqua non vera (re familiari <pb pagenum="46"/>hominibus, etiam optimis) &longs;tare nihil vetat. </s>

<s>Cùm ad<lb/>dis autem prætereà generale e&longs;&longs;e, vt pro numero dia<lb/>metrorum, quibus idem globus dimi&longs;&longs;us abfuerit à <lb/>lance, pondera cleuet &longs;uo paria; qua&longs;i cùm id præ<lb/>&longs;titerit in certo quodam numero, non valeat citra <lb/>illum plureis, vltrà pauciores eleuare; hoc e&longs;t, quod <lb/>peto mihi condones, vt dicere liceat, in veritatis gra<lb/>tiam, te aut &longs;atis non attendi&longs;&longs;e, aut alijs etiam ni<lb/>miùm credidi&longs;&longs;e. </s>

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<s>in cæteris tamen etiam <lb/>corporibus idem quoque &longs;eruata proportione accidere; vt &longs;i ex <lb/>quacumque di&longs;tantia æquale &longs;ibi pondus attollant, ex eadem <lb/>di&longs;tantia duplicata duplicatum, & ex triplicata <expan abbr="triplicat&utilde;">triplicatum</expan> <lb/>attollant, atque ita con&longs;equenter, ob eandem rationem; cui <lb/>rationi ip&longs;a quoque experientia &longs;uffragetur, &c. </s>

<s>hac ta<lb/>men differentia, quòd in globis, diameter altitudines præ<lb/>cisè definiat, vnde pondus ip&longs;orum multiplicetur, in cæteris <lb/>figuris non item; &longs;ed in illis altitudines diametris ip&longs;arum <lb/>&longs;int minores; ratio verò po&longs;tulet vt vniuer&longs;im in figuris om<lb/>nibus tales altitudines diametro &longs;phæræ eiu&longs;dem molis, ac <lb/>ponderis inueniantur æquales.<emph.end type="italics"/> Nihil, inquam, e&longs;t opus <lb/>vt ad i&longs;tud dicam; cùm neque &longs;uffragari experien<lb/>tiam videam, neque ip&longs;e globus, quicum corpora <lb/>aliarum figurarum confers, habeat pro men&longs;ura præ-<pb pagenum="52"/>ci&longs;a illius altitudinis, ex qua &longs;uo nutu cadens, æquale <lb/>&longs;ibi pondus attollat, &longs;uam diametrum; &longs;ed potiùs duo<lb/>decimam circiter &longs;uæ diametri partem; neque aliun<lb/>de eadem diameter præcisè definiat altitudines, vnde <lb/>pondus, &longs;eu impetus multiplicetur, euadatque tri<lb/>plus ex tripla, quadruplus ex quadrupla, &c. </s>

<s>hac ta<lb/>men differentia, quòd in globis, diameter altitudines præ<lb/>cisè definiat, vnde pondus ip&longs;orum multiplicetur, in cæteris <lb/>figuris non item; &longs;ed in illis altitudines diametris ip&longs;arum <lb/>&longs;int minores; ratio verò po&longs;tulet vt vniuer&longs;im in figuris om<lb/>nibus tales altitudines diametro &longs;phæræ eiu&longs;dem molis, ac <lb/>ponderis inueniantur æquales.<emph.end type="italics"/></s><s> Nihil, inquam, e&longs;t opus <lb/>vt ad i&longs;tud dicam; cùm neque &longs;uffragari experien<lb/>tiam videam, neque ip&longs;e globus, quicum corpora <lb/>aliarum figurarum confers, habeat pro men&longs;ura præ-<pb pagenum="52"/>ci&longs;a illius altitudinis, ex qua &longs;uo nutu cadens, æquale <lb/>&longs;ibi pondus attollat, &longs;uam diametrum; &longs;ed potiùs duo<lb/>decimam circiter &longs;uæ diametri partem; neque aliun<lb/>de eadem diameter præcisè definiat altitudines, vnde <lb/>pondus, &longs;eu impetus multiplicetur, euadatque tri<lb/>plus ex tripla, quadruplus ex quadrupla, &c. </s>

<s>&longs;ed id <lb/>potiù faciat progre&longs;&longs;io numerorum imparium, qua<lb/>dratorumve, ad quos terminantur. </s>

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<s>Sequitur iam Secundum membrum Po<lb/>&longs;terioris capitis, quod tibi fuit præcipus &longs;copus. <lb/></s>

<s>Videlicet ita concludis. <emph type="italics"/>Atque ex his iam manife&longs;tè, at<lb/>que euidenter con&longs;tat, celeritatem motus in naturali grauium <lb/>de&longs;cen&longs;u per aërem, &longs;eclu&longs;is externis impedimentis, vniformi <lb/>&longs;emper incremento augeri, & in spatijs æqualibus cre&longs;cere <lb/>æqualiter: ita &longs;cilicet, vt ex dupla di&longs;tantia, celeritas dupla, <lb/>& ex tripla di&longs;tantia, celeritas tripla, atque ita deinceps, <lb/>eadem ratione, maior &longs;emper celeritas habeatur: ni&longs;i fortè <lb/>eò v&longs;que iam progre&longs;&longs;a e&longs;&longs;et celeritas, vt nec celeriùs <expan abbr="a&etilde;r">aerr</expan> di<lb/>uidi, nec citiùs rarefieri, & accurrere ad replendum va<lb/>cuum naturaliter po&longs;&longs;et.<emph.end type="italics"/> Et po&longs;teà: <emph type="italics"/>Ex quo vlteriùs il<lb/>lud etiam con&longs;tat, quàm non rectè<emph.end type="italics"/> G<emph type="italics"/>alileus, vulgò receptam <lb/>motus æquabiliter accelerati definitionem eam reiecerit, qua <lb/>motus eiu&longs;modi is dicitur; qui spatijs æqualibus, æqualia cele<lb/>ritatis augmenta acquirit; & quàm o&longs;citanter idem halluci-<emph.end type="italics"/><pb pagenum="54"/><emph type="italics"/>natus &longs;it, cùm etiam in&longs;uper, clara, euidentíque demon&longs;tra<lb/>tione, eiu&longs;dem &longs;e fal&longs;itatem, impoßibilitatémque o&longs;tendi&longs;&longs;e, <lb/>tam facilè &longs;ibi, atque incon&longs;uliè per&longs;ua&longs;it: cùm aperta iam, <lb/>indubitatáque experientiâ con&longs;tet, in naturali grauium de&longs;<lb/>cen&longs;u, æqualibus spatijs, æqualia celeritatis augmenta perpe<lb/>tuò acquiri, &longs;emperque velocitates, emen&longs;aque ab initio mo<lb/>tus spatia, in eadem ratione reperiri.<emph.end type="italics"/> Ad i&longs;ta verò vides <lb/>profectò quid &longs;it iam promptum re&longs;pondere; cùm <lb/>tantum abe&longs;t, vt aperta indubitatáque experientia de<lb/>finitionem illam vulgarem, aut incrementa velocitatis <lb/>pro ip&longs;a &longs;patiorum ratione &longs;tabiliat, quin illam potiùs <lb/>planè euertat, & Galileanum ita confirmet, vt mani<lb/>fe&longs;tò exinde con&longs;tet incrementa velocitatis acquiri <lb/>duntaxat æqualia æqualibus temporibus; acqui&longs;ita <lb/>verò, &longs;eu &longs;uperata &longs;patia e&longs;&longs;e vt ip&longs;orum temporum <lb/>quadrata. </s>

<s>Videlicet ita concludis. <emph type="italics"/>Atque ex his iam manife&longs;tè, at<lb/>que euidenter con&longs;tat, celeritatem motus in naturali grauium <lb/>de&longs;cen&longs;u per aërem, &longs;eclu&longs;is externis impedimentis, vniformi <lb/>&longs;emper incremento augeri, & in spatijs æqualibus cre&longs;cere <lb/>æqualiter: ita &longs;cilicet, vt ex dupla di&longs;tantia, celeritas dupla, <lb/>& ex tripla di&longs;tantia, celeritas tripla, atque ita deinceps, <lb/>eadem ratione, maior &longs;emper celeritas habeatur: ni&longs;i fortè <lb/>eò v&longs;que iam progre&longs;&longs;a e&longs;&longs;et celeritas, vt nec celeriùs <expan abbr="a&etilde;r">aerr</expan> di<lb/>uidi, nec citiùs rarefieri, & accurrere ad replendum va<lb/>cuum naturaliter po&longs;&longs;et.<emph.end type="italics"/></s><s> Et po&longs;teà: <emph type="italics"/>Ex quo vlteriùs il<lb/>lud etiam con&longs;tat, quàm non rectè<emph.end type="italics"/> G<emph type="italics"/>alileus, vulgò receptam <lb/>motus æquabiliter accelerati definitionem eam reiecerit, qua <lb/>motus eiu&longs;modi is dicitur; qui spatijs æqualibus, æqualia cele<lb/>ritatis augmenta acquirit; & quàm o&longs;citanter idem halluci-<emph.end type="italics"/><pb pagenum="54"/><emph type="italics"/>natus &longs;it, cùm etiam in&longs;uper, clara, euidentíque demon&longs;tra<lb/>tione, eiu&longs;dem &longs;e fal&longs;itatem, impoßibilitatémque o&longs;tendi&longs;&longs;e, <lb/>tam facilè &longs;ibi, atque incon&longs;uliè per&longs;ua&longs;it: cùm aperta iam, <lb/>indubitatáque experientiâ con&longs;tet, in naturali grauium de&longs;<lb/>cen&longs;u, æqualibus spatijs, æqualia celeritatis augmenta perpe<lb/>tuò acquiri, &longs;emperque velocitates, emen&longs;aque ab initio mo<lb/>tus spatia, in eadem ratione reperiri.<emph.end type="italics"/></s><s> Ad i&longs;ta verò vides <lb/>profectò quid &longs;it iam promptum re&longs;pondere; cùm <lb/>tantum abe&longs;t, vt aperta indubitatáque experientia de<lb/>finitionem illam vulgarem, aut incrementa velocitatis <lb/>pro ip&longs;a &longs;patiorum ratione &longs;tabiliat, quin illam potiùs <lb/>planè euertat, & Galileanum ita confirmet, vt mani<lb/>fe&longs;tò exinde con&longs;tet incrementa velocitatis acquiri <lb/>duntaxat æqualia æqualibus temporibus; acqui&longs;ita <lb/>verò, &longs;eu &longs;uperata &longs;patia e&longs;&longs;e vt ip&longs;orum temporum <lb/>quadrata. </s>

<s>Ex quo fit, vt allatis illis antè argumen<lb/>tis, quibus permouebar, vt coniicerem percu&longs;&longs;ionem, <lb/>atque idcircò impetum, velocitatémque rei deciden<lb/>tis maiorem duplò non haberi, ni&longs;i ex altitudine qua<lb/>drupla, triplum, ni&longs;i ex nonupla, quadruplum, ni&longs;i ex <lb/>&longs;exdecupla, i&longs;tud iam nouum acce&longs;&longs;erit. </s>

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<s>Pro&longs;equeris deinde &longs;ic. <emph type="italics"/>Porrò cùm celeritas <lb/>motus in naturali de&longs;cen&longs;u grauium, non modò ad locum, &longs;ed <lb/>ad tempus quoque re&longs;pectum includat, iamque de altero <expan abbr="dictã">dictam</expan> <lb/>&longs;it, qua videlicet ratione, celeritas &longs;patijs æqualibus augea<lb/>tur; vt ne quid ad perfectam motus accelerati notitiam de<lb/>&longs;it, nece&longs;&longs;arium e&longs;t, vt de &longs;patiis quoque, quæ temporibus <lb/>æqualibus percurruntur, quam inter &longs;e rationem ob&longs;eruent, <lb/>reliqua di&longs;putatione inquiramus, & ex ii&longs;dem quoque expe<lb/>rientiis definiamus.<emph.end type="italics"/> Hoc iam loco, optimè Vir, agno&longs;<lb/>cere potes originem mali. </s>

<s>Pro&longs;equeris deinde &longs;ic. <emph type="italics"/>Porrò cùm celeritas <lb/>motus in naturali de&longs;cen&longs;u grauium, non modò ad locum, &longs;ed <lb/>ad tempus quoque re&longs;pectum includat, iamque de altero <expan abbr="dictã">dictam</expan> <lb/>&longs;it, qua videlicet ratione, celeritas &longs;patijs æqualibus augea<lb/>tur; vt ne quid ad perfectam motus accelerati notitiam de<lb/>&longs;it, nece&longs;&longs;arium e&longs;t, vt de &longs;patiis quoque, quæ temporibus <lb/>æqualibus percurruntur, quam inter &longs;e rationem ob&longs;eruent, <lb/>reliqua di&longs;putatione inquiramus, & ex ii&longs;dem quoque expe<lb/>rientiis definiamus.<emph.end type="italics"/></s><s> Hoc iam loco, optimè Vir, agno&longs;<lb/>cere potes originem mali. </s>

<s>Nempe labes tota vide<lb/>tur ex definitione vulgari contracta, quatenus ratio<lb/>nem incre&longs;centis celeritatis ita cum &longs;patio comparat, <lb/>vt nullam interim in&longs;tituat comparationem cum tem<lb/>pore, &longs;ine quo tamen neque celeritas, neque acce<lb/>leratio intelligi pote&longs;t. </s>

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<s>Subdis con&longs;equenter; <emph type="italics"/>Quod vt certiùs <lb/>fiat, primùm occurrendum est errori, qui facilè obrepere <lb/>potest, &longs;i quæ de cele itatis augmento in &longs;patiis æqualibus <lb/>antè demonstrata &longs;unt, minùs accuratè perpendantur. </s>

<s>Cùm <lb/>enim ex &longs;uperioribus iam euidenter con&longs;tet, in naturali gra<lb/>uium de&longs;cen&longs;u, &longs;emper ex dupla di&longs;tantia, celeritatem ha<lb/>beri duplam; & ex tripla distantia, triplam; atque ita <lb/>deinceps, eadem ratione celeritatem augeri: nihil procliuius <lb/>e&longs;&longs;e potest, quàm vt quis exi&longs;timet, accelerationem <gap/><lb/>fieri per &longs;ubdiui&longs;ionem primi cuiu&longs;libet temporis, in paricis <lb/>&longs;emper minores, pro multitudine, & ratione &longs;patiorum æqua<lb/>lium, quæ motu decurruntur; ita videlicet, vt pars &longs;ecunda <lb/>spatij, ab&longs;oluatur dimidia parte temporis, quo prima pars <lb/>decur&longs;a est; & tertia pars &longs;patij, tertia parte eiu&longs;dem primi <lb/>temporis percurratur, & ita de cæteris: maximè cùm in hac <lb/>etiam hypothe&longs;i, &longs;patia & velocitates in eadem e&longs;&longs;e ratione, <lb/>& quod con&longs;equens e&longs;t, ex impeta quoque decidentium corpo<lb/>rum hac ratione inuariato, iidem omnes, quos experientia <lb/>docet effectus haberi, primo a&longs;pectu videantur.<emph.end type="italics"/> Heic pro<lb/>fectò rur&longs;us mirari tuam &longs;agacitatem par e&longs;t, qua<lb/>tenus eam non fugit error qui ex po&longs;itione à te a&longs;<lb/>&longs;erta con&longs;equitur; tamet&longs;i ip&longs;e non con&longs;equi ex iis, <lb/>quæ &longs;ubiicis, contendas. </s>

<s>Cùm <lb/>enim ex &longs;uperioribus iam euidenter con&longs;tet, in naturali gra<lb/>uium de&longs;cen&longs;u, &longs;emper ex dupla di&longs;tantia, celeritatem ha<lb/>beri duplam; & ex tripla distantia, triplam; atque ita <lb/>deinceps, eadem ratione celeritatem augeri: nihil procliuius <lb/>e&longs;&longs;e potest, quàm vt quis exi&longs;timet, accelerationem <gap/><lb/>fieri per &longs;ubdiui&longs;ionem primi cuiu&longs;libet temporis, in paricis <lb/>&longs;emper minores, pro multitudine, & ratione &longs;patiorum æqua<lb/>lium, quæ motu decurruntur; ita videlicet, vt pars &longs;ecunda <lb/>spatij, ab&longs;oluatur dimidia parte temporis, quo prima pars <lb/>decur&longs;a est; & tertia pars &longs;patij, tertia parte eiu&longs;dem primi <lb/>temporis percurratur, & ita de cæteris: maximè cùm in hac <lb/>etiam hypothe&longs;i, &longs;patia & velocitates in eadem e&longs;&longs;e ratione, <lb/>& quod con&longs;equens e&longs;t, ex impeta quoque decidentium corpo<lb/>rum hac ratione inuariato, iidem omnes, quos experientia <lb/>docet effectus haberi, primo a&longs;pectu videantur.<emph.end type="italics"/></s><s> Heic pro<lb/>fectò rur&longs;us mirari tuam &longs;agacitatem par e&longs;t, qua<lb/>tenus eam non fugit error qui ex po&longs;itione à te a&longs;<lb/>&longs;erta con&longs;equitur; tamet&longs;i ip&longs;e non con&longs;equi ex iis, <lb/>quæ &longs;ubiicis, contendas. </s>

<s>Me quod attinet, is e&longs;t <lb/>ip&longs;emet, quem deduxi aliàs aduer&longs;us Michaelem <lb/>Varronem, qui primus, quod &longs;ciam, eandem po&longs;itio<lb/>nem ante annos plus minùs &longs;exaginta defendit; de<lb/>clarando ex ea id incommodi inter cætera con&longs;equi, <lb/>vt, quemadmodum antè in&longs;inuaui, &longs;patia acqui&longs;ita <lb/>in &longs;ine æqualis cuiu&longs;libet temporis numeranda &longs;int, <lb/>vt difformiter, &longs;ic in plu&longs;quàm tripla ratione. </s>

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<s>XXXII. </s>

<s>Demon&longs;tras ip&longs;e alia ratione (&longs;ed nimi<lb/>rùm aduer&longs;um te) non fieri accelerationem pro &longs;ub<lb/>diui&longs;ione i&longs;ta temporis. <emph type="italics"/>Si igitur,<emph.end type="italics"/> inquis, <emph type="italics"/>accelera io <lb/>motus per eam primi temporis &longs;ubdiui&longs;ionem fieret, de qua<emph.end type="italics"/><pb pagenum="60"/><emph type="italics"/>heic &longs;ermo e&longs;t, pars &longs;ecunda DE tribus minutis percurri <lb/>deberet, hoc e&longs;t dimidia parte primi temporis; & pars ter<lb/>tia EF duobus minutis, nempe tertia parte eiu&longs;aem primi <lb/>temporis, & ita de cæteris.<emph.end type="italics"/> Quamobrem verò id non <lb/>fieret; cùm &longs;uppo&longs;ito tuo illo principio de velocita<lb/>tibus &longs;e&longs;e habentibus vt &longs;patijs, & nullus &longs;it paralo<lb/>gi&longs;mus, & res &longs;ponte &longs;ua &longs;e prodat, neque videatur <lb/>euerti po&longs;&longs;e, abs te, vt mox tentas euertere, ni&longs;i tua <lb/>ip&longs;ius euertas principia, & fal&longs;itatem prodens con&longs;e<lb/>quentis, quod tamen ex tuis principiis tam nece&longs;&longs;a<lb/>riò deducitur, videaris etiam prodere fal&longs;itatem ante<lb/>cedentis? </s>

<s>Demon&longs;tras ip&longs;e alia ratione (&longs;ed nimi<lb/>rùm aduer&longs;um te) non fieri accelerationem pro &longs;ub<lb/>diui&longs;ione i&longs;ta temporis. <emph type="italics"/>Si igitur,<emph.end type="italics"/> inquis, <emph type="italics"/>accelera io <lb/>motus per eam primi temporis &longs;ubdiui&longs;ionem fieret, de qua<emph.end type="italics"/><pb pagenum="60"/><emph type="italics"/>heic &longs;ermo e&longs;t, pars &longs;ecunda DE tribus minutis percurri <lb/>deberet, hoc e&longs;t dimidia parte primi temporis; & pars ter<lb/>tia EF duobus minutis, nempe tertia parte eiu&longs;aem primi <lb/>temporis, & ita de cæteris.<emph.end type="italics"/></s><s> Quamobrem verò id non <lb/>fieret; cùm &longs;uppo&longs;ito tuo illo principio de velocita<lb/>tibus &longs;e&longs;e habentibus vt &longs;patijs, & nullus &longs;it paralo<lb/>gi&longs;mus, & res &longs;ponte &longs;ua &longs;e prodat, neque videatur <lb/>euerti po&longs;&longs;e, abs te, vt mox tentas euertere, ni&longs;i tua <lb/>ip&longs;ius euertas principia, & fal&longs;itatem prodens con&longs;e<lb/>quentis, quod tamen ex tuis principiis tam nece&longs;&longs;a<lb/>riò deducitur, videaris etiam prodere fal&longs;itatem ante<lb/>cedentis? </s>

<s>Pergis itaque, <emph type="italics"/>At rem non ita accidere facilè <lb/>intelligimus, diui&longs;a bifariam parte AD in S, & parte <lb/>item DE &longs;imiliter in X. </s>

<s>Tunc enim ob eandem ratio<lb/>nem nece&longs;&longs;e fuerit, vt pars SD percurratur in dimidio <lb/>eius temporis, quo pars AS decurritur; & DX in ter<lb/>tia parte, itemque XE in quarta parte eiu&longs;dem temporis, <lb/>vt manife&longs;tum e&longs;t.<emph.end type="italics"/> Quor&longs;um verò id nece&longs;&longs;e non fue<lb/>rit; cùm eadem &longs;it ratio dimidij ad dimidium, quæ <lb/>totius ad totum, & nulla &longs;it ob&longs;eruatio, aut ratio, ex <lb/>qua aliud inferatur potiùs de partibus AD, DE, EF, <lb/>&c. </s>

<s>Tunc enim ob eandem ratio<lb/>nem nece&longs;&longs;e fuerit, vt pars SD percurratur in dimidio <lb/>eius temporis, quo pars AS decurritur; & DX in ter<lb/>tia parte, itemque XE in quarta parte eiu&longs;dem temporis, <lb/>vt manife&longs;tum e&longs;t.<emph.end type="italics"/></s><s> Quor&longs;um verò id nece&longs;&longs;e non fue<lb/>rit; cùm eadem &longs;it ratio dimidij ad dimidium, quæ <lb/>totius ad totum, & nulla &longs;it ob&longs;eruatio, aut ratio, ex <lb/>qua aliud inferatur potiùs de partibus AD, DE, EF, <lb/>&c. </s>

<s>quàm de partibus AS, SD, DX, &c. </s>

<s>aut de <lb/>quibu&longs;libet minoribus, dummodò &longs;int omnes inter <lb/>&longs;e æquales? </s>

<s>Pergis iterum, C<emph type="italics"/>ùm igitur &longs;upponamus <lb/>totam AD minutis &longs;ex pertran&longs;iri, nece&longs;&longs;e erit, vt decur<lb/>&longs;us per AS quatuor minuta, & de&longs;cen&longs;us per SD duo <lb/>tantum minuta in&longs;umat: vt &longs;cilicet ea ratione tempus de&longs;<lb/>cen&longs;us per SD &longs;it dimidia pars temporis in de&longs;cen&longs;u per AS <lb/>in&longs;umpti; ideoque etiam pars DX minuti.<emph.end type="italics"/> 1 <gap/> <emph type="italics"/>nempe tertia <lb/>parte temporis AS; & pars XE minuto vno, &longs;iue<emph.end type="italics"/><pb pagenum="61"/><emph type="italics"/>quarta parte eiu&longs;dem temporis percurreretur; &longs;icque de&longs;cen<lb/>&longs;us per totam DE minutis<emph.end type="italics"/> (2 <gap/>) <emph type="italics"/>ab&longs;olueretur.<emph.end type="italics"/> Quid ni <lb/>verò id quoque nece&longs;&longs;e non &longs;it, ex&longs;i&longs;tente &longs;emper <lb/>eadem ratione dimidiorum ad dimidia, quæ toto<lb/>rum ad tota? </s>

<s>Pergis iterum, C<emph type="italics"/>ùm igitur &longs;upponamus <lb/>totam AD minutis &longs;ex pertran&longs;iri, nece&longs;&longs;e erit, vt decur<lb/>&longs;us per AS quatuor minuta, & de&longs;cen&longs;us per SD duo <lb/>tantum minuta in&longs;umat: vt &longs;cilicet ea ratione tempus de&longs;<lb/>cen&longs;us per SD &longs;it dimidia pars temporis in de&longs;cen&longs;u per AS <lb/>in&longs;umpti; ideoque etiam pars DX minuti.<emph.end type="italics"/> 1 <gap/> <emph type="italics"/>nempe tertia <lb/>parte temporis AS; & pars XE minuto vno, &longs;iue<emph.end type="italics"/><pb pagenum="61"/><emph type="italics"/>quarta parte eiu&longs;dem temporis percurreretur; &longs;icque de&longs;cen<lb/>&longs;us per totam DE minutis<emph.end type="italics"/> (2 <gap/>) <emph type="italics"/>ab&longs;olueretur.<emph.end type="italics"/></s><s> Quid ni <lb/>verò id quoque nece&longs;&longs;e non &longs;it, ex&longs;i&longs;tente &longs;emper <lb/>eadem ratione dimidiorum ad dimidia, quæ toto<lb/>rum ad tota? </s>

<s>At <emph type="italics"/>paullò antè,<emph.end type="italics"/> inquis, <emph type="italics"/>&longs;uppo&longs;uimus ean<lb/>dem partem non ni&longs;i tribus minutis decurri.<emph.end type="italics"/> Id verò &longs;anè <lb/>non &longs;uppo&longs;ui&longs;ti, vt aliquid gratis conce&longs;&longs;um; &longs;ed vt <lb/>aliquid nece&longs;&longs;ariò cum tuis principiis cohærens. <lb/></s>

<s>At <emph type="italics"/>paullò antè,<emph.end type="italics"/> inquis, <emph type="italics"/>&longs;uppo&longs;uimus ean<lb/>dem partem non ni&longs;i tribus minutis decurri.<emph.end type="italics"/></s><s> Id verò &longs;anè <lb/>non &longs;uppo&longs;ui&longs;ti, vt aliquid gratis conce&longs;&longs;um; &longs;ed vt <lb/>aliquid nece&longs;&longs;ariò cum tuis principiis cohærens. <lb/></s>

<s>Quare & fit quidem, vt euincas rem e&longs;&longs;e impo&longs;&longs;ibi<lb/>lem, percurri partem DE dimidio eius temporis, quo <lb/>percurritur AD; &longs;ed euincas tamen aduer&longs;us teip&longs;um; <lb/>cùm ex hoc rursùs efficiatur, vt motu æquabiliter ac<lb/>celerato ex A in E, non fuerint in E acqui&longs;iti duo <lb/>celeritatis gradus, quemadmodum in D fuit acqui&longs;i<lb/>tus vnus, &longs;i mobile quidem per totam DE non &longs;it <lb/>motum duplò velocius, quàm per totam DA; atque <lb/>idcircò in dimidio temporis, durationeve minuto<lb/>rum trium. </s>

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<s>Et quia &longs;eruatâ analogià <lb/>PS percurri debet vno minuto cum triente, efficie<lb/>tur, vt non modò SD, verùm ip&longs;a quoque DE per<lb/>curratur rursùs non duobus minutis, &longs;ed vno&longs;olùm <lb/>cum triente; atque ita bifariam &longs;ecando, diminuendo<lb/>que in infinitum. </s>

<s>Adnoto deinde non tran&longs;ire te <lb/>vltrà comparationem partis DE cum parte SD, ne<lb/>que comparare ip&longs;am cum parte PS, vt mox factum <lb/>e&longs;t, & fieri po&longs;&longs;e nihil prohibet; cùm nulla &longs;it ratio, <lb/>ob <expan abbr="quã">quam</expan> in hac potiùs bi&longs;ectione, <expan abbr="quã">quam</expan> in vlteriore vlla <lb/>con&longs;i&longs;tatur; verùm a&longs;&longs;umere te &longs;olum, id <emph type="italics"/>tempus, quo <lb/>ab&longs;oluitur interuallum<emph.end type="italics"/> SD <emph type="italics"/>breuius e&longs;&longs;e tempore, quo pars <lb/>&longs;uperior<emph.end type="italics"/> AS <emph type="italics"/>tran&longs;curritur, alioquin de&longs;cen&longs;us &longs;ine accelera<lb/>tione vniformis e&longs;&longs;et;<emph.end type="italics"/> idque, vt inferas, <emph type="italics"/>partem primùm <lb/>de&longs;ignatam<emph.end type="italics"/> DE, <emph type="italics"/>cum eodem præcisè tempore percurratur, <lb/>quo interuallum<emph.end type="italics"/> SD, <emph type="italics"/>non in dimidio prioris temporis, &longs;ed <lb/>tempore breuiore ab&longs;olui.<emph.end type="italics"/> Adnoto, inquam, vt appareat, <lb/>cui fundamento &longs;uper-ex&longs;truas quicquid deinceps <lb/>ædificas, &longs;upponens nimirùm vt ratum principium <lb/>(quod obiter, & aliud agendo &longs;tabilieris) æqualita<lb/>tem temporis, quo pars SD, & ip&longs;ius dupla DE per<lb/>curruntur. </s>

<s>Adnoto deinde non tran&longs;ire te <lb/>vltrà comparationem partis DE cum parte SD, ne<lb/>que comparare ip&longs;am cum parte PS, vt mox factum <lb/>e&longs;t, & fieri po&longs;&longs;e nihil prohibet; cùm nulla &longs;it ratio, <lb/>ob <expan abbr="quã">quam</expan> in hac potiùs bi&longs;ectione, <expan abbr="quã">quam</expan> in vlteriore vlla <lb/>con&longs;i&longs;tatur; verùm a&longs;&longs;umere te &longs;olum, id <emph type="italics"/>tempus, quo <lb/>ab&longs;oluitur interuallum<emph.end type="italics"/> SD <emph type="italics"/>breuius e&longs;&longs;e tempore, quo pars <lb/>&longs;uperior<emph.end type="italics"/> AS <emph type="italics"/>tran&longs;curritur, alioquin de&longs;cen&longs;us &longs;ine accelera<lb/>tione vniformis e&longs;&longs;et;<emph.end type="italics"/> idque, vt inferas, <emph type="italics"/>partem primùm <lb/>de&longs;ignatam<emph.end type="italics"/> DE, <emph type="italics"/>cum eodem præcisè tempore percurratur, <lb/>quo interuallum<emph.end type="italics"/> SD, <emph type="italics"/>non in dimidio prioris temporis, &longs;ed <lb/>tempore breuiore ab&longs;olui.<emph.end type="italics"/></s><s> Adnoto, inquam, vt appareat, <lb/>cui fundamento &longs;uper-ex&longs;truas quicquid deinceps <lb/>ædificas, &longs;upponens nimirùm vt ratum principium <lb/>(quod obiter, & aliud agendo &longs;tabilieris) æqualita<lb/>tem temporis, quo pars SD, & ip&longs;ius dupla DE per<lb/>curruntur. </s>

<s><emph type="center"/><emph type="italics"/>DeTempore, quo R. P. colligit &longs;ingulas parteis decur &longs;umiri.<emph.end type="italics"/><emph.end type="center"/></s>

<s>XXXIV. </s>

<s>Etenim illicò &longs;ic habes; <emph type="italics"/>Sed ex his, <lb/>& eadem pror&longs;us ratione aliud demonstratur, quod ingentis, <lb/>atque admirabilis paradoxi loco non immeritò fortaßis habe<lb/>ri poßit, nempe &longs;i spatium, per quod corpus graue quod<lb/>cumque de&longs;cendit, in parteis quotlibet æqualeis diui&longs;um intel<lb/>ligatur, & primæ, ac &longs;upremæ partis etiam de&longs;ignetur<emph.end type="italics"/><pb pagenum="64"/><emph type="italics"/>dimidia pars, & tertia, & quarta, ac deinceps cæteræ, inci<lb/>piendo diui&longs;iones i&longs;tas omneis ab infimo eiu&longs;dem primæ par<lb/>tis puncto, donec totidem de&longs;ignatæ &longs;int, quo<gap/> in reliquo &longs;patio <lb/>partes æquales acceptæ fuerint: tum &longs;ingulæ partes buiu&longs;mo<lb/>di æquales tanto præcisè tempore à corpore graui<emph.end type="italics"/><lb/><figure id="fig17"></figure><lb/><emph type="italics"/>de&longs;cendente percurrantur, quanto partes ip&longs;is analo<lb/>gæ, ac respondentes in &longs;uprema parte<emph.end type="italics"/> (&longs;eu infe<lb/>riore eius dimidio) <emph type="italics"/>ab eodem corpore graui de<lb/>cur&longs;æ fuerint.<emph.end type="italics"/> Rem con&longs;equenter ita declaras; <lb/>S<emph type="italics"/>it &longs;patium<emph.end type="italics"/> AB (in &longs;chemate hoc) <emph type="italics"/>per quod <lb/>corpus graue de&longs;cendat, in parteis exempli gratiâ <lb/>&longs;ex æqualeis diui&longs;um in<emph.end type="italics"/> C, D, E, F, & G: <emph type="italics"/>primæ<lb/>que, ac &longs;upremæ partis<emph.end type="italics"/> AC, <emph type="italics"/>ex infimo eius pun<lb/>cto<emph.end type="italics"/> C <emph type="italics"/>de&longs;ignetur primùm media pars<emph.end type="italics"/> CH, <emph type="italics"/>dein<lb/>de tertia<emph.end type="italics"/> CI, <emph type="italics"/>& quarta<emph.end type="italics"/> CK, <emph type="italics"/>itemque quinta, & <lb/>&longs;exta<emph.end type="italics"/> CL, <emph type="italics"/>&<emph.end type="italics"/> CM. <emph type="italics"/>Dico corpus graue de&longs;cen<lb/>dens per<emph.end type="italics"/> AB <emph type="italics"/>tanto præcisè tempore pertran&longs;ire &longs;e<lb/>cundam partem<emph.end type="italics"/> CD, <emph type="italics"/>quanto dimidiam primæ par<lb/>tis<emph.end type="italics"/> HC, <emph type="italics"/>antè pertran&longs;iuit; & &longs;imiliter pari, atque <lb/>æquali tempore partem<emph.end type="italics"/> DE, <emph type="italics"/>quæ ordine tertia est, <lb/>& tertiam prim&ecedil; partis, nempe<emph.end type="italics"/> IC <emph type="italics"/>ab eodem cor<lb/>pore de&longs;cendente tran&longs;curri, & ita de c&ecedil;teris.<emph.end type="italics"/> Tunc <lb/>autem pergis. <emph type="italics"/>Et quidem de &longs;ecunda parte<emph.end type="italics"/> CD, <lb/><emph type="italics"/>eam non longiore tempore decurri, quàm quo prim&ecedil; <lb/>partis posterior dimidia pars tran&longs;ini&longs;&longs;a fuerit, iam <lb/>paulò antè o&longs;ten&longs;um est, nec maiore negotio idem <lb/>de c&ecedil;teris quoque partibus concludetur. </s>

<s>Etenim illicò &longs;ic habes; <emph type="italics"/>Sed ex his, <lb/>& eadem pror&longs;us ratione aliud demonstratur, quod ingentis, <lb/>atque admirabilis paradoxi loco non immeritò fortaßis habe<lb/>ri poßit, nempe &longs;i spatium, per quod corpus graue quod<lb/>cumque de&longs;cendit, in parteis quotlibet æqualeis diui&longs;um intel<lb/>ligatur, & primæ, ac &longs;upremæ partis etiam de&longs;ignetur<emph.end type="italics"/><pb pagenum="64"/><emph type="italics"/>dimidia pars, & tertia, & quarta, ac deinceps cæteræ, inci<lb/>piendo diui&longs;iones i&longs;tas omneis ab infimo eiu&longs;dem primæ par<lb/>tis puncto, donec totidem de&longs;ignatæ &longs;int, quo<gap/> in reliquo &longs;patio <lb/>partes æquales acceptæ fuerint: tum &longs;ingulæ partes buiu&longs;mo<lb/>di æquales tanto præcisè tempore à corpore graui<emph.end type="italics"/><lb/><figure id="fig17"></figure><lb/><emph type="italics"/>de&longs;cendente percurrantur, quanto partes ip&longs;is analo<lb/>gæ, ac respondentes in &longs;uprema parte<emph.end type="italics"/> (&longs;eu infe<lb/>riore eius dimidio) <emph type="italics"/>ab eodem corpore graui de<lb/>cur&longs;æ fuerint.<emph.end type="italics"/></s><s> Rem con&longs;equenter ita declaras; <lb/>S<emph type="italics"/>it &longs;patium<emph.end type="italics"/> AB (in &longs;chemate hoc) <emph type="italics"/>per quod <lb/>corpus graue de&longs;cendat, in parteis exempli gratiâ <lb/>&longs;ex æqualeis diui&longs;um in<emph.end type="italics"/> C, D, E, F, & G: <emph type="italics"/>primæ<lb/>que, ac &longs;upremæ partis<emph.end type="italics"/> AC, <emph type="italics"/>ex infimo eius pun<lb/>cto<emph.end type="italics"/> C <emph type="italics"/>de&longs;ignetur primùm media pars<emph.end type="italics"/> CH, <emph type="italics"/>dein<lb/>de tertia<emph.end type="italics"/> CI, <emph type="italics"/>& quarta<emph.end type="italics"/> CK, <emph type="italics"/>itemque quinta, & <lb/>&longs;exta<emph.end type="italics"/> CL, <emph type="italics"/>&<emph.end type="italics"/> CM. <emph type="italics"/>Dico corpus graue de&longs;cen<lb/>dens per<emph.end type="italics"/> AB <emph type="italics"/>tanto præcisè tempore pertran&longs;ire &longs;e<lb/>cundam partem<emph.end type="italics"/> CD, <emph type="italics"/>quanto dimidiam primæ par<lb/>tis<emph.end type="italics"/> HC, <emph type="italics"/>antè pertran&longs;iuit; & &longs;imiliter pari, atque <lb/>æquali tempore partem<emph.end type="italics"/> DE, <emph type="italics"/>quæ ordine tertia est, <lb/>& tertiam prim&ecedil; partis, nempe<emph.end type="italics"/> IC <emph type="italics"/>ab eodem cor<lb/>pore de&longs;cendente tran&longs;curri, & ita de c&ecedil;teris.<emph.end type="italics"/></s><s> Tunc <lb/>autem pergis. <emph type="italics"/>Et quidem de &longs;ecunda parte<emph.end type="italics"/> CD, <lb/><emph type="italics"/>eam non longiore tempore decurri, quàm quo prim&ecedil; <lb/>partis posterior dimidia pars tran&longs;ini&longs;&longs;a fuerit, iam <lb/>paulò antè o&longs;ten&longs;um est, nec maiore negotio idem <lb/>de c&ecedil;teris quoque partibus concludetur. </s>

<s>Sumpto <lb/>enim<emph.end type="italics"/> CN, <emph type="italics"/>&c.<emph.end type="italics"/></s>

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<s>Vt enim probes (re&longs;umpto iam recen<lb/>tiore &longs;chemate) tempus per tertiam partem DE æqua<lb/>le e&longs;&longs;e tempori per trientem primæ partis IC, <emph type="italics"/>Sumpto,<emph.end type="italics"/><lb/>inquis, CN <emph type="italics"/>æquali ip&longs;i<emph.end type="italics"/> CE, <emph type="italics"/>erit tota<emph.end type="italics"/> AD <emph type="italics"/>diui&longs;a in <lb/>treis parteis æqualeis<emph.end type="italics"/> AI, IN, <emph type="italics"/>&<emph.end type="italics"/> ND; <emph type="italics"/>eritque veloci<lb/>tas in<emph.end type="italics"/> D <emph type="italics"/>ad velocitatem in<emph.end type="italics"/> I, <emph type="italics"/>vt tota<emph.end type="italics"/> AD <emph type="italics"/>ad ip&longs;am<emph.end type="italics"/> AI, <emph type="italics"/>hoc <lb/>e&longs;t tripla. </s>

<s>Cumque ob eandem cau&longs;&longs;am velocitas quoque in<emph.end type="italics"/> E <lb/><emph type="italics"/>tripla etiam &longs;it velocitatis in<emph.end type="italics"/> C, <emph type="italics"/>erit velocitas per totam<emph.end type="italics"/> DE <lb/><emph type="italics"/>tripla velocitatis per totam<emph.end type="italics"/> IC, <emph type="italics"/>&longs;icut tota<emph.end type="italics"/> DE <emph type="italics"/>tripla e&longs;t ip&longs;ius<emph.end type="italics"/><lb/>IC; <emph type="italics"/>ac proinde percurrentur<emph.end type="italics"/> IC, <emph type="italics"/>&<emph.end type="italics"/> DE <emph type="italics"/>æquali tempore.<emph.end type="italics"/><pb pagenum="69"/>Et con&longs;equenter, vt pergas probate tempus per <lb/><figure id="fig19"></figure><lb/>quartam partem EF æquale e&longs;&longs;e tempori per <lb/>KC quadrantem primæ, <emph type="italics"/>Similiter,<emph.end type="italics"/> inquis, <emph type="italics"/>di<lb/>ui&longs;a bifariàm<emph.end type="italics"/> CD <emph type="italics"/>in<emph.end type="italics"/> O, <emph type="italics"/>&longs;umptoque quadr inte<emph.end type="italics"/><lb/>DP <emph type="italics"/>æquali ip&longs;i<emph.end type="italics"/> KC, <emph type="italics"/>tota<emph.end type="italics"/> AE <emph type="italics"/>diui&longs;a erit in par<lb/>teis quatuor æqualeis<emph.end type="italics"/> AK KO, OP, PE; <emph type="italics"/>ideó <lb/>que velocitas in<emph.end type="italics"/> E <emph type="italics"/>erit quadrupla velocitatis in<emph.end type="italics"/> K, <emph type="italics"/>vt <lb/>tota<emph.end type="italics"/> AE <emph type="italics"/>quadrupla e&longs;t ip&longs;ius<emph.end type="italics"/> AK. <emph type="italics"/>At velocitas <lb/>quoque in<emph.end type="italics"/> F <emph type="italics"/>ob eandem rationem quadrupla etiam e&longs;t <lb/>velocitatis in<emph.end type="italics"/> C; <emph type="italics"/>velocitas igitur per totam<emph.end type="italics"/> EF <lb/><emph type="italics"/>quadrupla e&longs;t velocitatis per totam<emph.end type="italics"/> KC, <emph type="italics"/>&longs;icut tota<emph.end type="italics"/><lb/>EF <emph type="italics"/>quadrupla e&longs;t ip&longs;ius<emph.end type="italics"/> KC. <emph type="italics"/>Percurrentur igitur<emph.end type="italics"/><lb/>KC, <emph type="italics"/>&<emph.end type="italics"/> EF <emph type="italics"/>æquali tempore.<emph.end type="italics"/> Sequitur, <emph type="italics"/>Ea <lb/>dem autem etiam ratio e&longs;t cæterarum omnium par<lb/>tium, vt facilè quilibet ex i&longs;tis per &longs;e intelliget.<emph.end type="italics"/> Con<lb/>cludis, <emph type="italics"/>Si &longs;patium igitur, per quod corpus quodcum<lb/>que graue de&longs;cendit, ea, qua dictum e&longs;t, ratione diui<lb/>&longs;um intelligatur, &longs;ingulæ partes huiu&longs;modi æquales tanto <lb/>præcisè tempore à corpore graui de&longs;cendente percur<lb/>rentur, quantò partes ip&longs;is analogæ ac re&longs;pondentes <lb/>in &longs;uprema parte<emph.end type="italics"/> (aut inferiore eius dimidio) <emph type="italics"/>de&longs;i <lb/>gnatæ ab eodem corpore graui decur&longs;æ fuerint, vt est <lb/>propo&longs;itum.<emph.end type="italics"/> Prætereo autem, quod &longs;ubinde de<lb/>claras te ad&longs;crip&longs;i&longs;&longs;e fini cuiu&longs;que &longs;ex partium <lb/>numerum integrum, incipiendo ab vnitate, <lb/>ad de&longs;ignandum velocitatis gradus illeic acqui&longs;itos, & <lb/>ex æquo factos cum decur&longs;is partibus; ad&longs;crip&longs;i&longs;&longs;e au<lb/>tem mediis interuallis &longs;ecundæ, & &longs;equentium partium <lb/>fractos numeros, ad de&longs;ignandum tempora, &longs;iue fra<lb/>ctiones temporis primi, quibus vnumquodque &longs;pa-<pb pagenum="70"/>tiorum primum con&longs;equentium percurritur. </s>

<s>Cumque ob eandem cau&longs;&longs;am velocitas quoque in<emph.end type="italics"/> E <lb/><emph type="italics"/>tripla etiam &longs;it velocitatis in<emph.end type="italics"/> C, <emph type="italics"/>erit velocitas per totam<emph.end type="italics"/> DE <lb/><emph type="italics"/>tripla velocitatis per totam<emph.end type="italics"/> IC, <emph type="italics"/>&longs;icut tota<emph.end type="italics"/> DE <emph type="italics"/>tripla e&longs;t ip&longs;ius<emph.end type="italics"/><lb/>IC; <emph type="italics"/>ac proinde percurrentur<emph.end type="italics"/> IC, <emph type="italics"/>&<emph.end type="italics"/> DE <emph type="italics"/>æquali tempore.<emph.end type="italics"/><pb pagenum="69"/>Et con&longs;equenter, vt pergas probate tempus per <lb/><figure id="fig19"></figure><lb/>quartam partem EF æquale e&longs;&longs;e tempori per <lb/>KC quadrantem primæ, <emph type="italics"/>Similiter,<emph.end type="italics"/> inquis, <emph type="italics"/>di<lb/>ui&longs;a bifariàm<emph.end type="italics"/> CD <emph type="italics"/>in<emph.end type="italics"/> O, <emph type="italics"/>&longs;umptoque quadr inte<emph.end type="italics"/><lb/>DP <emph type="italics"/>æquali ip&longs;i<emph.end type="italics"/> KC, <emph type="italics"/>tota<emph.end type="italics"/> AE <emph type="italics"/>diui&longs;a erit in par<lb/>teis quatuor æqualeis<emph.end type="italics"/> AK KO, OP, PE; <emph type="italics"/>ideó <lb/>que velocitas in<emph.end type="italics"/> E <emph type="italics"/>erit quadrupla velocitatis in<emph.end type="italics"/> K, <emph type="italics"/>vt <lb/>tota<emph.end type="italics"/> AE <emph type="italics"/>quadrupla e&longs;t ip&longs;ius<emph.end type="italics"/> AK. <emph type="italics"/>At velocitas <lb/>quoque in<emph.end type="italics"/> F <emph type="italics"/>ob eandem rationem quadrupla etiam e&longs;t <lb/>velocitatis in<emph.end type="italics"/> C; <emph type="italics"/>velocitas igitur per totam<emph.end type="italics"/> EF <lb/><emph type="italics"/>quadrupla e&longs;t velocitatis per totam<emph.end type="italics"/> KC, <emph type="italics"/>&longs;icut tota<emph.end type="italics"/><lb/>EF <emph type="italics"/>quadrupla e&longs;t ip&longs;ius<emph.end type="italics"/> KC. <emph type="italics"/>Percurrentur igitur<emph.end type="italics"/><lb/>KC, <emph type="italics"/>&<emph.end type="italics"/> EF <emph type="italics"/>æquali tempore.<emph.end type="italics"/></s><s> Sequitur, <emph type="italics"/>Ea <lb/>dem autem etiam ratio e&longs;t cæterarum omnium par<lb/>tium, vt facilè quilibet ex i&longs;tis per &longs;e intelliget.<emph.end type="italics"/></s><s> Con<lb/>cludis, <emph type="italics"/>Si &longs;patium igitur, per quod corpus quodcum<lb/>que graue de&longs;cendit, ea, qua dictum e&longs;t, ratione diui<lb/>&longs;um intelligatur, &longs;ingulæ partes huiu&longs;modi æquales tanto <lb/>præcisè tempore à corpore graui de&longs;cendente percur<lb/>rentur, quantò partes ip&longs;is analogæ ac re&longs;pondentes <lb/>in &longs;uprema parte<emph.end type="italics"/> (aut inferiore eius dimidio) <emph type="italics"/>de&longs;i <lb/>gnatæ ab eodem corpore graui decur&longs;æ fuerint, vt est <lb/>propo&longs;itum.<emph.end type="italics"/></s><s> Prætereo autem, quod &longs;ubinde de<lb/>claras te ad&longs;crip&longs;i&longs;&longs;e fini cuiu&longs;que &longs;ex partium <lb/>numerum integrum, incipiendo ab vnitate, <lb/>ad de&longs;ignandum velocitatis gradus illeic acqui&longs;itos, & <lb/>ex æquo factos cum decur&longs;is partibus; ad&longs;crip&longs;i&longs;&longs;e au<lb/>tem mediis interuallis &longs;ecundæ, & &longs;equentium partium <lb/>fractos numeros, ad de&longs;ignandum tempora, &longs;iue fra<lb/>ctiones temporis primi, quibus vnumquodque &longs;pa-<pb pagenum="70"/>tiorum primum con&longs;equentium percurritur. </s>

<s>XXXVIII. </s>

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<s>Supere&longs;t po&longs;tremum, &longs;iue tertium mem<lb/>brum, de Ratione continuò dupla, qua pertran&longs;iri <lb/>&longs;patia temporibus continuò æqualibus infers. </s>

<s>Primùm <lb/>autem, vbi adnota&longs;ti non po&longs;&longs;e quidem ex deductio<lb/>ne à te mox facta, <emph type="italics"/>ab&longs;olutè colligi quantum præcisè tem<lb/>poris graue ex aßignata altitudine de&longs;cendens in toto de&longs;<lb/>cen&longs;u in&longs;umat, ni&longs;i di&longs;tinctè etiam cogno&longs;eatur tempus de&longs;-<emph.end type="italics"/><pb pagenum="73"/><emph type="italics"/>cen&longs;us non tantum per totam primam partem<emph.end type="italics"/> AC (in nu<lb/>pero &longs;chemate) <emph type="italics"/>&longs;ed etiam &longs;eor&longs;um per<emph.end type="italics"/> AH, <emph type="italics"/>& per<emph.end type="italics"/> HC; <lb/><emph type="italics"/>quod multò difficilius e&longs;&longs;e arbitreris, quàm<emph.end type="italics"/> G<emph type="italics"/>alileo videatur; <lb/>at cognitis, aut præ&longs;uppo&longs;itis temporibus illis, facilè deinceps <lb/>totum tempus totius de&longs;cen&longs;us per quamcumque de&longs;ignatam <lb/>altitudinem determinari:<emph.end type="italics"/> id quod <emph type="italics"/>postmodum te osten&longs;u<lb/>rum recipis.<emph.end type="italics"/> Tum &longs;upponens me ex&longs;pectare <lb/><figure id="fig20"></figure><lb/>diutiùs, quid &longs;is dicturus de <emph type="italics"/>Ratione, qua &longs;e ha<lb/>bent &longs;patia æquali tempore emen&longs;a,<emph.end type="italics"/> &longs;ic infis, <emph type="italics"/>Aio <lb/>verò æqualibus temporibus &longs;patia decurri maiora <lb/>&longs;emper, ac maiora in Ratione dupla. </s>

<s>Primùm <lb/>autem, vbi adnota&longs;ti non po&longs;&longs;e quidem ex deductio<lb/>ne à te mox facta, <emph type="italics"/>ab&longs;olutè colligi quantum præcisè tem<lb/>poris graue ex aßignata altitudine de&longs;cendens in toto de&longs;<lb/>cen&longs;u in&longs;umat, ni&longs;i di&longs;tinctè etiam cogno&longs;eatur tempus de&longs;-<emph.end type="italics"/><pb pagenum="73"/><emph type="italics"/>cen&longs;us non tantum per totam primam partem<emph.end type="italics"/> AC (in nu<lb/>pero &longs;chemate) <emph type="italics"/>&longs;ed etiam &longs;eor&longs;um per<emph.end type="italics"/> AH, <emph type="italics"/>& per<emph.end type="italics"/> HC; <lb/><emph type="italics"/>quod multò difficilius e&longs;&longs;e arbitreris, quàm<emph.end type="italics"/> G<emph type="italics"/>alileo videatur; <lb/>at cognitis, aut præ&longs;uppo&longs;itis temporibus illis, facilè deinceps <lb/>totum tempus totius de&longs;cen&longs;us per quamcumque de&longs;ignatam <lb/>altitudinem determinari:<emph.end type="italics"/> id quod <emph type="italics"/>postmodum te osten&longs;u<lb/>rum recipis.<emph.end type="italics"/></s><s> Tum &longs;upponens me ex&longs;pectare <lb/><figure id="fig20"></figure><lb/>diutiùs, quid &longs;is dicturus de <emph type="italics"/>Ratione, qua &longs;e ha<lb/>bent &longs;patia æquali tempore emen&longs;a,<emph.end type="italics"/> &longs;ic infis, <emph type="italics"/>Aio <lb/>verò æqualibus temporibus &longs;patia decurri maiora <lb/>&longs;emper, ac maiora in Ratione dupla. </s>

<s>Diui&longs;o enim <lb/>spatio<emph.end type="italics"/> AB, <emph type="italics"/>per quod &longs;upponitur fieri de&longs;cen&longs;us, in <lb/>parteis quotcumque æqualeis in<emph.end type="italics"/> C, D, E, F, <emph type="italics"/>&c. </s>

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<s>Patere quin etiam, vt rogitem te, quî ea expedi<lb/>re, quæ à te deinceps &longs;ubiunguntur, valeas? </s>

<s>Compa<lb/>rans enim tempora, quibus partes omnes prim<gap/>m &longs;e<lb/>quentes percurruntur, cum temporibus, quibus vis <lb/>fragmenta po&longs;terioris illius dimidij &longs;igillatim &longs;umpta <lb/>percurri, i&longs;thæc habes verba, <emph type="italics"/>Sic tempus, quo primi in<lb/>terualli media pars inferior ab&longs;oluitur, & quo duæ &longs;equen<lb/>tes partes, nempe<emph.end type="italics"/> 3, <emph type="italics"/>&<emph.end type="italics"/> 4, <emph type="italics"/>&longs;igillatim tran&longs;currerentur; <lb/>itemque illud, quo quatuor &longs;equentes<emph.end type="italics"/> 5, 6, 7, <emph type="italics"/>&<emph.end type="italics"/> 8, <emph type="italics"/>vel <lb/>&longs;equentes octo<emph.end type="italics"/> 9, 10, 11, 12, 13, 14, 15, <emph type="italics"/>&<emph.end type="italics"/> 16, <emph type="italics"/>aut cæ<lb/>teræ con&longs;equenter, &longs;eor&longs;im tamen, & &longs;ucceßiuè ab&longs;olueren<lb/>tur.<emph.end type="italics"/> Quæ&longs;o te verò, quî id fieri, quod hac ratione <lb/>deducis valeat? </s>

<s>Compa<lb/>rans enim tempora, quibus partes omnes prim<gap/>m &longs;e<lb/>quentes percurruntur, cum temporibus, quibus vis <lb/>fragmenta po&longs;terioris illius dimidij &longs;igillatim &longs;umpta <lb/>percurri, i&longs;thæc habes verba, <emph type="italics"/>Sic tempus, quo primi in<lb/>terualli media pars inferior ab&longs;oluitur, & quo duæ &longs;equen<lb/>tes partes, nempe<emph.end type="italics"/> 3, <emph type="italics"/>&<emph.end type="italics"/> 4, <emph type="italics"/>&longs;igillatim tran&longs;currerentur; <lb/>itemque illud, quo quatuor &longs;equentes<emph.end type="italics"/> 5, 6, 7, <emph type="italics"/>&<emph.end type="italics"/> 8, <emph type="italics"/>vel <lb/>&longs;equentes octo<emph.end type="italics"/> 9, 10, 11, 12, 13, 14, 15, <emph type="italics"/>&<emph.end type="italics"/> 16, <emph type="italics"/>aut cæ<lb/>teræ con&longs;equenter, &longs;eor&longs;im tamen, & &longs;ucceßiuè ab&longs;olueren<lb/>tur.<emph.end type="italics"/></s><s> Quæ&longs;o te verò, quî id fieri, quod hac ratione <lb/>deducis valeat? </s>

<s>A&longs;&longs;ume enim integrum tempus, quod<lb/>cúmque volueris, vt ad illud referas qua&longs;cúmque heic <lb/>enumeras parteis, & peruidebis ratio-ne dupla id ip<lb/>&longs;um, quod moliris, ab&longs;oluat. </s>

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<s>Cùm tibi &longs;ubinde in animo e&longs;&longs;et &longs;pecimen <lb/>quoddam in&longs;igne dare huiu&longs;ce tuæ rationis duplæ, <lb/>ca&longs;um delegi&longs;ti globi ferrei ex Luna v&longs;que in centrum <lb/>Terræ. </s>

<s>Ac primùm quidem adnotas &longs;equi ex tua illa <lb/>ratione, G<emph type="italics"/>rauia omnia longè celeriùs deor&longs;um moueri, <lb/>quàm à<emph.end type="italics"/> G<emph type="italics"/>alileo con&longs;tituatur; quoniam cùm ex eius principiis <lb/>corpus graue quodcumque &longs;ex temporibus, exempli gratiâ, <lb/>inter &longs;e æqualibus de&longs;cendens, non ni&longs;i triginta &longs;ex interualla <lb/>æqualia percurrat; po&longs;ita aliunde acceleratione motus <lb/>æqualibus temporibus in ratione dupla, demon&longs;tratum<emph.end type="italics"/> à te <lb/>dicis <emph type="italics"/>nece&longs;&longs;e omninò e&longs;&longs;e, vt idem corpus graue &longs;ex ii&longs;dem <lb/>temporibus de&longs;cendens in terualla non tantum triginta &longs;ex, <lb/>&longs;ed &longs;exaginta tria decurrat.<emph.end type="italics"/> Verùm hac in re non e&longs;t <lb/>immoiandum, neque exaggeranda e&longs;t exorbitatio, <lb/>qua facta progre&longs;&longs;io in ratione dupla, vtcumque initio <lb/>moderata &longs;it, & progre&longs;&longs;ionem &longs;ecundum &longs;eriem nu<lb/>merorum imparium proximè circum&longs;tat; <gap/> eò tamen <lb/>omneis metas probabilitatis prætergreditur, cùm res <lb/>&longs;tatim pateat in ip&longs;o de ca&longs;u ex Luna exemplo. </s>

<s>Ac primùm quidem adnotas &longs;equi ex tua illa <lb/>ratione, G<emph type="italics"/>rauia omnia longè celeriùs deor&longs;um moueri, <lb/>quàm à<emph.end type="italics"/> G<emph type="italics"/>alileo con&longs;tituatur; quoniam cùm ex eius principiis <lb/>corpus graue quodcumque &longs;ex temporibus, exempli gratiâ, <lb/>inter &longs;e æqualibus de&longs;cendens, non ni&longs;i triginta &longs;ex interualla <lb/>æqualia percurrat; po&longs;ita aliunde acceleratione motus <lb/>æqualibus temporibus in ratione dupla, demon&longs;tratum<emph.end type="italics"/> à te <lb/>dicis <emph type="italics"/>nece&longs;&longs;e omninò e&longs;&longs;e, vt idem corpus graue &longs;ex ii&longs;dem <lb/>temporibus de&longs;cendens in terualla non tantum triginta &longs;ex, <lb/>&longs;ed &longs;exaginta tria decurrat.<emph.end type="italics"/></s><s> Verùm hac in re non e&longs;t <lb/>immoiandum, neque exaggeranda e&longs;t exorbitatio, <lb/>qua facta progre&longs;&longs;io in ratione dupla, vtcumque initio <lb/>moderata &longs;it, & progre&longs;&longs;ionem &longs;ecundum &longs;eriem nu<lb/>merorum imparium proximè circum&longs;tat; <gap/> eò tamen <lb/>omneis metas probabilitatis prætergreditur, cùm res <lb/>&longs;tatim pateat in ip&longs;o de ca&longs;u ex Luna exemplo. </s>

<s>Ecce <pb pagenum="80"/>enim quia Galileus, &longs;upponendo e&longs;&longs;e à Luna in cen<lb/>trum terræ milliaria 196000. ratiocinatur globum <lb/>ferreum è Luna dimi&longs;&longs;um peruenturum ad centrum <lb/>Terræ intra horas 3. & minuta 22. cum &longs;ecundis 4. <lb/>quatenus ex ob&longs;eruatione ab eo peracta decidit ini<lb/>tio, intra &longs;ecunda quinque, centum cubitis; ac perre<lb/>cturus e&longs;t deinceps iuxta progre&longs;&longs;ionem ab eo a&longs;&longs;i<lb/>gnatam: idcircò tu illa milliaria diuidens in pedes <lb/>980000000 (quanquam Galileus non pedes v&longs;urpa<lb/>uit, &longs;ed cubitos, quorum numerus foret 588000000) <lb/>& numerum reducens in pedum centena 9800000, <lb/>a&longs;&longs;umis 100 pedes (a&longs;&longs;ump&longs;it ille ex ob&longs;eruatione 100 <lb/>cubitos, qui continent pedes (166 2/3)) pro &longs;patio, quod <lb/>percurritur quinque &longs;ecundis, &longs;eu tempore vno, qua<lb/>lia &longs;unt duodecim in vno minuto, & 24 in duobus mi<lb/>nutis: ac tum extendendo 24. hæc tempora, tribuis <lb/>primo 100, &longs;ecundo 200, tertio 400, quarto 800, at<lb/>que ita ingeminando, quov&longs;que vige&longs;imo quarto tri<lb/>buas 838860800: & colligis po&longs;tea omnium &longs;um<lb/>mam 1677721500, numerum videlicet pedum, qui <lb/>percurruntur intra duo minuta. </s>

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<s>Videris deinde fidem liberare circa id, <lb/>quod facturum te receperas de tempore determinan<lb/>do, quo duo illa primæ partis percurruntur dimidia; <lb/>vt quo habito di&longs;tinctè deinde præ i&longs;um tempus cog<lb/>no&longs;ceremus, quo decidens graue de&longs;ignatum &longs;patium <lb/>&longs;uo de&longs;cen&longs;u percurteret. </s>

<s>Dicis autem primò, G<emph type="italics"/>alileum <lb/>quidem id fidenter promittere, dum ait &longs;e iteratis &longs;æpiùs ac <lb/>diligenter experient is ob&longs;erua&longs;&longs;e globum ferreum ex altitud ne <lb/>cubitorum centum decidentem quinque &longs;ecundis horæ minutis <lb/>totum illud &longs;patium decurri&longs;&longs;e: verùm, cùm idem non minùs<emph.end type="italics"/><pb pagenum="83"/><emph type="italics"/>audacter etiam affirmet &longs;e item eadem methodo expertum <lb/>e&longs;&longs;e spatia &ecedil;qualibus temporibus emen&longs;a eam inter &longs;e ratio<lb/>nem ob&longs;eruare, quæ inter numeros omneis impareis ab vni<lb/>tate continua &longs;erie procedenteis inuenitur; & in hac tamen <lb/>po&longs;teriore ob&longs;eruatione vehementer errauerit, magnoperè <lb/>verendum e&longs;&longs;e, ne in priore quoque non minùs hallucinatus <lb/>&longs;it.<emph.end type="italics"/> Dicis deinde, <emph type="italics"/>Satis non e&longs;&longs;e, &longs;i tempus habeatur, quo <lb/>prima quælibet pars de&longs;ignati spatij tran&longs;mittitur, ni&longs;i tem<lb/>pus quoque cogno&longs;catur, quo pars &longs;equens priori æqualis, vel <lb/>duæ medietates prim&ecedil; &longs;eor&longs;im decurruntur; quod tamen <lb/>exactè determinare,<emph.end type="italics"/> inquis, <emph type="italics"/>per quam difficile arbitror, ob <lb/>cau&longs;&longs;as iam &longs;æpiùs adductas.<emph.end type="italics"/> Et quænam quidem fue<lb/>rint huiu&longs;modi cau&longs;&longs;æ non commemini; &longs;ed interim <lb/>tamen candorem commendo, quo dicis Tertiò, <emph type="italics"/>te qua<lb/>cúmque diligentia adhibita nihil habere potui&longs;&longs;e, in quo in<lb/>tellectus conquie&longs;ceret:<emph.end type="italics"/> ac author es; vt &longs;i aliquis &longs;e id <lb/>f&oelig;liciùs a&longs;&longs;equi po&longs;&longs;e confidat, <emph type="italics"/>turrim &longs;atis excel&longs;am <lb/>eligat, puta<emph.end type="italics"/> 200 <emph type="italics"/>pedum; ac deinde aliam altitudinem duplò <lb/>præcisè minorem, pedum videlicet centum; & ex vtraque <lb/>altitudine, tempus de&longs;cen&longs;us exactißimè inquirat; tum mino<lb/>re tempore, ex maiore &longs;ubducto, re&longs;iduum daturum tempus <lb/>de&longs;cen&longs;us per turris maioris centum pedes infimos: tempus <lb/>verò illud minus, quo idem corpus ex &longs;ola centum pedum al<lb/>titudine de&longs;cendet, &ecedil;quale tempori futurum, quo ex maiori <lb/>quoque altitudine, per centum pedes &longs;uperiores de&longs;cenderit.<emph.end type="italics"/></s>

<s>Dicis autem primò, G<emph type="italics"/>alileum <lb/>quidem id fidenter promittere, dum ait &longs;e iteratis &longs;æpiùs ac <lb/>diligenter experient is ob&longs;erua&longs;&longs;e globum ferreum ex altitud ne <lb/>cubitorum centum decidentem quinque &longs;ecundis horæ minutis <lb/>totum illud &longs;patium decurri&longs;&longs;e: verùm, cùm idem non minùs<emph.end type="italics"/><pb pagenum="83"/><emph type="italics"/>audacter etiam affirmet &longs;e item eadem methodo expertum <lb/>e&longs;&longs;e spatia &ecedil;qualibus temporibus emen&longs;a eam inter &longs;e ratio<lb/>nem ob&longs;eruare, quæ inter numeros omneis impareis ab vni<lb/>tate continua &longs;erie procedenteis inuenitur; & in hac tamen <lb/>po&longs;teriore ob&longs;eruatione vehementer errauerit, magnoperè <lb/>verendum e&longs;&longs;e, ne in priore quoque non minùs hallucinatus <lb/>&longs;it.<emph.end type="italics"/></s><s> Dicis deinde, <emph type="italics"/>Satis non e&longs;&longs;e, &longs;i tempus habeatur, quo <lb/>prima quælibet pars de&longs;ignati spatij tran&longs;mittitur, ni&longs;i tem<lb/>pus quoque cogno&longs;catur, quo pars &longs;equens priori æqualis, vel <lb/>duæ medietates prim&ecedil; &longs;eor&longs;im decurruntur; quod tamen <lb/>exactè determinare,<emph.end type="italics"/> inquis, <emph type="italics"/>per quam difficile arbitror, ob <lb/>cau&longs;&longs;as iam &longs;æpiùs adductas.<emph.end type="italics"/></s><s> Et quænam quidem fue<lb/>rint huiu&longs;modi cau&longs;&longs;æ non commemini; &longs;ed interim <lb/>tamen candorem commendo, quo dicis Tertiò, <emph type="italics"/>te qua<lb/>cúmque diligentia adhibita nihil habere potui&longs;&longs;e, in quo in<lb/>tellectus conquie&longs;ceret:<emph.end type="italics"/> ac author es; vt &longs;i aliquis &longs;e id <lb/>f&oelig;liciùs a&longs;&longs;equi po&longs;&longs;e confidat, <emph type="italics"/>turrim &longs;atis excel&longs;am <lb/>eligat, puta<emph.end type="italics"/> 200 <emph type="italics"/>pedum; ac deinde aliam altitudinem duplò <lb/>præcisè minorem, pedum videlicet centum; & ex vtraque <lb/>altitudine, tempus de&longs;cen&longs;us exactißimè inquirat; tum mino<lb/>re tempore, ex maiore &longs;ubducto, re&longs;iduum daturum tempus <lb/>de&longs;cen&longs;us per turris maioris centum pedes infimos: tempus <lb/>verò illud minus, quo idem corpus ex &longs;ola centum pedum al<lb/>titudine de&longs;cendet, &ecedil;quale tempori futurum, quo ex maiori <lb/>quoque altitudine, per centum pedes &longs;uperiores de&longs;cenderit.<emph.end type="italics"/></s>

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<s>Ad &longs;ecundum quod <lb/>&longs;pectat, determinauit ille, quo præcisè tempore &longs;ecun<lb/>da &longs;patij pars, ac dimidium primæ, & quævis alia per<lb/>curreretur, ex a&longs;&longs;ignato tempore, quo pars prima de<lb/>curritur. </s>

<s>O&longs;tendit nimirum ex &longs;uis principijs, <emph type="italics"/>Si à <lb/>lationis principio duo quælibet spatia &longs;umantur, tempora <lb/>ip&longs;orum fore inter &longs;e, vt alterum eorum ad spatium medium <lb/>proportionale inter ip&longs;a.<emph.end type="italics"/> Adeò vt, &longs;i inter AB pri<lb/>mam partem, & AC aggregatum primæ cum <lb/><figure id="fig21"></figure><lb/>&longs;ecunda inuenias mediam proportionalem AD, <lb/>tempus ca&longs;us per AB, ad tempus ca&longs;us per AC, <lb/>futurum &longs;it vt AB, ad AD. </s>

<s>O&longs;tendit nimirum ex &longs;uis principijs, <emph type="italics"/>Si à <lb/>lationis principio duo quælibet spatia &longs;umantur, tempora <lb/>ip&longs;orum fore inter &longs;e, vt alterum eorum ad spatium medium <lb/>proportionale inter ip&longs;a.<emph.end type="italics"/></s><s> Adeò vt, &longs;i inter AB pri<lb/>mam partem, & AC aggregatum primæ cum <lb/><figure id="fig21"></figure><lb/>&longs;ecunda inuenias mediam proportionalem AD, <lb/>tempus ca&longs;us per AB, ad tempus ca&longs;us per AC, <lb/>futurum &longs;it vt AB, ad AD. </s>

<s>Nimirùm id <lb/>con&longs;equitur ex eo, quòd &longs;patia &longs;int inter &longs;e <lb/>in duplicata temporum ratione; &longs;eu vt quadra<lb/>ta temporum; quódque &longs;it per&longs;picuum ratio<lb/>nem &longs;patij AC ad &longs;patium AB e&longs;&longs;e duplam <lb/>rationis AC, ad AD, &longs;eu eandem, quam ha<lb/>bent quadrata AC, & AD. </s>

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<s>XLVII. </s>

<s>Iam ad finem properans, <emph type="italics"/>omittere<emph.end type="italics"/> te dicis, <lb/><emph type="italics"/>quæ etiam de Motu accelerato examinari po&longs;&longs;ent, vt, qu&ecedil;, qua<lb/>li&longs;que &longs;it cau&longs;&longs;a accelerationis in naturali de&longs;cen&longs;u grauium: <lb/>cur corpora, &longs;altem, quæ eiu&longs;dem figuræ, & homogenea &longs;int, <lb/>cuiu&longs;cumque, & quantumlibet in&ecedil;qualis ponderis illa fuerint, <lb/>deorsùm nihilominùs &ecedil;quali celeritate de&longs;cendant: aliàque <lb/>eiu&longs;mo li, qu&ecedil; tibi quidem in promptu &longs;int, & alio loco, ac <lb/>tempore opportuniùs forta&longs;&longs;e proferenda in publicum: &longs;ed in<lb/>terim h&ecedil;c pr&ecedil;libanda puta&longs;&longs;e, qu&ecedil; non mo ò ad reuincendos<emph.end type="italics"/><lb/>G<emph type="italics"/>alilei errores opportuna, &longs;ed ad veram quoque, ac germa<lb/>nam accelerati motus naturam aperiendam nece&longs;&longs;aria vide<lb/>rentur.<emph.end type="italics"/> Quo rursùs loco, nihil e&longs;t, quod addam, neque <lb/>cur importunè rogem, quamobrem non cen&longs;ueris <pb pagenum="86"/><expan abbr="&longs;ubiiciend&utilde;">&longs;ubiiciendum</expan> aliquid e&longs;&longs;e de quæ&longs;tionibus illis Phy&longs;icis <lb/>ac duabus præ&longs;ertim heic commemoratis; cùm id fe<lb/>cerit maximè &longs;perandum, qui titulus e&longs;t <emph type="italics"/>Phy&longs;ica demon<lb/>&longs;tratio<emph.end type="italics"/> præ&longs;criptus. </s>

<s>Iam ad finem properans, <emph type="italics"/>omittere<emph.end type="italics"/> te dicis, <lb/><emph type="italics"/>quæ etiam de Motu accelerato examinari po&longs;&longs;ent, vt, qu&ecedil;, qua<lb/>li&longs;que &longs;it cau&longs;&longs;a accelerationis in naturali de&longs;cen&longs;u grauium: <lb/>cur corpora, &longs;altem, quæ eiu&longs;dem figuræ, & homogenea &longs;int, <lb/>cuiu&longs;cumque, & quantumlibet in&ecedil;qualis ponderis illa fuerint, <lb/>deorsùm nihilominùs &ecedil;quali celeritate de&longs;cendant: aliàque <lb/>eiu&longs;mo li, qu&ecedil; tibi quidem in promptu &longs;int, & alio loco, ac <lb/>tempore opportuniùs forta&longs;&longs;e proferenda in publicum: &longs;ed in<lb/>terim h&ecedil;c pr&ecedil;libanda puta&longs;&longs;e, qu&ecedil; non mo ò ad reuincendos<emph.end type="italics"/><lb/>G<emph type="italics"/>alilei errores opportuna, &longs;ed ad veram quoque, ac germa<lb/>nam accelerati motus naturam aperiendam nece&longs;&longs;aria vide<lb/>rentur.<emph.end type="italics"/></s><s> Quo rursùs loco, nihil e&longs;t, quod addam, neque <lb/>cur importunè rogem, quamobrem non cen&longs;ueris <pb pagenum="86"/><expan abbr="&longs;ubiiciend&utilde;">&longs;ubiiciendum</expan> aliquid e&longs;&longs;e de quæ&longs;tionibus illis Phy&longs;icis <lb/>ac duabus præ&longs;ertim heic commemoratis; cùm id fe<lb/>cerit maximè &longs;perandum, qui titulus e&longs;t <emph type="italics"/>Phy&longs;ica demon<lb/>&longs;tratio<emph.end type="italics"/> præ&longs;criptus. </s>

<s>Scilicet tibi liberum fuit ex&longs;pecta<lb/>re tempus, quoddam opportunius; ac mihi &longs;anè op<lb/>pidò nimiùm pro tua comitate tribui&longs;ti, cùm faciens <lb/>editionis &longs;pem, id futurum inter&longs;erui&longs;ti, <emph type="italics"/>maximè, &longs;i <lb/>cognoueris i&longs;ta viris eruditis, mihique imprimis minimè di&longs;<lb/>plicui&longs;&longs;e.<emph.end type="italics"/> Ac intelligo quidem non fui&longs;&longs;e cur tibi pla<lb/>cerent, quæ de ii&longs;dem quæ&longs;tionibus in priore mearum <lb/>illarum Epi&longs;tolarum commentus &longs;um, ac cætera inter, <lb/>quod adnixus fui explicare Phy&longs;icam cau&longs;&longs;am, ob <lb/>quam cadens graue primo momento per vnam or<lb/>gyiam, cadit in &longs;ecundo per treis, in tertio per quin<lb/>que, &c. </s>

<s>Scilicet tibi liberum fuit ex&longs;pecta<lb/>re tempus, quoddam opportunius; ac mihi &longs;anè op<lb/>pidò nimiùm pro tua comitate tribui&longs;ti, cùm faciens <lb/>editionis &longs;pem, id futurum inter&longs;erui&longs;ti, <emph type="italics"/>maximè, &longs;i <lb/>cognoueris i&longs;ta viris eruditis, mihique imprimis minimè di&longs;<lb/>plicui&longs;&longs;e.<emph.end type="italics"/></s><s> Ac intelligo quidem non fui&longs;&longs;e cur tibi pla<lb/>cerent, quæ de ii&longs;dem quæ&longs;tionibus in priore mearum <lb/>illarum Epi&longs;tolarum commentus &longs;um, ac cætera inter, <lb/>quod adnixus fui explicare Phy&longs;icam cau&longs;&longs;am, ob <lb/>quam cadens graue primo momento per vnam or<lb/>gyiam, cadit in &longs;ecundo per treis, in tertio per quin<lb/>que, &c. </s>

<s>Verùm ratio iam nulla &longs;ube&longs;t, quorsùm aut <lb/>quicquam repetam, aut obiectionem, &longs;i quampiam es <lb/>propo&longs;iturus præoccupem; cùm paratus aliunde &longs;im <lb/>& manus dare, & habere gratiam, quam maximam <lb/>voueo, meliora docenti. </s>

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<s>Habes denique eam quoque ratio<lb/>nem, qu&ecedil; inter spatia &ecedil;qualibus temporibus emen&longs;a reperi<lb/>tur, indubitatis experientiis, certis, euidentibú&longs;que rationibus <lb/>demon&longs;tratam. </s>

<s>Qu&ecedil; &longs;i, vt &longs;pero, tibi accepta, probataque fue<lb/>rint, non exiguum huius oper&ecedil; pretium me con&longs;ecutum e&longs;&longs;e <lb/>arbitrabor.<emph.end type="italics"/> Ad hæc verò omnia, Optime virorum, <lb/>nihil regerere in animo e&longs;t: cùm illa &longs;atis, &longs;uperque <lb/>&longs;int, quæ circa &longs;ingula edi&longs;&longs;erui. </s>

<s>Qu&ecedil; &longs;i, vt &longs;pero, tibi accepta, probataque fue<lb/>rint, non exiguum huius oper&ecedil; pretium me con&longs;ecutum e&longs;&longs;e <lb/>arbitrabor.<emph.end type="italics"/></s><s> Ad hæc verò omnia, Optime virorum, <lb/>nihil regerere in animo e&longs;t: cùm illa &longs;atis, &longs;uperque <lb/>&longs;int, quæ circa &longs;ingula edi&longs;&longs;erui. </s>

<s>E&longs;t &longs;olùm, quòd <lb/>gratias agam vberes, pro in&longs;igni illo affectu, quem <lb/>ante duos annos in me te&longs;tari dignatus es, quemque <pb pagenum="88"/>expre&longs;&longs;i&longs;ti nunc etiam, pretium collocans operæ, <lb/>quam meam &longs;pera&longs;ti comprobationem. </s>

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<s>Dicere vis &longs;anè circa explicandum vtriu&longs;que opi<lb/>nionis modum quatenus etiam opinionem, quam tu <lb/>defendis ita expo&longs;ui, vt ip&longs;e cam exponeres (tamet&longs;i <lb/>po&longs;teà me non ingre&longs;&longs;um in penetralia controuer&longs;iæ <lb/>dicas) alioquin enim circa rem ip&longs;am planum e&longs;t, <lb/>quantum di&longs;&longs;entiamus; cùm tu gradus velocitatis in <lb/>acceleratione grauium decidentium acqui&longs;itæ habere <lb/>&longs;e velis vt tran&longs;acta &longs;patia, non vt tempora; ego vnà <lb/>cum Galileo &longs;e vt tran&longs;acta tempora, non verò vt <lb/>&longs;patia habere opiner: ac tu defendas &longs;patia æqualibus <lb/>temporibus in dupla continuò ratione percurri; ego <lb/>&longs;patia decurri cen&longs;eam æqualibus temporibus iuxta <lb/>progre&longs;&longs;ionem numerorum imparium ab vnitate in<lb/>c&oelig;ptorum. </s>

<s>Porrò quia ad illu&longs;trationem totius <lb/>controuer&longs;iæ de&longs;iderari adhùc videtur ratio illius Ti<lb/>tuli, quo fuit libellus à te in&longs;criptus, <emph type="italics"/>Phy&longs;ica Demonstra<lb/>tio, qua ratio, men&longs;ura, modus, ac potentia accelerationis mo<lb/>tus in naturali de&longs;cen&longs;u grauium determinantur, Aduer&longs;us <lb/>nuper excogitatam à Galileo<emph.end type="italics"/> G<emph type="italics"/>alilei Florentino Philo&longs;opho, <lb/>ac Mathematico de eodem motu P&longs;eudo &longs;cientiam<emph.end type="italics"/> (&longs;iqui<lb/>dem non pauci tuo libro <emph type="italics"/>lege<emph.end type="italics"/> pellicto quæ&longs;ierunt ex me, <lb/>quamobrem tu illum Demon&longs;trationem indigita&longs;&longs;es, <lb/>quod non &longs;atis per&longs;picerent, qua forma con&longs;tare De<lb/>mon&longs;tratio po&longs;&longs;et) ideò videtur operæ-pretium rem <lb/>heic &longs;upplere; ac tantò magis, quantò iam etiam titu<lb/>lus e&longs;t tuus, <emph type="italics"/>Vindici&ecedil; Phy&longs;ic&ecedil; Demon&longs;trationis.<emph.end type="italics"/> Itaque, <lb/>vt Demon&longs;trationem, quantum quidem a&longs;&longs;equor, toto <lb/>ex opere eliciam, ea videtur huiu&longs;modi. </s>

<s>Porrò quia ad illu&longs;trationem totius <lb/>controuer&longs;iæ de&longs;iderari adhùc videtur ratio illius Ti<lb/>tuli, quo fuit libellus à te in&longs;criptus, <emph type="italics"/>Phy&longs;ica Demonstra<lb/>tio, qua ratio, men&longs;ura, modus, ac potentia accelerationis mo<lb/>tus in naturali de&longs;cen&longs;u grauium determinantur, Aduer&longs;us <lb/>nuper excogitatam à Galileo<emph.end type="italics"/> G<emph type="italics"/>alilei Florentino Philo&longs;opho, <lb/>ac Mathematico de eodem motu P&longs;eudo &longs;cientiam<emph.end type="italics"/> (&longs;iqui<lb/>dem non pauci tuo libro <emph type="italics"/>lege<emph.end type="italics"/> pellicto quæ&longs;ierunt ex me, <lb/>quamobrem tu illum Demon&longs;trationem indigita&longs;&longs;es, <lb/>quod non &longs;atis per&longs;picerent, qua forma con&longs;tare De<lb/>mon&longs;tratio po&longs;&longs;et) ideò videtur operæ-pretium rem <lb/>heic &longs;upplere; ac tantò magis, quantò iam etiam titu<lb/>lus e&longs;t tuus, <emph type="italics"/>Vindici&ecedil; Phy&longs;ic&ecedil; Demon&longs;trationis.<emph.end type="italics"/></s><s> Itaque, <lb/>vt Demon&longs;trationem, quantum quidem a&longs;&longs;equor, toto <lb/>ex opere eliciam, ea videtur huiu&longs;modi. </s>

<s><emph type="italics"/>Si in motu accelerato grauium decidentium velocitates <lb/>acqui&longs;it&ecedil; &longs;e habent, vt emen&longs;a &longs;patia, nece&longs;&longs;e e&longs;t spatia<emph.end type="italics"/><pb pagenum="95"/><emph type="italics"/>decurri temporibus æqualibus in ratione continuò dupla:<emph.end type="italics"/></s>

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<s>At imprimis istud non reprehendo; &longs;ed quòd &longs;uam illam <lb/>definitionem nouam nec &longs;ufficienter, nec ea, qua par e&longs;&longs;et, <lb/>ratione confirmauerit.<emph.end type="italics"/></s>

<s>Ni&longs;i tu illud reprehendis; non videbaris ergo dicere <pb pagenum="98"/><emph type="italics"/>debere fui&longs;&longs;e ab eo fal&longs;am accelerati motus definitionem <lb/>institutam.<emph.end type="italics"/> Quòd fueris autem cau&longs;atus ip&longs;um <emph type="italics"/>&longs;uam <lb/>illam Definitionem experientia certa, ac euidenti non con<lb/>firma&longs;&longs;e;<emph.end type="italics"/> agno&longs;ce quæ&longs;o tu-ne certiore, ac euiden<lb/>tiore <emph type="italics"/>tuam<emph.end type="italics"/> confirmâris. <emph type="italics"/>Tuam,<emph.end type="italics"/> inquam; namlicet eam <lb/>&longs;emper e&longs;&longs;e repetas <emph type="italics"/>vulgò receptam communemque;<emph.end type="italics"/> ec<lb/>qui <expan abbr="nã">nam</expan> tamen illi &longs;unt, qui eodem t<gap/><expan abbr="&utilde;">um</expan> modo definiunt? <lb/></s>

<s>Ni&longs;i tu illud reprehendis; non videbaris ergo dicere <pb pagenum="98"/><emph type="italics"/>debere fui&longs;&longs;e ab eo fal&longs;am accelerati motus definitionem <lb/>institutam.<emph.end type="italics"/></s><s> Quòd fueris autem cau&longs;atus ip&longs;um <emph type="italics"/>&longs;uam <lb/>illam Definitionem experientia certa, ac euidenti non con<lb/>firma&longs;&longs;e;<emph.end type="italics"/> agno&longs;ce quæ&longs;o tu-ne certiore, ac euiden<lb/>tiore <emph type="italics"/>tuam<emph.end type="italics"/> confirmâris. <emph type="italics"/>Tuam,<emph.end type="italics"/> inquam; namlicet eam <lb/>&longs;emper e&longs;&longs;e repetas <emph type="italics"/>vulgò receptam communemque;<emph.end type="italics"/> ec<lb/>qui <expan abbr="nã">nam</expan> tamen illi &longs;unt, qui eodem t<gap/><expan abbr="&utilde;">um</expan> modo definiunt? <lb/></s>

<s>Galileus certè eam non vt receptam, communemque <lb/>impugnauit, &longs;ed vt eam, quæ po&longs;&longs;et fortè ab aliquo ex<lb/>cogitari. </s>

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<s>Cùm igitur in vtraque <lb/>hypothe&longs;i eadem omninò velocitatis acceleratio habeatur, cur <lb/>prior à te constituta perfectam omnibus numeris<emph.end type="italics"/> G<emph type="italics"/>alilei de<lb/>finitionem o&longs;tendat; vulgatam autem defi utionem po&longs;terior <lb/>hypothe&longs;is pari ratione perfectam non euincat?<emph.end type="italics"/></s>

<s>Cau&longs;&longs;am in&longs;inuaui tum mox, tum verbis illis, quæ <lb/>præmi&longs;eram, <emph type="italics"/>Quippe memini&longs;&longs;e, aut potiùs adnota&longs;&longs;e dili<lb/>genter oportet agi heic de motu æquabiliter accelerato, &longs;iue <lb/>cuius celeritas continenter, vniformiterque incre&longs;cat, neque <lb/>vllum &longs;it momentum con&longs;equentis temporis, in quo motus non <lb/>&longs;it velocior, quàm in quouis antecedente, & in quo non eadem <lb/>ratione ip&longs;a velocitas augeatur.<emph.end type="italics"/> Nempe memini <emph type="italics"/>Tempo<lb/>ris,<emph.end type="italics"/> ob rationem po&longs;teà deductam, vbi tu primùm de <lb/>eo egi&longs;ti, admonendo fui&longs;&longs;e originem mali, quòd in <lb/>definitione vulgari, &longs;eu tua nulla e&longs;&longs;et facta <expan abbr="m&etilde;tio">mentio</expan> tem<lb/>poris, &longs;ine quo tamen neque celeritas, neque accele<lb/>ratio (& maximè quidem vniformis) intelligi po&longs;&longs;it. <lb/></s>

<s>Cau&longs;&longs;am in&longs;inuaui tum mox, tum verbis illis, quæ <lb/>præmi&longs;eram, <emph type="italics"/>Quippe memini&longs;&longs;e, aut potiùs adnota&longs;&longs;e dili<lb/>genter oportet agi heic de motu æquabiliter accelerato, &longs;iue <lb/>cuius celeritas continenter, vniformiterque incre&longs;cat, neque <lb/>vllum &longs;it momentum con&longs;equentis temporis, in quo motus non <lb/>&longs;it velocior, quàm in quouis antecedente, & in quo non eadem <lb/>ratione ip&longs;a velocitas augeatur.<emph.end type="italics"/></s><s> Nempe memini <emph type="italics"/>Tempo<lb/>ris,<emph.end type="italics"/> ob rationem po&longs;teà deductam, vbi tu primùm de <lb/>eo egi&longs;ti, admonendo fui&longs;&longs;e originem mali, quòd in <lb/>definitione vulgari, &longs;eu tua nulla e&longs;&longs;et facta <expan abbr="m&etilde;tio">mentio</expan> tem<lb/>poris, &longs;ine quo tamen neque celeritas, neque accele<lb/>ratio (& maximè quidem vniformis) intelligi po&longs;&longs;it. <lb/></s>

<s>Obieci illeic, <emph type="italics"/>Si velocitas attendatur &longs;olùm penes &longs;patia, <lb/>debere &longs;emper id mobile, quod decem percurrerit &longs;tadia, dici <lb/>moueri celeriter, & &longs;emper id, quod vnicum percurrerit, tar<lb/>dè, cum contingere tamen poßit, vt quod percurrit vnicum, <lb/>moueatur decuplò velociùs, quàm illud, quod percurrit decem.<emph.end type="italics"/><lb/>Addo heic &longs;olùm; &longs;i AC &longs;it &longs;patium, & mobile di&longs;ce<lb/>dens ab A acceleretur v&longs;que ad E per parteis integri <lb/>minuti; & motu non interrupto accelerari pergat ab <lb/>E in G, &longs;ed per parteis integræ horæ; ac rursùs motu <lb/>non interrupto accelerari pergat à G in I, &longs;ed per par<lb/>teis integri &longs;ecundi; rur&longs;u&longs;que etiam non interrupto <pb pagenum="101"/>motu, accelerari pergat ab I, in L, &longs;ed per parteis in<lb/>tegri die<gap/>: quæ&longs;o, dices-ne huiu&longs;modi accelerationem <lb/>e&longs;&longs;e vn formem? </s>

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<s>Ex quibus planè efficitur, definitionem accelerati motus <lb/>quamcúmque inde veram, perfectamque non probari, quòd <lb/>ea ratione concepta &longs;it, qua vniformis acceleratio exprima<lb/>tur.<emph.end type="italics"/></s>

<s>Id, quod dicis videri me &longs;upponere, reuerâ &longs;uppo<lb/>no: & quod ais <emph type="italics"/>notum omnibus progreßiones Geometricas <lb/>non minùs e&longs;&longs;e vniformeis, quàm Arithmeticas,<emph.end type="italics"/> mihi &longs;al<lb/>tem notum non e&longs;t (<emph type="italics"/>qualemcumque me habiturus &longs;is<emph.end type="italics"/>) vt <lb/>neque capio id, quod ais, <emph type="italics"/>ad vniformem motus acceleratio<lb/>nem &longs;atis e&longs;&longs;e, &longs;i incrementa velocitatis continuò maiora in <lb/>quacumque ratione Geometrica acquirantur.<emph.end type="italics"/> Sed nempe <lb/>videris tu mihi <emph type="italics"/>vniformitatem<emph.end type="italics"/> cum <emph type="italics"/>conformitate<emph.end type="italics"/> confun-<pb pagenum="107"/>dere; & quia videtur <emph type="italics"/>conformitas<emph.end type="italics"/> idem &longs;onare, quod <lb/><emph type="italics"/>proportio,<emph.end type="italics"/> confundere quoque cum <emph type="italics"/>proportione vnifor<lb/>mitatem:<emph.end type="italics"/> cùm videatur tamen <emph type="italics"/>Vniformitas<emph.end type="italics"/> relatio e&longs;&longs;e <lb/>identitatis, ob vnum, eundemque tenorem, in vna, <lb/>atque eademre; <emph type="italics"/>Proportio<emph.end type="italics"/> autem e&longs;&longs;e potiùs &longs;imilitu<lb/>dinis relatio, quæ in rebus alioquin diuer&longs;is, &longs;iue di&longs;&longs;i<lb/>tis reperiatur. </s>

<s>Id, quod dicis videri me &longs;upponere, reuerâ &longs;uppo<lb/>no: & quod ais <emph type="italics"/>notum omnibus progreßiones Geometricas <lb/>non minùs e&longs;&longs;e vniformeis, quàm Arithmeticas,<emph.end type="italics"/> mihi &longs;al<lb/>tem notum non e&longs;t (<emph type="italics"/>qualemcumque me habiturus &longs;is<emph.end type="italics"/>) vt <lb/>neque capio id, quod ais, <emph type="italics"/>ad vniformem motus acceleratio<lb/>nem &longs;atis e&longs;&longs;e, &longs;i incrementa velocitatis continuò maiora in <lb/>quacumque ratione Geometrica acquirantur.<emph.end type="italics"/></s><s> Sed nempe <lb/>videris tu mihi <emph type="italics"/>vniformitatem<emph.end type="italics"/> cum <emph type="italics"/>conformitate<emph.end type="italics"/> confun-<pb pagenum="107"/>dere; & quia videtur <emph type="italics"/>conformitas<emph.end type="italics"/> idem &longs;onare, quod <lb/><emph type="italics"/>proportio,<emph.end type="italics"/> confundere quoque cum <emph type="italics"/>proportione vnifor<lb/>mitatem:<emph.end type="italics"/> cùm videatur tamen <emph type="italics"/>Vniformitas<emph.end type="italics"/> relatio e&longs;&longs;e <lb/>identitatis, ob vnum, eundemque tenorem, in vna, <lb/>atque eademre; <emph type="italics"/>Proportio<emph.end type="italics"/> autem e&longs;&longs;e potiùs &longs;imilitu<lb/>dinis relatio, quæ in rebus alioquin diuer&longs;is, &longs;iue di&longs;&longs;i<lb/>tis reperiatur. </s>

<s>Ex hoc quippe e&longs;t, cur dicatur inter <lb/>fontem, & radicem, non <emph type="italics"/>vniformitas,<emph.end type="italics"/> &longs;ed <emph type="italics"/>proportio<emph.end type="italics"/> e&longs;<lb/>&longs;e: & in colore pennarum cycni, non <emph type="italics"/>proportio,<emph.end type="italics"/> &longs;ed <lb/><emph type="italics"/>vniformitas:<emph.end type="italics"/> ac eodem ex capite e&longs;t, cur in progre&longs;&longs;io<lb/>ne Geometrica rationem vnius ad quàtuor, quatuor ad <lb/>&longs;exdecim, &longs;exdecim ad &longs;exaginta quatuor, dicamus <lb/>e&longs;&longs;e <emph type="italics"/>proportionem,<emph.end type="italics"/> non verò vniformitatem; & in pro<lb/>gre&longs;&longs;ione Arithmetica vnius duorum, trium, quatuor, <lb/>vel duorum, quatuor, &longs;ex, octo; vel trium &longs;ex, nouem, <lb/>duodecim, &c. <emph type="italics"/>vniformitatem<emph.end type="italics"/> e&longs;&longs;e, & non <emph type="italics"/>proportionem<emph.end type="italics"/><lb/>dicamus. </s>

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<s>eam rationem, qua idem Galileus communiorem motus <lb/>vniformiter accelerati definitionem ab&longs;urditatis arguit, à <lb/>paralogi&longs;mo excu&longs;are: &longs;ed fru&longs;tra huius cau&longs;&longs;æ pairocinium <lb/>&longs;u&longs;cipis, cùm nec eam obtinere, nec &longs;atis plau&longs;ibiliter eam de<lb/>fendere poßis. </s>

<s>Hæc porrò e&longs;t<emph.end type="italics"/> G<emph type="italics"/>alilei ratio.<emph.end type="italics"/> Si accelera<lb/>tio motus in de&longs;cen&longs;u grauium æqualibus &longs;patiis, <lb/>æqualia &longs;umeret velocitatis incrementa, e&longs;&longs;ent velo-<pb pagenum="111"/>citates inter &longs;e, vt emen&longs;a &longs;patia: at quoties velocitates <lb/>inter &longs;e &longs;unt, vt emen&longs;a &longs;patia, debent nece&longs;&longs;ariò ea <lb/>&longs;patia aut eodem, aut æquali tempore percurri. </s>

<s>Hæc porrò e&longs;t<emph.end type="italics"/> G<emph type="italics"/>alilei ratio.<emph.end type="italics"/></s><s> Si accelera<lb/>tio motus in de&longs;cen&longs;u grauium æqualibus &longs;patiis, <lb/>æqualia &longs;umeret velocitatis incrementa, e&longs;&longs;ent velo-<pb pagenum="111"/>citates inter &longs;e, vt emen&longs;a &longs;patia: at quoties velocitates <lb/>inter &longs;e &longs;unt, vt emen&longs;a &longs;patia, debent nece&longs;&longs;ariò ea <lb/>&longs;patia aut eodem, aut æquali tempore percurri. </s>

<s>Si igi<lb/>tur velocitas acqui&longs;ita per totam AC, eam rationem <lb/>habeat ad velocitatem acqui&longs;itam per AB, <lb/><figure id="fig25"></figure><lb/>quam &longs;patium AC, ad &longs;patium AB, nece&longs;&longs;e e&longs;t, <lb/>vt totum &longs;patium AC eodem, aut æquali tem<lb/>pore decurratur, quo &longs;patium AB ab&longs;oluitur. <lb/></s>

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<s>Si <lb/>enim intriangulo æqualia spatia de&longs;ignentur<emph.end type="italics"/> AD, DE, EF, <lb/><emph type="italics"/>&c. </s>

<s>& in<emph.end type="italics"/> D <emph type="italics"/>acqui&longs;itus &longs;upponatur vnus<emph.end type="italics"/><lb/><figure id="fig26"></figure><lb/><emph type="italics"/>gradus, & in<emph.end type="italics"/> E <emph type="italics"/>duo, & tres in<emph.end type="italics"/> F, <emph type="italics"/>manife&longs;tum <lb/>e&longs;t duos gradus, ad quos acceleratio perueni&longs;&longs;e <lb/>ponitur in<emph.end type="italics"/> E, <emph type="italics"/>e&longs;&longs;e ad vnum gradum acqui&longs;i<lb/>tum in<emph.end type="italics"/> D, <emph type="italics"/>vt &longs;patium<emph.end type="italics"/> AE <emph type="italics"/>ad spatium<emph.end type="italics"/> AD; <lb/><emph type="italics"/>& &longs;imiliter gradus treis, qui in<emph.end type="italics"/> F <emph type="italics"/>&longs;upponun<lb/>tur terminare celeritatis augmentum, e&longs;&longs;e ad <lb/>gradum vnum ip&longs;ius<emph.end type="italics"/> D, <emph type="italics"/>vel ad duos ip&longs;ius<emph.end type="italics"/> E, <lb/><emph type="italics"/>vt<emph.end type="italics"/> AF, <emph type="italics"/>ad<emph.end type="italics"/> AD, <emph type="italics"/>vel<emph.end type="italics"/> AE. <emph type="italics"/>Et hoc quidem <lb/>&longs;en&longs;u, &longs;i primam illam<emph.end type="italics"/> G<emph type="italics"/>alilei v&longs;urpares, vera omninò e&longs;&longs;et, <lb/>ac nece&longs;&longs;aria, &longs;ed A&longs;&longs;umptio, quæ &longs;ub&longs;umitur, fal&longs;a e&longs;&longs;et at<lb/>que impoßibilis; nempe hæc.<emph.end type="italics"/> At quoties velocitates inter <lb/>&longs;e &longs;unt vt emen&longs;a &longs;patia (<emph type="italics"/>in &longs;en&longs;u proximè aßignato<emph.end type="italics"/>) de<lb/>bent nece&longs;&longs;ariò ea &longs;patia aut eodem, aut æquali tem<lb/>pore percurri: <emph type="italics"/>Sicque iam hac ex parte<emph.end type="italics"/> G<emph type="italics"/>alilei licet ratio<lb/>cinatio corruit. </s>

<s>& in<emph.end type="italics"/> D <emph type="italics"/>acqui&longs;itus &longs;upponatur vnus<emph.end type="italics"/><lb/><figure id="fig26"></figure><lb/><emph type="italics"/>gradus, & in<emph.end type="italics"/> E <emph type="italics"/>duo, & tres in<emph.end type="italics"/> F, <emph type="italics"/>manife&longs;tum <lb/>e&longs;t duos gradus, ad quos acceleratio perueni&longs;&longs;e <lb/>ponitur in<emph.end type="italics"/> E, <emph type="italics"/>e&longs;&longs;e ad vnum gradum acqui&longs;i<lb/>tum in<emph.end type="italics"/> D, <emph type="italics"/>vt &longs;patium<emph.end type="italics"/> AE <emph type="italics"/>ad spatium<emph.end type="italics"/> AD; <lb/><emph type="italics"/>& &longs;imiliter gradus treis, qui in<emph.end type="italics"/> F <emph type="italics"/>&longs;upponun<lb/>tur terminare celeritatis augmentum, e&longs;&longs;e ad <lb/>gradum vnum ip&longs;ius<emph.end type="italics"/> D, <emph type="italics"/>vel ad duos ip&longs;ius<emph.end type="italics"/> E, <lb/><emph type="italics"/>vt<emph.end type="italics"/> AF, <emph type="italics"/>ad<emph.end type="italics"/> AD, <emph type="italics"/>vel<emph.end type="italics"/> AE. <emph type="italics"/>Et hoc quidem <lb/>&longs;en&longs;u, &longs;i primam illam<emph.end type="italics"/> G<emph type="italics"/>alilei v&longs;urpares, vera omninò e&longs;&longs;et, <lb/>ac nece&longs;&longs;aria, &longs;ed A&longs;&longs;umptio, quæ &longs;ub&longs;umitur, fal&longs;a e&longs;&longs;et at<lb/>que impoßibilis; nempe hæc.<emph.end type="italics"/></s><s> At quoties velocitates inter <lb/>&longs;e &longs;unt vt emen&longs;a &longs;patia (<emph type="italics"/>in &longs;en&longs;u proximè aßignato<emph.end type="italics"/>) de<lb/>bent nece&longs;&longs;ariò ea &longs;patia aut eodem, aut æquali tem<lb/>pore percurri: <emph type="italics"/>Sicque iam hac ex parte<emph.end type="italics"/> G<emph type="italics"/>alilei licet ratio<lb/>cinatio corruit. </s>

<s>Sed alius item e&longs;&longs;e pote&longs;t primæ illius Propo<lb/>&longs;itionis &longs;en&longs;us, vt &longs;eilicet quoties acceleratio velocitatis in de&longs;<lb/>cen&longs;u grauium æqualibus &longs;patiis æqualia incrementa acquirit, <lb/>integræ velocitates &longs;ecundum &longs;e totas, & qua&longs;libet &longs;ui parteis <lb/>analogas aeceptæ, & con&longs;iderata, & non tantum acqui&longs;itæ <lb/>partibus &longs;patii æqualibus incrementa, eam ab initio ad finem <lb/>inter &longs;e rationem ob&longs;eruent, quam emen&longs;a &longs;patia. </s>

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<s>An videri potes operosè quidem, &longs;ed nequicquam <lb/>tamen explicare conatum, vt Paralogi&longs;mum o&longs;tendas, <lb/>quem quanta moderatione potueram non fui&longs;&longs;e à te <pb pagenum="115"/>o&longs;ten&longs;um innueram; bonitatem tuam implorando, &longs;i <lb/>fortè liceret mihi dicere, videri po&longs;&longs;e cuipiam, te eum <lb/>potiùs e&longs;&longs;e, qui incideres in Paralogi&longs;mum? </s>

<s>Quippe <lb/>huiu&longs;modi de re &longs;ola hæc verba habueras, quæ non <lb/>pigebit repetere, <emph type="italics"/>Vt &longs;i graue de&longs;cendens per AB, tem<lb/>pus quodcumque in&longs;umat, puta quadrantem: ac deinde BC <lb/>ip&longs;i AB æquale, dimidio quadrante percurrat: quis neget in<emph.end type="italics"/><lb/>C <emph type="italics"/>duplam haberi velocitatem eius, quæ fuit in B? Et-tamen <lb/>idem graue totam AC, & dimidium eius AB eodem tem<lb/>pore non percurreret.<emph.end type="italics"/> Scilicet i&longs;thæc ip&longs;a &longs;unt, ob quæ <expan abbr="c&utilde;">cum</expan> <lb/>ego dixerim, videri te <emph type="italics"/>Rem controuer&longs;am pro principio <lb/>a&longs;&longs;umere:<emph.end type="italics"/> ais iam te fui&longs;&longs;e breuiter loquutum, quod pu<lb/>târis me <emph type="italics"/>intelligentem<emph.end type="italics"/> &longs;atis, vt paucis multa caperem: <lb/>nunc autem, quia contigit &longs;ecus, & &longs;altem virum <emph type="italics"/>animo <lb/>præoccupatum<emph.end type="italics"/> es alloquutus, e&longs;&longs;e rem exactiùs, fu&longs;iu&longs;<lb/>que dicendam. </s>

<s>Quippe <lb/>huiu&longs;modi de re &longs;ola hæc verba habueras, quæ non <lb/>pigebit repetere, <emph type="italics"/>Vt &longs;i graue de&longs;cendens per AB, tem<lb/>pus quodcumque in&longs;umat, puta quadrantem: ac deinde BC <lb/>ip&longs;i AB æquale, dimidio quadrante percurrat: quis neget in<emph.end type="italics"/><lb/>C <emph type="italics"/>duplam haberi velocitatem eius, quæ fuit in B? Et-tamen <lb/>idem graue totam AC, & dimidium eius AB eodem tem<lb/>pore non percurreret.<emph.end type="italics"/></s><s> Scilicet i&longs;thæc ip&longs;a &longs;unt, ob quæ <expan abbr="c&utilde;">cum</expan> <lb/>ego dixerim, videri te <emph type="italics"/>Rem controuer&longs;am pro principio <lb/>a&longs;&longs;umere:<emph.end type="italics"/> ais iam te fui&longs;&longs;e breuiter loquutum, quod pu<lb/>târis me <emph type="italics"/>intelligentem<emph.end type="italics"/> &longs;atis, vt paucis multa caperem: <lb/>nunc autem, quia contigit &longs;ecus, & &longs;altem virum <emph type="italics"/>animo <lb/>præoccupatum<emph.end type="italics"/> es alloquutus, e&longs;&longs;e rem exactiùs, fu&longs;iu&longs;<lb/>que dicendam. </s>

<s>Age itaque tu adeò humanus, vt te hu<lb/>ius meæ hebetudinis, præoccupationi&longs;que mi&longs;e<lb/>reat, patere &longs;altem lentè incedam, viamque pertentem; <lb/>&longs;i quà po&longs;&longs;im te con&longs;equi. </s>

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<s>Quia <lb/>verò tu ad A&longs;&longs;umptionem (Propo&longs;itionis nomine) hæc <lb/>refers; age quid id &longs;it peruideamus. </s>

<s>A&longs;&longs;umptio e&longs;t, <emph type="italics"/>Si acceleratio motus in de&longs;cen&longs;u gra<lb/>uium æqualibus &longs;patiis æqualia &longs;umeret velocitatis incremen<lb/>ta, e&longs;&longs;ent velocitates inter &longs;e, vt emen&longs;a spatia.<emph.end type="italics"/> Tu illam <lb/>explanaturus duplicem ip&longs;i &longs;en&longs;um attribuis. <emph type="italics"/>Et prior <lb/>quidem i&longs;te est,<emph.end type="italics"/> inquis, <emph type="italics"/>&longs;i acceleratio motus in de&longs;cen&longs;u gra<lb/>uium æqualibus &longs;patijs æqualia &longs;umat velocitatis augmenta, <lb/>nece&longs;&longs;e est, vt hæc eadem augmenta quibu&longs;libet spatij parti<lb/>bus acqui&longs;ita, eandem inter &longs;e rationem ob&longs;eruent, quàm <lb/>emen&longs;a &longs;patia.<emph.end type="italics"/> At ego non &longs;um Oedipus, pote&longs;que ip&longs;e <lb/>cau&longs;&longs;ari te non affari intelligentem: &longs;iquidem non ita <lb/>&longs;um &longs;olers, vt per&longs;picere valeam, quid diuer&longs;itatis, aut <lb/>explanationis, &longs;en&longs;us hic, quem facis &longs;pecialem, <lb/>contineat. </s>

<s>A&longs;&longs;umptio e&longs;t, <emph type="italics"/>Si acceleratio motus in de&longs;cen&longs;u gra<lb/>uium æqualibus &longs;patiis æqualia &longs;umeret velocitatis incremen<lb/>ta, e&longs;&longs;ent velocitates inter &longs;e, vt emen&longs;a spatia.<emph.end type="italics"/></s><s> Tu illam <lb/>explanaturus duplicem ip&longs;i &longs;en&longs;um attribuis. <emph type="italics"/>Et prior <lb/>quidem i&longs;te est,<emph.end type="italics"/> inquis, <emph type="italics"/>&longs;i acceleratio motus in de&longs;cen&longs;u gra<lb/>uium æqualibus &longs;patijs æqualia &longs;umat velocitatis augmenta, <lb/>nece&longs;&longs;e est, vt hæc eadem augmenta quibu&longs;libet spatij parti<lb/>bus acqui&longs;ita, eandem inter &longs;e rationem ob&longs;eruent, quàm <lb/>emen&longs;a &longs;patia.<emph.end type="italics"/></s><s> At ego non &longs;um Oedipus, pote&longs;que ip&longs;e <lb/>cau&longs;&longs;ari te non affari intelligentem: &longs;iquidem non ita <lb/>&longs;um &longs;olers, vt per&longs;picere valeam, quid diuer&longs;itatis, aut <lb/>explanationis, &longs;en&longs;us hic, quem facis &longs;pecialem, <lb/>contineat. </s>

<s>Po&longs;terior, <emph type="italics"/>vt &longs;cilicet,<emph.end type="italics"/> inquis, <emph type="italics"/>quoties accelera<lb/>tio velocitatis in de&longs;cen&longs;u grauium æqualibus spatiis æqualia <lb/>incrementa acquirit, integræ velocitates &longs;ecundum &longs;e totas, & <lb/>qua&longs;libet &longs;ui parteis analogas acceptæ, & con&longs;ideratæ, & non <lb/>tantum acqui&longs;ita partibus &longs;patii æqualibus incrementa, ea <lb/>ab initio ad finem inter &longs;e rationem ob&longs;eruent, quam emen&longs;a <lb/>&longs;patia.<emph.end type="italics"/> Hæc paulò ob&longs;curiùs, fortè propter illud, <emph type="italics"/>& <lb/>non tantum acqui&longs;ita partibus spatii æqualibus incrementa,<emph.end type="italics"/><lb/>quod ad priorem &longs;en&longs;um attinens, cen&longs;ui&longs;ti hui<gap/> <expan abbr="inter-&longs;erend&utilde;">inter<lb/>&longs;erendum</expan>. </s>

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<s>Quippe heic agitur de Motu, cuius acceleratio fiat, <lb/>&longs;eu celeritas, velocitas-ve incre&longs;cat &longs;ucce&longs;&longs;ione conti<lb/>nua, non quacumque, &longs;ed æquabili. </s>

<s>Nam illa qui<lb/>dem acceleratio, quam antè obiiciebam po&longs;&longs;e accipi, <lb/>primò &longs;ecundum parteis minuti, deinde &longs;ecundum <lb/>parteis horæ, tum &longs;ecundum parteis &longs;ecundi, tandem <lb/><expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> parteis diei, aut quæuis alia huiu&longs;modi; talis, <lb/>inquam, acceleratio continua &longs;ucce&longs;&longs;ione fieret, atta<lb/>men difformi, inæquabili, qualemque ip&longs;e non es ad<lb/>mi&longs;&longs;urus, cùm ab initio v&longs;que controuer&longs;iæ &longs;tatueris <lb/>definiti <emph type="italics"/>motum æquabiliter acceleratum eum, qui æqualibus <lb/>spatijs æqualia celeritatis augmenta acquirat.<emph.end type="italics"/> Circa Con&longs;e<lb/>quens, moneo &longs;olùm te aut debui&longs;&longs;e in&longs;erere, aut iam <lb/>debere &longs;upponere mentionem partium <emph type="italics"/>analogarum;<emph.end type="italics"/><lb/>qua&longs;i nimirùm e&longs;&longs;e debeat, aut &longs;altem intelligi huiu&longs;<lb/>modi Con&longs;equens. </s>

<s>Nam illa qui<lb/>dem acceleratio, quam antè obiiciebam po&longs;&longs;e accipi, <lb/>primò &longs;ecundum parteis minuti, deinde &longs;ecundum <lb/>parteis horæ, tum &longs;ecundum parteis &longs;ecundi, tandem <lb/><expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> parteis diei, aut quæuis alia huiu&longs;modi; talis, <lb/>inquam, acceleratio continua &longs;ucce&longs;&longs;ione fieret, atta<lb/>men difformi, inæquabili, qualemque ip&longs;e non es ad<lb/>mi&longs;&longs;urus, cùm ab initio v&longs;que controuer&longs;iæ &longs;tatueris <lb/>definiti <emph type="italics"/>motum æquabiliter acceleratum eum, qui æqualibus <lb/>spatijs æqualia celeritatis augmenta acquirat.<emph.end type="italics"/></s><s> Circa Con&longs;e<lb/>quens, moneo &longs;olùm te aut debui&longs;&longs;e in&longs;erere, aut iam <lb/>debere &longs;upponere mentionem partium <emph type="italics"/>analogarum;<emph.end type="italics"/><lb/>qua&longs;i nimirùm e&longs;&longs;e debeat, aut &longs;altem intelligi huiu&longs;<lb/>modi Con&longs;equens. </s>

<s><emph type="italics"/>Ergo velocitas de&longs;cen&longs;us per totam A<emph.end type="italics"/>C <emph type="italics"/>ab initio ad fi<lb/>nem, & &longs;ecundum qua&longs;libet eius parteis con&longs;iderata perpetuò <lb/>dupla e&longs;t velocitatis de&longs;cen&longs;us eiu&longs;dem mobilis per totam AB <lb/>ab initio ad finem, & &longs;ecundum qua&longs;libet eius parteis, parti<lb/>bus ip&longs;ius AC analogas, con&longs;ideratæ.<emph.end type="italics"/></s>

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<s>Dicis <lb/><emph type="italics"/>me id falsò a&longs;&longs;umere;<emph.end type="italics"/> ego verò non falsò a&longs;&longs;umo, qui <lb/>ne a&longs;&longs;umo quidem, &longs;ed &longs;olum con&longs;equi demon&longs;tro, vt<lb/>cumque po&longs;tquàm id demon&longs;traui, &longs;ub&longs;umere deinde <lb/>po&longs;&longs;im, vt o&longs;tendam te tibi repugnare, quòd <expan abbr="c&utilde;">cum</expan> fatea<lb/>ris AC, & AB inæqualibus percurri temporibus, prin<lb/>cipium tamen id defendas, ex quo fateri &longs;imul cogaris <lb/>eodem, aut æquali tempore percurri. </s>

<s>Itaque cùm <lb/>heic non agatur de veritate Con&longs;equentis, &longs;ed de ne<lb/>ce&longs;&longs;itate, qua con&longs;equitur, ac tu deberes o&longs;tendere <lb/>nece&longs;&longs;ariò non con&longs;equi, & declarare in quo peceá<lb/>rim, inferendo fore velocitatem per totam AC du<lb/>plam velocitatis per totam AB, nihil aliud habes, <lb/><expan abbr="quã">quam</expan>, <emph type="italics"/>non e&longs;&longs;e duplam.<emph.end type="italics"/> Quod perinde e&longs;t, ac &longs;i te ponen<lb/>te illud Antecedens, <emph type="italics"/>Plato e&longs;t lapis,<emph.end type="italics"/> ego inferam i&longs;tud <pb pagenum="122"/>Con&longs;equens, igitur <emph type="italics"/>Plato &longs;en&longs;u caret:<emph.end type="italics"/> & te negante <lb/>con&longs;equutionem, illam ex eo probem, <emph type="italics"/>quòd lapis &longs;en&longs;u <lb/>careat:<emph.end type="italics"/> ac tum dicas Con&longs;equens <emph type="italics"/>non rectè inferri;<emph.end type="italics"/> & <lb/>compul&longs;us ad id probandum, nihil tamen aliud <lb/>quàm hoc dicas, <emph type="italics"/>Plato enim &longs;en&longs;u non caret, vt falsò, <lb/>a&longs;&longs;umis, &longs;ed planè &longs;en&longs;u præditus e&longs;t.<emph.end type="italics"/> Videlicet quæ&longs;tio <lb/>non erit de veritate Con&longs;equentis, nam ego quoque <lb/>Platonem &longs;en&longs;u carere fal&longs;um reputabo: &longs;ed de nece&longs;<lb/>&longs;itate con&longs;equutionis, quam tu infirmare deberes, ne <lb/>euerteret tuum Antecedens; neque ego falsò a&longs;&longs;u<lb/>mam, carere Platonem &longs;en&longs;u, qui ne a&longs;&longs;umam quidem: <lb/>&longs;ed nece&longs;&longs;ariò &longs;olummodò, & vt conclu&longs;ionem dedu<lb/>cam; tamet&longs;i <expan abbr="deduct&utilde;">deductum</expan> a&longs;&longs;umere po&longs;&longs;im, vt o&longs;tendam te <lb/>contradicere tibi ip&longs;i, tanquam coactum a&longs;&longs;erere Pla<lb/>tonem &longs;en&longs;u de&longs;titui, quem a&longs;&longs;eras præditum &longs;en&longs;u. </s>

<s>Itaque cùm <lb/>heic non agatur de veritate Con&longs;equentis, &longs;ed de ne<lb/>ce&longs;&longs;itate, qua con&longs;equitur, ac tu deberes o&longs;tendere <lb/>nece&longs;&longs;ariò non con&longs;equi, & declarare in quo peceá<lb/>rim, inferendo fore velocitatem per totam AC du<lb/>plam velocitatis per totam AB, nihil aliud habes, <lb/><expan abbr="quã">quam</expan>, <emph type="italics"/>non e&longs;&longs;e duplam.<emph.end type="italics"/></s><s> Quod perinde e&longs;t, ac &longs;i te ponen<lb/>te illud Antecedens, <emph type="italics"/>Plato e&longs;t lapis,<emph.end type="italics"/> ego inferam i&longs;tud <pb pagenum="122"/>Con&longs;equens, igitur <emph type="italics"/>Plato &longs;en&longs;u caret:<emph.end type="italics"/> & te negante <lb/>con&longs;equutionem, illam ex eo probem, <emph type="italics"/>quòd lapis &longs;en&longs;u <lb/>careat:<emph.end type="italics"/> ac tum dicas Con&longs;equens <emph type="italics"/>non rectè inferri;<emph.end type="italics"/> & <lb/>compul&longs;us ad id probandum, nihil tamen aliud <lb/>quàm hoc dicas, <emph type="italics"/>Plato enim &longs;en&longs;u non caret, vt falsò, <lb/>a&longs;&longs;umis, &longs;ed planè &longs;en&longs;u præditus e&longs;t.<emph.end type="italics"/></s><s> Videlicet quæ&longs;tio <lb/>non erit de veritate Con&longs;equentis, nam ego quoque <lb/>Platonem &longs;en&longs;u carere fal&longs;um reputabo: &longs;ed de nece&longs;<lb/>&longs;itate con&longs;equutionis, quam tu infirmare deberes, ne <lb/>euerteret tuum Antecedens; neque ego falsò a&longs;&longs;u<lb/>mam, carere Platonem &longs;en&longs;u, qui ne a&longs;&longs;umam quidem: <lb/>&longs;ed nece&longs;&longs;ariò &longs;olummodò, & vt conclu&longs;ionem dedu<lb/>cam; tamet&longs;i <expan abbr="deduct&utilde;">deductum</expan> a&longs;&longs;umere po&longs;&longs;im, vt o&longs;tendam te <lb/>contradicere tibi ip&longs;i, tanquam coactum a&longs;&longs;erere Pla<lb/>tonem &longs;en&longs;u de&longs;titui, quem a&longs;&longs;eras præditum &longs;en&longs;u. </s>

<s>Pergis porrò, <emph type="italics"/><expan abbr="N&etilde;pe">Nempe</expan> volumus, & nece&longs;&longs;ariò exigimus (quod <lb/>ip&longs;a quoque rei natura po&longs;tulat) vt motus, qui per totam<emph.end type="italics"/><lb/>AC, <emph type="italics"/>& per partem<emph.end type="italics"/> AB, <emph type="italics"/>&longs;iue per æqualem<emph.end type="italics"/> DE, <emph type="italics"/>eadem <lb/>planè velocitate incipiat, & eadem velocitate progrediatur, <lb/>per totam<emph.end type="italics"/> AB, <emph type="italics"/>& per ip&longs;am<emph.end type="italics"/> DE, <emph type="italics"/>ex<emph.end type="italics"/> B <emph type="italics"/>verò ita velocitas <lb/>augeatur, vt tandem in<emph.end type="italics"/> C <emph type="italics"/>dupla inueniatur eius, quæ fuit in<emph.end type="italics"/><lb/>B, <emph type="italics"/>vel in<emph.end type="italics"/> E. At, optime Vir, quod vis quidem, & <lb/>exigis, vt <emph type="italics"/>c&oelig;ptus ex A motus,<emph.end type="italics"/> &longs;iue progre&longs;&longs;urus &longs;it v&longs;que <lb/>ad C, &longs;iue de&longs;iturus in B, <emph type="italics"/>eadem planè velocitate incipiat, <lb/>& progrediatur v&longs;que ad B,<emph.end type="italics"/> idip&longs;um e&longs;t, quod po&longs;tulat <lb/>ip&longs;a quoque rei natura (vtcumque po&longs;teà cau&longs;&longs;eris me <lb/>non in&longs;pexi&longs;&longs;e illam penitiùs.) Quod autem vis, & <lb/>exigis, vt velocitas ex B ita augeatur, vt tandem in <lb/>C dupla inueniatur eius, quæ fuit in B, idip&longs;um iam <lb/>e&longs;t, quod o&longs;ten&longs;um e&longs;t tantùm auer&longs;ari Naturam, <pb pagenum="123"/>quantùm auer&longs;atur motum in&longs;tantancum. </s>

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<s>& in<emph.end type="italics"/> D <emph type="italics"/>acqui&longs;itus &longs;upponatur vnus <lb/>gradus, & in<emph.end type="italics"/> E <emph type="italics"/>duo, & tres in<emph.end type="italics"/> F; <emph type="italics"/>manife<lb/>&longs;tum e&longs;t d<gap/>os gradus, ad quos acceleratio per<lb/>ueni&longs;&longs;e ponitur in<emph.end type="italics"/> E, <emph type="italics"/>e&longs;&longs;e ad vnum gradum <lb/>acqui&longs;itum in<emph.end type="italics"/> D, <emph type="italics"/>vt spatium<emph.end type="italics"/> AE, <emph type="italics"/>ad spa<lb/>tium. </s>

<s>AD.<emph.end type="italics"/> Deprehendere enim &longs;tatim <lb/>licet, quemadmodum idip&longs;um &longs;upponas, quod pror<lb/>sùs controuertitur: nempe in E e&longs;&longs;e duos gradus, vbi <lb/>vnus fuerit in D. </s>

<s>AD.<emph.end type="italics"/></s><s> Deprehendere enim &longs;tatim <lb/>licet, quemadmodum idip&longs;um &longs;upponas, quod pror<lb/>sùs controuertitur: nempe in E e&longs;&longs;e duos gradus, vbi <lb/>vnus fuerit in D. </s>

<s>Ni&longs;i verò hoc e&longs;t; quid nam tandem <lb/>e&longs;t, quod dicunt petere principium? </s>

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<s>Nam, vt mutares terminos, de quibus, vt ais, contro. <lb/></s>

<s>uer&longs;ia e&longs;t, debueras idip&longs;um, quod ego ratiocinando <lb/>habui pro <emph type="italics"/>Spatio,<emph.end type="italics"/> habere pro <emph type="italics"/>Tempore,<emph.end type="italics"/> quod pro <emph type="italics"/>Tempo<lb/>re,<emph.end type="italics"/> habere pro <emph type="italics"/>Spatio,<emph.end type="italics"/> cùm alterum alter arguamus, <lb/>quòd velocitas exæquetur à me quidem <emph type="italics"/>Tempori,<emph.end type="italics"/> à te <lb/>verò <emph type="italics"/>Spatio.<emph.end type="italics"/> Sic autem accepta linea PM pro tempo<lb/>re AD, & PN pro tempore AB, pro&longs;equi potu<gap/>es <lb/>hoc modo. </s>

<s>uer&longs;ia e&longs;t, debueras idip&longs;um, quod ego ratiocinando <lb/>habui pro <emph type="italics"/>Spatio,<emph.end type="italics"/> habere pro <emph type="italics"/>Tempore,<emph.end type="italics"/> quod pro <emph type="italics"/>Tempo<lb/>re,<emph.end type="italics"/> habere pro <emph type="italics"/>Spatio,<emph.end type="italics"/> cùm alterum alter arguamus, <lb/>quòd velocitas exæquetur à me quidem <emph type="italics"/>Tempori,<emph.end type="italics"/> à te <lb/>verò <emph type="italics"/>Spatio.<emph.end type="italics"/></s><s> Sic autem accepta linea PM pro tempo<lb/>re AD, & PN pro tempore AB, pro&longs;equi potu<gap/>es <lb/>hoc modo. </s>

<s><emph type="italics"/>Nam vt modo ratiocinandi tuo etiam vtar, &longs;umpto quo<lb/>piam alio tempore<emph.end type="italics"/> RO, <emph type="italics"/>tempori<emph.end type="italics"/> PM <emph type="italics"/>æquali, con<gap/>mus <lb/>duo mobilia, quorum vnum per<emph.end type="italics"/> PN <emph type="italics"/>eodem &longs;patio moueri<emph.end type="italics"/><pb pagenum="129"/><emph type="italics"/>incipiat velocitate dupla, quo alterum per<emph.end type="italics"/> RO <emph type="italics"/>de&longs;cendit <lb/>velocitate &longs;ubdupla; tum nece&longs;&longs;e fuerit, vt quibu&longs;libet &longs;pa<lb/>tij partibus continuò momenta temporis<emph.end type="italics"/> PM <emph type="italics"/>duplò matora <lb/>percurrantur, quam &longs;int momenta temporis<emph.end type="italics"/> RO, <emph type="italics"/>quæ ab <lb/>aliò mobili ii&longs;dem partibus &longs;ubdupla velocitate decurruntur. <lb/></s>

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<s>Pri<lb/>mum illud verum e&longs;&longs;e nihil repugnat, at &longs;ecundum istud fal<lb/>&longs;um, & impoßibile est; quod &longs;i rectè<emph.end type="italics"/> G<emph type="italics"/>alileus aduerti&longs;&longs;et, <lb/>Paralogi&longs;mum nobis pro demon&longs;tratione non obtru&longs;i&longs;&longs;et.<emph.end type="italics"/></s>

<s>Verumtamen, ne confunde quæ&longs;o tempora cum <lb/>&longs;patiis; cum ais aliud e&longs;&longs;e <emph type="italics"/>æqualibus &longs;iue &longs;patiis, &longs;iue tem<lb/>poribus, &c.<emph.end type="italics"/> Siquidem & facta ratiocinatione nihil <lb/>conclu&longs;i&longs;ti contra tempora, vt te puta&longs;ti concludere; <lb/>&longs;ed &longs;olùm contra &longs;patia, quatenus à me fuerant impe<lb/>tita: & tempora aliunde cum velocitatibus comparata <lb/>nullam agno&longs;cunt di&longs;tinctionem, qualem te putas in<lb/>uehere: cùm & totæ velocitates, & ip&longs;arum partes, &longs;eu <lb/>augmenta eandem &longs;emper proportionem cum tempo<lb/>ribus, partibu&longs;que corum analogis &longs;eruent. </s>

<s>Verumtamen, ne confunde quæ&longs;o tempora cum <lb/>&longs;patiis; cum ais aliud e&longs;&longs;e <emph type="italics"/>æqualibus &longs;iue &longs;patiis, &longs;iue tem<lb/>poribus, &c.<emph.end type="italics"/></s><s> Siquidem & facta ratiocinatione nihil <lb/>conclu&longs;i&longs;ti contra tempora, vt te puta&longs;ti concludere; <lb/>&longs;ed &longs;olùm contra &longs;patia, quatenus à me fuerant impe<lb/>tita: & tempora aliunde cum velocitatibus comparata <lb/>nullam agno&longs;cunt di&longs;tinctionem, qualem te putas in<lb/>uehere: cùm & totæ velocitates, & ip&longs;arum partes, &longs;eu <lb/>augmenta eandem &longs;emper proportionem cum tempo<lb/>ribus, partibu&longs;que corum analogis &longs;eruent. </s>

<s>Quin<lb/>etiam, quod &longs;pectat ad &longs;patia, declaratum iam e&longs;t, <lb/>quàm irrito conamine &longs;ic di&longs;tinguas, quatenus de mo<lb/>tu non quomodocumque, &longs;ed æquabiliter accelerato <pb pagenum="131"/>agitur; &longs;tupendumque e&longs;t, te in eo hærere, quòd Gali<lb/>leus non aduerterit fal&longs;um, ac impo&longs;&longs;ibile e&longs;&longs;e, quod <lb/>&longs;ecundum ais, hoc e&longs;t, <emph type="italics"/>velocitates ip&longs;as integras, &c.<emph.end type="italics"/> &longs;i<lb/>quidem i&longs;tud e&longs;&longs;e fal&longs;um, impo&longs;&longs;ibileque non modò <lb/>aduertit, &longs;ed etiam o&longs;tendit, quod tu recu&longs;as aduertere, <lb/>con&longs;equi ex ea, quam tu &longs;equeris, opinione. </s>

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<s>Su&longs;ceperas ip&longs;e o<gap/>tendendum <lb/>in illa Galilei A&longs;&longs;umptione Paralogi&longs;mum, & præmi<lb/>&longs;eras, <emph type="italics"/>non vno modo tantum, &longs;ed pluribus intelligi po&longs;&longs;e, <lb/>quomodo velocitates &longs;int inter &longs;e, vt emen&longs;a spatia; licet <lb/>eadem spatia, neque eodem, neque æquali tempore percur<lb/>rantur:<emph.end type="italics"/> ac tum deligens modum vnum, qui præ cæte<lb/>ris id præ&longs;taret, atque idcircò <gap/>&longs;&longs;umptionem Paralo<lb/>gi&longs;mi conuinceret, i&longs;thæc met &longs;ub<gap/>eci&longs;ti verba, <emph type="italics"/>Vt <gap/><lb/>graue de&longs;cendens per AB, tempus quodcumque in&longs;umat, putà <lb/>quadrantem; ac deinde BC ip&longs;i AB æquale dimidio qua<lb/>drante percurrat; quis neget in<emph.end type="italics"/> C <emph type="italics"/>duplam haberi velocita<lb/>tem eius, quæ fuit in B? </s>

<s>Et tamen idem graue totam AC, <lb/>& dimidium eius AB eodem tempore non percurreret.<emph.end type="italics"/><lb/>Subinde autem qua&longs;i re ab&longs;olutè cófecta pro&longs;equutus <lb/>es, <emph type="italics"/>A&longs;&longs;umptio igitur Galilei fal&longs;a e&longs;t, & totæ eius ratiocinatio <lb/>merus Paralogi&longs;mus.<emph.end type="italics"/> Quæ&longs;o ergo te, quid tibi affinxi? <lb/></s>

<s>Et tamen idem graue totam AC, <lb/>& dimidium eius AB eodem tempore non percurreret.<emph.end type="italics"/><lb/>Subinde autem qua&longs;i re ab&longs;olutè cófecta pro&longs;equutus <lb/>es, <emph type="italics"/>A&longs;&longs;umptio igitur Galilei fal&longs;a e&longs;t, & totæ eius ratiocinatio <lb/>merus Paralogi&longs;mus.<emph.end type="italics"/></s><s> Quæ&longs;o ergo te, quid tibi affinxi? <lb/></s>

<s>Agno&longs;cis tua verba, an non? <emph type="italics"/>Propo&longs;itionem,<emph.end type="italics"/> inquis, <emph type="italics"/>fal<lb/>&longs;am, ac impoßibilem?<emph.end type="italics"/> E&longs;to verò, illam iam fal&longs;am, ac <lb/>impo&longs;&longs;ibilem agno&longs;eas; at tunc &longs;altem veram, atque <lb/>nece&longs;&longs;ariam habui&longs;ti, cùm illa &longs;ola v&longs;us fueris ad o&longs;ten<lb/>dendum Paralogi&longs;mum. </s>

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<s>Vnum, <lb/>cur adeò &longs;olemniter prouoca&longs;&longs;es me <emph type="italics"/>ad facileis, claras, <lb/>indubitatas Experientias,<emph.end type="italics"/> quæ controuer&longs;iæ caput face<lb/>rent, ac Demon&longs;trationem tuam, &longs;cientiamque totam <lb/>con&longs;tabilirent: cùm ecce habens vnicam, videri iis <lb/>po&longs;&longs;es, qui rerum amantes verbis non capiuntur, ita <lb/>o&longs;citanter illam peregi&longs;&longs;e, vt nihil e&longs;&longs;et minùs, quàm <pb pagenum="147"/>quod diceretur. </s>

<s>Profectò ni&longs;i v&longs;us fui&longs;&longs;es voce <emph type="italics"/>Præ<lb/>ci&longs;ionis,<emph.end type="italics"/> alii&longs;que con&longs;imilibus, videri dumtaxat potui&longs;<lb/>&longs;es opinione præoccupatus, ac præ illius a more, volui&longs;<lb/>&longs;e non opinionem experientiæ, &longs;ed experientiam <lb/>opinioni accom modare: Nunc autem non video, cur <lb/>tot paginis, tantoque apparatu in&longs;titeris (etiam tot <lb/>cautiones adhibendas iis, qui rem experiri &longs;crupulo<lb/>&longs;iùs vellent, præ&longs;cribens) vt te expertum crederemus, <lb/><emph type="italics"/>naturam illud in globo peculiare ac proprium e&longs;&longs;e volui&longs;&longs;e, <lb/>vt eius diameter præci&longs;a e&longs;&longs;et men&longs;ura illius altitudinis, ex <lb/>qua, &c.<emph.end type="italics"/> ac iterùm, <emph type="italics"/>hanc e&longs;&longs;e inter globos, & alias figu<lb/>ras differentiam, quòd in globis diameter altitudines præcis è <lb/>definiat, vnde pondus, &c.<emph.end type="italics"/> Alterum, cur huiu&longs;imodi Ex<lb/>perimento deprehen&longs;o fal&longs;o; hoc e&longs;t, cùm verùm iam <lb/>non &longs;it, vt contenderas, <emph type="italics"/>con&longs;tare Experientiâ corpus graue <lb/>quodcumque ex qualibet altitudine per aërem cadens, & <lb/>percutiens vt libet, perpetuò ex altitudine dupla dupla præcisè <lb/>ampliùs, & ex tripla, quadruplave di&longs;tantia, triplò, qua<lb/>druplove fortiùs percutere;<emph.end type="italics"/> cur, inquam, pergas etiam<lb/>num eam Ratiocinationem habere, imò & acriter <lb/>tueri pro Phy&longs;ica Demon&longs;tratione, quam non alij <lb/>fundamento, quàm huic vnico Experimento &longs;uper<lb/>ex&longs;truxeris? </s>

<s>Profectò ni&longs;i v&longs;us fui&longs;&longs;es voce <emph type="italics"/>Præ<lb/>ci&longs;ionis,<emph.end type="italics"/> alii&longs;que con&longs;imilibus, videri dumtaxat potui&longs;<lb/>&longs;es opinione præoccupatus, ac præ illius a more, volui&longs;<lb/>&longs;e non opinionem experientiæ, &longs;ed experientiam <lb/>opinioni accom modare: Nunc autem non video, cur <lb/>tot paginis, tantoque apparatu in&longs;titeris (etiam tot <lb/>cautiones adhibendas iis, qui rem experiri &longs;crupulo<lb/>&longs;iùs vellent, præ&longs;cribens) vt te expertum crederemus, <lb/><emph type="italics"/>naturam illud in globo peculiare ac proprium e&longs;&longs;e volui&longs;&longs;e, <lb/>vt eius diameter præci&longs;a e&longs;&longs;et men&longs;ura illius altitudinis, ex <lb/>qua, &c.<emph.end type="italics"/> ac iterùm, <emph type="italics"/>hanc e&longs;&longs;e inter globos, & alias figu<lb/>ras differentiam, quòd in globis diameter altitudines præcis è <lb/>definiat, vnde pondus, &c.<emph.end type="italics"/></s><s> Alterum, cur huiu&longs;imodi Ex<lb/>perimento deprehen&longs;o fal&longs;o; hoc e&longs;t, cùm verùm iam <lb/>non &longs;it, vt contenderas, <emph type="italics"/>con&longs;tare Experientiâ corpus graue <lb/>quodcumque ex qualibet altitudine per aërem cadens, & <lb/>percutiens vt libet, perpetuò ex altitudine dupla dupla præcisè <lb/>ampliùs, & ex tripla, quadruplave di&longs;tantia, triplò, qua<lb/>druplove fortiùs percutere;<emph.end type="italics"/> cur, inquam, pergas etiam<lb/>num eam Ratiocinationem habere, imò & acriter <lb/>tueri pro Phy&longs;ica Demon&longs;tratione, quam non alij <lb/>fundamento, quàm huic vnico Experimento &longs;uper<lb/>ex&longs;truxeris? </s>

<s>Hoc &longs;anè e&longs;t, quod mihi videtur faten<lb/>dum &longs;imùl ingenuè fui&longs;&longs;e, ac parcendum &longs;imùl labo<lb/>ri, quo æque te exerceres, ac me, quemque declinare <lb/>potucras, &longs;i neque meam Re&longs;pon&longs;ionem, neque tuas <lb/>Vindicias e&longs;&longs;e cuulgandas cen&longs;ui&longs;&longs;es; cùm alioquin <lb/>iam de&longs;titutus omni argumento, quo Demon&longs;tra<lb/>tionem &longs;uffulcias, ludere videaris omnem operam, dum <lb/>operosè adeò in ea propugnanda de&longs;udas. </s><pb pagenum="148"/>

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<s>Accedamus propiùs ad hypothe&longs;in. </s>

<s>O&longs;tendere <lb/>volui velocitatis gradus men&longs;urandos non e&longs;&longs;e, vt tu <lb/>a&longs;&longs;erebas, penes globorum diametros, quæ men&longs;ura<lb/>rent &longs;ingulos ca&longs;us. <emph type="italics"/>Sunto enim,<emph.end type="italics"/> inquam, <emph type="italics"/>globi, verbi <lb/>caußâ, duo ex eadem materia, quorum vnus &longs;it diametro<emph.end type="italics"/><pb pagenum="156"/><emph type="italics"/>decies maiore, quàm alius, & dimittatur vterque ex eadem<gap/><lb/>altitudine: tunc, quia minor decidet per diametros decuplò <lb/>plureis, quàm mator, fiet, vt attollat pondera &longs;ibi æqualia <lb/>decuplò multipliciora, quàm attollat maior ex &longs;ibi æqualibus: <lb/>Quare & &longs;equitur, vtper idem &longs;patium feratur decuplò ve<lb/>lociùs, ac decuplò citiùs, temporeve decies breuiore perue<lb/>niat ad lancem, quàm maior: hoc autem con&longs;tat quàm fal&longs;um <lb/>&longs;it; cùm, &c.<emph.end type="italics"/> Con&longs;idera iam, an quid dicerem, non ad<lb/>uerterim. </s>

<s>O&longs;tendere <lb/>volui velocitatis gradus men&longs;urandos non e&longs;&longs;e, vt tu <lb/>a&longs;&longs;erebas, penes globorum diametros, quæ men&longs;ura<lb/>rent &longs;ingulos ca&longs;us. <emph type="italics"/>Sunto enim,<emph.end type="italics"/> inquam, <emph type="italics"/>globi, verbi <lb/>caußâ, duo ex eadem materia, quorum vnus &longs;it diametro<emph.end type="italics"/><pb pagenum="156"/><emph type="italics"/>decies maiore, quàm alius, & dimittatur vterque ex eadem<gap/><lb/>altitudine: tunc, quia minor decidet per diametros decuplò <lb/>plureis, quàm mator, fiet, vt attollat pondera &longs;ibi æqualia <lb/>decuplò multipliciora, quàm attollat maior ex &longs;ibi æqualibus: <lb/>Quare & &longs;equitur, vtper idem &longs;patium feratur decuplò ve<lb/>lociùs, ac decuplò citiùs, temporeve decies breuiore perue<lb/>niat ad lancem, quàm maior: hoc autem con&longs;tat quàm fal&longs;um <lb/>&longs;it; cùm, &c.<emph.end type="italics"/></s><s> Con&longs;idera iam, an quid dicerem, non ad<lb/>uerterim. </s>

<s>E&longs;to pondus maioris globi mille vnciarum, <lb/>& clatus globus vna &longs;ui diametro &longs;upra lancem, in eam <lb/>dimittatur; tum gradum velocitatis iuxta te acqui&longs;ie<lb/>rit, quo lancem percutiens alteram attollat cum pon<lb/>dere vnciarum mille, præter æquilibrium. </s>

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<s>Atque ego quidem &longs;ic ad rem <lb/>aduerti. </s>

<s>Ais iam tu, <emph type="italics"/>meam &longs;agacitatem non aduerti&longs;&longs;e, à <lb/>maiore globo vnius diametri de&longs;cen&longs;u tantum velocitatis ac<lb/>quiri, quantum à minore globo decem diametrorum de&longs;cen&longs;u <lb/>acquiritur.<emph.end type="italics"/> Verùm cùm ego aduerterim rem &longs;e reip&longs;a <lb/>ita habere: aduerti tamen &longs;imùl id aduer&longs;ari tuis de<lb/>cretis, vnde & tua &longs;agacitas aduerti&longs;&longs;e duntaxat vide<lb/>tur quid fieret, non verò quid ex propriis a&longs;&longs;ertionibus <lb/>&longs;equeretur. </s>

<s>Ais iam tu, <emph type="italics"/>meam &longs;agacitatem non aduerti&longs;&longs;e, à <lb/>maiore globo vnius diametri de&longs;cen&longs;u tantum velocitatis ac<lb/>quiri, quantum à minore globo decem diametrorum de&longs;cen&longs;u <lb/>acquiritur.<emph.end type="italics"/></s><s> Verùm cùm ego aduerterim rem &longs;e reip&longs;a <lb/>ita habere: aduerti tamen &longs;imùl id aduer&longs;ari tuis de<lb/>cretis, vnde & tua &longs;agacitas aduerti&longs;&longs;e duntaxat vide<lb/>tur quid fieret, non verò quid ex propriis a&longs;&longs;ertionibus <lb/>&longs;equeretur. </s>

<s>Pergis <emph type="italics"/>nihil omninò referre, &longs;i ex duabus ve<lb/>locitatibus inter &longs;e æqualibus altera plureis in parteis &longs;ub<lb/>diuidatur. </s>

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<s>Quàm falsò repetas hanc Propo&longs;itionem tibi <lb/>à me affictam, feci abundè manife&longs;tum, cùm id <lb/>obiter non &longs;um prætergre&longs;&longs;us, quod tu citato <pb pagenum="161"/>loco, hoc e&longs;t, in articulum xii, attigeras obiter &longs;olùm. <lb/></s>

<s>Quippe tuis verbis recitatis, & deducta occa&longs;ione, ob <lb/>quam illa texueras, demon&longs;tratum e&longs;t tuam fui&longs;&longs;e, <lb/>quam iam inficiaris, expre&longs;&longs;am &longs;ententiam; heincque <lb/>adeò probatum manet me non modò probabili, &longs;ed <lb/>conuincenti etiam ratione (ni&longs;i te velis Paralogi&longs;tam, <lb/>quod ab&longs;it vt cen&longs;eam, ridiculo&longs;i&longs;&longs;imum haberi) ac <lb/>non meo iure, &longs;ed ex tuis verbis hanc &longs;uppo&longs;itionem, <lb/>qua&longs;i tuam &longs;upponere, G<emph type="italics"/>raue de&longs;cendens per spatium <lb/>AB in parteis quotlibet æqualeis diui&longs;um, percurrere partem <lb/>&longs;ecundam DE<emph.end type="italics"/> (quæ illeic fuit BC) <emph type="italics"/>in dimidio eius tem<lb/>poris, quo percurritur prior pars AD<emph.end type="italics"/> (quæ illeic AB) & <lb/>quod idem e&longs;t, <emph type="italics"/>partem DE percurri veiocitate dupla eius, <lb/>velocitatis, qua tran&longs;curritur AD.<emph.end type="italics"/> Sequitur. </s>

<s><emph type="italics"/>At Primum, quid amabò, caußæ est, cur cùm antè nume<lb/>ro tuæ Re&longs;pon&longs;ionis X. volueris velocitatem per totam AE <lb/>duplam e&longs;&longs;e velocitatis per primam partem AD, idque ex <lb/>meis quoque principiis nece&longs;&longs;arium e&longs;&longs;e a&longs;&longs;erueris: nunc, mutato <lb/>con&longs;ilio, velocitatem per &longs;olam partem DE velocitatis per <lb/>partem AD acqui&longs;itæ duplam e&longs;&longs;e contendas: & quidem, vt <lb/>ais, ex principiis item meis?<emph.end type="italics"/></s>

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<s>Hem! quid profero? </s>

<s>Videlicet Primò tefal&longs;a v&longs;ur<lb/>pare principia, neque alia lege concludere ex ip&longs;is ve<lb/>rum, quàm &longs;i quis ex eo, quod a&longs;&longs;umat <emph type="italics"/>arbores omneis <lb/>e&longs;&longs;e in cælo,<emph.end type="italics"/> & <emph type="italics"/>Lunam e&longs;&longs;e arborem,<emph.end type="italics"/> concludat <emph type="italics"/>Lunam <lb/>e&longs;&longs;e in cælo.<emph.end type="italics"/> Secundò, committere te, vt vulgo aiunt, cir<lb/>culum, incidereve in Diallelum; vti obiter in&longs;inuatum <lb/>e&longs;t, & tota ex &longs;erie tui operis con&longs;tat. </s>

<s>Videlicet Primò tefal&longs;a v&longs;ur<lb/>pare principia, neque alia lege concludere ex ip&longs;is ve<lb/>rum, quàm &longs;i quis ex eo, quod a&longs;&longs;umat <emph type="italics"/>arbores omneis <lb/>e&longs;&longs;e in cælo,<emph.end type="italics"/> & <emph type="italics"/>Lunam e&longs;&longs;e arborem,<emph.end type="italics"/> concludat <emph type="italics"/>Lunam <lb/>e&longs;&longs;e in cælo.<emph.end type="italics"/></s><s> Secundò, committere te, vt vulgo aiunt, cir<lb/>culum, incidereve in Diallelum; vti obiter in&longs;inuatum <lb/>e&longs;t, & tota ex &longs;erie tui operis con&longs;tat. </s>

<s>Tertiò, te noua <lb/>contradictione temetip&longs;um inuoluere, dum coactus vi <lb/>&longs;uperioris dilemmatis, dicere teneris velocitatem per <lb/>DE duplam e&longs;&longs;e velocitatis per AD, & nunc a&longs;&longs;umis, <lb/>aut te proba&longs;&longs;e contendis eandem velocitatem per <lb/>DE duplam e&longs;&longs;e velocitatis per SD, quod &longs;it &longs;olùm di<lb/>midium ip&longs;ius DE. </s>

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<s>Conquereris, quòd, <lb/><emph type="italics"/>meo iure, & &longs;ine vlla demon&longs;tratione, aut veri&longs;imilitudine di<lb/>xerim, atque inculcârim tua decretainde maximè reuelli, quòd <lb/>adeò pugnantia exijs concludantur.<emph.end type="italics"/> (nam quòd alioquin <lb/>tanquam de con&longs;tanti victoria triumphârim, hoc e&longs;t, <lb/>ex&longs;ultabundus ge&longs;tierim, & qua&longs;i thra&longs;ofuerim gloria<lb/>tus; id vt à me alienum e&longs;t, ita Deo propitio, nu&longs;quam <lb/>deprehendes.) Itaque id-ne ab&longs;que iure, & &longs;ine vlla <lb/>demon&longs;tratione, aut veri&longs;imilitudine fecerim, perui<lb/>deamus. </s>

<s>Verba tua fuerant vt retuli, articulo XXXI. <lb/><emph type="italics"/>Cùm enim ex &longs;uperioribus iam euidenter co<gap/> in naturali <lb/>grauium de&longs;cen&longs;u &longs;emper ex dupla di&longs;tantia celeritatem haberi <lb/>duplam, & ex tripla di&longs;tantia triplam, atque ita deinceps ea<lb/>dem ratione celeritatem augeri; nihil procliuius e&longs;&longs;e potest, <lb/>quàm vt quis existimet accelerationem illam fieri per &longs;ubdi<lb/>ui&longs;ionem primi cuiu&longs;libet temporis in parteis &longs;emper minores, <lb/>pro multitudine, & ratione spatiorum æqualium, quæ motu<emph.end type="italics"/><pb pagenum="168"/><emph type="italics"/>decurruntur: ita videlicet, vt pars &longs;ecunda spatii ab&longs;oluatur <lb/>dimidia parte temporis, quo prima decur&longs;a e&longs;t: & tertia pars <lb/>&longs;patii tertia parte eiu&longs;dem primi temporis percurratur, & ita <lb/>de cæteris.<emph.end type="italics"/> Excepi ego, <emph type="italics"/>heic profectò rur&longs;us mirari tuam <lb/>&longs;agacitatem par e&longs;t, quatenùs eam non fugit error, qui ex po&longs;i<lb/>tione à te a&longs;&longs;erta con&longs;equitur, tamet&longs;i ip&longs;e non con&longs;equi, ex iis, <lb/>quæ &longs;equuntur, contendas.<emph.end type="italics"/> Duo heic fuerunt: <emph type="italics"/>Vnum,<emph.end type="italics"/> Er<lb/>rorem e&longs;&longs;e, quòd &longs;ecundum &longs;patium æquale percurra<lb/>tur dimidio illius temporis, quo primum; tertium trien<lb/>te, quartum quadrante, atque ita de reliquis: <emph type="italics"/>Alterum,<emph.end type="italics"/><lb/>huiu&longs;modi errorem con&longs;equi ex tua pofitione, quòd <lb/>celeritates &longs;e habeant vt &longs;patia, atque adeò, quod ex <lb/>duplo di&longs;tantiæ celeritas habeatur dupla, ex triplo tri<lb/>pla, &c. </s>

<s>Verba tua fuerant vt retuli, articulo XXXI. <lb/><emph type="italics"/>Cùm enim ex &longs;uperioribus iam euidenter co<gap/> in naturali <lb/>grauium de&longs;cen&longs;u &longs;emper ex dupla di&longs;tantia celeritatem haberi <lb/>duplam, & ex tripla di&longs;tantia triplam, atque ita deinceps ea<lb/>dem ratione celeritatem augeri; nihil procliuius e&longs;&longs;e potest, <lb/>quàm vt quis existimet accelerationem illam fieri per &longs;ubdi<lb/>ui&longs;ionem primi cuiu&longs;libet temporis in parteis &longs;emper minores, <lb/>pro multitudine, & ratione spatiorum æqualium, quæ motu<emph.end type="italics"/><pb pagenum="168"/><emph type="italics"/>decurruntur: ita videlicet, vt pars &longs;ecunda spatii ab&longs;oluatur <lb/>dimidia parte temporis, quo prima decur&longs;a e&longs;t: & tertia pars <lb/>&longs;patii tertia parte eiu&longs;dem primi temporis percurratur, & ita <lb/>de cæteris.<emph.end type="italics"/></s><s> Excepi ego, <emph type="italics"/>heic profectò rur&longs;us mirari tuam <lb/>&longs;agacitatem par e&longs;t, quatenùs eam non fugit error, qui ex po&longs;i<lb/>tione à te a&longs;&longs;erta con&longs;equitur, tamet&longs;i ip&longs;e non con&longs;equi, ex iis, <lb/>quæ &longs;equuntur, contendas.<emph.end type="italics"/></s><s> Duo heic fuerunt: <emph type="italics"/>Vnum,<emph.end type="italics"/> Er<lb/>rorem e&longs;&longs;e, quòd &longs;ecundum &longs;patium æquale percurra<lb/>tur dimidio illius temporis, quo primum; tertium trien<lb/>te, quartum quadrante, atque ita de reliquis: <emph type="italics"/>Alterum,<emph.end type="italics"/><lb/>huiu&longs;modi errorem con&longs;equi ex tua pofitione, quòd <lb/>celeritates &longs;e habeant vt &longs;patia, atque adeò, quod ex <lb/>duplo di&longs;tantiæ celeritas habeatur dupla, ex triplo tri<lb/>pla, &c. </s>

<s>Et <emph type="italics"/>de Priore<emph.end type="italics"/> quidem non fuit controuer&longs;ia, <lb/>cùm tu e&longs;&longs;e errorem & confe&longs;&longs;us fueris, & aliquot <lb/>etiam argumentis o&longs;tenderis. <emph type="italics"/>De Po&longs;teriore<emph.end type="italics"/> tota lis <lb/>fuit, an nempe huiu&longs;modi error tuis ex principiis, &longs;eu <lb/>ex po&longs;itione mox memorata &longs;equeretur, an-non. </s>

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<s>Et cùm fuerim conte&longs;tatus in mea &longs;eu demon&longs;tratio<lb/>ne, &longs;eu veri&longs;imili ratione nullum &longs;ube&longs;&longs;e paralogi&longs;<lb/>mum; cur tu, &longs;i quempiam e&longs;&longs;e puta&longs;ti, verè &longs;ube&longs;&longs;e <lb/>non o&longs;tendi&longs;ti? </s>

<s>Nam quòd fueris ratiocinatus ex con<lb/>clu&longs;ione illa <expan abbr="quã">quam</expan> &longs;tatutum à te principium dixi&longs;ti, ve<lb/>locitatem per &longs;ecundam partem non e&longs;&longs;e duplam ve<lb/>locitatis per primam, id non arguit illud non &longs;equi ex <lb/>alio tuo principio, ex quo aliunde etiam potuerit per <lb/>media quæpiam alia mendo&longs;a illa conclu&longs;io trahi: ac <lb/>poti&longs;&longs;imùm, cum &longs;it adeò verum, quod dicitur vulgò, <lb/><emph type="italics"/>ex po&longs;ito vno ab&longs;urdo con&longs;equi po&longs;&longs;e innumera.<emph.end type="italics"/> Quam<lb/>obrem neque vllus exinde concludi pote&longs;t paralogi&longs;<lb/>mus; neque non con&longs;tat quàm variè tua ratiocinatio <lb/>peccet, quámque mea illa confiimetur ex confecto <lb/>dilemmate, quod repetere nihil e&longs;t nece&longs;&longs;e. </s>

<s>Nam quòd fueris ratiocinatus ex con<lb/>clu&longs;ione illa <expan abbr="quã">quam</expan> &longs;tatutum à te principium dixi&longs;ti, ve<lb/>locitatem per &longs;ecundam partem non e&longs;&longs;e duplam ve<lb/>locitatis per primam, id non arguit illud non &longs;equi ex <lb/>alio tuo principio, ex quo aliunde etiam potuerit per <lb/>media quæpiam alia mendo&longs;a illa conclu&longs;io trahi: ac <lb/>poti&longs;&longs;imùm, cum &longs;it adeò verum, quod dicitur vulgò, <lb/><emph type="italics"/>ex po&longs;ito vno ab&longs;urdo con&longs;equi po&longs;&longs;e innumera.<emph.end type="italics"/></s><s> Quam<lb/>obrem neque vllus exinde concludi pote&longs;t paralogi&longs;<lb/>mus; neque non con&longs;tat quàm variè tua ratiocinatio <lb/>peccet, quámque mea illa confiimetur ex confecto <lb/>dilemmate, quod repetere nihil e&longs;t nece&longs;&longs;e. </s>

<s>Quæ&longs;o <lb/>etiam, potueri&longs;-ne paulò antè exaggerere <emph type="italics"/>debui&longs;&longs;e me <lb/>primùm demon&longs;trare ea, quæ à te tanquam fal&longs;a reiecta vi<lb/>de bam, ex con&longs;titutis à te principiis nihilominus &longs;equi, ante<lb/>quam eadem, vt tua decreta impeterem,<emph.end type="italics"/> &c. </s>

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<s>Mi&longs;&longs;um autem facio, vt non modo hoc præterm &longs;eris, <lb/>&longs;ed di&longs;&longs;imulâris etiam incommodum ex hac po&longs;itione <lb/>deductum de Progre&longs;&longs;ione illa &longs;patiorum plu&longs;quam <lb/>tripla eodem articulo &longs;upputata; ni&longs;i quod ad calcem <pb pagenum="170"/>eius obiter memini&longs;ti, non tanquam incommodi, &longs;ed <lb/>tanquam veræ progre&longs;&longs;ionis, quam vano labore re<lb/>qui&longs;ierim. </s>

<s>Ad duosarticulos &longs;equenteis, nempe XXXII, & XXXIII, <lb/>poti&longs;&longs;imùm &longs;pectat, quod rursùs es ante conque&longs;tus <lb/><emph type="italics"/>me non &longs;olùm contra expre&longs;&longs;am Epi&longs;tolæ tuæ &longs;ententiam, &longs;ed <lb/>contra euidentem quoque demon&longs;trationis lucem velle à te ea <lb/>dici, quæ verbis expreßis negas, quæque fal&longs;a e&longs;&longs;e non tantum <lb/>pronuncias, &longs;ed clare etiam, atque euidenter demon&longs;tras.<emph.end type="italics"/> At <lb/>quomodo quæ&longs;o dicere id potes; cùm ex iam dictis <lb/>quæ&longs;tio &longs;it duplex; <emph type="italics"/>vna,<emph.end type="italics"/> an &longs;it error, percurri &longs;ecundum <lb/>&longs;patium dimidio temporis, quo primum, tertium trien<lb/>re, &c. <emph type="italics"/>altera,<emph.end type="italics"/> an is error &longs;equatur ex tuis principiis. <lb/></s>

<s>Ad duosarticulos &longs;equenteis, nempe XXXII, & XXXIII, <lb/>poti&longs;&longs;imùm &longs;pectat, quod rursùs es ante conque&longs;tus <lb/><emph type="italics"/>me non &longs;olùm contra expre&longs;&longs;am Epi&longs;tolæ tuæ &longs;ententiam, &longs;ed <lb/>contra euidentem quoque demon&longs;trationis lucem velle à te ea <lb/>dici, quæ verbis expreßis negas, quæque fal&longs;a e&longs;&longs;e non tantum <lb/>pronuncias, &longs;ed clare etiam, atque euidenter demon&longs;tras.<emph.end type="italics"/></s><s> At <lb/>quomodo quæ&longs;o dicere id potes; cùm ex iam dictis <lb/>quæ&longs;tio &longs;it duplex; <emph type="italics"/>vna,<emph.end type="italics"/> an &longs;it error, percurri &longs;ecundum <lb/>&longs;patium dimidio temporis, quo primum, tertium trien<lb/>re, &c. <emph type="italics"/>altera,<emph.end type="italics"/> an is error &longs;equatur ex tuis principiis. <lb/></s>

<s>Tu verò &longs;ic me impetas, qua&longs;i litem tibi mouerim de <lb/>prima, non autem &longs;olùm de &longs;ecunda; & cùm deberes <lb/>ip&longs;e tueri errorem non &longs;equi ex tuis principiis, qua &longs;ola <lb/>de re agitur; o&longs;tendas &longs;olùm errorem e&longs;&longs;e; qua de re nu&ltail; <lb/>la e&longs;t controuer&longs;ia? </s>

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<s>An dicere igitur potes, <emph type="italics"/>me con<lb/>tra expre&longs;&longs;am &longs;ententiam, & demon&longs;trationem tuam velle <lb/>te ea dicere, quæ verbis expreßis pronuncias, &c.<emph.end type="italics"/> cùm non <lb/>modò noluerim, verùm ne cogitârim quidem. </s>

<s>Sic <lb/>cùm articulo XXXIII. o&longs;tendi&longs;&longs;es rur&longs;us tuo modo, ex <lb/>comparatione &longs;ecundæ partis cum inferiore primæ di-<pb pagenum="171"/>midio con&longs;equi aliud In<lb/>commodum: non repugnaui ego &longs;imiliter, quin tuo modo <lb/>o&longs;tendi&longs;&longs;es; imò & expre&longs;sè admi&longs;i incommodum, <lb/>qua&longs;i à te o&longs;ten&longs;um; & excepi &longs;olùm <emph type="italics"/>nihil e&longs;&longs;e, quod ma<lb/>gis principij fal&longs;itatem proderet, quàm tot repugnantium, at<lb/>que ab&longs;urdorum capitum deductio.<emph.end type="italics"/> An ergo etiam illeic <lb/>negaui te dicere quæ diceres, aut demon&longs;trare, quæ de<lb/>mon&longs;trares: & non potiùs &longs;emper in eo &longs;olùm fui, quòd <lb/>cognitus error à te in &longs;eip&longs;o, & in con&longs;equente multi<lb/>plici incommodo; non foret tamen per&longs;pectus in <lb/>cau&longs;&longs;a, &longs;eu in principio antecedente: eo modo, quo po<lb/>te&longs;t deformitas pueri agno&longs;ci, & probro haberi ab eo, <lb/>qui pote&longs;t non agno&longs;cere e&longs;&longs;e &longs;e illius <expan abbr="parent&etilde;">parentem</expan>; & fami<lb/>liare illud e&longs;t, <emph type="italics"/>mutato nomine, de te fabula narratur?<emph.end type="italics"/> <expan abbr="Ver&utilde;">Verum</expan> <lb/>hæc &longs;atis, vt inde con&longs;ter, tua-ne fuerit iu&longs;ta quercla. </s>

<s>Sic <lb/>cùm articulo XXXIII. o&longs;tendi&longs;&longs;es rur&longs;us tuo modo, ex <lb/>comparatione &longs;ecundæ partis cum inferiore primæ di-<pb pagenum="171"/>midio con&longs;equi aliud In<lb/>commodum: non repugnaui ego &longs;imiliter, quin tuo modo <lb/>o&longs;tendi&longs;&longs;es; imò & expre&longs;sè admi&longs;i incommodum, <lb/>qua&longs;i à te o&longs;ten&longs;um; & excepi &longs;olùm <emph type="italics"/>nihil e&longs;&longs;e, quod ma<lb/>gis principij fal&longs;itatem proderet, quàm tot repugnantium, at<lb/>que ab&longs;urdorum capitum deductio.<emph.end type="italics"/></s><s> An ergo etiam illeic <lb/>negaui te dicere quæ diceres, aut demon&longs;trare, quæ de<lb/>mon&longs;trares: & non potiùs &longs;emper in eo &longs;olùm fui, quòd <lb/>cognitus error à te in &longs;eip&longs;o, & in con&longs;equente multi<lb/>plici incommodo; non foret tamen per&longs;pectus in <lb/>cau&longs;&longs;a, &longs;eu in principio antecedente: eo modo, quo po<lb/>te&longs;t deformitas pueri agno&longs;ci, & probro haberi ab eo, <lb/>qui pote&longs;t non agno&longs;cere e&longs;&longs;e &longs;e illius <expan abbr="parent&etilde;">parentem</expan>; & fami<lb/>liare illud e&longs;t, <emph type="italics"/>mutato nomine, de te fabula narratur?<emph.end type="italics"/> <expan abbr="Ver&utilde;">Verum</expan> <lb/>hæc &longs;atis, vt inde con&longs;ter, tua-ne fuerit iu&longs;ta quercla. </s>

<s><emph type="italics"/>Vt porrò ex tuis etiam, &<emph.end type="italics"/> G<emph type="italics"/>alilei principiis rem euincam, <lb/>& eapropemodum omnia, quæ tam acriter nobis obiectas, & <lb/>tanquam ab&longs;urda tantopere in&longs;ectaris, tibi nobi&longs;cum e&longs;&longs;e <lb/>communia demon&longs;trem. </s>

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<s><emph type="italics"/>Vides igitur in tua quoque, &<emph.end type="italics"/> G<emph type="italics"/>alilei &longs;ententia perinde, <lb/>atque eadem ratione, qua in no&longs;tra, velocitatem &longs;ecunda parte<emph.end type="italics"/><lb/>DE <emph type="italics"/>acqui&longs;itam non totius velocitatis acqui&longs;itæ in prima parte<emph.end type="italics"/><lb/>AD <emph type="italics"/>duplam e&longs;&longs;e, &longs;ed velocitatis acqui&longs;itæ in vltima eius me<lb/>dietate<emph.end type="italics"/> SD. </s><pb pagenum="176"/>

<s>Nego, <emph type="italics"/>videre me perinde, atque eadem ratione.<emph.end type="italics"/> Nam <lb/>in mea quidem, & Galilei &longs;ententia &longs;umendo has <lb/>parteis DE, AD, SD pro partibus <lb/><figure id="fig40"></figure><lb/>temporis, res e&longs;t nece&longs;&longs;aria; at in tua, <lb/>&longs;umendo ea&longs;dem pro partibus &longs;patij, <lb/>o&longs;ten&longs;um iam e&longs;t velocitatem per DE <lb/>debere e&longs;&longs;e duplam velocitatis per AD. <lb/></s>

<s>Nego, <emph type="italics"/>videre me perinde, atque eadem ratione.<emph.end type="italics"/></s><s> Nam <lb/>in mea quidem, & Galilei &longs;ententia &longs;umendo has <lb/>parteis DE, AD, SD pro partibus <lb/><figure id="fig40"></figure><lb/>temporis, res e&longs;t nece&longs;&longs;aria; at in tua, <lb/>&longs;umendo ea&longs;dem pro partibus &longs;patij, <lb/>o&longs;ten&longs;um iam e&longs;t velocitatem per DE <lb/>debere e&longs;&longs;e duplam velocitatis per AD. <lb/></s>

<s>Et o&longs;tendetur paulò pò&longs;t non probari <lb/>duplam velocitatis per SD, ni&longs;i ip&longs;um<lb/>met petendo principium. </s>

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<s>Itaque & &longs;emper monui, & <expan abbr="iter&utilde;">iterum</expan> moneo moneboque <lb/>iterùm, nihil e&longs;&longs;e opus, vt e&longs;&longs;e probes fal&longs;um, <emph type="italics"/>Partem <lb/>&longs;ecundam spatii percurri dimidio temporis, quo primam:<emph.end type="italics"/> &longs;ed <lb/>opus e&longs;&longs;e, vt o&longs;tendas id non e&longs;&longs;e tuum, hoc e&longs;t non ex<lb/>pre&longs;sè a&longs;&longs;umptum à te vt verum, nece&longs;&longs;ariumque prin<lb/>cipium, quo Paralogi&longs;mi Galileum argueres; & non <lb/>nece&longs;&longs;ariò con&longs;equi ex eo, quod defendis velocitates <lb/>&longs;e habere vt &longs;patia. </s>

<s>Nempe hoc po&longs;terius <emph type="italics"/>fundamentum<emph.end type="italics"/><lb/>e&longs;t, quòd vt <emph type="italics"/>male iactum euertendum &longs;it,<emph.end type="italics"/> &longs;i contendas qui<lb/>dem, vt tam illud <emph type="italics"/>ab&longs;urdum,<emph.end type="italics"/> quàm <emph type="italics"/>tota &longs;uperex&longs;tructa mo<lb/>les corruat.<emph.end type="italics"/> Quod interim putas ab&longs;urdum euer&longs;um, <lb/>non tantùm quatenus obiectum e&longs;t tibi articulo XII. <lb/>&longs;ed etiam quatenus obiicitur po&longs;teà articulo xlii. </s>

<s>Nempe hoc po&longs;terius <emph type="italics"/>fundamentum<emph.end type="italics"/><lb/>e&longs;t, quòd vt <emph type="italics"/>male iactum euertendum &longs;it,<emph.end type="italics"/> &longs;i contendas qui<lb/>dem, vt tam illud <emph type="italics"/>ab&longs;urdum,<emph.end type="italics"/> quàm <emph type="italics"/>tota &longs;uperex&longs;tructa mo<lb/>les corruat.<emph.end type="italics"/></s><s> Quod interim putas ab&longs;urdum euer&longs;um, <lb/>non tantùm quatenus obiectum e&longs;t tibi articulo XII. <lb/>&longs;ed etiam quatenus obiicitur po&longs;teà articulo xlii. </s>

<s>id <lb/>haud rectè putas. </s>

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<s>Mi&longs;&longs;um autem facio, quod <lb/>ais de mea, & Galilei &longs;ententia, quandò ex paulò antè <lb/>deductis adeò manife&longs;tè intelligitur, fore vt potiùs ma<lb/>ri flammam, & terram cælo commi&longs;ceas, quàm ex Ga<lb/>lilei contextu, aut mea Re&longs;pon&longs;ione id probes, quod <lb/>heic a&longs;&longs;eris, aut euincere valeas cuertere me agnitam à <lb/>me veritatem. </s>

<s>Quod &longs;upere&longs;t autem cùm tua &longs;enten<lb/>tia tum ver&longs;ibus hi&longs;ce, tum hactenus toties repetita &longs;it, <lb/><emph type="italics"/>velocitatem tota &longs;ecunda parte<emph.end type="italics"/> DE <emph type="italics"/>acquifitam præcisè du<lb/>plam e&longs;&longs;e totius velocitatis per inferiorem primæ partis medie<lb/>tatem<emph.end type="italics"/> SD <emph type="italics"/>acqui&longs;itæ fimiliterque, &c.<emph.end type="italics"/> Quæ&longs;ote primùm, <lb/>quomodo nam ip&longs;am hactenùs &longs;tabilii&longs;ti? </s>

<s>Quod &longs;upere&longs;t autem cùm tua &longs;enten<lb/>tia tum ver&longs;ibus hi&longs;ce, tum hactenus toties repetita &longs;it, <lb/><emph type="italics"/>velocitatem tota &longs;ecunda parte<emph.end type="italics"/> DE <emph type="italics"/>acquifitam præcisè du<lb/>plam e&longs;&longs;e totius velocitatis per inferiorem primæ partis medie<lb/>tatem<emph.end type="italics"/> SD <emph type="italics"/>acqui&longs;itæ fimiliterque, &c.<emph.end type="italics"/></s><s> Quæ&longs;ote primùm, <lb/>quomodo nam ip&longs;am hactenùs &longs;tabilii&longs;ti? </s>

<s>Nam &longs;i <lb/>to r<gap/>u<gap/>ra &longs;tabilii&longs;&longs;e probes, fru&longs;trà &longs;it omnis meus la-<pb pagenum="183"/>bor: &longs;i verò non probes, fru&longs;trà omnis tuus. </s>

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<s>A&longs;&longs;umptâ illeic lineâ AB, diui&longs;a in parteis æqua<lb/>leis AD, DE, &c. </s>

<s>ac prima parte bi&longs;ecti in S, <lb/><figure id="fig41"></figure><lb/>expre&longs;&longs;a &longs;ententia hi&longs;ce verbis ex&longs;tat <emph type="italics"/>Tota<emph.end type="italics"/> DE <lb/><emph type="italics"/>eodem præcisè tempore, quo pars<emph.end type="italics"/> SD <emph type="italics"/>tran&longs;curritur.<emph.end type="italics"/><lb/>Tum probatio hæc additur, <emph type="italics"/>Cùm enim<emph.end type="italics"/> AD <emph type="italics"/>du<lb/>pla ponatur ip&longs;ius<emph.end type="italics"/> AS, <emph type="italics"/>& &longs;imiliter<emph.end type="italics"/> AE <emph type="italics"/>dupla &longs;it <lb/>ip&longs;ius<emph.end type="italics"/> AD, <emph type="italics"/>nece&longs;&longs;e e&longs;t, vt velocitas in<emph.end type="italics"/> D, <emph type="italics"/>dupla &longs;it <lb/>velocitatis in<emph.end type="italics"/> S, <emph type="italics"/>& velocitas in<emph.end type="italics"/> E <emph type="italics"/>eodem modo du<lb/>pla reperiatur velocitatis in D.<emph.end type="italics"/> Deducis con&longs;e<lb/>quenter velocitatem per totam DE e&longs;&longs;e du<lb/>plam velocitatis per totam SD: &longs;ed quod caput <lb/>e&longs;t, peruideamus. </s>

<s>ac prima parte bi&longs;ecti in S, <lb/><figure id="fig41"></figure><lb/>expre&longs;&longs;a &longs;ententia hi&longs;ce verbis ex&longs;tat <emph type="italics"/>Tota<emph.end type="italics"/> DE <lb/><emph type="italics"/>eodem præcisè tempore, quo pars<emph.end type="italics"/> SD <emph type="italics"/>tran&longs;curritur.<emph.end type="italics"/><lb/>Tum probatio hæc additur, <emph type="italics"/>Cùm enim<emph.end type="italics"/> AD <emph type="italics"/>du<lb/>pla ponatur ip&longs;ius<emph.end type="italics"/> AS, <emph type="italics"/>& &longs;imiliter<emph.end type="italics"/> AE <emph type="italics"/>dupla &longs;it <lb/>ip&longs;ius<emph.end type="italics"/> AD, <emph type="italics"/>nece&longs;&longs;e e&longs;t, vt velocitas in<emph.end type="italics"/> D, <emph type="italics"/>dupla &longs;it <lb/>velocitatis in<emph.end type="italics"/> S, <emph type="italics"/>& velocitas in<emph.end type="italics"/> E <emph type="italics"/>eodem modo du<lb/>pla reperiatur velocitatis in D.<emph.end type="italics"/></s><s> Deducis con&longs;e<lb/>quenter velocitatem per totam DE e&longs;&longs;e du<lb/>plam velocitatis per totam SD: &longs;ed quod caput <lb/>e&longs;t, peruideamus. </s>

<s>Nece&longs;&longs;e dicis <emph type="italics"/>velocitatem in<emph.end type="italics"/><lb/>D, <emph type="italics"/>e&longs;&longs;e duplam velocitatis in<emph.end type="italics"/> S, <emph type="italics"/>& velocitatem in<emph.end type="italics"/> E <lb/><emph type="italics"/>velocitatis in<emph.end type="italics"/> D, eo argumento, <emph type="italics"/>quòd<emph.end type="italics"/> AD <emph type="italics"/>dupla <lb/>&longs;it ip&longs;ius<emph.end type="italics"/> AS, <emph type="italics"/>&<emph.end type="italics"/> AE <emph type="italics"/>ip&longs;ius<emph.end type="italics"/> AD. </s>

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<s>Nam hoc opus, hic labor e&longs;t. </s>

<s>Quomodò, <lb/>inquam, ex eo, quòd <emph type="italics"/>spatium<emph.end type="italics"/> AD <emph type="italics"/>duplum &longs;it spatij<emph.end type="italics"/><lb/>AS, <emph type="italics"/>&longs;patium<emph.end type="italics"/> AE <emph type="italics"/>spatij<emph.end type="italics"/> AD, &longs;equi nece&longs;&longs;ariò, <emph type="italics"/>vt <lb/>velocitas in D dupla &longs;it velocitatis in S, & velocitas in<emph.end type="italics"/><pb pagenum="184"/><emph type="italics"/>E, velocitatis in D?<emph.end type="italics"/> Id &longs;anè non probas, &longs;ed &longs;olùm <lb/>&longs;upponis ex eo vim habere, <emph type="italics"/>quòd velocitates &longs;icut spa<lb/>tia &longs;int.<emph.end type="italics"/> Atqui hæc ip&longs;a e&longs;t controuer&longs;ia, <emph type="italics"/>an velocita<lb/>tes inter &longs;e &longs;icut &longs;patia &longs;int:<emph.end type="italics"/> neque idip&longs;um, quod opus <lb/>e&longs;t, probas, &longs;ed omninò principium petis, &longs;eu ip&longs;am <lb/>quæ&longs;tionem, remve controuer&longs;am pro principio a&longs;&longs;u<lb/>mis. </s>

<s>Quomodò, <lb/>inquam, ex eo, quòd <emph type="italics"/>spatium<emph.end type="italics"/> AD <emph type="italics"/>duplum &longs;it spatij<emph.end type="italics"/><lb/>AS, <emph type="italics"/>&longs;patium<emph.end type="italics"/> AE <emph type="italics"/>spatij<emph.end type="italics"/> AD, &longs;equi nece&longs;&longs;ariò, <emph type="italics"/>vt <lb/>velocitas in D dupla &longs;it velocitatis in S, & velocitas in<emph.end type="italics"/><pb pagenum="184"/><emph type="italics"/>E, velocitatis in D?<emph.end type="italics"/> Id &longs;anè non probas, &longs;ed &longs;olùm <lb/>&longs;upponis ex eo vim habere, <emph type="italics"/>quòd velocitates &longs;icut spa<lb/>tia &longs;int.<emph.end type="italics"/></s><s> Atqui hæc ip&longs;a e&longs;t controuer&longs;ia, <emph type="italics"/>an velocita<lb/>tes inter &longs;e &longs;icut &longs;patia &longs;int:<emph.end type="italics"/> neque idip&longs;um, quod opus <lb/>e&longs;t, probas, &longs;ed omninò principium petis, &longs;eu ip&longs;am <lb/>quæ&longs;tionem, remve controuer&longs;am pro principio a&longs;&longs;u<lb/>mis. </s>

<s>An verò dices te proba&longs;&longs;e, <emph type="italics"/>velocitates e&longs;&longs;e vt &longs;pa<lb/>tia?<emph.end type="italics"/> Sed quæ&longs;o, vbi-nam? </s>

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<s>An vbi volui&longs;ti arguere Galileum Pa<lb/>ralogi&longs;mi? </s>

<s>At abundè iam <expan abbr="declarat&utilde;">declaratum</expan> e&longs;t te potiùs v&longs;um <lb/>paralogi&longs;mo, cùm rur&longs;us nihil aliud, quàm principium <lb/>petieris: vt taceam te, &longs;i quid habui&longs;ti probationis, id<lb/>po&longs;teà nega&longs;&longs;e: quando nega&longs;ti <emph type="italics"/>&longs;i prima pars spatij per<lb/>curratur quadrante, percurri &longs;ecundam dimidio quadrantis,<emph.end type="italics"/><lb/>An vbi demùm protuli&longs;ti <emph type="italics"/>tuum de Bilance Experimen<lb/>tum?<emph.end type="italics"/> Certè i&longs;ta vna probatio fuit tua, neque potes pro<lb/>ferre locum, in quo alia ratione probaueris <emph type="italics"/>velocitates <lb/>&longs;e habere vt spatia.<emph.end type="italics"/> Atqui & fal&longs;um deprehen&longs;um Ex<lb/>perimentum tuum e&longs;t; & quæ germana fuit Experien<lb/>tia fal&longs;um conuicit <emph type="italics"/>velocitates &longs;e inter &longs;e habere vt <lb/>spatia.<emph.end type="italics"/> Itaque ex his &longs;equitur, non modo nece&longs;&longs;e non <lb/>e&longs;&longs;e: &longs;ed fal&longs;um etiam, atque adeò prorsùs impo&longs;&longs;ibile, <lb/>vt <emph type="italics"/>velocitas in D, dupla &longs;it velocitatis in S, & velocitas in <lb/>E, velocitatis in D.<emph.end type="italics"/></s>

<s>At abundè iam <expan abbr="declarat&utilde;">declaratum</expan> e&longs;t te potiùs v&longs;um <lb/>paralogi&longs;mo, cùm rur&longs;us nihil aliud, quàm principium <lb/>petieris: vt taceam te, &longs;i quid habui&longs;ti probationis, id<lb/>po&longs;teà nega&longs;&longs;e: quando nega&longs;ti <emph type="italics"/>&longs;i prima pars spatij per<lb/>curratur quadrante, percurri &longs;ecundam dimidio quadrantis,<emph.end type="italics"/><lb/>An vbi demùm protuli&longs;ti <emph type="italics"/>tuum de Bilance Experimen<lb/>tum?<emph.end type="italics"/> Certè i&longs;ta vna probatio fuit tua, neque potes pro<lb/>ferre locum, in quo alia ratione probaueris <emph type="italics"/>velocitates <lb/>&longs;e habere vt spatia.<emph.end type="italics"/></s><s> Atqui & fal&longs;um deprehen&longs;um Ex<lb/>perimentum tuum e&longs;t; & quæ germana fuit Experien<lb/>tia fal&longs;um conuicit <emph type="italics"/>velocitates &longs;e inter &longs;e habere vt <lb/>spatia.<emph.end type="italics"/></s><s> Itaque ex his &longs;equitur, non modo nece&longs;&longs;e non <lb/>e&longs;&longs;e: &longs;ed fal&longs;um etiam, atque adeò prorsùs impo&longs;&longs;ibile, <lb/>vt <emph type="italics"/>velocitas in D, dupla &longs;it velocitatis in S, & velocitas in <lb/>E, velocitatis in D.<emph.end type="italics"/></s>

<s>Cùm ergo non modò probatum non &longs;it, &longs;ed fal<lb/>&longs;um quoque & impo&longs;&longs;ibile ip&longs;a Experientia &longs;uffra<lb/>gante o&longs;ten&longs;um, <emph type="italics"/>velocitatem tota &longs;ecunda parte<emph.end type="italics"/> DE <lb/><emph type="italics"/>acqui&longs;itam pr&ecedil;cisè duplam e&longs;&longs;e totius velocitatis per inferio<lb/>rem primæ partis medietatem<emph.end type="italics"/> SD, <emph type="italics"/>acqui&longs;itæ, &longs;imiliterque, &c.<emph.end type="italics"/><lb/>Quæ&longs;o quî adhûc valeas talem &longs;ententiam defendere, <pb pagenum="185"/>querique, quòd nullum non mouerim lapidem <emph type="italics"/>ad euer<lb/>tendum hanc veritatem?<emph.end type="italics"/> Atque ego quidem, quòd ex<lb/>inde inferres, <emph type="italics"/>Tempus, quo percurritur DE, e&longs;&longs;e præcisè <lb/>æquale tempori, quo percurritur SD,<emph.end type="italics"/> ob duplam nempe <lb/>velocitatem, &longs;icuti &longs;patium duplum e&longs;t, huiu&longs;cemodi <lb/>lapides, & articulis quidem XXXV. ac XXXVI. moui, I. <lb/>fore, vt &longs;uppo&longs;ito tempore, quo percurritur SD, <lb/>minutorum v. </s>

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<s>Et cùm volueris ip&longs;e po&longs;teà videri huma<lb/>nior, dum legens IC, adnota&longs;ti <emph type="italics"/>dicere me volui&longs;&longs;e HC<emph.end type="italics"/><lb/>(quanqùam dicere nolui HC, &longs;ed ND, tribus inte<lb/>gris ver&longs;ibus, ad illud v&longs;que, <emph type="italics"/>vt tu concludis,<emph.end type="italics"/> qui in &longs;eheda <lb/>fuere, ob idem initium, ca&longs;u prætermi&longs;&longs;is) cùm, <expan abbr="inquã">inquam</expan>, <lb/>illeic humanior fueris, cur heic quoque e&longs;&longs;e nolui&longs;ti? <lb/></s>

<s>Debui&longs;ti ergo potiùs re&longs;titutâ literâ D, o&longs;tendere me <lb/>impropriè loquutum, qua&longs;i ignorantem diui&longs;ionem <lb/>rationis e&longs;&longs;e <emph type="italics"/>&longs;umptionem exce&longs;&longs;us, quo antecedens &longs;uperat <lb/>con&longs;equens, ad ip&longs;ummet con&longs;equens:<emph.end type="italics"/> hoc e&longs;t, <emph type="italics"/>e&longs;&longs;e compa<lb/>rationem differentiæ terminorum cum ip&longs;orum alterutro.<emph.end type="italics"/> Sed <lb/>ita nimirùm agere fuit cordi, vt dicere po&longs;&longs;es, quamuis <lb/>vt par e&longs;t, di&longs;ponerentur termini, nihil me hac ratione <lb/>conclu&longs;urum, ni&longs;i prius &longs;upponerem <emph type="italics"/>velocitatem per to<lb/>tam<emph.end type="italics"/> AE <emph type="italics"/>duplam e&longs;&longs;e velocitatis acqui&longs;itæ per<emph.end type="italics"/> DE, <emph type="italics"/>quod ta<lb/>men fal&longs;um non ignorarem.<emph.end type="italics"/> Ego verò fal&longs;um <expan abbr="quid&etilde;">quidem</expan> e&longs;&longs;e, <lb/>&longs;ed & tuum e&longs;&longs;e non ignoro: ac ne ex &longs;uperiùs dedu<lb/>ctis argumentum repetam, paucis o&longs;tendo nihil e&longs;&longs;e <lb/>hac &longs;uppo&longs;itione, aut omninò vlla tergiuer&longs;atione <lb/>opus. </s>

<s>Debui&longs;ti ergo potiùs re&longs;titutâ literâ D, o&longs;tendere me <lb/>impropriè loquutum, qua&longs;i ignorantem diui&longs;ionem <lb/>rationis e&longs;&longs;e <emph type="italics"/>&longs;umptionem exce&longs;&longs;us, quo antecedens &longs;uperat <lb/>con&longs;equens, ad ip&longs;ummet con&longs;equens:<emph.end type="italics"/> hoc e&longs;t, <emph type="italics"/>e&longs;&longs;e compa<lb/>rationem differentiæ terminorum cum ip&longs;orum alterutro.<emph.end type="italics"/></s><s> Sed <lb/>ita nimirùm agere fuit cordi, vt dicere po&longs;&longs;es, quamuis <lb/>vt par e&longs;t, di&longs;ponerentur termini, nihil me hac ratione <lb/>conclu&longs;urum, ni&longs;i prius &longs;upponerem <emph type="italics"/>velocitatem per to<lb/>tam<emph.end type="italics"/> AE <emph type="italics"/>duplam e&longs;&longs;e velocitatis acqui&longs;itæ per<emph.end type="italics"/> DE, <emph type="italics"/>quod ta<lb/>men fal&longs;um non ignorarem.<emph.end type="italics"/></s><s> Ego verò fal&longs;um <expan abbr="quid&etilde;">quidem</expan> e&longs;&longs;e, <lb/>&longs;ed & tuum e&longs;&longs;e non ignoro: ac ne ex &longs;uperiùs dedu<lb/>ctis argumentum repetam, paucis o&longs;tendo nihil e&longs;&longs;e <lb/>hac &longs;uppo&longs;itione, aut omninò vlla tergiuer&longs;atione <lb/>opus. </s>

<s>Ex verbis paulò antè ex tua di&longs;&longs;ertatione reci<lb/>tatis, negare non potes, quin hoc totum tuum &longs;it: <pb pagenum="187"/><emph type="italics"/>vt<emph.end type="italics"/> AE, <emph type="italics"/>ad<emph.end type="italics"/> AD, <emph type="italics"/>ita<emph.end type="italics"/> AD <emph type="italics"/>ad<emph.end type="italics"/> AS. Quamobrem, aut <lb/>neges oportet ratiocinia Geometrica, aut fatearis le<lb/>gitimè diuidendo ita concludi, <emph type="italics"/>vt<emph.end type="italics"/> AS, <emph type="italics"/>ad<emph.end type="italics"/> SD; <emph type="italics"/>ita<emph.end type="italics"/> AD <lb/><emph type="italics"/>ad<emph.end type="italics"/> DE. </s>

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<s>Cùm deduxe<lb/>rim verò incommoda varia ex eo, quòd liceat <expan abbr="dimi-di&utilde;">dimi<lb/>dium</expan> prius in duo alia dimidia &longs;ubdiuidere, & prius i&longs;to<lb/>rum in duo alia, & &longs;ic con&longs;equenter: quid tu ad ea om<lb/>nia? </s>

<s>Nempe <emph type="italics"/>po&longs;&longs;e quidem id dimidium &longs;ubdiuidi: verùm <lb/>e&longs;&longs;e tandem alicubi &longs;tandum: cùm diui&longs;io e&longs;&longs;e infinita non po&longs;<lb/>&longs;it.<emph.end type="italics"/> Age itaque peruideamus quid hac re&longs;pon&longs;ione ef<lb/>ficias. </s>

<s>Nempe <emph type="italics"/>po&longs;&longs;e quidem id dimidium &longs;ubdiuidi: verùm <lb/>e&longs;&longs;e tandem alicubi &longs;tandum: cùm diui&longs;io e&longs;&longs;e infinita non po&longs;<lb/>&longs;it.<emph.end type="italics"/></s><s> Age itaque peruideamus quid hac re&longs;pon&longs;ione ef<lb/>ficias. </s>

<s>Dicis <emph type="italics"/>e&longs;&longs;e tandem alicubi &longs;tandum, quòd diui&longs;io e&longs;&longs;e <lb/>infinita non poßit:<emph.end type="italics"/> igitur per te licebit non &longs;tare, quo v&longs;<lb/>que diui&longs;io finita non erit, ac partes &longs;upererunt, per <pb pagenum="194"/>quas progredi diuidendo liceat? </s>

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<s>An-non proinde cùm l inea AD contexta erit <lb/>ex duobus punctis? </s>

<s>Prouidens tu quæ po&longs;&longs;ent exinde iure vrgeri in<lb/>commoda, præoccupa&longs;ti, <emph type="italics"/>partem AS accipiendam e&longs;&longs;e <lb/>vt quid Phy&longs;icum, quod mente quidem, &longs;eu Mathematicè <lb/>diui&longs;ibile in parteis infinitas &longs;it: &longs;ed non ita tamen, vt accelera<lb/>tio variari &longs;ecundum eas poßit; quippe quæ effectus Phy&longs;i<lb/>cus cùm &longs;it, non-ni&longs;i per parteis &longs;en&longs;ibileis metienda videa<lb/>tur.<emph.end type="italics"/> Aequiuocatio e&longs;&longs;e quædam po&longs;&longs;et circa vocem <lb/><emph type="italics"/>&longs;en&longs;ibileis;<emph.end type="italics"/> verùm &longs;ic accipio, qua&longs;i tu per illam intelle<lb/>xeris parteis <emph type="italics"/>Phy&longs;icas,<emph.end type="italics"/> hoc e&longs;t reuerâ ex&longs;i&longs;tenteis in <lb/>rerum natura; nempe vt opponantur Mathematicis, <lb/>&longs;iue iis, quas mente confictas dixi&longs;ti. </s>

<s>Prouidens tu quæ po&longs;&longs;ent exinde iure vrgeri in<lb/>commoda, præoccupa&longs;ti, <emph type="italics"/>partem AS accipiendam e&longs;&longs;e <lb/>vt quid Phy&longs;icum, quod mente quidem, &longs;eu Mathematicè <lb/>diui&longs;ibile in parteis infinitas &longs;it: &longs;ed non ita tamen, vt accelera<lb/>tio variari &longs;ecundum eas poßit; quippe quæ effectus Phy&longs;i<lb/>cus cùm &longs;it, non-ni&longs;i per parteis &longs;en&longs;ibileis metienda videa<lb/>tur.<emph.end type="italics"/></s><s> Aequiuocatio e&longs;&longs;e quædam po&longs;&longs;et circa vocem <lb/><emph type="italics"/>&longs;en&longs;ibileis;<emph.end type="italics"/> verùm &longs;ic accipio, qua&longs;i tu per illam intelle<lb/>xeris parteis <emph type="italics"/>Phy&longs;icas,<emph.end type="italics"/> hoc e&longs;t reuerâ ex&longs;i&longs;tenteis in <lb/>rerum natura; nempe vt opponantur Mathematicis, <lb/>&longs;iue iis, quas mente confictas dixi&longs;ti. </s>

<s>Nam &longs;i alioquin <lb/>diceres <emph type="italics"/>&longs;en&longs;ibileis,<emph.end type="italics"/> qua&longs;i &longs;en&longs;u perceptibileis, notum e&longs;t <lb/>naturam non e&longs;&longs;e metiendam in &longs;uis adeò &longs;ubtilibus <lb/>operationibus iuxta &longs;en&longs;us captum. </s>

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<s>Cùm non po&longs;&longs;is: vide quàm fru&longs;trà <lb/>eò confugeris, vt <emph type="italics"/>&longs;tandum alicubi &longs;it, quòd diui&longs;io e&longs;&longs;e infi<lb/>nita non poßit.<emph.end type="italics"/></s>

<s>Hanc iterùm difficultatem qua&longs;i præ&longs;entiens, præ<lb/>uenien&longs;que, <emph type="italics"/>quid ni,<emph.end type="italics"/> inquis, <emph type="italics"/>iam primùm in ea parte con<lb/>&longs;i&longs;tamus, ex qua totius motus accelerati ratio perfectè intelli<lb/>gatur?<emph.end type="italics"/> Dicere ergo vis, non e&longs;&longs;e ex&longs;pectandum, ad <lb/>hoc vt con&longs;i&longs;tamus, quov&longs;que ad eam diui&longs;ionem per<lb/>uenerimus, ex qua partes AS, & SD &longs;int duo puncta <lb/>Phy&longs;ica, &longs;eu duæ Phy&longs;icè indiui&longs;ibiles partes: &longs;ed in illa <lb/>&longs;tandum, in qua tam AS, quàm SD con&longs;tent adhùc ex <lb/>tot Phy&longs;icis partibus, <emph type="italics"/>vt ex ijs ratio accelerati motus per<lb/>fectè intelligatur.<emph.end type="italics"/> At imprimis, &longs;i ita &longs;it, fru&longs;trà ergo <lb/>dicis alicubi &longs;tandum, <emph type="italics"/>quòd diui&longs;io e&longs;&longs;e infinita non poßit:<emph.end type="italics"/><lb/>cùm etiam diui&longs;ione ex&longs;i&longs;tente non infinita, progredi <lb/>adhûc vlteriùs liceat: atque idcircò vigent adhûc in<lb/>commoda omnia, quæ obiecta &longs;unt: quandò pote&longs;t <pb pagenum="196"/>adhûc pars AS, &longs;ubdiuidi in plura, pluraque dimidia. <lb/></s>

<s>Hanc iterùm difficultatem qua&longs;i præ&longs;entiens, præ<lb/>uenien&longs;que, <emph type="italics"/>quid ni,<emph.end type="italics"/> inquis, <emph type="italics"/>iam primùm in ea parte con<lb/>&longs;i&longs;tamus, ex qua totius motus accelerati ratio perfectè intelli<lb/>gatur?<emph.end type="italics"/> Dicere ergo vis, non e&longs;&longs;e ex&longs;pectandum, ad <lb/>hoc vt con&longs;i&longs;tamus, quov&longs;que ad eam diui&longs;ionem per<lb/>uenerimus, ex qua partes AS, & SD &longs;int duo puncta <lb/>Phy&longs;ica, &longs;eu duæ Phy&longs;icè indiui&longs;ibiles partes: &longs;ed in illa <lb/>&longs;tandum, in qua tam AS, quàm SD con&longs;tent adhùc ex <lb/>tot Phy&longs;icis partibus, <emph type="italics"/>vt ex ijs ratio accelerati motus per<lb/>fectè intelligatur.<emph.end type="italics"/></s><s> At imprimis, &longs;i ita &longs;it, fru&longs;trà ergo <lb/>dicis alicubi &longs;tandum, <emph type="italics"/>quòd diui&longs;io e&longs;&longs;e infinita non poßit:<emph.end type="italics"/><lb/>cùm etiam diui&longs;ione ex&longs;i&longs;tente non infinita, progredi <lb/>adhûc vlteriùs liceat: atque idcircò vigent adhûc in<lb/>commoda omnia, quæ obiecta &longs;unt: quandò pote&longs;t <pb pagenum="196"/>adhûc pars AS, &longs;ubdiuidi in plura, pluraque dimidia. <lb/></s>

<s>Deinde, cùm in dimidio SD, tot requiris parteis, vt <lb/><emph type="italics"/>ex ip&longs;is ratio accelerati motus perfectè intelligatur:<emph.end type="italics"/> quot<lb/>nam quæ&longs;o &longs;unt, quas requiris? </s>

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<s>&longs;ex, quas nempe recen&longs;es, dum rationem motus <lb/>accelerati explicas per trientem, quadrantem, per quin<lb/>tam, perque &longs;extam parteis tantum? </s>

<s>Sanè vel ne&longs;ciens <lb/>tot requiris, vt innumerabiles &longs;int; & tum ab&longs;is longi&longs;<lb/>&longs;imè ab eo, vt cau&longs;&longs;eris &longs;tandum, quòd <emph type="italics"/>diui&longs;io e&longs;&longs;e infinita <lb/>non poßit,<emph.end type="italics"/> qua&longs;i vel in fine, vel certe non longè à fine <lb/>con&longs;i&longs;tendum &longs;it: tum etiam ab eo, vt ex cognitis par<lb/>tibus <emph type="italics"/>ratio motus intelligatur.<emph.end type="italics"/> Rem vt experiamur, ac<lb/>cipiamus, ecce, ca&longs;um globi ferrei (quod tuum po&longs;teà <lb/>exemplum e&longs;t) ex cælo Lunæ in centrum terræ: atque <lb/>in ip&longs;o talem partem, <emph type="italics"/>in qua iam primum,<emph.end type="italics"/> vt ais, <emph type="italics"/>con&longs;i&longs;ta<lb/>mus.<emph.end type="italics"/> Cùm tuo ex decreto, men&longs;ura durationis om<lb/>nium partium i&longs;ti primæ æqualium &longs;it æqualis duratio <lb/>totidem minutiorum partium &longs;igillatim acceptarum <lb/>in inferiore eius dimidio: ergo inferius eius dimidium <lb/>diui&longs;ibile e&longs;t in tot parteis, non Mathematicas, men<lb/>teve confictas, &longs;ed Phy&longs;icas, &longs;iue in ip&longs;a rerum natura <lb/>ex&longs;i&longs;tenteis, quot partes &longs;unt à cælo Lunæ, v&longs;que in <lb/>centrum terræ, ip&longs;i AD æquales. </s>

<s>Sanè vel ne&longs;ciens <lb/>tot requiris, vt innumerabiles &longs;int; & tum ab&longs;is longi&longs;<lb/>&longs;imè ab eo, vt cau&longs;&longs;eris &longs;tandum, quòd <emph type="italics"/>diui&longs;io e&longs;&longs;e infinita <lb/>non poßit,<emph.end type="italics"/> qua&longs;i vel in fine, vel certe non longè à fine <lb/>con&longs;i&longs;tendum &longs;it: tum etiam ab eo, vt ex cognitis par<lb/>tibus <emph type="italics"/>ratio motus intelligatur.<emph.end type="italics"/></s><s> Rem vt experiamur, ac<lb/>cipiamus, ecce, ca&longs;um globi ferrei (quod tuum po&longs;teà <lb/>exemplum e&longs;t) ex cælo Lunæ in centrum terræ: atque <lb/>in ip&longs;o talem partem, <emph type="italics"/>in qua iam primum,<emph.end type="italics"/> vt ais, <emph type="italics"/>con&longs;i&longs;ta<lb/>mus.<emph.end type="italics"/> Cùm tuo ex decreto, men&longs;ura durationis om<lb/>nium partium i&longs;ti primæ æqualium &longs;it æqualis duratio <lb/>totidem minutiorum partium &longs;igillatim acceptarum <lb/>in inferiore eius dimidio: ergo inferius eius dimidium <lb/>diui&longs;ibile e&longs;t in tot parteis, non Mathematicas, men<lb/>teve confictas, &longs;ed Phy&longs;icas, &longs;iue in ip&longs;a rerum natura <lb/>ex&longs;i&longs;tenteis, quot partes &longs;unt à cælo Lunæ, v&longs;que in <lb/>centrum terræ, ip&longs;i AD æquales. </s>

<s>Hæ verò partes quot<lb/>nam &longs;unt? </s>

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<s>Vide&longs;-ne <lb/>ergo quàm procùl ab&longs;it à diui&longs;ionum fine ea pars, <emph type="italics"/>in <lb/>qua iam primùm,<emph.end type="italics"/> vt ais, <emph type="italics"/>con&longs;istamus?<emph.end type="italics"/></s>

<s>Subiicis, <emph type="italics"/>non &longs;entire te cum<emph.end type="italics"/> G<emph type="italics"/>alileo, & me, graue <lb/>de&longs;cendens, statim à quiete, atque in omnibus, ac &longs;ingulis mo<lb/>mentis accelerare motum.<emph.end type="italics"/> Quot ergo putas momenta, <lb/>&longs;eu Phy&longs;icas temporis parteis ab&longs;que acceleratione <lb/>tran&longs;iri? </s>

<s>Subiicis, <emph type="italics"/>non &longs;entire te cum<emph.end type="italics"/> G<emph type="italics"/>alileo, & me, graue <lb/>de&longs;cendens, statim à quiete, atque in omnibus, ac &longs;ingulis mo<lb/>mentis accelerare motum.<emph.end type="italics"/></s><s> Quot ergo putas momenta, <lb/>&longs;eu Phy&longs;icas temporis parteis ab&longs;que acceleratione <lb/>tran&longs;iri? </s>

<s>Tot certè, quot &longs;unt innumerabiles illæ par<lb/>tes, quæ &longs;unt <expan abbr="nõ">non</expan> in priore minùs, quàm in po&longs;teriore di<lb/>midio di&longs;tinctæ: neque enim illæ, ni&longs;i &longs;ucce&longs;&longs;iuè, & vna <lb/>po&longs;t aliam, atque adeò di&longs;tinctis temporis partibus per<lb/>curruntur. </s>

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<s>aërem: <lb/>neque enim prius accelerari motum à grauitate inchoatum, <lb/>quàm à medii accurrentis, &longs;eque à tergo claudentis motu, eó<lb/>que iam notabili re&longs;i&longs;tentia &longs;uperetur.<emph.end type="italics"/> Quo loco rursùs <lb/>æquiuocatio in nomine <emph type="italics"/>notabilis.<emph.end type="italics"/> Nam <emph type="italics"/>notabilem<emph.end type="italics"/> intel<lb/>ligis aut naturæ, aut nobis. </s>

<s>aërem: <lb/>neque enim prius accelerari motum à grauitate inchoatum, <lb/>quàm à medii accurrentis, &longs;eque à tergo claudentis motu, eó<lb/>que iam notabili re&longs;i&longs;tentia &longs;uperetur.<emph.end type="italics"/></s><s> Quo loco rursùs <lb/>æquiuocatio in nomine <emph type="italics"/>notabilis.<emph.end type="italics"/> Nam <emph type="italics"/>notabilem<emph.end type="italics"/> intel<lb/>ligis aut naturæ, aut nobis. </s>

<s>Et nobis quidem <emph type="italics"/>notabilem<emph.end type="italics"/><pb pagenum="198"/>non debes intelligere: cùm natura no&longs;træ <emph type="italics"/>notationi<emph.end type="italics"/> non <lb/>alligetur; & priu&longs;quam no&longs;tra per&longs;picacia <emph type="italics"/>notare<emph.end type="italics"/> quic<lb/>quam valeat, natura iam tran&longs;ierit per innumerabi<lb/>leis parteis. </s>

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<s>Qua&longs;i non po&longs;&longs;it motus <emph type="italics"/>notabilis<emph.end type="italics"/> e&longs;&longs;e paulò antè <lb/>medium, aut non-ni&longs;i paulò pò&longs;t medium? </s>

<s>E&longs;t ne <lb/>aliquod argumentum, quo probes i&longs;tam tuam cau&longs;&longs;am <lb/>nihil omninò agere, nihil &longs;uperare re&longs;i&longs;tentiæ, per tot <lb/>illas partium &longs;patij, tempori&longs;que myriadas, quæ toti <lb/>priori dimidio tribuuntur, &longs;tatim autem ac mobile at<lb/>tigit primam po&longs;terioris, incipere & agere, & re&longs;i&longs;ten<lb/>tiam &longs;uperare? <emph type="italics"/>Requiritur,<emph.end type="italics"/> inquis, <emph type="italics"/>pars temporis, ac spa<lb/>tii non Mathematicè minima, &longs;ed Phy&longs;icè notabilis.<emph.end type="italics"/> Aduer<lb/>&longs;atiuam hanc non capio: cùm videretur debere pars <lb/>dici, aut <emph type="italics"/>Mathematicè notabilis,<emph.end type="italics"/> aut <emph type="italics"/>Phy&longs;icè minima:<emph.end type="italics"/> &longs;ed <lb/>quicquid &longs;it, vis eam Phy&longs;icè notabilem e&longs;&longs;e; quid inde <lb/>concludis? <emph type="italics"/>Heinc e&longs;t,<emph.end type="italics"/> inquis, <emph type="italics"/>cur accelerationis ratio à <lb/>primo &longs;patii percurren li puncto non tutò inchoetur.<emph.end type="italics"/> Non <lb/>tutò inchoetur? </s>

<s>E&longs;t ne <lb/>aliquod argumentum, quo probes i&longs;tam tuam cau&longs;&longs;am <lb/>nihil omninò agere, nihil &longs;uperare re&longs;i&longs;tentiæ, per tot <lb/>illas partium &longs;patij, tempori&longs;que myriadas, quæ toti <lb/>priori dimidio tribuuntur, &longs;tatim autem ac mobile at<lb/>tigit primam po&longs;terioris, incipere & agere, & re&longs;i&longs;ten<lb/>tiam &longs;uperare? <emph type="italics"/>Requiritur,<emph.end type="italics"/> inquis, <emph type="italics"/>pars temporis, ac spa<lb/>tii non Mathematicè minima, &longs;ed Phy&longs;icè notabilis.<emph.end type="italics"/></s><s> Aduer<lb/>&longs;atiuam hanc non capio: cùm videretur debere pars <lb/>dici, aut <emph type="italics"/>Mathematicè notabilis,<emph.end type="italics"/> aut <emph type="italics"/>Phy&longs;icè minima:<emph.end type="italics"/> &longs;ed <lb/>quicquid &longs;it, vis eam Phy&longs;icè notabilem e&longs;&longs;e; quid inde <lb/>concludis? <emph type="italics"/>Heinc e&longs;t,<emph.end type="italics"/> inquis, <emph type="italics"/>cur accelerationis ratio à <lb/>primo &longs;patii percurren li puncto non tutò inchoetur.<emph.end type="italics"/></s><s> Non <lb/>tutò inchoetur? </s>

<s>Imò, vnde tutiùs inchoetur, quàm <lb/>vnde e&longs;t periculi nihil? </s>

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<s>Igitur per te <lb/>AC, & NC, &longs;ecundum &longs;e totas velocitate ea<lb/>dem percurruntur; &longs;untque idcircò inter &longs;e <lb/>æquales. </s>

<s>Tu ergo vim con&longs;equutionis ex inte<lb/>gro antecedente diffimulans, infers &longs;olùm ex <lb/>duplo &longs;patij, & temporis æqualitate, velocitates <lb/>e&longs;&longs;e vt &longs;patia: ac retices quod intere&longs;t, quodque <lb/>&longs;ubnotatum fuit, cùm &longs;ubiunxi, <emph type="italics"/>con&longs;equi, vt <lb/>velocitates per AC, & NC, acqui&longs;itæ &longs;int pror&longs;us <lb/>æquales: ac proinde vt AC, & NC, hoc est totum, & <lb/>pars eodem tempore percurrantur, &c.<emph.end type="italics"/> Sequitur. </s>

<s><emph type="italics"/>Numero xli. </s>

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<s>Quid tu ad i&longs;ta <lb/>igitur? </s>

<s>Dicis me, <emph type="italics"/>non &longs;olùm re&longs;pectum partium ad parteis <lb/>temporis exigere, quas neque ego, neque alius qui&longs;quam aßi<lb/>gnare poßit: &longs;ed tempora etiam illis ad&longs;cribere, quæ nullo <lb/>modo ip&longs;is conuenire non ignorem.<emph.end type="italics"/> Verumtamen, quæ<lb/>&longs;tio non e&longs;t de eo, quod ego, aut alius præ&longs;tare po&longs;&longs;i<lb/>mus, aut non po&longs;&longs;imus, in a&longs;&longs;ignandis temporibus, quæ <lb/>partibus quibu&longs;que conueniant: quanquam Galileum <lb/>quidem imitatus, &longs;umpto quocumque tempore primæ <lb/>parti debito, a&longs;&longs;ignaui tempus, quod exigitur ad &longs;ecun<lb/>dam, & quod ad vtrumque primæ partis dimidium, <lb/>paratus idem prorsùs præ&longs;tare circa quælibet tempora, <lb/>quarumcum que voles partium cætetarum, iuxta gene<lb/>rale &longs;cilicet Effatum, quod articulo <expan abbr="Re&longs;põ&longs;ionis">Re&longs;pon&longs;ionis</expan> XXXVI. <lb/>retuli, & in quod nihil fuit, quod à te obiiceretur. <lb/></s>

<s>Dicis me, <emph type="italics"/>non &longs;olùm re&longs;pectum partium ad parteis <lb/>temporis exigere, quas neque ego, neque alius qui&longs;quam aßi<lb/>gnare poßit: &longs;ed tempora etiam illis ad&longs;cribere, quæ nullo <lb/>modo ip&longs;is conuenire non ignorem.<emph.end type="italics"/></s><s> Verumtamen, quæ<lb/>&longs;tio non e&longs;t de eo, quod ego, aut alius præ&longs;tare po&longs;&longs;i<lb/>mus, aut non po&longs;&longs;imus, in a&longs;&longs;ignandis temporibus, quæ <lb/>partibus quibu&longs;que conueniant: quanquam Galileum <lb/>quidem imitatus, &longs;umpto quocumque tempore primæ <lb/>parti debito, a&longs;&longs;ignaui tempus, quod exigitur ad &longs;ecun<lb/>dam, & quod ad vtrumque primæ partis dimidium, <lb/>paratus idem prorsùs præ&longs;tare circa quælibet tempora, <lb/>quarumcum que voles partium cætetarum, iuxta gene<lb/>rale &longs;cilicet Effatum, quod articulo <expan abbr="Re&longs;põ&longs;ionis">Re&longs;pon&longs;ionis</expan> XXXVI. <lb/>retuli, & in quod nihil fuit, quod à te obiiceretur. <lb/></s>

<s>Non item e&longs;t quæ&longs;tio, an tempora quæ partibus ad&longs;cri<lb/>bo, ip&longs;is nullo modo conuenire ignorem, an &longs;ciam (&longs;cio <lb/>enim e&longs;&longs;e longè alià, prout ex citato moxloco intelligi <lb/>pote&longs;t) &longs;ed an ea ad&longs;cribam iuxta tua principia. </s>

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<s>Quidnam verò e&longs;t, <lb/>quod &longs;ubiungis? </s>

<s>I&longs;tud nimirùm: <emph type="italics"/>cùm ex tuis, &<emph.end type="italics"/> G<emph type="italics"/>a<lb/>lilei principiis dimidia parte primi temporis quarta pars tan<lb/>tum spatii &longs;uperior decurratur, & reliqua dimidia parte tem<lb/>poris tres inferiores spatii quadrantes ab&longs;oluantur.<emph.end type="italics"/> Sed <lb/>quæ&longs;tio heic non e&longs;t, quid Galileus, & ego &longs;entiamus: <lb/>ea de re enim &longs;atis iam con&longs;tat: verùm, an quod tibi <lb/>obiicio, &longs;it tuum, &longs;iue iuxta tua decreta, an non? </s>

<s>I&longs;tud nimirùm: <emph type="italics"/>cùm ex tuis, &<emph.end type="italics"/> G<emph type="italics"/>a<lb/>lilei principiis dimidia parte primi temporis quarta pars tan<lb/>tum spatii &longs;uperior decurratur, & reliqua dimidia parte tem<lb/>poris tres inferiores spatii quadrantes ab&longs;oluantur.<emph.end type="italics"/></s><s> Sed <lb/>quæ&longs;tio heic non e&longs;t, quid Galileus, & ego &longs;entiamus: <lb/>ea de re enim &longs;atis iam con&longs;tat: verùm, an quod tibi <lb/>obiicio, &longs;it tuum, &longs;iue iuxta tua decreta, an non? </s>

<s>Cùm <lb/>non fuerit, quod re&longs;ponderes, his tamen verbis con<lb/>clu&longs;i&longs;ti, <emph type="italics"/>Vide ergo, quid ex tam ab&longs;urda hypothe&longs;i conclu<lb/>dere poßis.<emph.end type="italics"/> Ego verò, <emph type="italics"/>Imò tuvide,<emph.end type="italics"/> inquam, <emph type="italics"/>quid ex hypo<lb/>the&longs;i tam ab&longs;urda, cum tua &longs;it, conclu&longs;erim, & ad conclu&longs;io<lb/>nem re&longs;ponde, &longs;i poßis.<emph.end type="italics"/> Pergis. </s>

<s>Cùm <lb/>non fuerit, quod re&longs;ponderes, his tamen verbis con<lb/>clu&longs;i&longs;ti, <emph type="italics"/>Vide ergo, quid ex tam ab&longs;urda hypothe&longs;i conclu<lb/>dere poßis.<emph.end type="italics"/></s><s> Ego verò, <emph type="italics"/>Imò tuvide,<emph.end type="italics"/> inquam, <emph type="italics"/>quid ex hypo<lb/>the&longs;i tam ab&longs;urda, cum tua &longs;it, conclu&longs;erim, & ad conclu&longs;io<lb/>nem re&longs;ponde, &longs;i poßis.<emph.end type="italics"/></s><s> Pergis. </s>

<s><emph type="italics"/>Vt verò etiam numero xlij. </s>

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<s>Cùm verò ip&longs;e &longs;olam iam attractricem <lb/>retineam, à qua continenter agente, & impre&longs;&longs;ione non <lb/>pereunte, acceleratio motus fiat; opinatis tu grauita<lb/>tem ad accelerationem nihil facere: &longs;ed inalteratam &longs;ic <lb/>per&longs;euerare, vt ex &longs;e motum vniformem, & æquabilem <lb/>faciat: &longs;olum autem aërem &longs;e&longs;e à tergo concludentem <lb/>e&longs;&longs;e accelerationis cau&longs;&longs;am. </s>

<s>Heinc nempe &longs;uperiùs tua <lb/>hæc verba fuerunt. <emph type="italics"/>Acceleratio omnis à medio &longs;olo e&longs;t: vn<lb/>de de&longs;cen&longs;us in vacuo &longs;ui &longs;emper &longs;imilis, atque vniformis <lb/>ex&longs;i&longs;teret: &longs;icut tunc quoque tota cau&longs;&longs;a de&longs;cen&longs;us, nempe graui<lb/>tas, &longs;emper eadem, ac &longs;ui &longs;imilis per &longs;eueraret.<emph.end type="italics"/> Itaque cùm <lb/>di&longs;&longs;en&longs;us &longs;it circa tuam vtramque cau&longs;&longs;am, ecce de <lb/>vtraque pauca hæc attingo. </s><pb pagenum="215"/>

<s>Heinc nempe &longs;uperiùs tua <lb/>hæc verba fuerunt. <emph type="italics"/>Acceleratio omnis à medio &longs;olo e&longs;t: vn<lb/>de de&longs;cen&longs;us in vacuo &longs;ui &longs;emper &longs;imilis, atque vniformis <lb/>ex&longs;i&longs;teret: &longs;icut tunc quoque tota cau&longs;&longs;a de&longs;cen&longs;us, nempe graui<lb/>tas, &longs;emper eadem, ac &longs;ui &longs;imilis per &longs;eueraret.<emph.end type="italics"/></s><s> Itaque cùm <lb/>di&longs;&longs;en&longs;us &longs;it circa tuam vtramque cau&longs;&longs;am, ecce de <lb/>vtraque pauca hæc attingo. </s><pb pagenum="215"/>

<s>Et ab Aëre quidem vt incipiam, non immanifc&longs;tum <lb/>videtur ip&longs;um nihil po&longs;&longs;e ad accelerationem conferre; <lb/>quin-etiam potiùs officere, tantum abe&longs;t, vt aër &longs;olus <lb/>&longs;it accelerationis cau&longs;&longs;a. </s>

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<s>Sed <lb/>& quæ&longs;o te, nonne ip&longs;e fateris re&longs;i&longs;tere aërem? </s>

<s>Dixi&longs;ti <pb pagenum="216"/>videlicet <emph type="italics"/>motum, eiu&longs;que accelerationem effectum e&longs;&longs;e <lb/>Phy&longs;icum, qui per parteis maiores, aut minores pro ratione <lb/>ponderis, & re&longs;i&longs;tentia medij metiendus videatur.<emph.end type="italics"/> Igitut <lb/>aër non tantum re&longs;i&longs;tit &longs;upernè, vt omnes admittunt, <lb/>&longs;ed etiam infernè, vt tu quoque admittis (& certè vi<lb/>detur tantò maior e&longs;&longs;e debere infernè re&longs;i&longs;tentia, quan<lb/>tò aër cra&longs;&longs;ior e&longs;t, & propter terram &longs;uppo&longs;itam diffici<lb/>liùs diffundi, ac dilabi pote&longs;t; &longs;ed hoc parùm e&longs;t.) Aut <lb/>ergo re&longs;i&longs;tentia aëris infernè e&longs;t maior, quàm impul&longs;io <lb/>&longs;upernè, aut æqualis, aut minor. </s>

<s>Dixi&longs;ti <pb pagenum="216"/>videlicet <emph type="italics"/>motum, eiu&longs;que accelerationem effectum e&longs;&longs;e <lb/>Phy&longs;icum, qui per parteis maiores, aut minores pro ratione <lb/>ponderis, & re&longs;i&longs;tentia medij metiendus videatur.<emph.end type="italics"/></s><s> Igitut <lb/>aër non tantum re&longs;i&longs;tit &longs;upernè, vt omnes admittunt, <lb/>&longs;ed etiam infernè, vt tu quoque admittis (& certè vi<lb/>detur tantò maior e&longs;&longs;e debere infernè re&longs;i&longs;tentia, quan<lb/>tò aër cra&longs;&longs;ior e&longs;t, & propter terram &longs;uppo&longs;itam diffici<lb/>liùs diffundi, ac dilabi pote&longs;t; &longs;ed hoc parùm e&longs;t.) Aut <lb/>ergo re&longs;i&longs;tentia aëris infernè e&longs;t maior, quàm impul&longs;io <lb/>&longs;upernè, aut æqualis, aut minor. </s>

<s>Si dicas maiorem; <lb/>igitur motus rei cadentis non accelerationem ab aëre, <lb/>&longs;ed retardationem patietur. </s>

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<s>Cùm tu igitur duas illas <emph type="italics"/>de Motu impre&longs;&longs;o à Motore <lb/>tran&longs;lato<emph.end type="italics"/> à me con&longs;criptas Epi&longs;tolas reuocaueris in exa<lb/>men; po&longs;tquàm exhibui&longs;ti in&longs;ignia &longs;ingularis bene<lb/>uolentiæ, & comitatis te&longs;timonia: tum explicare ag<lb/>gre&longs;&longs;us es, quæ improba&longs;ti circa Priorem. </s>

<s>Imprimis <lb/>verò, quòd comprobârim illud Galilei decretum, <lb/><emph type="italics"/>Motum corporum decidentium &longs;ic accelerari, vt &longs;uperatæ<emph.end type="italics"/><pb pagenum="229"/><emph type="italics"/>æqualibus temporibus spatia incre&longs;cant, &longs;icut numeri ab vni<lb/>tate impares,<emph.end type="italics"/> dicis me, <emph type="italics"/>Si illud quidem decretum in examen <lb/>adduxi&longs;&longs;em, per&longs;pecturum fui&longs;&longs;e & fal&longs;um, & Paralogi&longs;mo <lb/>euidente confirmatum.<emph.end type="italics"/> Ego verò neque inficior hallu<lb/>cinari potui&longs;&longs;e me; neque me habeo adeò &longs;olertem, vt <lb/>Paralogi&longs;mum à te in&longs;inuatum etiamnùm pervideam. <lb/></s>

<s>Imprimis <lb/>verò, quòd comprobârim illud Galilei decretum, <lb/><emph type="italics"/>Motum corporum decidentium &longs;ic accelerari, vt &longs;uperatæ<emph.end type="italics"/><pb pagenum="229"/><emph type="italics"/>æqualibus temporibus spatia incre&longs;cant, &longs;icut numeri ab vni<lb/>tate impares,<emph.end type="italics"/> dicis me, <emph type="italics"/>Si illud quidem decretum in examen <lb/>adduxi&longs;&longs;em, per&longs;pecturum fui&longs;&longs;e & fal&longs;um, & Paralogi&longs;mo <lb/>euidente confirmatum.<emph.end type="italics"/></s><s> Ego verò neque inficior hallu<lb/>cinari potui&longs;&longs;e me; neque me habeo adeò &longs;olertem, vt <lb/>Paralogi&longs;mum à te in&longs;inuatum etiamnùm pervideam. <lb/></s>

<s>Peruelle proinde ip&longs;um o&longs;tendi&longs;&longs;es, atque adeò &longs;ubin<lb/>dica&longs;&longs;es, qua ergo alia proportione accelerationem de<lb/>cidentium fieri, aut experiundo notaueris, aut deduxe<lb/>ris demon&longs;trando. </s>

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<s>Quod <lb/>ad rationem; quia nondum per&longs;pexi, quem ip&longs;e te ais <lb/>per&longs;pexi&longs;&longs;e Paralogi&longs;mum: ideo <foreign lang="greek">e/pe/xw</foreign>, expectoque, <lb/>quou&longs;que eximias lucubrationes vulgaueris, quas pol<lb/>liceris aduer&longs;us ea, quæ à Galileo de Motu edi&longs;&longs;eruntur <lb/>Dialogo tertio. </s>

<s>III. Deinde, cùm ip&longs;e elicio, <emph type="italics"/>Vim impellentem mobils <lb/>&longs;ur&longs;um, non modò non de&longs;trui, &longs;ed ne vlla quidem ratione im<lb/>minui à vi impellente in latus,<emph.end type="italics"/> dicis, <emph type="italics"/>Me non inuenturum <lb/>fidem apud harum rerum peritos, apud quos receptum e&longs;t, Mo<lb/>bile quodcumque duobus motibus in diuer&longs;as partes actum, <lb/>tantò &longs;egniùs deferri in vnum terminum, quantò fortiùs is <lb/>alterum tendit.<emph.end type="italics"/> Ego verò, cui cordi e&longs;t, non tam peri<lb/>tis quid per&longs;uadere, quàm addi&longs;cere ab ijs aliquid; id <lb/>expeto &longs;olùm, vt per&longs;picuè doceant, quod po&longs;&longs;im ca<lb/>pere per&longs;picuè. </s>

<s>III. Deinde, cùm ip&longs;e elicio, <emph type="italics"/>Vim impellentem mobils <lb/>&longs;ur&longs;um, non modò non de&longs;trui, &longs;ed ne vlla quidem ratione im<lb/>minui à vi impellente in latus,<emph.end type="italics"/> dicis, <emph type="italics"/>Me non inuenturum <lb/>fidem apud harum rerum peritos, apud quos receptum e&longs;t, Mo<lb/>bile quodcumque duobus motibus in diuer&longs;as partes actum, <lb/>tantò &longs;egniùs deferri in vnum terminum, quantò fortiùs is <lb/>alterum tendit.<emph.end type="italics"/></s><s> Ego verò, cui cordi e&longs;t, non tam peri<lb/>tis quid per&longs;uadere, quàm addi&longs;cere ab ijs aliquid; id <lb/>expeto &longs;olùm, vt per&longs;picuè doceant, quod po&longs;&longs;im ca<lb/>pere per&longs;picuè. </s>

<s>Et, quod &longs;pectat quidem ad tuum <lb/>Effatum, &longs;i dum Mobile reipsâ mouetur, di&longs;iunctum<lb/>que e&longs;t à motore, veluti lapis per aërem, &longs;uperueniat <lb/>vis aliqua, vt venti, aut manus, quæ ip&longs;um deflectat: <lb/>agno&longs;co eo ca&longs;u vim primò impre&longs;&longs;am imminutum iri, <lb/>& mobile, ad quem terminum de&longs;tinabatur, non per<lb/>uenturum. </s>

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<s>Seligis con&longs;equenter nonnulla, quæ dicis <emph type="italics"/>me <lb/>nimia facilitate admittere, quæque viris eruditis, ac pijs minùs <lb/>placitura videantur.<emph.end type="italics"/> Quo &longs;anè loco, &longs;i aliquid ex ijs, quæ <lb/>admitto, pietati repugnet, id prorsùs deuoueo; vt <lb/>quod imprudenti, neque repugnantiam intelligenti <lb/>&longs;e&longs;e obtrudat; agno&longs;cóque te &longs;ummopere lenem, dum <lb/><emph type="italics"/>nimiam<emph.end type="italics"/> potiùs <emph type="italics"/>facilitatem,<emph.end type="italics"/> quàm <emph type="italics"/>temeritatem,<emph.end type="italics"/> aut aliud <lb/>quid dicis: quanquam quid tale hactenus, mihi acci<lb/>derit, non peruideo. </s>

<s>Seligis con&longs;equenter nonnulla, quæ dicis <emph type="italics"/>me <lb/>nimia facilitate admittere, quæque viris eruditis, ac pijs minùs <lb/>placitura videantur.<emph.end type="italics"/></s><s> Quo &longs;anè loco, &longs;i aliquid ex ijs, quæ <lb/>admitto, pietati repugnet, id prorsùs deuoueo; vt <lb/>quod imprudenti, neque repugnantiam intelligenti <lb/>&longs;e&longs;e obtrudat; agno&longs;cóque te &longs;ummopere lenem, dum <lb/><emph type="italics"/>nimiam<emph.end type="italics"/> potiùs <emph type="italics"/>facilitatem,<emph.end type="italics"/> quàm <emph type="italics"/>temeritatem,<emph.end type="italics"/> aut aliud <lb/>quid dicis: quanquam quid tale hactenus, mihi acci<lb/>derit, non peruideo. </s>

<s>Ad cætera, quæ merè &longs;ùnt na<lb/>turalia, quod attinet; non nego quidem ea me phi<lb/>lo&longs;ophari libertate, vt non vni alicui Sectæ erudito<lb/>rum, vt vocas, hære&longs;cam: &longs;ed &longs;i quid alij aut dicant, <lb/>aut dicere po&longs;&longs;e videantur, quod magis probabile &longs;it, <lb/>id veluti magis probabile &longs;equar: at quoniam &longs;olo <lb/>veritatis amore ita comparor, non e&longs;t, cur verear, <emph type="italics"/>ne <lb/>quid nimis.<emph.end type="italics"/> Neque verò is &longs;um, qui Platonis, Ari&longs;tote<lb/>li&longs;que (aut &longs;i quos putas e&longs;&longs;e illis eruditiores) &longs;annis <lb/>mouear: ac præ&longs;ertim, cùm ip&longs;i me voce, factóque do<lb/>cuerint, <emph type="italics"/>Rem &longs;anctam e&longs;&longs;e, nihil habere &longs;tudio veritatis an<lb/>tiquius.<emph.end type="italics"/> Non &longs;anè, quòd ego proptereà &longs;equi me <pb pagenum="236"/>ip&longs;am veritatem, tanquam à me certò arreptam, pro<lb/>&longs;itear: &longs;ed quòd omnibus exploratis, & &longs;equutus id, <lb/>quod &longs;imilitudinem maiorem cum ip&longs;a habere mihi <lb/>vi&longs;um e&longs;t, tum videar mihi cumulatè eo defunctus of<lb/>ficio, quod exigit ip&longs;a eius reuerentia. </s>

<s>Ad cætera, quæ merè &longs;ùnt na<lb/>turalia, quod attinet; non nego quidem ea me phi<lb/>lo&longs;ophari libertate, vt non vni alicui Sectæ erudito<lb/>rum, vt vocas, hære&longs;cam: &longs;ed &longs;i quid alij aut dicant, <lb/>aut dicere po&longs;&longs;e videantur, quod magis probabile &longs;it, <lb/>id veluti magis probabile &longs;equar: at quoniam &longs;olo <lb/>veritatis amore ita comparor, non e&longs;t, cur verear, <emph type="italics"/>ne <lb/>quid nimis.<emph.end type="italics"/></s><s> Neque verò is &longs;um, qui Platonis, Ari&longs;tote<lb/>li&longs;que (aut &longs;i quos putas e&longs;&longs;e illis eruditiores) &longs;annis <lb/>mouear: ac præ&longs;ertim, cùm ip&longs;i me voce, factóque do<lb/>cuerint, <emph type="italics"/>Rem &longs;anctam e&longs;&longs;e, nihil habere &longs;tudio veritatis an<lb/>tiquius.<emph.end type="italics"/></s><s> Non &longs;anè, quòd ego proptereà &longs;equi me <pb pagenum="236"/>ip&longs;am veritatem, tanquam à me certò arreptam, pro<lb/>&longs;itear: &longs;ed quòd omnibus exploratis, & &longs;equutus id, <lb/>quod &longs;imilitudinem maiorem cum ip&longs;a habere mihi <lb/>vi&longs;um e&longs;t, tum videar mihi cumulatè eo defunctus of<lb/>ficio, quod exigit ip&longs;a eius reuerentia. </s>

<s>Ex quo pro<lb/>inde &longs;it, vt &longs;i illi quidem, quos eruditos intelligis, ip<lb/>&longs;am veritatem facerent apertam, nemo me citiùs non <lb/>pedibus modò, &longs;ed manibus quoque, & corpore toto <lb/>iret, prorueretque in eorum &longs;ententiam: verùm quia <lb/>dum &longs;uis inhærent principiis, nihilo nobis veritatem <lb/>reuclatiorem faciunt: quid di&longs;pliceat, &longs;i à me aliæ, at<lb/>que aliæ pul&longs;entur fores? </s>

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<s>Idem porrò dicendum e&longs;t circa id, quod miraris <lb/><emph type="italics"/>de volutione globi &longs;upra planum.<emph.end type="italics"/> Neque enim dixi il<lb/>lam e&longs;&longs;e ab&longs;olutè naturalem, qua&longs;i nullo modo ab alio <lb/>&longs;it: &longs;ed &longs;olùm comparatione motus, quo globus per <lb/>aërem tran&longs;adigitur, quique &longs;it præ&longs;ertim dicendus <lb/>violentus. </s>

<s>Idem porrò dicendum e&longs;t circa id, quod miraris <lb/><emph type="italics"/>de volutione globi &longs;upra planum.<emph.end type="italics"/></s><s> Neque enim dixi il<lb/>lam e&longs;&longs;e ab&longs;olutè naturalem, qua&longs;i nullo modo ab alio <lb/>&longs;it: &longs;ed &longs;olùm comparatione motus, quo globus per <lb/>aërem tran&longs;adigitur, quique &longs;it præ&longs;ertim dicendus <lb/>violentus. </s>

<s>Scilicet globus, quà globus e&longs;t, &longs;eu ex figuræ <lb/>&longs;uæ natura, ad volutionem e&longs;t comparatus, imò com<lb/>parati&longs;&longs;imus; volutionem, inquam, quæ peragitur non <lb/>modò in loco, &longs;eu &longs;upra axem &longs;u&longs;tentantem, vt Ari&longs;to<lb/>teles admittit: &longs;ed maximè etiam per locum, &longs;eu &longs;u<lb/>pra planum horizontale, quod & &longs;u&longs;tentat, & nihil <lb/>re&longs;i&longs;tit; cùm aliunde tamen ex eodem Ari&longs;totele, nul<lb/>lum &longs;it corpus globo ineptius ad motum <foreign lang="greek">ei)s <gap/> w<gap/>e\n</foreign><lb/><emph type="italics"/>antror&longs;um,<emph.end type="italics"/> & qualis e&longs;t eorum, quæ per &longs;e mouentur. <lb/></s>

<s>Heinc proinde &longs;it, vt de globo &longs;upra planum con&longs;titu<lb/>to liceat dicere, illum ad motum &longs;upra planum, &longs;eu ad <lb/>volutionem ita propendere, vt minimo pul&longs;u, ac ve<lb/>luti nutu talem motum &longs;ubeat, ip&longs;oque ita afficiatur, <lb/>vt depo&longs;iturus illum nunquam &longs;it, ni&longs;i planum defece<lb/>rit, aut facta aliunde fuerit re&longs;i&longs;tentia. </s>

<s>Ni&longs;i verò ille <lb/>motus non e&longs;t dicendus maximè &longs;ecundum mobilis <lb/>naturam, qui &longs;emel inditus, &longs;it ex &longs;e perpetuus, ac præ<lb/>tereà æquabilis, vniu&longs;que tenoris? <emph type="italics"/>At,<emph.end type="italics"/> inquis, <emph type="italics"/>natu-<emph.end type="italics"/><pb pagenum="239"/><emph type="italics"/>ralis nondicitur motus, ni&longs;i ab interno principio, ip&longs;aque rei <lb/>natura effectiuè procedat.<emph.end type="italics"/> Sed quid-ni ille quoque di<lb/>catur, qui ab externo e&longs;t, effectiuéque ab alio e&longs;t; &longs;i mo<lb/>dò <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> mobilis <expan abbr="naturã">naturam</expan>, ac di&longs;po&longs;itionem, non ve<lb/>rò contra illam &longs;it; & qua&longs;i fiat, quod dicitur, <foreign lang="greek"><gap/>sont<gap/><lb/>o)t<gap/>w<gap/><gap/>n</foreign>; <emph type="italics"/>in&longs;tigare iam fe&longs;tinantem?<emph.end type="italics"/> Et nonne ip&longs;e <lb/>fateris cum Ari&longs;totele motum rerum grauium e&longs;&longs;e na<lb/>turalem, quem ille tamen vult ab externo, non ab in<lb/>terno e&longs;&longs;e principio? </s>

<s>Ni&longs;i verò ille <lb/>motus non e&longs;t dicendus maximè &longs;ecundum mobilis <lb/>naturam, qui &longs;emel inditus, &longs;it ex &longs;e perpetuus, ac præ<lb/>tereà æquabilis, vniu&longs;que tenoris? <emph type="italics"/>At,<emph.end type="italics"/> inquis, <emph type="italics"/>natu-<emph.end type="italics"/><pb pagenum="239"/><emph type="italics"/>ralis nondicitur motus, ni&longs;i ab interno principio, ip&longs;aque rei <lb/>natura effectiuè procedat.<emph.end type="italics"/></s><s> Sed quid-ni ille quoque di<lb/>catur, qui ab externo e&longs;t, effectiuéque ab alio e&longs;t; &longs;i mo<lb/>dò <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> mobilis <expan abbr="naturã">naturam</expan>, ac di&longs;po&longs;itionem, non ve<lb/>rò contra illam &longs;it; & qua&longs;i fiat, quod dicitur, <foreign lang="greek"><gap/>sont<gap/><lb/>o)t<gap/>w<gap/><gap/>n</foreign>; <emph type="italics"/>in&longs;tigare iam fe&longs;tinantem?<emph.end type="italics"/> Et nonne ip&longs;e <lb/>fateris cum Ari&longs;totele motum rerum grauium e&longs;&longs;e na<lb/>turalem, quem ille tamen vult ab externo, non ab in<lb/>terno e&longs;&longs;e principio? </s>

<s>Et nonne proinde eius verba <lb/>&longs;unt, <foreign lang="greek">t<gap/> e)p) a)/llou xinoum<gap/>o/wn, ta\ m_/) fu/s<gap/>, ta\ d<gap/><lb/><gap/>a\ fu/sin xi/n<gap/></foreign>; <emph type="italics"/>eorum, quæ ab alio mouentur, alia qui<lb/>dem naturâ, alia verò prater naturam moueri?<emph.end type="italics"/> Ac ad<lb/>uerti quidem, imò expre&longs;sè dixi, <emph type="italics"/>alias globi parteis deor<lb/>&longs;um tendere, alias &longs;ur&longs;um:<emph.end type="italics"/> &longs;ed & hoc ip&longs;um e&longs;t, quod fa<lb/>cere cen&longs;ui ad æquabilitatem motus; vt dum globus <lb/>non ampliùs &longs;ur&longs;um, quàm deorsùm, nec deorsùm, <lb/>quàm &longs;ursùm fertur, motusinterim ab&longs;que vlla aut ac<lb/>celeratione, aut retardatione per&longs;eueret. </s>

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<s>Dicis po&longs;teà, <emph type="italics"/>forè, vt mihi Eruditi omnes conce<lb/>dant accelerationem e&longs;&longs;e violentam, &longs;i illam, vt quid &longs;uper<lb/>ueniens, mente &longs;ecernamus ab ip&longs;o de&longs;cen&longs;u.<emph.end type="italics"/> Non e&longs;t porrò <lb/>cur dubites, quin ip&longs;e quoque mente &longs;ecernam motum <lb/>illum &longs;implicem, quo lapis fertur deor&longs;um, quemque <lb/>tu de&longs;cen&longs;um appellas, ab omnibus, qui &longs;uperueniunt, <lb/>giadibus accelerationis. </s>

<s>Dicis po&longs;teà, <emph type="italics"/>forè, vt mihi Eruditi omnes conce<lb/>dant accelerationem e&longs;&longs;e violentam, &longs;i illam, vt quid &longs;uper<lb/>ueniens, mente &longs;ecernamus ab ip&longs;o de&longs;cen&longs;u.<emph.end type="italics"/></s><s> Non e&longs;t porrò <lb/>cur dubites, quin ip&longs;e quoque mente &longs;ecernam motum <lb/>illum &longs;implicem, quo lapis fertur deor&longs;um, quemque <lb/>tu de&longs;cen&longs;um appellas, ab omnibus, qui &longs;uperueniunt, <lb/>giadibus accelerationis. </s>

<s>Quippe id abunde expre&longs;&longs;i, <lb/>cùm dixi <emph type="italics"/>eum motum, &longs;eclu&longs;a acceleratione, fore ex &longs;e æqua<lb/>bilem, &longs;ed imperceptibilem tamen, ob incredibilem &longs;egnitiem.<emph.end type="italics"/><lb/>Non e&longs;t proinde etiam, cur hæreas, quin illum e&longs;&longs;e na<lb/>turalem, & &longs;ine reluctatione agno&longs;cam; quippe qui <lb/>eum faciam, quantum e&longs;t ex &longs;e, æquabilem, perpetuum, <lb/>ac talem, qui &longs;it imprimendus etiam lapidi ex&longs;i&longs;tenti <lb/>in vacuo, vbi mobile nullam habet ad motum repu<lb/>gnantiam, quocumque ver&longs;um tandem agatur: verum <lb/>quòd eiu&longs;modi motus cen&longs;eri naturalis po&longs;&longs;it, non id<lb/>circò cen&longs;eo ca&longs;um lapidis habendum e&longs;&longs;e naturalem. <lb/></s>

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<s>Et, qui fieri pote&longs;t, vt grauitas <lb/>dicatur e&longs;&longs;e organum internæ naturæ, ac effectiuum <lb/>motus deorsùm cùm grauitas tota, & motus totu ob<lb/>&longs;eruabilis procedat à cau&longs;&longs;a externa? </s>

<s>Heinc dum re<lb/>quiris, <emph type="italics"/>quid ab&longs;urdum, impoßibileve ea in re ag<gap/>o<gap/>cam?<emph.end type="italics"/><lb/>Sanè vel hoc vnum di<gap/>i&longs;&longs;e, inculca&longs;&longs;e ve potiùs, e&longs;t la<lb/>tis. <emph type="italics"/>Tellus ip&longs;a,<emph.end type="italics"/> inquis, <emph type="italics"/>&longs;i loco tantisper dimoueatur, vt in <lb/>vehementioribus eius commotionibus, à qua alia Tellure in <lb/>pri&longs;tinum locum retrahitur?<emph.end type="italics"/> Sed ego quidem nondum <lb/>accepi Terram v&longs;quam &longs;ic contremui&longs;&longs;e, &longs;eu vehemen<lb/>tem adeò illius commotionem fui&longs;&longs;e, vt mota loco tota <lb/>fuerit (ni&longs;i fortè tremorem illum, qui contigit Chri&longs;to <lb/>patiente, &longs;ed pr&ecedil;ter naturæ tamen ordinem, intellexeris) <lb/>tuque ip&longs;e &longs;tatim pò&longs;t dicis <emph type="italics"/>illam &longs;ic affectare &longs;uum <expan abbr="loc&utilde;">locum</expan>, vt <lb/>nullis <expan abbr="cõcu&longs;&longs;a">concu&longs;&longs;a</expan> motibus ab eo dimoueri valeat.<emph.end type="italics"/> Quare <expan abbr="c&utilde;">cum</expan> omnes <lb/>Terræ tremores particulares e&longs;&longs;e videantur; quæ Terræ <lb/>vis retrahit glebas, retrahet etiam maiores parteis, quæ <lb/>aliqua vehementiore &longs;ucce&longs;&longs;ione fuerint commotæ. </s>

<s>Heinc dum re<lb/>quiris, <emph type="italics"/>quid ab&longs;urdum, impoßibileve ea in re ag<gap/>o<gap/>cam?<emph.end type="italics"/><lb/>Sanè vel hoc vnum di<gap/>i&longs;&longs;e, inculca&longs;&longs;e ve potiùs, e&longs;t la<lb/>tis. <emph type="italics"/>Tellus ip&longs;a,<emph.end type="italics"/> inquis, <emph type="italics"/>&longs;i loco tantisper dimoueatur, vt in <lb/>vehementioribus eius commotionibus, à qua alia Tellure in <lb/>pri&longs;tinum locum retrahitur?<emph.end type="italics"/> Sed ego quidem nondum <lb/>accepi Terram v&longs;quam &longs;ic contremui&longs;&longs;e, &longs;eu vehemen<lb/>tem adeò illius commotionem fui&longs;&longs;e, vt mota loco tota <lb/>fuerit (ni&longs;i fortè tremorem illum, qui contigit Chri&longs;to <lb/>patiente, &longs;ed pr&ecedil;ter naturæ tamen ordinem, intellexeris) <lb/>tuque ip&longs;e &longs;tatim pò&longs;t dicis <emph type="italics"/>illam &longs;ic affectare &longs;uum <expan abbr="loc&utilde;">locum</expan>, vt <lb/>nullis <expan abbr="cõcu&longs;&longs;a">concu&longs;&longs;a</expan> motibus ab eo dimoueri valeat.<emph.end type="italics"/></s><s> Quare <expan abbr="c&utilde;">cum</expan> omnes <lb/>Terræ tremores particulares e&longs;&longs;e videantur; quæ Terræ <lb/>vis retrahit glebas, retrahet etiam maiores parteis, quæ <lb/>aliqua vehementiore &longs;ucce&longs;&longs;ione fuerint commotæ. </s>

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<s>Subdis, <emph type="italics"/>Putas enim di&longs;rupto fornice, totàque <lb/>&longs;i placet, Terrâin arenulas redactà, eam non confluxuram ad <lb/>centrum?<emph.end type="italics"/> Ego quidem non puto, qui putare non po&longs;<lb/>&longs;unt monteis, aliaque Terræ loca di&longs;rumpi, inque are<lb/>nulas redigi, vt compleant &longs;uppo&longs;itas &longs;pecus, crypta&longs;<lb/>que aut aqua, aut aëre plenas: idque, ni&longs;i fortè, vt dixi, <lb/>&longs;upponas eandem vim deterere Terram in arenulas, <lb/>quæ excauárit fornicem; quo ca&longs;u, quæ e&longs;&longs;et in arenu<lb/>lis &longs;uper&longs;tes magnetica vis &longs;ic eas mutuò pelliceret, vt & <lb/>in crypten confluerent, & aquam, aëremve inde abi<lb/>gerent; &longs;i modò &longs;uppo&longs;ueris quoque rimas, exitumve <lb/>patere. </s>

<s>Pergis adhûc, <emph type="italics"/>confluerent &longs;anè, & quidem non <lb/>ab alio corpore attracta, &longs;ed &longs;ponte naturæ, & à principio <lb/>interno, atque innato.<emph.end type="italics"/> Verumtamen confluere po&longs;&longs;ent <lb/>attractæ à &longs;einuicem, vt & iam confluunt ferri ramen<lb/>ta, quæ magneticam combiberunt vim. </s>

<s>Pergis adhûc, <emph type="italics"/>confluerent &longs;anè, & quidem non <lb/>ab alio corpore attracta, &longs;ed &longs;ponte naturæ, & à principio <lb/>interno, atque innato.<emph.end type="italics"/></s><s> Verumtamen confluere po&longs;&longs;ent <lb/>attractæ à &longs;einuicem, vt & iam confluunt ferri ramen<lb/>ta, quæ magneticam combiberunt vim. </s>

<s>Concludis, <lb/>C<emph type="italics"/>ur de cæteris igitur grauibus idem &longs;imili ratione non <lb/>dicatur?<emph.end type="italics"/> Dico, quia fiunt in cæteris &longs;en&longs;ibiliora experi<lb/>menta, ex quibus liceat aliquid veri&longs;imilius coniectari. </s>

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<s>In&longs;ectaris deinde Magneticam illam, &longs;eu <lb/>attractricem Terræ vim; opinari&longs;que <emph type="italics"/>me ridere in &longs;inu, <lb/>dum inui&longs;ibileis vncinos, harpagones, chelas, funei&longs;que ten&longs;os, <lb/>& tractorios fingo.<emph.end type="italics"/> Sed quod me quidem attinet, non <lb/>diuendo &longs;anè ha&longs;ce meas commentationes, &longs;eu vt antè <pb pagenum="255"/>dicebam, nugas, vt quidpiam germanum, ac indu<lb/>bium; at &longs;impliciùs ago, quàm vt rideam; quippe me <lb/>potiùs mi&longs;eret natiuæ imbecillitatis, cùm nihil ha<lb/>beam præclarius, quo meam, aut alterius &longs;ciendi auidi<lb/>tatem pa&longs;cam. </s>

<s>In&longs;ectaris deinde Magneticam illam, &longs;eu <lb/>attractricem Terræ vim; opinari&longs;que <emph type="italics"/>me ridere in &longs;inu, <lb/>dum inui&longs;ibileis vncinos, harpagones, chelas, funei&longs;que ten&longs;os, <lb/>& tractorios fingo.<emph.end type="italics"/></s><s> Sed quod me quidem attinet, non <lb/>diuendo &longs;anè ha&longs;ce meas commentationes, &longs;eu vt antè <pb pagenum="255"/>dicebam, nugas, vt quidpiam germanum, ac indu<lb/>bium; at &longs;impliciùs ago, quàm vt rideam; quippe me <lb/>potiùs mi&longs;eret natiuæ imbecillitatis, cùm nihil ha<lb/>beam præclarius, quo meam, aut alterius &longs;ciendi auidi<lb/>tatem pa&longs;cam. </s>

<s>Obiicis, <emph type="italics"/>non e&longs;&longs;e, cur magnetieam ferri <lb/>vulgò dictam attractionem in exemplum adducam; quòd <lb/>Magnes, & &longs;errum non &longs;ictis illis meis hurpagonibus, aut <lb/>inui&longs;ibilibus catenis, qua&longs;i vi adducta; &longs;ed vtrumque &longs;ponte <lb/>naturæ incitata in mutuos amplexus accurrant.<emph.end type="italics"/> Id verò <lb/>&longs;anè per-eleganter; &longs;ed quid mihi facias, qui &longs;im ita <lb/>hebes, vt vim vocibus &longs;ubiectam non capiam. </s>

<s>Obiicis, <emph type="italics"/>non e&longs;&longs;e, cur magnetieam ferri <lb/>vulgò dictam attractionem in exemplum adducam; quòd <lb/>Magnes, & &longs;errum non &longs;ictis illis meis hurpagonibus, aut <lb/>inui&longs;ibilibus catenis, qua&longs;i vi adducta; &longs;ed vtrumque &longs;ponte <lb/>naturæ incitata in mutuos amplexus accurrant.<emph.end type="italics"/></s><s> Id verò <lb/>&longs;anè per-eleganter; &longs;ed quid mihi facias, qui &longs;im ita <lb/>hebes, vt vim vocibus &longs;ubiectam non capiam. </s>

<s>Dicis <lb/><emph type="italics"/>vtrumque accurrere in mutuos amplexus:<emph.end type="italics"/> &longs;ed hoc totum <lb/>effectus e&longs;t, de cuius cau&longs;&longs;a ambigitur. </s>

<s>Cau&longs;&longs;am ergo <lb/>interiicis, <emph type="italics"/>quia &longs;ponte naturæ incitantur.<emph.end type="italics"/> At cùm hæc vi<lb/>deatur e&longs;&longs;e generalis, inarti&longs;iciali&longs;que Re&longs;pon&longs;io, qua <lb/>ad omnia vtimur, quorum cau&longs;&longs;as ignoramus; non vi<lb/>deo profectò, quò tu, Vir acuti&longs;&longs;imus, collincees. </s>

<s>Cau&longs;&longs;am ergo <lb/>interiicis, <emph type="italics"/>quia &longs;ponte naturæ incitantur.<emph.end type="italics"/></s><s> At cùm hæc vi<lb/>deatur e&longs;&longs;e generalis, inarti&longs;iciali&longs;que Re&longs;pon&longs;io, qua <lb/>ad omnia vtimur, quorum cau&longs;&longs;as ignoramus; non vi<lb/>deo profectò, quò tu, Vir acuti&longs;&longs;imus, collincees. </s>

<s>Quippe <lb/>velle te dicere nihil aliud, quàm quod e&longs;t vulgò in ore <lb/>omnium, <emph type="italics"/>quia talis est rei natura; quia id &longs;ponte naturæ <lb/>fit; quia hoc natura ip&longs;a &longs;cit,<emph.end type="italics"/> cæteraque huiu&longs;modi; mihi <lb/>in animum non induco. </s>

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<s>An non, vt fiat incitatio, e&longs;&longs;e alia pars inci<lb/>tans, & alia incitata debet? </s>

<s>Idem certè mouere &longs;eip&longs;um, <lb/>ni&longs;i parteis habeat mouentem, & motam, cùm iis, quos <lb/>tu vocas Eruditos, aduer&longs;atur; tum communi etiam no<lb/>tioni repugnat, cui Ari&longs;toteles inhærens, impo&longs;&longs;ibilo <lb/>e&longs;&longs;e cen&longs;et, vt id &longs;eip&longs;um moueat, quod e&longs;t <foreign lang="greek">s<gap/>exe\<gap/></foreign>, <lb/><emph type="italics"/>continuum<emph.end type="italics"/> &longs;<gap/>u <emph type="italics"/>vniu&longs;modi, rigidum, inarticulatum.<emph.end type="italics"/> Non<lb/>ne verò &longs;unt huius generis tam Magnes, quàm Ferrum? <lb/></s>

<s>Idem certè mouere &longs;eip&longs;um, <lb/>ni&longs;i parteis habeat mouentem, & motam, cùm iis, quos <lb/>tu vocas Eruditos, aduer&longs;atur; tum communi etiam no<lb/>tioni repugnat, cui Ari&longs;toteles inhærens, impo&longs;&longs;ibilo <lb/>e&longs;&longs;e cen&longs;et, vt id &longs;eip&longs;um moueat, quod e&longs;t <foreign lang="greek">s<gap/>exe\<gap/></foreign>, <lb/><emph type="italics"/>continuum<emph.end type="italics"/> &longs;<gap/>u <emph type="italics"/>vniu&longs;modi, rigidum, inarticulatum.<emph.end type="italics"/></s><s> Non<lb/>ne verò &longs;unt huius generis tam Magnes, quàm Ferrum? <lb/></s>

<s>De altero ergo vt &longs;olùm loquamur, quænam in Ferro <lb/>parsincitans? </s>

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<s>Ac dum homo quidem trahitur ab homine, <lb/>communis e&longs;t notio, debere id fieri aut manu demi&longs;&longs;a, <lb/>aut chorda, aut vncino, aut alio &longs;imili in&longs;trumento: <lb/>cur & dum Ferrum à Magnete; putemus id fieri ab&longs;que <lb/>organo vllo intercepto? </s>

<s>XVIII. Sugillas, quòd hæc organa dicuntur à me <lb/><emph type="italics"/>in&longs;en&longs;ilia.<emph.end type="italics"/> Sed nempe, &longs;i &longs;en&longs;ilia e&longs;&longs;ent, in ijs di&longs;qui<lb/>rendis non laboraremus. </s>

<s>XVIII. Sugillas, quòd hæc organa dicuntur à me <lb/><emph type="italics"/>in&longs;en&longs;ilia.<emph.end type="italics"/></s><s> Sed nempe, &longs;i &longs;en&longs;ilia e&longs;&longs;ent, in ijs di&longs;qui<lb/>rendis non laboraremus. </s>

<s>Quod in&longs;en&longs;ilia verò dican<lb/>tur, non ideò tamen nulla &longs;unt; magi&longs;quam nulli non <lb/>&longs;unt vitales, animale&longs;que &longs;piritus, qui licet in&longs;en&longs;iles <lb/>&longs;int, cau&longs;&longs;æ &longs;unt tamen tot motuum, quos in animali<lb/>bus ob&longs;eruamus. </s>

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<s>Ni<lb/>hil, inquam, nece&longs;&longs;e e&longs;t, vt hæc, & &longs;imilia quædam <pb pagenum="261"/>pro&longs;equar, quandò tu ea rides, & iure forta&longs;&longs;is; &longs;ed <lb/>non ea ratione, quæ &longs;it mihi facta per&longs;picua. </s>

<s>Dicis, <lb/><emph type="italics"/>&longs;i vincula in&longs;en&longs;ilia &longs;unt, non e&longs;&longs;e cur timeam Magnetem &longs;entiri <lb/>à Ferro.<emph.end type="italics"/> At tu ludere, opinor, non vis ab æquiuoco: <lb/>qua&longs;i ego heic aliud appellem in&longs;en&longs;ibile, quàm quod <lb/>præ &longs;ui exilitate eiu&longs;modi e&longs;t, vt nec videri oculis, nec <lb/>palpari manibus po&longs;&longs;it? </s>

<s>Dicis, <lb/><emph type="italics"/>&longs;i vincula in&longs;en&longs;ilia &longs;unt, non e&longs;&longs;e cur timeam Magnetem &longs;entiri <lb/>à Ferro.<emph.end type="italics"/></s><s> At tu ludere, opinor, non vis ab æquiuoco: <lb/>qua&longs;i ego heic aliud appellem in&longs;en&longs;ibile, quàm quod <lb/>præ &longs;ui exilitate eiu&longs;modi e&longs;t, vt nec videri oculis, nec <lb/>palpari manibus po&longs;&longs;it? </s>

<s>Hoc certè modo ip&longs;as quo<lb/>que, quas vocant &longs;pecies intentionaleis, in&longs;en&longs;ibileis <lb/>dicimus; quatenus adeò &longs;ubtiles &longs;unt, vt videri ip&longs;æ ab <lb/>oculo nequeant. </s>

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<s>Rogas con&longs;equenter, <emph type="italics"/>Cur verear negraue deor&longs;um, & <lb/>Ferrum ad Magnetem, cæteraque corpora ad electrica, &longs;ine <lb/>&longs;en&longs;u concurrere non poßint?<emph.end type="italics"/> Sed quamobrem verear, ex<lb/>po&longs;itum habes. </s>

<s>XIX. Pergis, <emph type="italics"/>Ad hos certè effectus abundè &longs;ufficit re<lb/>bus omnibus à &longs;apientißimo earum opifice indita naturalis <lb/>inclinatio ad con&longs;eruationem, perfectionemque propriam; ad<lb/>de, &longs;i veles, ad con&longs;eruandum vniuer&longs;i ordinem, vt opus non<emph.end type="italics"/><pb pagenum="262"/><emph type="italics"/>&longs;it ad figmenta hæc tua confugere.<emph.end type="italics"/> Sed, Vir religio&longs;i&longs;&longs;ime, <lb/>inter nos non ambigitur, &longs;it-ne naturalis inclinatio <lb/>hi&longs;ce rebus ab Opifice &longs;apienti&longs;&longs;imo indita; quippe <lb/>quali&longs;cumque ea &longs;it, tam ego illam e&longs;&longs;e à Deo agno&longs;<lb/>co, & fateor, quam tu: &longs;ed hoc &longs;olùm ambigitur, qua<lb/>lis nimirùm illa &longs;it? </s>

<s>XIX. Pergis, <emph type="italics"/>Ad hos certè effectus abundè &longs;ufficit re<lb/>bus omnibus à &longs;apientißimo earum opifice indita naturalis <lb/>inclinatio ad con&longs;eruationem, perfectionemque propriam; ad<lb/>de, &longs;i veles, ad con&longs;eruandum vniuer&longs;i ordinem, vt opus non<emph.end type="italics"/><pb pagenum="262"/><emph type="italics"/>&longs;it ad figmenta hæc tua confugere.<emph.end type="italics"/></s><s> Sed, Vir religio&longs;i&longs;&longs;ime, <lb/>inter nos non ambigitur, &longs;it-ne naturalis inclinatio <lb/>hi&longs;ce rebus ab Opifice &longs;apienti&longs;&longs;imo indita; quippe <lb/>quali&longs;cumque ea &longs;it, tam ego illam e&longs;&longs;e à Deo agno&longs;<lb/>co, & fateor, quam tu: &longs;ed hoc &longs;olùm ambigitur, qua<lb/>lis nimirùm illa &longs;it? </s>

<s>An non repugnantia? </s>

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<s>Pergis, <emph type="italics"/>Finge vim à <lb/>te impre&longs;&longs;am e&longs;&longs;e eiu&longs;modi, quæ varijs impedimentis &longs;i&longs;ti qui<lb/>dem poßit, &longs;ed non de&longs;trui, aut etiam minui; an non &longs;ublato <lb/>impedimento motum redintegraret?<emph.end type="italics"/> Sed cùm damnes ip&longs;e <lb/>figmenta, quor&longs;um po&longs;tulas, vt illa adaugeam? </s>

<s>Ne<lb/>que enim vim po&longs;&longs;e &longs;i&longs;ti, quin &longs;imùl de&longs;truatur, pro<lb/>babile puto. <emph type="italics"/>Talis,<emph.end type="italics"/> inquis, <emph type="italics"/>omninò naturalis rerum in-<emph.end type="italics"/><pb pagenum="264"/><emph type="italics"/>clinatio e&longs;t; nec babes vnde impoßibilem, aut ip&longs;is etiam gra<lb/>uibus reipsâ inditam non e&longs;&longs;e concludas.<emph.end type="italics"/> Sed quamobrem <lb/>talem non habeam, ac eam præ&longs;ertim, quæ grauibus <lb/>indita e&longs;t; tum in ip&longs;is Epi&longs;tolis, tum in iis, quæ hacte<lb/>nus deduxi, inculcatum &longs;atis. </s>

<s>Ne<lb/>que enim vim po&longs;&longs;e &longs;i&longs;ti, quin &longs;imùl de&longs;truatur, pro<lb/>babile puto. <emph type="italics"/>Talis,<emph.end type="italics"/> inquis, <emph type="italics"/>omninò naturalis rerum in-<emph.end type="italics"/><pb pagenum="264"/><emph type="italics"/>clinatio e&longs;t; nec babes vnde impoßibilem, aut ip&longs;is etiam gra<lb/>uibus reipsâ inditam non e&longs;&longs;e concludas.<emph.end type="italics"/></s><s> Sed quamobrem <lb/>talem non habeam, ac eam præ&longs;ertim, quæ grauibus <lb/>indita e&longs;t; tum in ip&longs;is Epi&longs;tolis, tum in iis, quæ hacte<lb/>nus deduxi, inculcatum &longs;atis. </s>

<s>Vnde & cùm &longs;ic rogas, <lb/><emph type="italics"/>Cur eam ergo agno&longs;cere detrectas, & ad inania illa tua <lb/>figmenta recurris?<emph.end type="italics"/> Dictum &longs;atis, &longs;uperque e&longs;t, cur, & <lb/>qualis &longs;it, quam detrectem; & cur veritatis amore nul<lb/>lum non moueam lapidem, vt &longs;altem, &longs;i qua eius vm<lb/>bra, aut &longs;imilitudo occurrat, experiar. </s>

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<s>Quippe oportet non i&longs;ta modò atro <lb/>lapillo &longs;ubnotare, &longs;ed etiam quicquid dici pote&longs;t ab <lb/>vniuer&longs;is Phy&longs;icis, &longs;i nihil planè dicendum e&longs;t, quod <lb/>pari ratione non po&longs;&longs;it tran&longs;duci, parique modo acci<lb/>pi; vt &longs;i nihil di&longs;tinguendum foret inter id, quod fit <lb/>&longs;olis naturæ viribus, & id, quod fit, fierive pote&longs;t &longs;uper<lb/>naturali virtute. </s>

<s>Cau&longs;&longs;aris primùm, <emph type="italics"/>quòd Democriti, <lb/>& Epicuri Atomos tanto iam tempore à Regno Philo&longs;ophico <lb/>merito &longs;uo ex&longs;ulanteis, & tot iam &longs;æculorum, ac &longs;apientum <lb/>omnium præiudicio damnatas reuocare ab ex&longs;ilio, iterumque <lb/>in Academiam retrudere moliar.<emph.end type="italics"/> At ego nihil molior, <lb/>méque eum non habeo, qui retrudere, reuocareve ali<lb/>quid valeam: &longs;ed quia veritatis de&longs;iderio teneor, & il<lb/>lam tamen (&longs;eu hebetudo, &longs;eu inf&oelig;licitas mea e&longs;t) non <lb/>reperio in Philo&longs;ophico, quod tu dicis, Regno; idcircò <pb pagenum="268"/>exploro, num illi qui ex&longs;ulant, ac fortè merito non &longs;uo, <lb/>o&longs;tendere quædam ve&longs;tigia propiora, ac tutiora po&longs;<lb/>&longs;int. </s>

<s>Cau&longs;&longs;aris primùm, <emph type="italics"/>quòd Democriti, <lb/>& Epicuri Atomos tanto iam tempore à Regno Philo&longs;ophico <lb/>merito &longs;uo ex&longs;ulanteis, & tot iam &longs;æculorum, ac &longs;apientum <lb/>omnium præiudicio damnatas reuocare ab ex&longs;ilio, iterumque <lb/>in Academiam retrudere moliar.<emph.end type="italics"/></s><s> At ego nihil molior, <lb/>méque eum non habeo, qui retrudere, reuocareve ali<lb/>quid valeam: &longs;ed quia veritatis de&longs;iderio teneor, & il<lb/>lam tamen (&longs;eu hebetudo, &longs;eu inf&oelig;licitas mea e&longs;t) non <lb/>reperio in Philo&longs;ophico, quod tu dicis, Regno; idcircò <pb pagenum="268"/>exploro, num illi qui ex&longs;ulant, ac fortè merito non &longs;uo, <lb/>o&longs;tendere quædam ve&longs;tigia propiora, ac tutiora po&longs;<lb/>&longs;int. </s>

<s>Et Epicuro quidem, vt pote iuniori, te&longs;timonium <lb/>dicere Ari&longs;toteles non potuit; &longs;ed Democrito tamen <lb/>dixit, cùm cum non commendauit modò, &longs;ed prætulit <lb/>etiam Platoni, quem aliunde Sancti Patres Ari&longs;toteli <lb/>ip&longs;i prætulerunt: quantumcumque ip&longs;e deinde recla<lb/>mantibus Patribus, <expan abbr="Philo&longs;ophic&utilde;">Philo&longs;ophicum</expan> Regnum obtinue<lb/>rit, ex&longs;ulante &longs;imùl cum aliis Platone. </s>

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<s>Et &longs;tatim quidem pò&longs;t admones, <emph type="italics"/>præter ha<lb/>litus calidos, frigidos, humidos, odoratos, ac &longs;apidos, è <lb/>plæri&longs;que corporibus ex&longs;piratos, velle vniuer&longs;im quo dictum e&longs;t <lb/>modo, de in&longs;en&longs;ibilibus corporibus ratiocinari, non videri e&longs;&longs;e <lb/>&longs;apientiæ, ac eruditionis meæ.<emph.end type="italics"/> Verùm, cùm id ego acci<lb/>piam, vt in&longs;ignem quandam tuæ erga me beneuolen<lb/>tiæ te&longs;tationem (nimirùm, cùm ego neque &longs;apiens &longs;im, <lb/>neque audire eruditus merear, volui&longs;ti tamen his voci<lb/>bus, pro tua bonitate, lenire cen&longs;uram) quod &longs;upere&longs;t, <lb/>non video &longs;anè, cur res &longs;pectata Phy&longs;icè à &longs;apientiæ <lb/>&longs;tudio aliena cen&longs;eatur. </s>

<s>Et &longs;tatim quidem pò&longs;t admones, <emph type="italics"/>præter ha<lb/>litus calidos, frigidos, humidos, odoratos, ac &longs;apidos, è <lb/>plæri&longs;que corporibus ex&longs;piratos, velle vniuer&longs;im quo dictum e&longs;t <lb/>modo, de in&longs;en&longs;ibilibus corporibus ratiocinari, non videri e&longs;&longs;e <lb/>&longs;apientiæ, ac eruditionis meæ.<emph.end type="italics"/></s><s> Verùm, cùm id ego acci<lb/>piam, vt in&longs;ignem quandam tuæ erga me beneuolen<lb/>tiæ te&longs;tationem (nimirùm, cùm ego neque &longs;apiens &longs;im, <lb/>neque audire eruditus merear, volui&longs;ti tamen his voci<lb/>bus, pro tua bonitate, lenire cen&longs;uram) quod &longs;upere&longs;t, <lb/>non video &longs;anè, cur res &longs;pectata Phy&longs;icè à &longs;apientiæ <lb/>&longs;tudio aliena cen&longs;eatur. </s>

<s>Quantum vis enim tu &longs;ecus <lb/>putes, dum contendis &longs;ufficere, &longs;i quis halitus calidos, <lb/>alió&longs;que ex&longs;pirari dicat: non ideo tamen improban<lb/>dum, &longs;i quis requirat prætereà è quibus principiis qui&longs;<lb/>que halitus &longs;it &longs;ingulariter contextus: &longs;i dicere proinde <lb/>po&longs;&longs;it, qualia requirantur principia, vt calidus, non <lb/>alius &longs;it; quomodo actionem eliciat, vt calefacere cen<lb/>&longs;eatur; quid imprimat rei patienti, vt dicatur illam ca<lb/>lefacere; aliaque id genus complura. </s>

<s>Certè, vt præ<lb/>teream quos apud Platonem Socrates habet inter Sa<lb/>pienteis, Empedoclem, Heraclitum, Protagoram, <lb/>omnei&longs;que, præter Parmenidem, antiquiores (etiam <lb/>Homerum, & Epicharmum) quo&longs;que declarat fui&longs;&longs;e <lb/>ratione con&longs;imili philo&longs;ophatos, ac præcipuè dum <lb/>qualitates, cæteraque, nihil e&longs;&longs;e aliud, quàm motiones <lb/>exi&longs;timârunt: vt illos, inquam, præteream, &, vt de vno <lb/>Democrito, de quo iam dixi aliquid, loquar; Ecce, ne <lb/>Ari&longs;toteles quidem, licet in hi&longs;ce Elementis, qualitati<lb/>bu&longs;que vulgaribus con&longs;titerit, de&longs;ipere illum putauit; <pb pagenum="270"/>&longs;ed extulit potiùs, quòd hac ratione philo&longs;ophatus, <lb/><emph type="italics"/>res no&longs;&longs;e &longs;uperficie tenus<emph.end type="italics"/> <foreign lang="greek">w<gap/>a\ th_s e)pipolh_s</foreign> <emph type="italics"/>contentus non <lb/>fuerit, nihilque, quantum potuit, intactum præterm &longs;erit,<emph.end type="italics"/><lb/><foreign lang="greek">e)/oike <gap/> a)plu/twn f<gap/>nt<gap/>so<gap/>. </foreign></s>

<s>Non e&longs;t verò etiam De<lb/>mocritus de&longs;ipere Plutarcho vi&longs;us, cùm ip&longs;um vnà, ac <lb/>Platonem Ari&longs;toteli ex eo prætulit, <emph type="italics"/>quòd cau&longs;&longs;as caloris, <lb/>& grauitatis inquirentes, non in ip&longs;is terra, & igne &longs;pecula<lb/>tionem finierint, &longs;ed ad ip&longs;a v&longs;que principia &longs;ola mente contem<lb/>plabilia, ea, quæ &longs;en&longs;ibilia &longs;unt, deducentes, fuerint ad v&longs;que <lb/>minima, & qua&longs;i &longs;emina,<emph.end type="italics"/> <foreign lang="greek">mox<gap/> e)laxi/<gap/>wn <gap/>(s<gap/> spe<gap/>ma/ twn</foreign><lb/><emph type="italics"/>progreßi.<emph.end type="italics"/> Non item M. Tullio, cuius verba &longs;unt: <emph type="italics"/>Quid <lb/>loquar de Democrito? </s>

<s>Non e&longs;t verò etiam De<lb/>mocritus de&longs;ipere Plutarcho vi&longs;us, cùm ip&longs;um vnà, ac <lb/>Platonem Ari&longs;toteli ex eo prætulit, <emph type="italics"/>quòd cau&longs;&longs;as caloris, <lb/>& grauitatis inquirentes, non in ip&longs;is terra, & igne &longs;pecula<lb/>tionem finierint, &longs;ed ad ip&longs;a v&longs;que principia &longs;ola mente contem<lb/>plabilia, ea, quæ &longs;en&longs;ibilia &longs;unt, deducentes, fuerint ad v&longs;que <lb/>minima, & qua&longs;i &longs;emina,<emph.end type="italics"/> <foreign lang="greek">mox<gap/> e)laxi/<gap/>wn <gap/>(s<gap/> spe<gap/>ma/ twn</foreign><lb/><emph type="italics"/>progreßi.<emph.end type="italics"/></s><s> Non item M. Tullio, cuius verba &longs;unt: <emph type="italics"/>Quid <lb/>loquar de Democrito? </s>

<s>Quem cum eo conferre po&longs;&longs;um, non modò <lb/>ingenij magnitudine, &longs;ed etiam animi? </s>

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<s>XXIII. </s>

<s>Ecce enim in&longs;tas (& humaniter &longs;anè) <emph type="italics"/>An <lb/>meam &longs;agacitatem fugiat, quò tandem v&longs;que &longs;emel inducta <lb/>hæcper&longs;ua&longs;io proce&longs;&longs;ura videatur?<emph.end type="italics"/> Sed fugit profectò, &longs;i <lb/>putas vlteriùs, quàm quò pote&longs;t procedere Ari&longs;toteleæ <lb/>per&longs;ua&longs;io. <emph type="italics"/>Si,<emph.end type="italics"/> inquis, <emph type="italics"/>ortus, atque interitus nihil aliud vi<lb/>dentur, præter localeis atomorum, vel<emph.end type="italics"/> (vt me loqui mitiùs <lb/>dicis) <emph type="italics"/>tenuißimorum, atque in&longs;en&longs;ibilium principiorum mo<lb/>tiones, de Formis &longs;ub&longs;tantialibus conclamatum e&longs;t.<emph.end type="italics"/> Et non <lb/>adiicis quidem quid incommodi con&longs;equatur, &longs;i eò v&longs;<lb/>que proce&longs;&longs;um fuerit: &longs;ed coniector tamen in&longs;inuare <pb pagenum="271"/>te, quod periculum &longs;ube&longs;&longs;e videtur, ne prætereà ad Ani<lb/>mam v&longs;que rationalem procedatur. </s>

<s>Ecce enim in&longs;tas (& humaniter &longs;anè) <emph type="italics"/>An <lb/>meam &longs;agacitatem fugiat, quò tandem v&longs;que &longs;emel inducta <lb/>hæcper&longs;ua&longs;io proce&longs;&longs;ura videatur?<emph.end type="italics"/> Sed fugit profectò, &longs;i <lb/>putas vlteriùs, quàm quò pote&longs;t procedere Ari&longs;toteleæ <lb/>per&longs;ua&longs;io. <emph type="italics"/>Si,<emph.end type="italics"/> inquis, <emph type="italics"/>ortus, atque interitus nihil aliud vi<lb/>dentur, præter localeis atomorum, vel<emph.end type="italics"/> (vt me loqui mitiùs <lb/>dicis) <emph type="italics"/>tenuißimorum, atque in&longs;en&longs;ibilium principiorum mo<lb/>tiones, de Formis &longs;ub&longs;tantialibus conclamatum e&longs;t.<emph.end type="italics"/></s><s> Et non <lb/>adiicis quidem quid incommodi con&longs;equatur, &longs;i eò v&longs;<lb/>que proce&longs;&longs;um fuerit: &longs;ed coniector tamen in&longs;inuare <pb pagenum="271"/>te, quod periculum &longs;ube&longs;&longs;e videtur, ne prætereà ad Ani<lb/>mam v&longs;que rationalem procedatur. </s>

<s>At vides &longs;anè <lb/>periculum pari ratione deuitatum iri, qua & deuitatur <lb/>in Ari&longs;toteleis &longs;cholis. </s>

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<s>Venio nunc ad ea, quæ habes in &longs;ecundam <lb/>Epi&longs;tolam. </s>

<s>Memoras imprimis, quod initio dixi, <lb/><emph type="italics"/>Exob&longs;eruatis circa Motum à Motore tran&longs;lato impre&longs;&longs;um, <lb/>videri infirmum reddi argumentum, quo &longs;olemus vulgò quie<lb/>tem a&longs;&longs;erere globo Telluris.<emph.end type="italics"/> Et po&longs;tquàm addidi&longs;ti, <emph type="italics"/>idem <lb/><expan abbr="argument&utilde;">argumentum</expan> etiam inde nullum conuinci,<emph.end type="italics"/> id notas, quod e&longs;t <lb/>à me dictum, <emph type="italics"/>Non eò me proptereà adduci, vt inde pronun<lb/>ciem moueri haud dubiè Tellurem: &longs;ed &longs;olùm vt in&longs;inuem <lb/>conquirendam e&longs;&longs;e rationem veri&longs;imiliorem:<emph.end type="italics"/> ac tum &longs;ubdis; <lb/><emph type="italics"/>Bene habet. </s>

<s>Memoras imprimis, quod initio dixi, <lb/><emph type="italics"/>Exob&longs;eruatis circa Motum à Motore tran&longs;lato impre&longs;&longs;um, <lb/>videri infirmum reddi argumentum, quo &longs;olemus vulgò quie<lb/>tem a&longs;&longs;erere globo Telluris.<emph.end type="italics"/></s><s> Et po&longs;tquàm addidi&longs;ti, <emph type="italics"/>idem <lb/><expan abbr="argument&utilde;">argumentum</expan> etiam inde nullum conuinci,<emph.end type="italics"/> id notas, quod e&longs;t <lb/>à me dictum, <emph type="italics"/>Non eò me proptereà adduci, vt inde pronun<lb/>ciem moueri haud dubiè Tellurem: &longs;ed &longs;olùm vt in&longs;inuem <lb/>conquirendam e&longs;&longs;e rationem veri&longs;imiliorem:<emph.end type="italics"/> ac tum &longs;ubdis; <lb/><emph type="italics"/>Bene habet. </s>

<s>Si &longs;copus i&longs;te tuus est, collima&longs;ti: pluribus <lb/>opus non e&longs;t; adeptoque iam fine fru&longs;trà, ac inutiliter labo<lb/>ras.<emph.end type="italics"/> Sed ohe! humanitas tua adeóne euadit &longs;euera, vt <lb/>&longs;cribenti ad amicum ex&longs;patiari non liceat, nec præoc<lb/>cupare, &longs;i quid ille fortè aut requi&longs;iturus, aut quomo<lb/>documque habiturus e&longs;&longs;e iucundum videatur? </s>

<s>Si &longs;copus i&longs;te tuus est, collima&longs;ti: pluribus <lb/>opus non e&longs;t; adeptoque iam fine fru&longs;trà, ac inutiliter labo<lb/>ras.<emph.end type="italics"/></s><s> Sed ohe! humanitas tua adeóne euadit &longs;euera, vt <lb/>&longs;cribenti ad amicum ex&longs;patiari non liceat, nec præoc<lb/>cupare, &longs;i quid ille fortè aut requi&longs;iturus, aut quomo<lb/>documque habiturus e&longs;&longs;e iucundum videatur? </s>

<s>An-non <lb/>&longs;pecialis, vt Dialogorum, &longs;ic Epi&longs;tolarum e&longs;t mos; & <lb/>ille quidem non qualis e&longs;&longs;e angu&longs;ta &longs;olet &longs;emita, &longs;ed po<lb/>tiùs qualis regia via, imò & qualis apertus campus? </s>

<s>Alia <lb/>&longs;anè &longs;unt genera &longs;cribendi, quæ pro cuiu&longs;que in&longs;tituto <lb/>certis legibus, qua&longs;i frænis, atque catenis compe&longs;cun<lb/>tur; at genus Epi&longs;tolicum &longs;olutum, liberumque e&longs;t; & <lb/>cùm liceat in cæteris variè per vices digredi; facere in <lb/>Epi&longs;tolis etiam <foreign lang="greek">p<gap/>re<gap/> on e)/r<gap/>n</foreign> licet <emph type="italics"/>Frustrà, ac inutiliter<emph.end type="italics"/><pb pagenum="277"/><emph type="italics"/>laboro?<emph.end type="italics"/> Bene &longs;altem e&longs;t, quòd mihi e&longs;t vni iactura tem<lb/>poris ferenda; quanquam & tuum affectum probo, <lb/>dum &longs;ollicitus es, ne fru&longs;trà pretio&longs;am adeò rem de<lb/>teram. </s>

<s>Rogas con&longs;equenter, S<emph type="italics"/>i nihil ampliùs quæro, ec<lb/>quid rei &longs;it, quòd plurimorum &longs;imilium conglobatione præmi&longs;&longs;a <lb/>&longs;ic interrogem:<emph.end type="italics"/> C<emph type="italics"/>ur non ratione eadem &longs;uadente fiat vero&longs;imi<lb/>lius, probabilius, magis con&longs;entaneum, moueri Terram ver&longs;us <lb/>ortum, ac totam Mundi machinam, &longs;ideraque omnia &longs;alutare <lb/>ex ordine; quàm totam illam machinam, totque, & tanta &longs;i<lb/>dera circum ip&longs;am ire, eamque &longs;alutare?<emph.end type="italics"/> Rogas &, <emph type="italics"/>Quid &longs;it, <lb/>quod tantopere vrgeo, atque exaggero, maiora ex Solis, fixa<lb/>rumque, quàm ex Telluris motu ab &longs;urda &longs;equi, atque incom<lb/>moda?<emph.end type="italics"/> Rur&longs;us &, C<emph type="italics"/>ur adeò &longs;tudiosè cætera quoque omnia<emph.end type="italics"/><lb/>C<emph type="italics"/>opernicanorum argumenta congeram, &longs;i hoc &longs;olùm conten<lb/>dam, vulgatum illud aliorum Philo&longs;ophorum à proiectilium <lb/>motu petitum argumentum infirmum e&longs;&longs;e, atque inualidum?<emph.end type="italics"/><lb/>Tandem &, C<emph type="italics"/>ur etiam de Telluris eiu&longs;dem circa Solem mo<lb/>tu tam prolixam, nec ad prædictum finem nece&longs;&longs;ariam adiun<lb/>gam disputationem, in qua non modò Copernicanorum argu<lb/>menta omnia, & rationes qua po&longs;&longs;um, & valeo dicendi facul<lb/>tate<emph.end type="italics"/> (& hoc quoque e&longs;t tuæ humanitatis) <emph type="italics"/>&longs;tabilire, & <lb/>confirmare, &longs;ed aliorum quoque obiectiones infirmare pari &longs;tu<lb/>dio, & contentione moliar?<emph.end type="italics"/> Sed vno verbo ip&longs;emet cau&longs;<lb/>&longs;am iam recita&longs;ti illis verbis, quibus me id &longs;olùm dixi <lb/>facere, <emph type="italics"/>vt in&longs;inüarem conquirendam e&longs;&longs;e rationem veri&longs;imi<lb/>liorem.<emph.end type="italics"/> Atqui conuicta illa ratione ex proiectilibus <lb/>de&longs;umpta quie&longs;cendum fuit, nec aliæ mouendæ: Ve<lb/>rùm aliæ quoque vi&longs;æ &longs;unt mouen dæ; nequeid omninò <lb/>abs re, atque incohærenter factum. </s>

<s>Rogas con&longs;equenter, S<emph type="italics"/>i nihil ampliùs quæro, ec<lb/>quid rei &longs;it, quòd plurimorum &longs;imilium conglobatione præmi&longs;&longs;a <lb/>&longs;ic interrogem:<emph.end type="italics"/> C<emph type="italics"/>ur non ratione eadem &longs;uadente fiat vero&longs;imi<lb/>lius, probabilius, magis con&longs;entaneum, moueri Terram ver&longs;us <lb/>ortum, ac totam Mundi machinam, &longs;ideraque omnia &longs;alutare <lb/>ex ordine; quàm totam illam machinam, totque, & tanta &longs;i<lb/>dera circum ip&longs;am ire, eamque &longs;alutare?<emph.end type="italics"/> Rogas &, <emph type="italics"/>Quid &longs;it, <lb/>quod tantopere vrgeo, atque exaggero, maiora ex Solis, fixa<lb/>rumque, quàm ex Telluris motu ab &longs;urda &longs;equi, atque incom<lb/>moda?<emph.end type="italics"/> Rur&longs;us &, C<emph type="italics"/>ur adeò &longs;tudiosè cætera quoque omnia<emph.end type="italics"/><lb/>C<emph type="italics"/>opernicanorum argumenta congeram, &longs;i hoc &longs;olùm conten<lb/>dam, vulgatum illud aliorum Philo&longs;ophorum à proiectilium <lb/>motu petitum argumentum infirmum e&longs;&longs;e, atque inualidum?<emph.end type="italics"/><lb/>Tandem &, C<emph type="italics"/>ur etiam de Telluris eiu&longs;dem circa Solem mo<lb/>tu tam prolixam, nec ad prædictum finem nece&longs;&longs;ariam adiun<lb/>gam disputationem, in qua non modò Copernicanorum argu<lb/>menta omnia, & rationes qua po&longs;&longs;um, & valeo dicendi facul<lb/>tate<emph.end type="italics"/> (& hoc quoque e&longs;t tuæ humanitatis) <emph type="italics"/>&longs;tabilire, & <lb/>confirmare, &longs;ed aliorum quoque obiectiones infirmare pari &longs;tu<lb/>dio, & contentione moliar?<emph.end type="italics"/> Sed vno verbo ip&longs;emet cau&longs;<lb/>&longs;am iam recita&longs;ti illis verbis, quibus me id &longs;olùm dixi <lb/>facere, <emph type="italics"/>vt in&longs;inüarem conquirendam e&longs;&longs;e rationem veri&longs;imi<lb/>liorem.<emph.end type="italics"/></s><s> Atqui conuicta illa ratione ex proiectilibus <lb/>de&longs;umpta quie&longs;cendum fuit, nec aliæ mouendæ: Ve<lb/>rùm aliæ quoque vi&longs;æ &longs;unt mouen dæ; nequeid omninò <lb/>abs re, atque incohærenter factum. </s>

<s>Quia enim iure <lb/>obiici potuit, fru&longs;trà in&longs;inüari à me conquirendas e&longs;&longs;e <pb pagenum="278"/>alias rationes, cùm illæ iam & conqui&longs;itæ, & adinuen<lb/>tæ fuerint; ideò vi&longs;us &longs;um non debere cæteras intactas <lb/>prætermittere, vt o&longs;tenderem quatenus eas quoque ar<lb/>bitrarer e&longs;&longs;e infirmas. </s>

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<s>Alios, qui a&longs;&longs;umunt, vberiore quadam, atque <lb/>concinniore methodo vides agere: ego quidvis com<lb/>memoraui breuiter, ac præpo&longs;terè; quippe vt &longs;e fors <lb/>obtulit, mentique, & manui properanti obiecit. </s>

<s>XXVIII. Sequitur, <emph type="italics"/>Tolerandum fortaßis, & certè non <lb/>ita inconueniens vi&longs;um iri, &longs;i cum Heraclide Pontico, & <lb/>Ecphanto Pythagoreo Terram in medio Vniuer&longs;i constitutam <lb/>quotidiano tantum motu circa proprium axem moueri conten<lb/>derem; &longs;ic enim concitatißimum illum Siderum motum, qui <lb/>plæri&longs;que<emph.end type="italics"/> C<emph type="italics"/>opernici &longs;ectatoribus di&longs;plicui&longs;&longs;e vi&longs;us e&longs;t maximè, <lb/>tollerem; ac &longs;atis moderatum, quo Sacris literis faciliùs &longs;atis-<emph.end type="italics"/><pb pagenum="279"/><emph type="italics"/>facerem, tam errantium, quàm inerrantium Siderum motum, <lb/>quem proprium vocant, retinerem; atque in portento&longs;a, quæ ex <lb/>Copernici opinione &longs;equuntur, incommoda, atque ab&longs;urda non <lb/>inciderem.<emph.end type="italics"/> Heic verò tu me &longs;ic alloqueris, qua&longs;i ego <lb/>Philolai, aut Ari&longs;tarchi &longs;ententiam amplectar, & rem <lb/>proinde faciam minùs tolerabilem, quàm &longs;i &longs;equerer <lb/>hancà te <expan abbr="præ&longs;criptã">præ&longs;criptam</expan>. </s>

<s>XXVIII. Sequitur, <emph type="italics"/>Tolerandum fortaßis, & certè non <lb/>ita inconueniens vi&longs;um iri, &longs;i cum Heraclide Pontico, & <lb/>Ecphanto Pythagoreo Terram in medio Vniuer&longs;i constitutam <lb/>quotidiano tantum motu circa proprium axem moueri conten<lb/>derem; &longs;ic enim concitatißimum illum Siderum motum, qui <lb/>plæri&longs;que<emph.end type="italics"/> C<emph type="italics"/>opernici &longs;ectatoribus di&longs;plicui&longs;&longs;e vi&longs;us e&longs;t maximè, <lb/>tollerem; ac &longs;atis moderatum, quo Sacris literis faciliùs &longs;atis-<emph.end type="italics"/><pb pagenum="279"/><emph type="italics"/>facerem, tam errantium, quàm inerrantium Siderum motum, <lb/>quem proprium vocant, retinerem; atque in portento&longs;a, quæ ex <lb/>Copernici opinione &longs;equuntur, incommoda, atque ab&longs;urda non <lb/>inciderem.<emph.end type="italics"/></s><s> Heic verò tu me &longs;ic alloqueris, qua&longs;i ego <lb/>Philolai, aut Ari&longs;tarchi &longs;ententiam amplectar, & rem <lb/>proinde faciam minùs tolerabilem, quàm &longs;i &longs;equerer <lb/>hancà te <expan abbr="præ&longs;criptã">præ&longs;criptam</expan>. </s>

<s>Ego verò neque me illam ample<lb/>cti profiteor, neque i&longs;tam habeo tolerabiliorem, pro<lb/>pter eadem Scripturæ loca, <emph type="italics"/>Terra in æternum &longs;tat; Fun<lb/>dasti Terram &longs;uper &longs;tabilitatem &longs;uam; Firmauit orbem Ter<lb/>ræ, qui non commouebitur:<emph.end type="italics"/> Itemque, O<emph type="italics"/>ritur Sol, & occidit: <lb/>Sol ne moueatur; Regre&longs;&longs;us e&longs;t Sol;<emph.end type="italics"/> & &longs;imilia: Quibus &longs;i <lb/>putas ex moderati, ac immoderati motus di&longs;tinctio<lb/>ne ab authoribus huius &longs;atisfieri: complana&longs;ti pe<lb/>nitus viam illius defen&longs;oribus, qui &longs;e tuebuntur, quòd <lb/>&longs;acra Scriptura dum patitur minus, non prohibeat ma<lb/>ius. </s>

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<s>Quod autem &longs;pectat ad portento&longs;a, quæ <lb/>dicis ab&longs;urda, & incommoda; ip&longs;i nulla e&longs;&longs;e agno&longs;cunt: <lb/>vnde & ni&longs;i aduer&longs;am habeant &longs;acræ Scripturæ autho<lb/>ritatem, exi&longs;timant &longs;e prorsùs nihil intolerabile tueri. <lb/></s>

<s>Sequitur adhûc, <emph type="italics"/>Memini&longs;&longs;e &longs;emper oportet nos non Philo&longs;o<lb/>phos tantum e&longs;&longs;e, &longs;ed etiam Chri&longs;tianos, Philo&longs;ophiamque <lb/>no&longs;tram nec debere, nec verò etiam po&longs;&longs;e à Chri&longs;tiana fide <lb/>di&longs;crepare.<emph.end type="italics"/> Id verò e&longs;t &longs;anè tua pietate dignum; ip&longs;eque <lb/>non modò a&longs;&longs;entior, verùm etiam palam profiteor, ac <pb pagenum="280"/>iuro. </s>

<s>Sequitur adhûc, <emph type="italics"/>Memini&longs;&longs;e &longs;emper oportet nos non Philo&longs;o<lb/>phos tantum e&longs;&longs;e, &longs;ed etiam Chri&longs;tianos, Philo&longs;ophiamque <lb/>no&longs;tram nec debere, nec verò etiam po&longs;&longs;e à Chri&longs;tiana fide <lb/>di&longs;crepare.<emph.end type="italics"/></s><s> Id verò e&longs;t &longs;anè tua pietate dignum; ip&longs;eque <lb/>non modò a&longs;&longs;entior, verùm etiam palam profiteor, ac <pb pagenum="280"/>iuro. </s>

<s>Id vnum &longs;upere&longs;t, vt no&longs;catur, quid Philo&longs;ophia <lb/>proferat à Chri&longs;tiana di&longs;crepans fide. </s>

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<s>Augu&longs;tinus allato exem<lb/>plo præclarè in&longs;inüat; cùm difficultate propo&longs;ita, <emph type="italics"/>Quo<lb/>modo non &longs;it <expan abbr="contrari&utilde;">contrarium</expan> ijs, qui figuram Sphæræ cælo tribuunt, <lb/>quod &longs;criptum est in libris no&longs;tris, Qui extendit cælum &longs;icut <lb/>Pellem?<emph.end type="italics"/> Re&longs;pondet; S<emph type="italics"/>it &longs;anè contrarium, &longs;i fal&longs;um e&longs;t, quod <lb/>illi dicunt; hoc enim verum e&longs;t, quod diuina dicit authoritas, <lb/>potiu&longs;quàm illud, quod humana infirmitas coniicit. </s>

<s>Sed &longs;i <lb/>fortè talibus illi documentis probare potuerint, vt dubitari inde <lb/>non debeat; demon&longs;trandum est, hoc, quod apud nos est de Pelle <lb/>dictum, veris illis rationibus non e&longs;&longs;e contrarium.<emph.end type="italics"/> Et rursùs, <lb/><emph type="italics"/><expan abbr="Tãdiù">Tandiù</expan> non e&longs;t extra fidem, donecveritate certißima refellatur. <lb/></s>

<s>Sed &longs;i <lb/>fortè talibus illi documentis probare potuerint, vt dubitari inde <lb/>non debeat; demon&longs;trandum est, hoc, quod apud nos est de Pelle <lb/>dictum, veris illis rationibus non e&longs;&longs;e contrarium.<emph.end type="italics"/></s><s> Et rursùs, <lb/><emph type="italics"/><expan abbr="Tãdiù">Tandiù</expan> non e&longs;t extra fidem, donecveritate certißima refellatur. <lb/></s>

<s>Quod &longs;i factum fuerit, non hoc habebat diuina Scriptura; &longs;ed <lb/>hoc &longs;en&longs;erat humana ignorantia.<emph.end type="italics"/> Haud-dubium proinde, <lb/>quin &longs;anctus Doctor, &longs;i in no&longs;tra incidi&longs;&longs;et tempora; <lb/>aut &longs;i eius temporibus fui&longs;&longs;et tota Terra, vt nuper e&longs;t <lb/>factum, circum-nauigata: tum agniturus Antipodas <lb/>fui&longs;&longs;et, tum ad humanam potiùs ignorantiam, quàm <lb/>ad Scripturæ diuinæ &longs;en&longs;um, præhabitam &longs;uam relatu<lb/>rus &longs;ententiam, quam vidi&longs;&longs;et certi&longs;&longs;ima experientiæ <lb/>veritate refelli. </s>

<s>Quod &longs;i factum fuerit, non hoc habebat diuina Scriptura; &longs;ed <lb/>hoc &longs;en&longs;erat humana ignorantia.<emph.end type="italics"/></s><s> Haud-dubium proinde, <lb/>quin &longs;anctus Doctor, &longs;i in no&longs;tra incidi&longs;&longs;et tempora; <lb/>aut &longs;i eius temporibus fui&longs;&longs;et tota Terra, vt nuper e&longs;t <lb/>factum, circum-nauigata: tum agniturus Antipodas <lb/>fui&longs;&longs;et, tum ad humanam potiùs ignorantiam, quàm <lb/>ad Scripturæ diuinæ &longs;en&longs;um, præhabitam &longs;uam relatu<lb/>rus &longs;ententiam, quam vidi&longs;&longs;et certi&longs;&longs;ima experientiæ <lb/>veritate refelli. </s>

<s>Quæ memoro &longs;olùm, vt intelligamus, <lb/>non quicquid Philo&longs;ophia docet, quod videatur prima <lb/>fronte à Literis &longs;acris e&longs;&longs;e di&longs;crepans, proptereà verè <lb/>di&longs;crepare. </s><pb pagenum="281"/>

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<s>Nec porrò <lb/>&longs;acrum ip&longs;um Textum, cùm dicit Solem, & cætera Si<lb/>dera facta, vt Terram illuminent, negare prop tereà, <lb/>quin ip&longs;a aliude &longs;int in &longs;eip&longs;is, ac præter lucem aliquid; <lb/>& id genus alia, quæ tamen non dicit, vt nec cætera, <lb/>quæ no&longs;&longs;e nihil intere&longs;t ad &longs;upernaturalem &longs;alutem. <lb/></s>

<s>Scilicet præclarè &longs;anctus ille Doctor, <emph type="italics"/>Breuiter,<emph.end type="italics"/> inquit, <lb/><emph type="italics"/>dicendum e&longs;t, hoc &longs;ci&longs;&longs;e Authores no&longs;tros, quod veritas habet: <lb/>&longs;ed Spiritum Dei, qui per ip&longs;os loquebatur, nolui&longs;&longs;e i&longs;ta docere <lb/>bomines, nulli ad &longs;alutem profutura.<emph.end type="italics"/> Eiu&longs;modi &longs;unt, alia<lb/>que affinia, quæ prædixi vereri me, ne illi fuerint re&longs;<lb/>pon&longs;uri. </s>

<s>Scilicet præclarè &longs;anctus ille Doctor, <emph type="italics"/>Breuiter,<emph.end type="italics"/> inquit, <lb/><emph type="italics"/>dicendum e&longs;t, hoc &longs;ci&longs;&longs;e Authores no&longs;tros, quod veritas habet: <lb/>&longs;ed Spiritum Dei, qui per ip&longs;os loquebatur, nolui&longs;&longs;e i&longs;ta docere <lb/>bomines, nulli ad &longs;alutem profutura.<emph.end type="italics"/></s><s> Eiu&longs;modi &longs;unt, alia<lb/>que affinia, quæ prædixi vereri me, ne illi fuerint re&longs;<lb/>pon&longs;uri. </s>

<s>XXXI. Subiicis, <emph type="italics"/>Vides igitur, quàm i&longs;ta periculosè in <lb/>publicum diuulgentur, & à viris præ&longs;ertim, qui &longs;ua authori<lb/>tate fidem facere videantur; & quàm non immeritò iam inde <lb/>à Copernici tempore Eccle&longs;ia &longs;emper huic &longs;e errori oppo&longs;ue<lb/>rit: eumque etiam nouißimè non<emph.end type="italics"/> C<emph type="italics"/>ardinales tantum aliqui, vt <lb/>ais, &longs;ed &longs;upremum Eccle&longs;iæ caput Pontificio decreto in Galileo <lb/>damnauerit, & vt ne in posterùm verbo, aut &longs;cripto docere<lb/>tur, &longs;anctißimè prohibuerit.<emph.end type="italics"/> Heic non repeto, quod illi <lb/>tuebuntur, non &longs;equi ex ea, quam diuulgant, &longs;ententia <lb/>id, quod tu times, periculum. </s>

<s>XXXI. Subiicis, <emph type="italics"/>Vides igitur, quàm i&longs;ta periculosè in <lb/>publicum diuulgentur, & à viris præ&longs;ertim, qui &longs;ua authori<lb/>tate fidem facere videantur; & quàm non immeritò iam inde <lb/>à Copernici tempore Eccle&longs;ia &longs;emper huic &longs;e errori oppo&longs;ue<lb/>rit: eumque etiam nouißimè non<emph.end type="italics"/> C<emph type="italics"/>ardinales tantum aliqui, vt <lb/>ais, &longs;ed &longs;upremum Eccle&longs;iæ caput Pontificio decreto in Galileo <lb/>damnauerit, & vt ne in posterùm verbo, aut &longs;cripto docere<lb/>tur, &longs;anctißimè prohibuerit.<emph.end type="italics"/></s><s> Heic non repeto, quod illi <lb/>tuebuntur, non &longs;equi ex ea, quam diuulgant, &longs;ententia <lb/>id, quod tu times, periculum. </s>

<s>Tria potiùs dico. </s>

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<s>XXXII. </s>

<s>Miraris deinde, <emph type="italics"/>Qua fronte erroris huius<emph.end type="italics"/><lb/>S<emph type="italics"/>ectatores exprobrent communi, &longs;aniorique &longs;ententiæ, quòd <lb/>ab&longs;urda quædam videatur inducere: cùm ip&longs;i infinita pro<lb/>pemodum ab&longs;urditatum portenta admittant; excolant<gap/><lb/>culicem, & elephantos deglutientes: ac notas me eorum tan<lb/>gere nonnulla, &longs;ed di&longs;plicere, quòd etiam excu&longs;em.<emph.end type="italics"/> Ego <lb/>verò ea non excu&longs;o; aut certè ea mihi mens e&longs;t, vt <lb/>non tam excu&longs;em, quàm proponam quod illi re&longs;<lb/>pondent; vt quæ nosip&longs;is obiicimus e&longs;&longs;e ab&longs;urda, non <lb/>e&longs;&longs;e per&longs;uadeant. </s>

<s>Miraris deinde, <emph type="italics"/>Qua fronte erroris huius<emph.end type="italics"/><lb/>S<emph type="italics"/>ectatores exprobrent communi, &longs;aniorique &longs;ententiæ, quòd <lb/>ab&longs;urda quædam videatur inducere: cùm ip&longs;i infinita pro<lb/>pemodum ab&longs;urditatum portenta admittant; excolant<gap/><lb/>culicem, & elephantos deglutientes: ac notas me eorum tan<lb/>gere nonnulla, &longs;ed di&longs;plicere, quòd etiam excu&longs;em.<emph.end type="italics"/></s><s> Ego <lb/>verò ea non excu&longs;o; aut certè ea mihi mens e&longs;t, vt <lb/>non tam excu&longs;em, quàm proponam quod illi re&longs;<lb/>pondent; vt quæ nosip&longs;is obiicimus e&longs;&longs;e ab&longs;urda, non <lb/>e&longs;&longs;e per&longs;uadeant. </s>

<s>Dicis, <emph type="italics"/>me &longs;altem agno&longs;cere motum <lb/>Terræ circa<emph.end type="italics"/> S<emph type="italics"/>olem &longs;u&longs;tineri non po&longs;&longs;e, ni&longs;i etiam admitta<lb/>tur magnum illum<emph.end type="italics"/> O<emph type="italics"/>rbem, per quem Tellus deferri fingitur, <lb/>instar puncti respectu cæli obtinere.<emph.end type="italics"/> Et agno&longs;co &longs;anè. <lb/><emph type="italics"/>At dißimulo,<emph.end type="italics"/> ais, <emph type="italics"/>aut certè eleuo quæ inde &longs;equuntur<emph.end type="italics"/><pb pagenum="289"/><emph type="italics"/>ab&longs;urda, vt quòd inerrantia<emph.end type="italics"/> S<emph type="italics"/>idera propemodùm omnia tam <lb/>prodigio&longs;æ molis admittenda &longs;int, vt earum &longs;emidiameter in<lb/>teriectam à Terræ centro ad<emph.end type="italics"/> S<emph type="italics"/>olis centrum di&longs;tantiam exce<lb/>dat.<emph.end type="italics"/> Ego verò id, vt mihi videtur, non di&longs;&longs;imulo; quòd <lb/>&longs;i eleuare vi&longs;us &longs;um; id alienæ &longs;ententiæ fuit. </s>

<s>Dicis, <emph type="italics"/>me &longs;altem agno&longs;cere motum <lb/>Terræ circa<emph.end type="italics"/> S<emph type="italics"/>olem &longs;u&longs;tineri non po&longs;&longs;e, ni&longs;i etiam admitta<lb/>tur magnum illum<emph.end type="italics"/> O<emph type="italics"/>rbem, per quem Tellus deferri fingitur, <lb/>instar puncti respectu cæli obtinere.<emph.end type="italics"/></s><s> Et agno&longs;co &longs;anè. <lb/><emph type="italics"/>At dißimulo,<emph.end type="italics"/> ais, <emph type="italics"/>aut certè eleuo quæ inde &longs;equuntur<emph.end type="italics"/><pb pagenum="289"/><emph type="italics"/>ab&longs;urda, vt quòd inerrantia<emph.end type="italics"/> S<emph type="italics"/>idera propemodùm omnia tam <lb/>prodigio&longs;æ molis admittenda &longs;int, vt earum &longs;emidiameter in<lb/>teriectam à Terræ centro ad<emph.end type="italics"/> S<emph type="italics"/>olis centrum di&longs;tantiam exce<lb/>dat.<emph.end type="italics"/></s><s> Ego verò id, vt mihi videtur, non di&longs;&longs;imulo; quòd <lb/>&longs;i eleuare vi&longs;us &longs;um; id alienæ &longs;ententiæ fuit. </s>

<s>Quan<lb/>quam me dixi&longs;&longs;e non commemini, Sidera inerrantia <lb/>Orbem magnum excedere; videlicet, potiu&longs; quàm <lb/>Solem, quem dixi quidem po&longs;&longs;e <emph type="italics"/>apparere,<emph.end type="italics"/> at non <emph type="italics"/>e&longs;&longs;e<emph.end type="italics"/><lb/>ip&longs;i æqualem. </s>

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<s>Quæ&longs;o te, inquam, Vir <lb/>Religio&longs;i&longs;&longs;ime, ecquid-nam illis dicturus &longs;im, cùm <lb/>hæc, & &longs;imilia reponent? </s><pb pagenum="291"/>

<s>XXXIII. Subiicitur; <emph type="italics"/>Eleuas certè plærdque alia, quæ <lb/>ex eadem Telluris circa Solem tran&longs;latione vlteriùs &longs;equuntur, <lb/>ab&longs;urda, à quibus tamen vt te expedias, fingis alia fortaßis <lb/>adhûc ab&longs;urdiora; vt, quòd illu&longs;triora illa, quæ in<emph.end type="italics"/> F<emph type="italics"/>irmamento <lb/>apparent Sidera credi poßint vt mole maiora, &longs;ic etiam Sole <lb/>ip&longs;o longè lucidiora: adeò tibi facile e&longs;t tot, tamque ingenteis <lb/>in cælo pro tua voluntate verbo vnico creare Soleis.<emph.end type="italics"/> Ego ve<lb/>ro & heic quoque tibi ad&longs;tipulor. </s>

<s>XXXIII. Subiicitur; <emph type="italics"/>Eleuas certè plærdque alia, quæ <lb/>ex eadem Telluris circa Solem tran&longs;latione vlteriùs &longs;equuntur, <lb/>ab&longs;urda, à quibus tamen vt te expedias, fingis alia fortaßis <lb/>adhûc ab&longs;urdiora; vt, quòd illu&longs;triora illa, quæ in<emph.end type="italics"/> F<emph type="italics"/>irmamento <lb/>apparent Sidera credi poßint vt mole maiora, &longs;ic etiam Sole <lb/>ip&longs;o longè lucidiora: adeò tibi facile e&longs;t tot, tamque ingenteis <lb/>in cælo pro tua voluntate verbo vnico creare Soleis.<emph.end type="italics"/></s><s> Ego ve<lb/>ro & heic quoque tibi ad&longs;tipulor. </s>

<s>Sed dic, amabò, <lb/>etiam hoc loco, quid illis re&longs;pon&longs;urus &longs;im, cùm ip&longs;i &longs;ic <lb/>in&longs;titerint. </s>

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<s>Subiungis verò; <emph type="italics"/>Similiter, quod etiam ais, <lb/>fieri po&longs;&longs;e, vt Sol hic no&longs;ter, quamvis comparatione &longs;uperio<lb/>rum<emph.end type="italics"/> S<emph type="italics"/>iderum adeò exiguus, ac penè nullus admittatur; ab im<lb/>men&longs;a tamen illa<emph.end type="italics"/> S<emph type="italics"/>iderum di&longs;tantia con&longs;picuus nihilominùs <lb/>appareat, ac tantæ etiam magnitudinis, quanta est tota regio <lb/>Planetaria<emph.end type="italics"/> (dixi, aut quantus magnus orbis) <emph type="italics"/>idque ob <lb/>lucem eius vegetam, diffu&longs;o&longs;que ip&longs;ius radios, quibus oculus <lb/>afficiendus e&longs;&longs;et; eo modo, quo flamma candelæ noctu spectata <lb/>ignis ingens apparet. </s>

<s>Id, inquam, ingenij tui admirabile qui<lb/>dem, &longs;ed incredibile figmentum e&longs;t, quod exemplo candelæ <lb/>comodè non probas.<emph.end type="italics"/> An porrò, cùm i&longs;tud videatur <emph type="italics"/>figmen<lb/>tum incredibile;<emph.end type="italics"/> patietur tua bonitas, vt proferam aliud, <lb/>quod cum i&longs;to connexum &longs;it, quodque, quantum con<lb/>iector, &longs;it incredibilius appariturum? </s>

<s>Id, inquam, ingenij tui admirabile qui<lb/>dem, &longs;ed incredibile figmentum e&longs;t, quod exemplo candelæ <lb/>comodè non probas.<emph.end type="italics"/></s><s> An porrò, cùm i&longs;tud videatur <emph type="italics"/>figmen<lb/>tum incredibile;<emph.end type="italics"/> patietur tua bonitas, vt proferam aliud, <lb/>quod cum i&longs;to connexum &longs;it, quodque, quantum con<lb/>iector, &longs;it incredibilius appariturum? </s>

<s>Quantum, pu<lb/>tas, &longs;i omnes di&longs;ci mille & viginti duarum Stellarum <lb/>vulgò agnitarum &longs;imùl iungerentur, aggregarenturve <lb/>in vnum; quantum putas, inquam, totalem di&longs;cum <lb/>conficerent? </s>

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<s>Ad te vt redeam, po&longs;tquàm præmi&longs;i&longs;ti, <lb/><emph type="italics"/>non probare me commodè figmentum exemplo candelæ,<emph.end type="italics"/> &longs;ic <lb/>pergis, <emph type="italics"/>Quæcùmque enim cau&longs;&longs;a &longs;it, cur flamma candelæ, ad <lb/>certam præ&longs;ertim di&longs;tantiam, &longs;emper auctior appareat: &longs;atis <lb/>certè tibi con&longs;tat Lunam, ac Martem, ip&longs;umque etiam Solem,<emph.end type="italics"/><pb pagenum="302"/><emph type="italics"/>cùm propiùs ad nos accedunt, non minores videri, &longs;ed maiores: <lb/>vbi verò longiùs à Terra remouentur, non maiores conspici, <lb/>&longs;ed apparere minores. </s>

<s>Vnde ergo, quæ&longs;o te, colligis<emph.end type="italics"/> S<emph type="italics"/>olem ex <lb/>immen&longs;a Siderum di&longs;tantia conspectum non modò maiorem <lb/>videndum, quàm nobis vicinioribus appareat, &longs;ed tantæ etiam <lb/>magnitudinis, vt regionem quoque Planetariam totam, atque <lb/>integram æquare videretur.<emph.end type="italics"/> Sed nimirùm, optime Vir, <lb/>cùm ip&longs;e cau&longs;&longs;am reticeas, cur candelæ flamma appa<lb/>reat per noctem adauctior; quòd &longs;agacitas illa tua, quan<lb/>tum coniicere par e&longs;t, difficultatem prouiderit, quæ ex<lb/>citari in vulgarem cau&longs;&longs;æ explicationem pote&longs;t; non <lb/>ea mihi tamen fuit prætermittenda, quæ e&longs;t probabi<lb/>li&longs;&longs;ima vi&longs;a, vt præoccupando declarare po&longs;&longs;em, quod <lb/>iam rogas me, vnde-nam putà colligam, Solem è Fixis <lb/>con&longs;pectum po&longs;&longs;e apparere æqualem regioni Planeta<lb/>riæ, &longs;icque maiorem, quàm heinc videri. </s>

<s>Vnde ergo, quæ&longs;o te, colligis<emph.end type="italics"/> S<emph type="italics"/>olem ex <lb/>immen&longs;a Siderum di&longs;tantia conspectum non modò maiorem <lb/>videndum, quàm nobis vicinioribus appareat, &longs;ed tantæ etiam <lb/>magnitudinis, vt regionem quoque Planetariam totam, atque <lb/>integram æquare videretur.<emph.end type="italics"/></s><s> Sed nimirùm, optime Vir, <lb/>cùm ip&longs;e cau&longs;&longs;am reticeas, cur candelæ flamma appa<lb/>reat per noctem adauctior; quòd &longs;agacitas illa tua, quan<lb/>tum coniicere par e&longs;t, difficultatem prouiderit, quæ ex<lb/>citari in vulgarem cau&longs;&longs;æ explicationem pote&longs;t; non <lb/>ea mihi tamen fuit prætermittenda, quæ e&longs;t probabi<lb/>li&longs;&longs;ima vi&longs;a, vt præoccupando declarare po&longs;&longs;em, quod <lb/>iam rogas me, vnde-nam putà colligam, Solem è Fixis <lb/>con&longs;pectum po&longs;&longs;e apparere æqualem regioni Planeta<lb/>riæ, &longs;icque maiorem, quàm heinc videri. </s>

<s>Siquidem <lb/>conatus idem explicare ex cau&longs;&longs;a vulgò reddita, vi&longs;us <lb/>mihi ip&longs;i ridiculus &longs;um ob illius inanitatem. </s>

<s>Ecce <lb/>enim dicere &longs;olent, <emph type="italics"/>aërem proximè circum&longs;tantem eâ vehe<lb/>mentiâ illu&longs;trari ob halituo&longs;as qua&longs;dam parteis è flamma con<lb/>tinuò diffugienteis, vt computetur in eandem flammam, parti<lb/>bus videlicet illis factis ad&longs;pectabilibus ex&longs;i&longs;tenti oculo procùl, <lb/>& in minore lumine; cùm è vicino, ab eximio flammæ &longs;plen<lb/>dore occultentur.<emph.end type="italics"/> At quomodo probare valeant e&longs;&longs;e has <lb/>halituo&longs;as parteis illu&longs;trationis eius capaceis, vt totum <lb/>aëreum &longs;patium, in quo &longs;unt, efficiant non minùs illu<lb/>&longs;tre, quàm flammam? </s>

<s>Ecce <lb/>enim dicere &longs;olent, <emph type="italics"/>aërem proximè circum&longs;tantem eâ vehe<lb/>mentiâ illu&longs;trari ob halituo&longs;as qua&longs;dam parteis è flamma con<lb/>tinuò diffugienteis, vt computetur in eandem flammam, parti<lb/>bus videlicet illis factis ad&longs;pectabilibus ex&longs;i&longs;tenti oculo procùl, <lb/>& in minore lumine; cùm è vicino, ab eximio flammæ &longs;plen<lb/>dore occultentur.<emph.end type="italics"/></s><s> At quomodo probare valeant e&longs;&longs;e has <lb/>halituo&longs;as parteis illu&longs;trationis eius capaceis, vt totum <lb/>aëreum &longs;patium, in quo &longs;unt, efficiant non minùs illu<lb/>&longs;tre, quàm flammam? </s>

<s>Nam non negabunt profectò <lb/>flammam e&longs;&longs;e centies, aut etiam millies &longs;plendidiorem <lb/>eo &longs;patio, quod ip&longs;am circum&longs;tat ad vnum, aut ad plu<lb/>reis palmos. </s>

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<s>Verba tua deinde &longs;unt, <emph type="italics"/>Dicis, atque audacter <lb/>affirmas<emph.end type="italics"/> G<emph type="italics"/>alileum ex aßignatis Telluris motibus ita Maris <lb/>æ&longs;tum expo&longs;ui&longs;&longs;e, vt videatur denique cau&longs;&longs;am eius germa<lb/>nam adinueni&longs;&longs;e.<emph.end type="italics"/> Quàm bene e&longs;t verò, quod verbo <emph type="italics"/>vi<lb/>deatur<emph.end type="italics"/> temperaui &longs;ententiam; ne dicere po&longs;&longs;es me id <lb/>non tantum <emph type="italics"/>audacter,<emph.end type="italics"/> verùm <emph type="italics"/>impudenter<emph.end type="italics"/> quoque affir<lb/>mare! Certè, religio&longs;i&longs;&longs;ime Vir, &longs;i me bene no&longs;ti, lon<lb/>gi&longs;&longs;imè ab&longs;um, vt in hi&longs;ce rebus, aut &longs;imilibus quid<lb/>piam a&longs;&longs;eueranter dicam; tantum à me abe&longs;t, vt faciam <lb/><emph type="italics"/>audacter.<emph.end type="italics"/> Nam & tamet&longs;i con&longs;uetudo loquendi non <lb/>&longs;emper patiatur, vt caueam, ne a&longs;&longs;erere videar aliquid <pb pagenum="307"/>(quod ne Socrates quidem &longs;e cauere profe&longs;&longs;us e&longs;t, <lb/><foreign lang="greek"><gap/>wo\ s<gap/>hq<gap/>as, kai\ ai)epishmss<gap/>gs g)na<gap/>kasme/nos</foreign>) <lb/>id tamen &longs;emper te&longs;tatum volo, quæcumque mea <lb/>phra&longs;is &longs;it, eam mihi in&longs;idere mentem, vt nihil planè <lb/>tanquam verum, & indubitatum affirmem, &longs;iue plu&longs;<lb/>quàm probabile, veri&longs;imileve profitear. </s>

<s>Verba tua deinde &longs;unt, <emph type="italics"/>Dicis, atque audacter <lb/>affirmas<emph.end type="italics"/> G<emph type="italics"/>alileum ex aßignatis Telluris motibus ita Maris <lb/>æ&longs;tum expo&longs;ui&longs;&longs;e, vt videatur denique cau&longs;&longs;am eius germa<lb/>nam adinueni&longs;&longs;e.<emph.end type="italics"/></s><s> Quàm bene e&longs;t verò, quod verbo <emph type="italics"/>vi<lb/>deatur<emph.end type="italics"/> temperaui &longs;ententiam; ne dicere po&longs;&longs;es me id <lb/>non tantum <emph type="italics"/>audacter,<emph.end type="italics"/> verùm <emph type="italics"/>impudenter<emph.end type="italics"/> quoque affir<lb/>mare! Certè, religio&longs;i&longs;&longs;ime Vir, &longs;i me bene no&longs;ti, lon<lb/>gi&longs;&longs;imè ab&longs;um, vt in hi&longs;ce rebus, aut &longs;imilibus quid<lb/>piam a&longs;&longs;eueranter dicam; tantum à me abe&longs;t, vt faciam <lb/><emph type="italics"/>audacter.<emph.end type="italics"/></s><s> Nam & tamet&longs;i con&longs;uetudo loquendi non <lb/>&longs;emper patiatur, vt caueam, ne a&longs;&longs;erere videar aliquid <pb pagenum="307"/>(quod ne Socrates quidem &longs;e cauere profe&longs;&longs;us e&longs;t, <lb/><foreign lang="greek"><gap/>wo\ s<gap/>hq<gap/>as, kai\ ai)epishmss<gap/>gs g)na<gap/>kasme/nos</foreign>) <lb/>id tamen &longs;emper te&longs;tatum volo, quæcumque mea <lb/>phra&longs;is &longs;it, eam mihi in&longs;idere mentem, vt nihil planè <lb/>tanquam verum, & indubitatum affirmem, &longs;iue plu&longs;<lb/>quàm probabile, veri&longs;imileve profitear. </s>

<s>Quantò verò <lb/>magis hoc loco id volui; vbi &longs;ententiam non tam pro<lb/>priam, quàm alienam expo&longs;ui! Heinc & quæ dicere <lb/>iam pergo, non vt propugnans &longs;ententiam, quæ mihi <lb/>rata fixa &longs;it: &longs;ed tanquam tentans quid iuxta ip&longs;am &longs;it <lb/>vero &longs;imile, in&longs;inuo: & dum tu &longs;ubdis, <emph type="italics"/>ne&longs;cire te, an ex <lb/>tarditate ingenij tui, an aliunde accidat, vt longè aliter, quàm <lb/>ego, hactenus hac in re &longs;en&longs;eris:<emph.end type="italics"/> id &longs;ic accipio, qua&longs;i velis <lb/>non me &longs;entire &longs;ecus, quàm te, quod ad rem ip&longs;am at<lb/>tinet; &longs;ed quod ad ea, quæ opinioni de motu Terræ <lb/>&longs;unt con&longs;entanea. </s>

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<s>Succedunt hæc verba, <emph type="italics"/>Imprimis enim ignorare <lb/>te non arbitror, etiam ex illis motibus cau&longs;&longs;am &longs;ufficientem <lb/>non reddi, cur circa<emph.end type="italics"/> Æ<emph type="italics"/>quinoctia æ&longs;tus fiant adeò magni præ <lb/>cæteris; cùm illis temporibus vix inæqualitas vlla in Telluris <lb/>motu appareat; & quæ minima in punctis<emph.end type="italics"/> Æ<emph type="italics"/>quinoctialibus <lb/>notatur, non &longs;ubitò, aut vna tantum die exoritur, &longs;ed paulla<lb/>tim, diuturnóque tempore accre&longs;cit: cùm æ&longs;tus illi tamen non <lb/>ita &longs;en&longs;im, & &longs;ucceßiuè v&longs;que ad aliquem maximum accre&longs;-<emph.end type="italics"/><pb pagenum="309"/><emph type="italics"/>cant, parique deinde &longs;ucceßione paullatim decre&longs;cant; nec <lb/>maiores item eo tempore æ&longs;tus fiant, quo Tellus in punctis<emph.end type="italics"/><lb/>Æ<emph type="italics"/>quinoctialibus con&longs;tituta, maiorem illam inæqualitatem <lb/>patitur: &longs;ed in plenilunio &longs;olùm proximè in&longs;equente.<emph.end type="italics"/> Et <lb/>fui&longs;ti tu &longs;anè arbitratu tuo in meam ignorantiam in<lb/>dulgens; qui etiam ignoro, quæ tu heic a&longs;&longs;umis. </s>

<s>Succedunt hæc verba, <emph type="italics"/>Imprimis enim ignorare <lb/>te non arbitror, etiam ex illis motibus cau&longs;&longs;am &longs;ufficientem <lb/>non reddi, cur circa<emph.end type="italics"/> Æ<emph type="italics"/>quinoctia æ&longs;tus fiant adeò magni præ <lb/>cæteris; cùm illis temporibus vix inæqualitas vlla in Telluris <lb/>motu appareat; & quæ minima in punctis<emph.end type="italics"/> Æ<emph type="italics"/>quinoctialibus <lb/>notatur, non &longs;ubitò, aut vna tantum die exoritur, &longs;ed paulla<lb/>tim, diuturnóque tempore accre&longs;cit: cùm æ&longs;tus illi tamen non <lb/>ita &longs;en&longs;im, & &longs;ucceßiuè v&longs;que ad aliquem maximum accre&longs;-<emph.end type="italics"/><pb pagenum="309"/><emph type="italics"/>cant, parique deinde &longs;ucceßione paullatim decre&longs;cant; nec <lb/>maiores item eo tempore æ&longs;tus fiant, quo Tellus in punctis<emph.end type="italics"/><lb/>Æ<emph type="italics"/>quinoctialibus con&longs;tituta, maiorem illam inæqualitatem <lb/>patitur: &longs;ed in plenilunio &longs;olùm proximè in&longs;equente.<emph.end type="italics"/></s><s> Et <lb/>fui&longs;ti tu &longs;anè arbitratu tuo in meam ignorantiam in<lb/>dulgens; qui etiam ignoro, quæ tu heic a&longs;&longs;umis. </s>

<s>Nam <lb/>primùm quidem, <emph type="italics"/>non e&longs;&longs;e quoddam paullatim factum in<lb/>crementum; &longs;ed repentè maximos æstus in Plenilunio<emph.end type="italics"/> Æ<emph type="italics"/>qui<lb/>noctium con&longs;equente contingere,<emph.end type="italics"/> hoc e&longs;t, quod neque <lb/>ob&longs;eruaui, neque ab alio quoquam accepi: cùm potiùs, <lb/>vt æ&longs;tus &longs;pectati per quadranteis men&longs;is, minimi circa <lb/>quadraturas, maximi circa &longs;yzygias, &longs;en&longs;im per inter<lb/>ceptos dies, & maximi ex minimis, & minimi ex ma<lb/>ximis euadunt; ita &longs;i &longs;pectentur per quadranteis anni, <lb/>audierim &longs;emper minimos fieri circa tempora inter <lb/>cardines tempe&longs;tatum media; maximos circa cardines <lb/>(ac præ&longs;ertim Æquinoctialeis) per tempora autem in<lb/>tercepta maximos &longs;en&longs;im ex minimis, minimos ex ma<lb/>ximis fieri: quantumcumque per aliquos dies ab&longs;que <lb/>apparente incremento, tam &longs;ub quadraturas, & &longs;yzy<lb/>gias, quàm &longs;ub Æquinoctia, Sol&longs;titiáque e&longs;&longs;e videan<lb/>tur. </s>

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<s>Congruum certè e&longs;t, vt &longs;i vniuersè <lb/>motus diurnus æ&longs;tum creat, ob inæqualitatem &longs;ibi ex <lb/>motu annuo &longs;uperuenientem; <expan abbr="alterat&utilde;">alteratum</expan> creet, ob &longs;uper<lb/>uenientem &longs;pecialem inæqualitatem ex ductu per Zo<lb/>diacum: quatenus vbi ille e&longs;t maximè obliquus, nempe <lb/>ad ip&longs;um Æquatorem, motus diurnus, qui e&longs;t &longs;emper <lb/>directè ad ortum, maximè reprimitur, hoc e&longs;t cohibe<lb/>tur, ne ver&longs;us ortum protendatur. </s>

<s>XLII. Pergis, <emph type="italics"/>Ex imaginariis illis motibus cau&longs;&longs;am non <lb/>reddi, cur in Pleniluniis Mare vehementiùs æ&longs;tuet, quàm tem<lb/>poribus reliquis.<emph.end type="italics"/> Verùm imprimis nihil e&longs;t nece&longs;&longs;e <lb/>cau&longs;&longs;am reddere illius effectus, quem verum e&longs;&longs;e mini<lb/>mè con&longs;tet: &longs;anè enim quæcumque &longs;it aliquorum <lb/>opinio, ob&longs;eruata tamen non de&longs;unt, quæ probent <pb pagenum="311"/><emph type="italics"/>non modò in India,<emph.end type="italics"/> de qua &longs;tatim loqueris, <emph type="italics"/>&longs;ed in ip&longs;a <expan abbr="quoq;">quoque</expan> <lb/>Europa<emph.end type="italics"/> e&longs;&longs;e Noui-lunareis æ&longs;tus Pleni-lunarib<emph type="sup"/>9<emph.end type="sup"/> &ecedil;&longs;tuo&longs;io<lb/>res. </s>

<s>XLII. Pergis, <emph type="italics"/>Ex imaginariis illis motibus cau&longs;&longs;am non <lb/>reddi, cur in Pleniluniis Mare vehementiùs æ&longs;tuet, quàm tem<lb/>poribus reliquis.<emph.end type="italics"/></s><s> Verùm imprimis nihil e&longs;t nece&longs;&longs;e <lb/>cau&longs;&longs;am reddere illius effectus, quem verum e&longs;&longs;e mini<lb/>mè con&longs;tet: &longs;anè enim quæcumque &longs;it aliquorum <lb/>opinio, ob&longs;eruata tamen non de&longs;unt, quæ probent <pb pagenum="311"/><emph type="italics"/>non modò in India,<emph.end type="italics"/> de qua &longs;tatim loqueris, <emph type="italics"/>&longs;ed in ip&longs;a <expan abbr="quoq;">quoque</expan> <lb/>Europa<emph.end type="italics"/> e&longs;&longs;e Noui-lunareis æ&longs;tus Pleni-lunarib<emph type="sup"/>9<emph.end type="sup"/> &ecedil;&longs;tuo&longs;io<lb/>res. </s>

<s>Deinde, vbi fuerit conce&longs;&longs;um, æ&longs;tuare vehementiùs <lb/>Mare Pleniluniorum temporibus; cau&longs;&longs;a ex illis moti<lb/>bus reddi poterit non prorsùs incongrua. </s>

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<s>XLIII. </s>

<s>Pergis adhûc; <emph type="italics"/>Neque profectò &longs;tatim acquie&longs;<lb/>cit animus, cùm ad ea, quæ aliter explicari nequeunt, vno <lb/>verbo re&longs;pondetur, hæc, & &longs;imilia ex particularibus locorum <lb/>affectionibus oriri.<emph.end type="italics"/> Porrò i&longs;tud non re&longs;pondetur, quod <lb/>&longs;pectat ad ea generaliora accidentia, quæ &longs;unt omnium <lb/>Marium, ac &longs;peciatim Indiæ, Europæque communia: <lb/>cuiu&longs;modi e&longs;t vehementia æ&longs;tus, tam in Sol&longs;titiis, & <lb/>Æquinoctiis, quàm in Nouiluniis, Plenilunii&longs;que in<lb/>ten&longs;ior: &longs;ed quod &longs;pectat ad accidentia, quæ locorum <lb/>Terræ particularium propria cùm &longs;int; quidni cau&longs;&longs;as <lb/>habere proprias ex particularibus locis po&longs;&longs;int? </s>

<s>Pergis adhûc; <emph type="italics"/>Neque profectò &longs;tatim acquie&longs;<lb/>cit animus, cùm ad ea, quæ aliter explicari nequeunt, vno <lb/>verbo re&longs;pondetur, hæc, & &longs;imilia ex particularibus locorum <lb/>affectionibus oriri.<emph.end type="italics"/></s><s> Porrò i&longs;tud non re&longs;pondetur, quod <lb/>&longs;pectat ad ea generaliora accidentia, quæ &longs;unt omnium <lb/>Marium, ac &longs;peciatim Indiæ, Europæque communia: <lb/>cuiu&longs;modi e&longs;t vehementia æ&longs;tus, tam in Sol&longs;titiis, & <lb/>Æquinoctiis, quàm in Nouiluniis, Plenilunii&longs;que in<lb/>ten&longs;ior: &longs;ed quod &longs;pectat ad accidentia, quæ locorum <lb/>Terræ particularium propria cùm &longs;int; quidni cau&longs;&longs;as <lb/>habere proprias ex particularibus locis po&longs;&longs;int? </s>

<s>Vt <lb/>enim dum nauicula aquæ &longs;emi-plena &longs;upra lacum pla<lb/>cidum inæquabiliter mouetur, ip&longs;a aqua fluit, ac re<lb/>fluit vniformiter, pro vniformitate inæqualitatis, &longs;i <lb/>nauicula quidem in interiore circumductu vniformi<lb/>ter deflexa, politaque ex&longs;titerit; Pari modo, &longs;i totum <lb/>Mare vna quadam Terræ cauitate ab occa&longs;u in ortum <lb/>producta, æquabiliterque deflexa contineretur, illius <lb/>fluxus, atque refluxus vniformiter fieret, quod attinet <lb/>quidem ad illa generaliora accidentia. </s>

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<s>Si hæc igitur di<lb/>uer&longs;itas motus cau&longs;&longs;a e&longs;&longs;et quotidianorum æ&longs;tuum, deberent <lb/>præcisè po&longs;t horas viginti quatuor recurrere, cùm vnâ ferè <lb/>horâ quotidie tardiùs recurrant. </s>

<s>Quò fit, vt &longs;ingulis men<lb/>&longs;ibus tunc mare maximè quie&longs;cat, cùm habita ratione motus <lb/>Telluris &longs;ummè feruere deberet; & contrà, tum vehementer <lb/>ferueat, cùm illud paccatè quie&longs;cere oporteret.<emph.end type="italics"/> Verùm vno <lb/>verbo in&longs;inuatum e&longs;t in Epi&longs;tolis naturam aquæ flui<lb/>dam ob&longs;tare, ne aqua circumferatur tam facilè, ac reli<lb/>qui globi compacta natura. </s>

<s>Quò fit, vt &longs;ingulis men<lb/>&longs;ibus tunc mare maximè quie&longs;cat, cùm habita ratione motus <lb/>Telluris &longs;ummè feruere deberet; & contrà, tum vehementer <lb/>ferueat, cùm illud paccatè quie&longs;cere oporteret.<emph.end type="italics"/></s><s> Verùm vno <lb/>verbo in&longs;inuatum e&longs;t in Epi&longs;tolis naturam aquæ flui<lb/>dam ob&longs;tare, ne aqua circumferatur tam facilè, ac reli<lb/>qui globi compacta natura. </s>

<s>Quippe cùm motus re<lb/>liqui globi non exqui&longs;itè obfecundet (&longs;cilicet, &longs;i ob<lb/>&longs;ecundaret, nullus æ&longs;tus ex&longs;i&longs;teret) ideò nece&longs;&longs;e e&longs;t <lb/>eius motum fieri non-nihil retardatiorem, & men&longs;urâ <lb/>quidem tarditatis acceptâ ex portione motus Lunæ <lb/>men&longs;trui addita diurno Telluris, quatenus ab ip&longs;o de<lb/>pendet, imò idem reipsâ e&longs;t. </s>

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