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version 1.15, 2002/08/22 15:44:06

version 1.16, 2002/09/09 22:04:07

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</info> <text> <front> </front> <body> <chap> <pb/>

<s><emph type="center"/><emph type="italics"/>PETRI GASSENDI<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>PETRI GASSENDI<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/>DE PROPORTIONE, <lb/>QVA GRAVIA DECIDENTIA <lb/>ACCELERANTVR.<emph.end type="center"/></s>

<s><emph type="center"/>EPISTOLÆ TRES.<emph.end type="center"/></s>

<s><emph type="center"/>EPISTOLÆ TRES.<emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Quibus ad totidem Epi&longs;tolas R. P.<emph.end type="italics"/> PETRI CAZRÆ<gap/><lb/><emph type="italics"/>Societatis<emph.end type="italics"/> IESV <emph type="italics"/>Re&longs;pondetur.<emph.end type="italics"/><emph.end type="center"/></s><figure/>

<s><emph type="center"/>PARISIIS,<emph.end type="center"/></s>

<s><emph type="center"/>PARISIIS,<emph.end type="center"/></s>

<s><emph type="center"/>Apud LVDOVICVM DE HEVQVEVILLE, via Iacobæa, <lb/>&longs;ub &longs;igno Pacis.<emph.end type="center"/><lb/><gap desc="hr tag"/></s>

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<s><emph type="center"/><emph type="italics"/>CVM PRIVILEGIO REGIS<emph.end type="italics"/><emph.end type="center"/></s><pb/><figure/>

<s><emph type="center"/>EPISTOLARVM<emph.end type="center"/></s>

<s><emph type="center"/>EPISTOLARVM<emph.end type="center"/><emph type="center"/>SVMMVLÆ.<emph.end type="center"/><lb/><gap desc="hr tag"/></s>

<s><emph type="center"/>SVMMVLÆ.<emph.end type="center"/><lb/><gap desc="hr tag"/></s>

<s><emph type="center"/>EPISTOLÆ PRIMÆ.<emph.end type="center"/></s>

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<s>Scribendi Occa&longs;io. </s>

<s><emph type="italics"/>CVm enim ante annos treis Author edidi&longs;&longs;et duas Epi&longs;to<lb/>las<emph.end type="italics"/> De Motu impre&longs;&longs;o à Motore tran&longs;lato <emph type="italics"/>in&longs;crip<lb/>tas, R. P. Cazræus Societatis<emph.end type="italics"/> IESV <emph type="italics"/>tum Diuionen&longs;is Collegij <lb/>Rector &longs;crip&longs;it ad ip&longs;um <expan abbr="Epi&longs;tolã">Epi&longs;tolam</expan>, qua reprehendit capita varia <lb/>tam circa cætera de Motu con&longs;cripta, quàm circa di&longs;putata &longs;pe<lb/>ciatim de Motu Terra attributo. </s>

<s>Cazræus Societatis<emph.end type="italics"/> IESV <emph type="italics"/>tum Diuionen&longs;is Collegij <lb/>Rector &longs;crip&longs;it ad ip&longs;um <expan abbr="Epi&longs;tolã">Epi&longs;tolam</expan>, qua reprehendit capita varia <lb/>tam circa cætera de Motu con&longs;cripta, quàm circa di&longs;putata &longs;pe<lb/>ciatim de Motu Terra attributo. </s>

<s>Itaque Author ad illum re&longs;<lb/>crip&longs;it eâ Epi&longs;tolâ, quæ heic babetur ordine tertia, quàmque pri<lb/>mam legere &longs;i libet, licet, imò & non <expan abbr="incongru&utilde;">incongruum</expan> e&longs;t. </s>

<s>Quia verò <lb/>R. P. cætera inter obiecerat, non fui&longs;&longs;e Authorem probatu<lb/>rum<emph.end type="italics"/> G<emph type="italics"/>alilei &longs;ententiam circa Proportionem, qua grauia de<lb/>cidentia accelerantur, &longs;i commi&longs;&longs;um à<emph.end type="italics"/> G<emph type="italics"/>alileo Paralogi&longs;mum <lb/>animaduerti&longs;&longs;et; & Author responderat &longs;e nec potui&longs;&longs;e nec<lb/>dum po&longs;&longs;e Paralogi&longs;mum vllum videre; ac optare adeò, <lb/>vt R. P. tum illum retegeret, tum proportionem quam crede<lb/>ret e&longs;&longs;e veriorem manife&longs;taret; idcircò R. P. con&longs;crip&longs;it, edi<lb/>ditque nuper Epistolam aliam hocce Titulo,<emph.end type="italics"/> Phy&longs;ica <pb/>Demon&longs;tratio, qua ratio, men&longs;ura, modus, ac poten<lb/>tia accelerationis motus in naturali de&longs;cen&longs;u grauium <lb/>determinantur; aduer&longs;us nuper excogitatam à <emph type="italics"/>G<emph.end type="italics"/>alileo <lb/>Galilei Florentino Philo&longs;opho, ac Mathe matico de <lb/>eodem motu P&longs;eudo &longs;cientiam. <emph type="italics"/>Hæc ergo Epi&longs;tola e&longs;t, <lb/>ad quam heic primùm Respondetur.<emph.end type="italics"/> A pag. </s>

<s>Status Controuer&longs;iæ. </s>

<s><emph type="italics"/>Quæritur nimirùm, An, cùm lapide, v. </s>

<s><emph type="italics"/>Quæritur nimirùm, An, cùm lapide, v. c. ex alto cadente, <lb/>accipere liceat primum quoddam spatium, vt vnam orgyiam; <lb/>& habe re pro momento, &longs;eu tempore primo illud quod effluit, <lb/>donec lapis per hanc orgyiam decidit: & pro gradu celeritatis <lb/>primo eam celeritatem, quæ in fine primi huius temporis acqui<lb/>&longs;ita e&longs;t: An inquam, acceptis deinceps æqualibus &longs;patijs, tempo<lb/>ribus, & gradibus, cen&longs;eri debeat lapis motu&longs;-ve ip&longs;ius tum <lb/>acqui&longs;u&longs;&longs;e duos celeritatis gradus, cùm e&longs;t &longs;uperata &longs;ecunda <lb/>orgyia, licet &longs;ecundum tempus nondum totum effluxerit, ac <lb/>pari modo treis, cùm tertia, quatuor cum quarta, &c. </s>

<s>ex alto cadente, <lb/>accipere liceat primum quoddam spatium, vt vnam orgyiam; <lb/>& habe re pro momento, &longs;eu tempore primo illud quod effluit, <lb/>donec lapis per hanc orgyiam decidit: & pro gradu celeritatis <lb/>primo eam celeritatem, quæ in fine primi huius temporis acqui<lb/>&longs;ita e&longs;t: An inquam, acceptis deinceps æqualibus &longs;patijs, tempo<lb/>ribus, & gradibus, cen&longs;eri debeat lapis motu&longs;-ve ip&longs;ius tum <lb/>acqui&longs;u&longs;&longs;e duos celeritatis gradus, cùm e&longs;t &longs;uperata &longs;ecunda <lb/>orgyia, licet &longs;ecundum tempus nondum totum effluxerit, ac <lb/>pari modo treis, cùm tertia, quatuor cum quarta, &c. </s>

<s>adeò vt <lb/>&longs;emper velocitates &longs;e habeant &longs;ieut &longs;patia, quòd R. P. conten<lb/>dit: An potiùs cen&longs;eride beat <expan abbr="t&utilde;">tum</expan> acqui&longs;u&longs;&longs;e duos celeritatis gra<lb/>dus, cùm effluxit &longs;ecundum tempus, licet plura spatia, quàm <lb/>duo &longs;uperata &longs;int: ac pari modo treis, cùm tertium, quatuor, <lb/><gap/>ùm quartum, &c. </s>

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<s>De Motus æquabiliter <lb/>accelerati definitione. </s>

<s><emph type="italics"/>Definit<emph.end type="italics"/> G<emph type="italics"/>alileus Motum æquabiliter acceleratum (qua<lb/>lis grauibus decidentibus competit) illum,<emph.end type="italics"/> qui à quiete rece<lb/>dens, temporibus æqualibus æqualia celeritatis mo<lb/>menta acquirit. <emph type="italics"/>Jd autem improbans R. P. contendit po<lb/>tiùs definiendum cum vulgari &longs;ententia illum,<emph.end type="italics"/> qui æquali<lb/>bus &longs;patiis æqualia celeritatis augmenta acqu<gap/>it. <emph type="italics"/>Quan<lb/>quam ex Galilei definitione præclarè intelligitur accelerationis <lb/>æquabilitas: prout incre&longs;<gap/>s celeritas &longs;e habet vt linea inter <lb/>latera memorati Trianguli ab apice v&longs;que in ba&longs;im incre&longs;cen<gap/><lb/>& hæc linea ideò incre&longs;cit æquabiliter, quòd &longs;ecundum parteis<lb/>laterum æqualeis (per quas dictum e&longs;t repræ&longs;entari tempora) <lb/>additamenta continuò æqualia acquirat.<emph.end type="italics"/> E<emph type="italics"/>x definitione au<lb/>tem R. </s>

<s>Patri probata, nihil tale potest intelligi: cùm nulla <lb/>facta temporis mentione, & &longs;umptis partibus lateris trianguli <lb/>pro spatiis, & interceptis triangulis pro celeritatis gradibus, <lb/>con&longs;tet, &longs;i totidem &longs;emper addantur triangula, quot lateris par<lb/>tes, creatum iri triangulum totalem, cuius area inæquabili&longs;<lb/>&longs;imè ab apice in ba&longs;im incre&longs;cat.<emph.end type="italics"/> A p. </s>

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<s>De Paralogi&longs;mo, <lb/>qui Galileo Definitionem &longs;puriam impugnan<lb/>ti obiicitur. </s>

<s><emph type="italics"/>Impugnat<emph.end type="italics"/> G<emph type="italics"/>alileus definitionem R. </s>

<s><emph type="italics"/>Impugnat<emph.end type="italics"/> G<emph type="italics"/>alileus definitionem R. </s>

<s>Patri probatam, <lb/>quòd &longs;i velocitates e&longs;&longs;ent, vt emen&longs;a &longs;patia, atque idcircò <lb/>&longs;patium v. c. duplum percurreretur velocitate dupla illius, qua <lb/>dimidium: &longs;equeretur duplum, & dimidium, &longs;eu totum, & <lb/>partem, eodem, aut æquali tempore percurri. </s>

<s>Patri probatam, <lb/>quòd &longs;i velocitates e&longs;&longs;ent, vt emen&longs;a &longs;patia, atque idcircò <lb/>&longs;patium v. </s>

<s>duplum percurreretur velocitate dupla illius, qua <lb/>dimidium: &longs;equeretur duplum, & dimidium, &longs;eu totum, & <lb/>partem, eodem, aut æquali tempore percurri. </s>

<s>Nempe &longs;eu <lb/>motus æquabilis, &longs;eu acceleratus æquabiliter &longs;it, non potest ce<lb/>leritas e&longs;&longs;e dupla per duplum &longs;patij, quin ea ex&longs;i&longs;tente vbique <lb/>dupla, duplæ partes percurrantur quibu&longs;libet temporibus, &longs;ic<lb/>que perueniatur eodem tempore ad dupli, & ad dimidij finem. <lb/></s>

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<s>At verò <lb/>heic quoque abs re præteritur primum primæ partis dimidium: <lb/>& maximè cùm requiratur, quæ accelerationis &longs;it ratio non <lb/>à medio v&longs;que primæ partis, &longs;ed ab eius v&longs;que initio. </s>

<s>Peruer<lb/>tit etiam R. P. </s>

<s>Peruer<lb/>tit etiam R. P. </s>

<s>Arithmeticam progreßionem, qua &longs;uperiùs <lb/>&longs;tatuens velocitates e&longs;&longs;e, vt &longs;patia, voluit vni parti integræ, non <lb/>eius dimidio competere vnum celeritatis gradum, duobus <lb/>duos, &c. </s>

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<s><emph type="center"/>EPISTOLÆ SECVNDÆ<emph.end type="center"/></s>

<s><emph type="center"/>EPISTOLÆ SECVNDÆ<emph.end type="center"/></s>

<s>Scribendi Occa&longs;io. </s>

<s><emph type="italics"/>Reu. Pater vi&longs;o &longs;uperioris Epistolæ autographo, ip&longs;am <lb/>edi non improbauit, &longs;i modò attexeretur alia, quam &longs;ubinde <lb/>&longs;crip&longs;it, in&longs;crip&longs;itque<emph.end type="italics"/> Vindicias Phy&longs;icæ Demon&longs;tratio<lb/>nis. <emph type="italics"/>Qùia verò R. P. profitetur &longs;e&longs;e in ea ignotam Autbori <lb/>veritatem maiori iam luce illu&longs;tratam aperire, & ab errore <lb/>vindicatam exhibere; ac aliunde queritur frequens ea &longs;ibi af<lb/>fingi quæ nec dixerit, nec ex traditis à &longs;e principijs potuerint <lb/>deduci; idcircò &longs;ic edi vi&longs;um e&longs;t Vindicias, vt Exceptio inter<lb/>&longs;eratur, ad explorandum quî fieri poßit, vt veritatem &longs;ic il<lb/>lu&longs;tratam, vindicatamque Author non videat, & ad eluen<lb/>dum labem illam, qua ad&longs;pergi per&longs;en&longs;it &longs;e, ob affictionem to<lb/>ties obiectam.<emph.end type="italics"/> A p. </s>

<s>Pater vi&longs;o &longs;uperioris Epistolæ autographo, ip&longs;am <lb/>edi non improbauit, &longs;i modò attexeretur alia, quam &longs;ubinde <lb/>&longs;crip&longs;it, in&longs;crip&longs;itque<emph.end type="italics"/> Vindicias Phy&longs;icæ Demon&longs;tratio<lb/>nis. <emph type="italics"/>Qùia verò R. P. profitetur &longs;e&longs;e in ea ignotam Autbori <lb/>veritatem maiori iam luce illu&longs;tratam aperire, & ab errore <lb/>vindicatam exhibere; ac aliunde queritur frequens ea &longs;ibi af<lb/>fingi quæ nec dixerit, nec ex traditis à &longs;e principijs potuerint <lb/>deduci; idcircò &longs;ic edi vi&longs;um e&longs;t Vindicias, vt Exceptio inter<lb/>&longs;eratur, ad explorandum quî fieri poßit, vt veritatem &longs;ic il<lb/>lu&longs;tratam, vindicatamque Author non videat, & ad eluen<lb/>dum labem illam, qua ad&longs;pergi per&longs;en&longs;it &longs;e, ob affictionem to<lb/>ties obiectam.<emph.end type="italics"/> A p. </s>

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<s>Neque enim po&longs;&longs;unt velocitatis gradus per triangulorum re<lb/>præ&longs;entari ba&longs;eis, &longs;i per parteis laterum repræ&longs;ententur &longs;patia, <lb/>vt R. P. vult; tum quòd nulla habita temporis mentione <gap/><lb/>t<gap/>g<gap/> poß<gap/> difformitas mira; tum quòd gradus &longs;emel acqui<lb/>&longs;itus aut perire debeat, aut nihil agere, neque poßit duplum <lb/>illius, qui acquiritur; tum quòd &longs;it futurum vt &longs;ecundo tempo<lb/>re octo penè spatia primo æqualia percurrantur. </s>

<s>Confundit <lb/>R. P. </s>

<s>Confundit <lb/>R. P. </s>

<s>Vniformitatem cum Proportione, dum progreßiones<emph.end type="italics"/><lb/>G<emph type="italics"/>eometricas non minùs e&longs;&longs;e vniformeis, quàm Arithmeticas <lb/>vult: ac in eadem rursùs incidit Incommoda, dum in difformi <lb/>Triangulo vult iteratò spatia per laterum parteis, potiu&longs;quàm <lb/>per triangulos interceptos repræ&longs;entari.<emph.end type="italics"/> A p. </s>

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<s>De Paralogi&longs;mo, <lb/>qui Galileo Definitionem &longs;puriam impugnan<lb/>ti obiicitur. </s>

<s><emph type="italics"/>Magno quidem molimine conatur R. P. </s>

<s><emph type="italics"/>Magno quidem molimine conatur R. P. </s>

<s>Paralogi&longs;mum <lb/>o&longs;tendere: &longs;ed fru&longs;trà nihilominùs; cùm &longs;eu varios &longs;en&longs;us <lb/>di&longs;tinguat, &longs;eu propo&longs;itiones retexat, &longs;eu con&longs;equutionem ex<lb/>pendat, nihil aliud rursùs, quàm quæ&longs;itum, &longs;eu principium (vt <lb/>fuerat illi <expan abbr="obiect&utilde;">obiectum</expan>) petat; aut in &longs;eip&longs;um etiam, vbi retorquere <lb/>quidpiam vult, mutato nomine, concludat. </s>

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<s>De <lb/>quodam lap&longs;u emendando circa cau&longs;&longs;am Phy<lb/>&longs;icam accelerati grauium motus. </s>

<s><emph type="italics"/>Quod R. P. in Vindicijs ad Artic. </s>

<s><emph type="italics"/>Quod R. P. in Vindicijs ad Artic. XL. de Phy&longs;ica<emph.end type="italics"/><pb/><emph type="italics"/>cau&longs;&longs;a accelerationis di&longs;&longs;erüerit, docendo &longs;olam grauitatem <lb/>e&longs;&longs;e cau&longs;&longs;am initij motus, & &longs;olùm medium, putà aërem e&longs;&longs;e <lb/>cau&longs;&longs;am accelerationis, quatenus à fronte re&longs;iliens, & à tergo <lb/>claudem, graue vrget; cùm alioquin &longs;ola grauitate agente, &longs;i<lb/>bique &longs;imili manente, vt in vacuo, de&longs;cen&longs;us foret vniformis, <lb/>&longs;imili&longs;que &longs;ui per&longs;eueraturus: idcircò an&longs;a & accepta, & in <lb/>hunc locum dimi&longs;&longs;a e&longs;t adiiciendi quidpiam de Phy&longs;ica cau&longs;&longs;a. <lb/></s>

<s>XL. de Phy&longs;ica<emph.end type="italics"/><pb/><emph type="italics"/>cau&longs;&longs;a accelerationis di&longs;&longs;erüerit, docendo &longs;olam grauitatem <lb/>e&longs;&longs;e cau&longs;&longs;am initij motus, & &longs;olùm medium, putà aërem e&longs;&longs;e <lb/>cau&longs;&longs;am accelerationis, quatenus à fronte re&longs;iliens, & à tergo <lb/>claudem, graue vrget; cùm alioquin &longs;ola grauitate agente, &longs;i<lb/>bique &longs;imili manente, vt in vacuo, de&longs;cen&longs;us foret vniformis, <lb/>&longs;imili&longs;que &longs;ui per&longs;eueraturus: idcircò an&longs;a & accepta, & in <lb/>hunc locum dimi&longs;&longs;a e&longs;t adiiciendi quidpiam de Phy&longs;ica cau&longs;&longs;a. <lb/></s>

<s>Nam primùm quidem paulò fu&longs;iùs deducitur lap&longs;us indicatus <lb/>ad calcem &longs;uperioris Epistolæ: declarando videlicet, quo pro<lb/>gre&longs;&longs;u tentatum fui&longs;&longs;et in Epi&longs;tolis<emph.end type="italics"/> de Motu impre&longs;&longs;o à <lb/>motore tran&longs;lato <emph type="italics"/>cau&longs;&longs;am dicere, quamobrem grauia acce<lb/>lerentur iuxta progreßionem numerorum imparium ab vnita<lb/>te inc&oelig;ptorum; & quemadmodum talis cau&longs;&longs;a fui&longs;&longs;et agnita <lb/>tum primo momento &longs;ola attractrix Terræ vis, quæ imprime<lb/>ret &longs;ingularem ictum: tum &longs;ecundo, & reliquis tam eadem <lb/>attractrix, quàm aër à tergo &longs;uccedens, in&longs;tan&longs;que, adeò vt <lb/>quolibet momento duo qua&longs;i ictus imprimerentur: &longs;icque & <lb/>primo momento vnus acquireretur velocitatis gradus, quo &longs;u<lb/>peraretur vnum &longs;patium: &longs;equente autem quolibet &longs;uper-ad<lb/>derentur duo, e&longs;&longs;entque proinde tres, quinque, &longs;eptem, &c. <lb/></s>

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<s>Quare & e&longs;&longs;e &longs;ecurus pote&longs;t <lb/>iri deinceps nihil inqui&longs;itum in ea, quæ &longs;e dicit habere <lb/>ob&longs;curiora, incertioraque; fore autem, vt &longs;olitum affectum, <lb/>venerationemque &longs;emper experiatur.<emph.end type="italics"/><pb/><gap desc="hr tag"/></s>

<s><emph type="center"/>EPISTOLÆ TERTIÆ.<emph.end type="center"/></s>

<s><emph type="center"/>EPISTOLÆ TERTIÆ.<emph.end type="center"/></s>

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<s>Fuerat & Po&longs;terior speciatim con&longs;cripta decla<lb/>randæ inanitati rationis illius, quæ aduer&longs;us A&longs;&longs;ertores motus <lb/>Telluris peti &longs;oleret ex eo, quòd &longs;agitta &longs;ursùm euibrata è <lb/>puppi, dum nauis moueretur, non in puppim recideret, &longs;ed in <lb/>aquam à tergo puppis, quæ interim &longs;ubducta foret: ac fuerat <lb/>con&longs;equenter o&longs;ten&longs;a imbecillitas aliarum rationum complu<lb/>rium, quæ &longs;olent ij&longs;demobiici. </s>

<s>Præstita, inquam, hæc fue<lb/>rant; cùm R. P. </s>

<s>Præstita, inquam, hæc fue<lb/>rant; cùm R. P. </s>

<s>Epi&longs;tolis vi&longs;is, ea ex vtraque impugnauit, <lb/>quæ potißimùm di&longs;plicuerunt.<emph.end type="italics"/> A p. </s>

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<s><emph type="italics"/>Qualem deinceps Paralogi&longs;mum R. P. detexerit, &longs;atis <lb/>est, &longs;uperque in Epi&longs;tolis &longs;uperioribus adnotatum. </s>

<s>Quod &longs;u<lb/>perest: cùm mota, v. </s>

<s>Quod &longs;u<lb/>perest: cùm mota, v. c. naui, lapis ex ea proiicitur &longs;ursùm; is <lb/>apparet quidem tam proiectori, quàm omnibus, qui in naui <lb/>&longs;unt, a&longs;cendere, de&longs;cenderéque &longs;ecundum perpendiculum: &longs;ed <lb/>reuerâ tamen a&longs;cendit, de&longs;cenditque obliquè (vti & apparet <lb/>quie&longs;centibus in littore) de&longs;cribit nempe lineam curuam, quam <lb/>dicunt parabolicam: cau&longs;&longs;aque e&longs;t, quia manus proiiciens vt<lb/>cumque &longs;ursùm moueri appareat, reuerâ tamen mouetur obli<lb/>què, deflexa nempe à motu nauis, qui illam, dum attollitur,<emph.end type="italics"/><pb/><emph type="italics"/>abducit vnà cum corpore ip&longs;ius proiectoris in latus, &longs;iue &longs;ecun<lb/>dum horizontem. </s>

<s>naui, lapis ex ea proiicitur &longs;ursùm; is <lb/>apparet quidem tam proiectori, quàm omnibus, qui in naui <lb/>&longs;unt, a&longs;cendere, de&longs;cenderéque &longs;ecundum perpendiculum: &longs;ed <lb/>reuerâ tamen a&longs;cendit, de&longs;cenditque obliquè (vti & apparet <lb/>quie&longs;centibus in littore) de&longs;cribit nempe lineam curuam, quam <lb/>dicunt parabolicam: cau&longs;&longs;aque e&longs;t, quia manus proiiciens vt<lb/>cumque &longs;ursùm moueri appareat, reuerâ tamen mouetur obli<lb/>què, deflexa nempe à motu nauis, qui illam, dum attollitur,<emph.end type="italics"/><pb/><emph type="italics"/>abducit vnà cum corpore ip&longs;ius proiectoris in latus, &longs;iue &longs;ecun<lb/>dum horizontem. </s>

<s>Et quoniam Author dixerat,<emph.end type="italics"/> Vim im<lb/>pellentem mobile &longs;ursùm, non modò non de&longs;trui, &longs;ed <lb/>ne vlla quidem ratione imminui à vi depellente in la<lb/>tus (<emph type="italics"/>quippe lapis ille neque minùs peruenit aliùm, quàm &longs;i <lb/>pari vi, naui quie&longs;cente, pro: iceretur à manu: vti neque mi<lb/>nùs in latus, quàm &longs;i immota manu veheretur &longs;olo motu nauis) <lb/>Idcircò R. P. i&longs;tud improbans, obiicit, quod e&longs;&longs;e apud peritos <lb/>Effatum ait,<emph.end type="italics"/> Mobile quodcumque duobus motibus in <lb/>diuer&longs;as parteis actis, tantò &longs;egniùs deferri in vnum <lb/>terminum, quantò fortiùs in alterum tendit. <emph type="italics"/>Sed cùm <lb/>hoc e&longs;&longs;e poßit verum, donec mobili iam &longs;eparato à motore &longs;u<lb/>peruenit vis, quæ ip&longs;um deflectat: fal&longs;um e&longs;t tamen, &longs;i nihil <lb/>noui à proiectore v&longs;que interueniat, in quo & vis ip&longs;ius pro<lb/>pria, & vis corporis ip&longs;um transferentis in vnam coïerint, quæ <lb/>tantùm &longs;it alterutrâ fortior, quantùm altera fortis e&longs;t; vt in <lb/>exemplo allato con&longs;tat, in quo quicquid e&longs;t motus &longs;ur&longs;um, à ma<lb/>nu est; quicquid motus prorsùm, à naui; & quod dee&longs;t virtuti <lb/>manus propriæ ad proiiciendum non minus altum &longs;ecundum li<lb/>neam curuam, quàm &longs;ecundum rectam, &longs;uppletur à vi tran&longs;<lb/>latitia nauis; vti & quod deest naui ad adigendum non mi<lb/>nus pror&longs;um &longs;ecundum curua, quàm &longs;ecundum rectam, <lb/>&longs;uppletur à vi proiectitia manus. </s>

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<s>Et <lb/>traducit quidem Authorem R. P. qua&longs;i a&longs;&longs;eruerit moueri Ter<lb/>ram non diurna modò reuolutione circa axem proprium, verùm <lb/>etiam annuo motu circa Solem: vnde & ait tolerabilius fui&longs;&longs;e, <lb/>etiam per &longs;acras Literas, &longs;i a&longs;&longs;ertus fui&longs;&longs;et diurnus dumtaxat. <lb/></s>

<s>Attamen, neque a&longs;&longs;erendo, &longs;ed proponendo &longs;olummodò de mo<lb/>tu Terræ actum e&longs;t; neque ea loca Scripturæ &longs;acræ, quæ aduer<lb/>&longs;us motum Terræ obiiciuntur, comperiuntur minùs aduer<lb/>&longs;us diurnum, quàm aduer&longs;us annuum e&longs;&longs;e comparata; neque <lb/>non præclare addit R. P. debere no&longs;tram Philo&longs;ophiam fidei <lb/>Chri&longs;tianæ e&longs;&longs;e con&longs;onam; &longs;ed &longs;upere&longs;t no&longs;&longs;e quid &longs;it di&longs;&longs;onum; <lb/>cùm non statim quicquid videtur repugnare Literis &longs;acris id<lb/>circò reuerà repugnat, vt rectè o&longs;tendit D. </s>

<s>Augu&longs;tinus ad<lb/>uer&longs;us eos, qui dicunt cælum Sphæricum, cùm Scriptura dicat<emph.end type="italics"/><lb/>exten&longs;um, vt pellem. </s>

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<s>De Con<lb/>&longs;equutionibus ex Terra Planetis inter&longs;ita <pb/>ductis, déque ignorata Copernicanæ opinionis <lb/>improbatione. </s>

<s>O<emph type="italics"/>biicit R. P. </s>

<s>O<emph type="italics"/>biicit R. P. </s>

<s>Si moueri Terram inter Planetas per<lb/>&longs;ua&longs;um &longs;it, creditum quoque iri ip&longs;am e&longs;&longs;e<emph.end type="italics"/> P<emph type="italics"/>lanetam; & e&longs;&longs;e in <lb/>alijs<emph.end type="italics"/> P<emph type="italics"/>lanetis, Stelli&longs;que &longs;uosincolas; ac iri <expan abbr="vocat&utilde;">vocatum</expan> in &longs;u&longs;picio<lb/>nem<emph.end type="italics"/> G<emph type="italics"/>ene&longs;in,<emph.end type="italics"/> I<emph type="italics"/>ncarnationem, Euangelium, fidem<emph.end type="italics"/> C<emph type="italics"/>hri&longs;tia<lb/>nam, quæ docet A&longs;tra non ad hominum, aliarumve rerum ha<lb/>bitationem e&longs;&longs;e facta, &longs;ed vt illuminent, f&oelig;cundentque Terram. <lb/></s>

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<s>1. l. 17. lege <emph type="italics"/>tantumdem.<emph.end type="italics"/> p 2. l. 16. <lb/><emph type="italics"/>heixc.<emph.end type="italics"/> p. </s>

<s>17. lege <emph type="italics"/>tantumdem.<emph.end type="italics"/> p 2. l. </s>

<s>16. <lb/><emph type="italics"/>heixc.<emph.end type="italics"/> p. </s>

<s>6. l. 4. <emph type="italics"/>at non.<emph.end type="italics"/> l. 22 XLVIII. fol. </s>

<s>22 XLVIII. fol. </s>

<s>1 l. 17. <emph type="italics"/>conficere.<emph.end type="italics"/><lb/>p. </s>

<s>17. <emph type="italics"/>conficere.<emph.end type="italics"/><lb/>p. </s>

<s>3 l. 2<gap/>. <emph type="italics"/>e<gap/>ruam Omi&longs;&longs;a in i<gap/>xtu.<emph.end type="italics"/> p. </s>

<s>2<gap/>. <emph type="italics"/>e<gap/>ruam Omi&longs;&longs;a in i<gap/>xtu.<emph.end type="italics"/> p. </s>

<s>242. 13. <lb/>octingenties. </s>

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<s>270. <lb/>24. An&longs;toteleæ &longs;ententiæ. </s>

<s>285, 2 ad hoc. <emph type="italics"/>In ip&longs;is Errata.<emph.end type="italics"/> l. </s>

<s>285, 2 ad hoc. <emph type="italics"/>In ip&longs;is Errata.<emph.end type="italics"/> l. 10. lege 128. 26. </s>

<s><emph type="center"/>DE PROPORTIONE, <lb/>QVA GRAVIA DECIDENTIA <lb/>ACCELERANTVR.<emph.end type="center"/></s>

<s><emph type="center"/>EPISTOLA PRIMA.<emph.end type="center"/><lb/><gap desc="hr tag"/></s>

<s><emph type="center"/>EPISTOLA PRIMA.<emph.end type="center"/><lb/><gap desc="hr tag"/></s>

<s><emph type="center"/><emph type="italics"/>ADMODVM REVERENDO, <lb/>& religio&longs;ißimo, doctißimoque Viro,<emph.end type="italics"/> P. <lb/>PETRO CAZRÆO <emph type="italics"/>Societatis<emph.end type="italics"/> IESV, <lb/><emph type="italics"/>Meten&longs;is Collegij Rectori &longs;apientißimo.<emph.end type="italics"/><emph.end type="center"/></s>

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

<s><emph type="center"/>PETRVS GASSENDVS S.<emph.end type="center"/>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>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> 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>Heinc e&longs;t, cur licet ni<lb/>hil in me &longs;it, quod qua&longs;i par pari rependam; adnitar <lb/>tamen, quantum licet, te&longs;tari gratitudinem, eandem <lb/>tecum r<gap/>m meditatus, ac eas dubitandi rationes, quæ <lb/>mihi &longs;e&longs;e inter legendum vltrò obtulere, reponens. <lb/></s>

<s>Quippe lógè ab&longs;um abeo, quem tu me e&longs;&longs;e protua illa <lb/>rara comitate volui&longs;ti, dum decreui&longs;ti <expan abbr="Iudic&etilde;">Iudicem</expan> tuæ hu<lb/>ius Demon&longs;trationis. </s>

<s>Is nimirùm &longs;um, qui aliud <lb/>nihil valeam, quàm difficultates qua&longs;dam excitare, ac <lb/>tibimet proponere, qui in hi&longs;ce rebus & diuti&longs;&longs;imè, & <lb/>curio&longs;i&longs;&longs;imè ver&longs;atus, ip&longs;as explanare facillimè po&longs;&longs;is. <lb/></s>

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<s>III. <expan abbr="Cæter&utilde;">Cæterum</expan> ea e&longs;t tua opinio, vt velocitates habeant <lb/>&longs;e quemadmodum &longs;patia; &longs;eu, vt tot gradus velocitatis <lb/>æquales primo acquirantur, quot &longs;unt partes æquales <lb/>&longs;patij, quæ po&longs;t primum, primoque gradu &longs;uperatum <lb/>decurruntur. </s>

<s>Siquidem toto &longs;patio diui&longs;o in decem <lb/>v. </s>

<s>Siquidem toto &longs;patio diui&longs;o in decem <lb/>v. c. orgyias; qualis, quantu&longs;que e&longs;t velocitatis gra<lb/>dus in fine primæ orgviæ acqui&longs;itus, taleis, tanto&longs;que <lb/>vis acqui&longs;itos in fine &longs;ecundæ duos, in fine tertiæ treis, <lb/>in fine quartæ quatuor, & ita deinceps, quov&longs;que in <pb pagenum="5"/>fine decimæ &longs;int decem. </s>

<s>orgyias; qualis, quantu&longs;que e&longs;t velocitatis gra<lb/>dus in fine primæ orgviæ acqui&longs;itus, taleis, tanto&longs;que <lb/>vis acqui&longs;itos in fine &longs;ecundæ duos, in fine tertiæ treis, <lb/>in fine quartæ quatuor, & ita deinceps, quov&longs;que in <pb pagenum="5"/>fine decimæ &longs;int decem. </s>

<s>At Galileus vult potiùs &longs;e ve<lb/>locitates habere &longs;icut tempora; &longs;iue gradus velocitatis <lb/>æqualeis primo tot acquiri, quot temporis partes pri<lb/>mæ æquales po&longs;t ip&longs;am fluunt. </s>

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<s>Itaque illud heic apponendo, vides primùm <pb pagenum="6"/>lineas AB, AC, angulum creanteis in A, &longs;ic diui&longs;as e&longs;&longs;e <lb/>heinc inde in parteis æqualeis, ad puncta D, E, F, G, H, <lb/>I, K, L (po&longs;&longs;ent autem in longè plureis continuatæ di<lb/>uidi) vt lineæ ductæ cùm inter ip&longs;a puncta, tùm ex ip&longs;is <lb/>in puncta M, N, O, totum &longs;patium KAL di&longs;pe&longs;cant <lb/>in triangula inter <lb/><figure id="fig2"/><lb/>&longs;e &longs;imilia, ac pror<lb/>sù æqualia. </s>

<s>Cùm <lb/>po&longs;&longs;imus porto <lb/>habere punctum <lb/>A pro initio tem<lb/>poris, pro initio <lb/>&longs;patij, pro initio <lb/>velocitatis, quæ <lb/>tria heic in motu <lb/>&longs;pectantur, ac vna <lb/>cùm ip&longs;o inci<lb/>piunt; Po&longs;&longs;umus imprimis habere parteis æqualeis al<lb/>terutrius, aut vtriu&longs;que lineæ AB, AC pro partibus, <lb/>&longs;iue momentis æqualibus temporis ab initio fluentis, <lb/>adeòproinde, vt AE, v. </s>

<s>repræ&longs;entet <expan abbr="prim&utilde;">primum</expan> momen<lb/>tum, EG &longs;ecundum, GI: tertium, IL quartum. <lb/></s>

<s>Po&longs;&longs;umus &longs;ecundò habere æqualia illa triangula pro <lb/>æqualibus &longs;patij partibus, quæ ab initio percurrun<lb/>tur; adeò vt ductâ &longs;eor&longs;im lineâ PQ ca&longs;um refe<lb/>rente per orgyias &longs;exdecim, Triangulum ADE <lb/>repræ&longs;entet primam orgyiam PR, quæ primò mo<lb/>mento percurritur; tria proxima, treis orgyias RS, <lb/>quæ &longs;ecundo; quinque &longs;equentia quinque orgyias <lb/>ST, quæ tertiò; & &longs;eptem &longs;uccedentia &longs;eptem or-<pb pagenum="7"/>gyias TQ, quæ quarto. </s>

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<s>Nam quod &longs;pectat quidem ad illam à te laudatam <lb/>definitionem, qua motus æquabiliter acceleratus de&longs;<lb/>cribitur is, <emph type="italics"/>Qui æqualibus spatiis æqualia celeritatis aug<lb/>menta acquirit:<emph.end type="italics"/> dic amabò quanam ratione concipere <lb/>exinde licear acceleratum æquabiliter motum? </s>

<s>E&longs;to <lb/>enim &longs;patium percurrendum v. </s>

<s>E&longs;to <lb/>enim &longs;patium percurrendum v. c. linea AB in par<lb/>teis æqualeis diui&longs;a ad puncta C, D, E, F, G, I, K. <lb/></s>

<s>linea AB in par<lb/>teis æqualeis diui&longs;a ad puncta C, D, E, F, G, I, K. <lb/></s>

<s>Decidat mobile ex A; & in C fine primæ partis ac<lb/>qui&longs;ierit primum velocitatis gradum; in D autem <pb pagenum="13"/>&longs;ecundum, quo ad priorem per&longs;euerantem iunctp <lb/><figure id="fig5"/><lb/>duo iam &longs;int: in E tertium, quo <lb/>iuncto ad duos &longs;uperiores, per<lb/>&longs;euerantei&longs;que &longs;int tres; in F <lb/>quartum, & ita porrò, quo<lb/>v&longs;que in B acqui&longs;ierit nonum, <lb/>quo iuncto cum octo antece<lb/>dentibus &longs;int nouem. </s>

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<s>Nihil e&longs;t <lb/>opus, vt de&longs;ude<gap/> ad o&longs;tendendum non increui&longs;&longs;e <lb/>velocitatem æquabiliter, eodemve tenore ex C in D, <lb/>quo inc&oelig;perat, perrexeratque v&longs;que in D; vt feci&longs;&longs;et <lb/>enim, oporteret de&longs;criptum e&longs;&longs;e non quadrangulum <lb/>LD con&longs;tans ex duobus triangulis; &longs;ed trapezion CN <lb/>con&longs;titutum ex tribus. </s>

<s>Eadem autem ratione mani<lb/>fe&longs;tum e&longs;t, &longs;i ad DE aptentur tria triangula, defutura <lb/>duo; &longs;i ad EF quatuor, defutura tria, & ita deinceps, <pb pagenum="14"/>quov&longs;que, &longs;i ad KB aptentur nouem, &longs;int defutura <lb/>octo; vt proinde intelligamus totidem dce&longs;&longs;e ad acce<lb/>lerationis æquabilitatem velocitatis gradus, quot nu<lb/>merare licet triangulos ad læuam è regione cuiu&longs;que <lb/>partis, complendo &longs;ummam triangulorum APB. <lb/></s>

<s>Con&longs;tare ergo videtur Motum æquabiliter accelera<lb/>tum definiti non po&longs;&longs;e illum, <emph type="italics"/>Qui æquabilibus &longs;patiis <lb/>æqualia celeritatis augmenta acquirat;<emph.end type="italics"/> &longs;ed potiùs illum, <lb/><emph type="italics"/>Qui acquirat æqualia æqualibus temporibus:<emph.end type="italics"/> atque idcircò <lb/>definitionem à Galileo traditam e&longs;&longs;e meritò præfe<lb/>rendam. </s>

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<s>Rem certe in <lb/>hunc modum concipio. </s>

<s>Intelligatur AC diui&longs;a in <lb/>duodecim parteis æqualcis, ac proinde eius dimidium <pb pagenum="16"/>AB, &longs;eu ip&longs;i æqualrs DE in &longs;ex: &longs;intque primùm <lb/>duo mobilia, quorum vnum di&longs;cedat ex A <lb/><figure id="fig7"/><lb/>ver&longs;us C, eodem momento, quo aliud ex D <lb/>ver&longs;us E. </s>

<s>Notum e&longs;t, &longs;i vtrumque quidem <lb/>ferretur non accelerato, &longs;ed æquabili motu, <lb/>euenturum e&longs;&longs;e, vt velocitate illius ex&longs;i&longs;tente <lb/>dupla ad velocitatem i&longs;tius, illud perueniret <lb/>in C eodem momento, quo i&longs;tud in E; quo<lb/>niam &longs;patium ab illo &longs;uperatum foret vbi<lb/>que ad &longs;patium ab i&longs;to &longs;uperatum duplum, hoc e&longs;t, <lb/>forent ab illo &longs;uperatæ duæ partes, cùm ab i&longs;to vna; <lb/>ab illo quatuor, cùm ab hoc duæ, &c. </s>

<s>quatenus &longs;pa<lb/>tia &longs;e haberent vbique vt velocitates, hoc e&longs;t veloci<lb/>tas per totam AC e&longs;&longs;et vbique dupla velocitatis per <lb/>totam DE. </s>

<s>quatenus &longs;pa<lb/>tia &longs;e haberent vbique vt velocitates, hoc e&longs;t veloci<lb/>tas per totam AC e&longs;&longs;et vbique dupla velocitatis per <lb/>totam DE. </s>

<s>At verò, quoniam heic agitur de motu <lb/>non æquabili, &longs;ed continenter accelerato; ita de&longs;cen<lb/>dant rur&longs;us mobilia eodem tempore, vnum ab A, <lb/>aliud à D, vt &longs;uccrefcentibus continuò velocitatis gra<lb/>dibus, illud perueniendo in C acqui&longs;ierit duodecim, <lb/>hoc perueniendo in E &longs;ex: Quæ&longs;o quid impediat, <lb/>quo minùs illud perueniat in C eodem tempore, quo <lb/>i&longs;tud in E? </s>

<s>Nam di&longs;crimen e&longs;t quidem inter mo<lb/>tum acceleratum, & æquabilem, quòd in æquabili <lb/>partes &longs;patiorum æquales percurrantur æqualibus <lb/>temporibus, vt &longs;ingulæ partes lineæ DE &longs;ingulis mi<lb/>nutis, & geminæ partes lineæ AC minutis item &longs;in<lb/>gulis; in accelerato non item: At in eo tamen motus <lb/>conueniunt, quòd vbique velocitas per totam AC <lb/>dupla &longs;it velocitatis per totam DE; & qua ratione <lb/>plures, plure&longs;que ex &longs;ingulis partibus lineæ DE <pb pagenum="17"/>percurruntur æqualibus temporibus, percurruntur <lb/>quoque plures, plure&longs;que ex geminatis lineæ AC. <lb/></s>

<s>Ex hoc autem &longs;it, vt quemadmodum in æquabili mo<lb/>tu, DE percurreb<gap/>tur &longs;ex minutis, & AC &longs;imiliter <lb/>&longs;ex, ob geminas parteis i&longs;tius corre&longs;pondenteis &longs;ingu<lb/>lis illius, ita in accelerato, &longs;i DE percurratur tribus <lb/>minutis, AC percurratur &longs;imiliter tribus; quòd dum <lb/>primo minuto percurritur pars illius vna, percurran<lb/>tur i&longs;tius duæ, ob ge minam velocitatem; & ob ean<lb/>dem cau&longs;&longs;am, dum &longs;ecundo minuto percurruntur <lb/>illius duæ, percurrantur i&longs;tius quatuor, dum tertio <lb/>demùm illius tres, percurrantur i&longs;tius &longs;ex. </s>

<s>Nim rùm <lb/>non alia ratione dici po&longs;&longs;ent habere &longs;e velocitates vt <lb/>&longs;patia: neque velocitas per totam AC dupla e&longs;&longs;et ve<lb/>locitatis per totam DE E&longs;to deinde vnicum mobile, <lb/>quod decedens ab A, tendat ver&longs;us C, & &longs;it rursùs <lb/>velocitas per totam AC dupla velocitatis per totam <lb/>AB, patet idem prorsùs dicendum de AC, re&longs;pectu <lb/>AB, quod dictum fuit de eadem re&longs;pectu DE. </s>

<s>Nam <lb/>in æquabili quidem motu oporteret mobile percur<lb/>rere &longs;imul, &longs;eu primo minuto primam, & &longs;ecundam <lb/>parteis; &longs;ecundo &longs;ecundam, & quartam; ac ita porrò <lb/>quov&longs;que &longs;exto, percurreret, &longs;eu attingeret &longs;imul <lb/>&longs;extam, atque duo &longs;ecimam. </s>

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<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"/><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>

<s>Tum globus idem in uit<emph.end type="italics"/> G<emph type="italics"/>alileus, non <lb/>&longs;olùm de&longs;cendet ad punctum B, &longs;ed eodem impetu vlteriùs <lb/>v&longs;que ad D, aut proximè ad illud, a&longs;cendet.<emph.end type="italics"/> S<emph type="italics"/>imiliter, &longs;i <lb/>globus idem è puncto E &longs;uspendatur, & item ad altitudinem<emph.end type="italics"/><pb pagenum="25"/><emph type="italics"/>eiu&longs;dem rectæ<emph.end type="italics"/> C<emph type="italics"/>D attollatur ad<emph.end type="italics"/> G, <emph type="italics"/>inde liberè dimi&longs;&longs;us, <lb/>pari modo ad eandem rectam CD, aut proximè ad eam <lb/>con&longs;cendet ver&longs;us H. Jmò, &longs;i ex F &longs;u&longs;pen&longs;us attollatur ad <lb/>I, inde feretur, v&longs;que ad K. </s>

<s>Per diuer&longs;os igitur illos arcus <lb/>decidens globus, &longs;emper ad æqualem altitudinem con&longs;cendit. <lb/></s>

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<s>Ex quo effici<lb/>tur, vt cùm res propriè attendenda non &longs;it, vbi cla<lb/>uus infra lineam defigitur, quòd tunc libratio &longs;implex <lb/>non &longs;it, &longs;ed mi&longs;tio duorum motuum, quorum im<lb/>petus &longs;e mutuò retundunt; &longs;it verò propriè atten<lb/>tenda, cùm clauo &longs;upra lineam defixo, vibrationis <lb/>motus &longs;implex e&longs;t; ideò non &longs;it exi&longs;timandum illam <lb/>qualemcumque interuallorum inæqualitatem in<lb/>terturbare negotium; ac poti&longs;&longs;imùm quidem, cùm <lb/>ip&longs;a ordinata &longs;int, ac eandem inter &longs;e, quàm fili, & <lb/>arcus prolixitates proportionem &longs;eruent. </s>

<s>Ad hæc, <lb/>id videtur præ&longs;ertim e&longs;&longs;e ob&longs;eruatione dignum in <lb/>his pendu orum vibrationibus, quòd, Si quatuor di<lb/>&longs;tinctos g obos quatuor di&longs;tinctis filis &longs;ic appendas, <lb/>vt primi longitudo &longs;it vnius, v. c. pedis, &longs;ecundi qua<lb/>tuor, tertij nouem, quarti &longs;exdecim; experturus &longs;is, <lb/>vbi omnes dimi&longs;&longs;i &longs;imul fuerint, quartum perfectu<lb/>rum vnam vibrationem eodem tempore, quo ter<lb/>tius interim perfecerit duas, &longs;ecundus treis, & primus <lb/>quatuor. </s>

<s>pedis, &longs;ecundi qua<lb/>tuor, tertij nouem, quarti &longs;exdecim; experturus &longs;is, <lb/>vbi omnes dimi&longs;&longs;i &longs;imul fuerint, quartum perfectu<lb/>rum vnam vibrationem eodem tempore, quo ter<lb/>tius interim perfecerit duas, &longs;ecundus treis, & primus <lb/>quatuor. </s>

<s>Scilicet exinde intelligitur, tum pendulo<lb/>rum vibrationes tantò &longs;egnius fieri, quantò earum <lb/>arcus planiores, &longs;iue inclinatiores &longs;unt; tum inclina<lb/>tiones arcuum men&longs;uratas &longs;ecundum varias perpen<lb/>diculi, &longs;eu fili longitudines, habere &longs;e perinde vt qua<lb/>drata temporum, ac vibrationes habere &longs;e recipro<gap/><lb/>vt ip&longs;as radices; &longs;icque rem eximiè quadrare ad &longs;u<lb/>periùs expo&longs;itam motus æquabilis rationem; tum <lb/>globum quartum non acquirere impetum ad eleua<lb/>tionem nece&longs;&longs;arium, ni&longs;i tempore duplo tertij, tri<lb/>plo &longs;ecundi, quadruplo primi; ac e&longs;&longs;e quidem im-<pb pagenum="28"/>petus omnium globorum inter &longs;e æqualeis; &longs;ed <expan abbr="quõ">quom</expan> <lb/>tempore impetus exprimitur à quarto &longs;emel, exprimi <lb/>à tert<gap/>o bis, à &longs;ecundo ter, à primo quater, &c. </s>

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<s>Et tamen, neque te <lb/>vel &longs;emel ip&longs;am explora&longs;&longs;e, fal&longs;amque comperi&longs;&longs;e di<lb/>cis, neque vllam rationem profers: &longs;ed cau&longs;aris &longs;olum<lb/>modo explorandi difficultatem; quam & repetis, <lb/>dum po&longs;tquam retuli&longs;ti tempora ab illo notata, no<lb/>tatis nempe, expen&longs;i&longs;que ponderibus aquæ, quæ è <lb/>clep&longs;ydra interim fluxi&longs;&longs;et: <emph type="italics"/>Quippe nemo,<emph.end type="italics"/> inquis, <emph type="italics"/>non <lb/>videt, quàm hic ob&longs;eruandi modus incertus &longs;it, & quàm <lb/>difficile, ne dicam impoßibile, tempus vtriu&longs;que illius de&longs;<lb/>cen&longs;us ad exactam men&longs;uram exigere, vel eo maximè no<lb/>mine, quòd in tanta celeritate initia, & fines horum mo<lb/>tuum &longs;atis præcisè aduerti, notarique po&longs;&longs;e non videantur.<emph.end type="italics"/><lb/>Sed nihil e&longs;t opus in&longs;i&longs;tam ad arguendum id non <lb/>&longs;ufficere; ni&longs;i aliunde aut resfactu impo&longs;&longs;ibilis de<lb/>mon&longs;tretur; aut ob&longs;eruator probetur fui&longs;&longs;e malæ fidei, <lb/>ac indiligens, & difficultates præcauere ne&longs;cius. </s>

<s>Ad<lb/>derem quemadmodum ip&longs;e rem explorare fuerim <lb/>conatus, tum dimi&longs;&longs;o per aërem globo, tum dela<lb/>bente globulo per tubulos vitreos etiam orgyiis dua<lb/>bus longiores, facto&longs;que nunc magis, nunc minùs de<lb/>cliueis, & adnotatis partibus æquis tum ad parietem, <lb/>&longs;ecundum quem globus decideret, tum ad vtram<lb/>que oram alueoli in tigno excauati, & tubulum quem<lb/>que continentis; ac &longs;imul adhibitis &longs;ociis, qui adno<lb/>tarent &longs;inguli parteis &longs;ingulas, quæ interim pertran<lb/>&longs;irentur, dum ip&longs;e temporis momenta nunc pul&longs;atio<lb/>nibus arteriæ, nunc itibus, reditibu&longs;que penduli di-<pb pagenum="32"/>&longs;tincta, vocibus mono&longs;yllabis cuique illorum &longs;igilla<lb/>tim a&longs;&longs;ignatis &longs;igni&longs;icarem: verùm memini rem ad te <lb/>per&longs;criptam; & circa hæc nimius iam &longs;um. </s>

<s><emph type="center"/><emph type="italics"/>De Experimentis circa ictum, impetumue grauium caden<lb/>tium, ad explorandum impetus-ne vt &longs;patium incre&longs;cat.<emph.end type="italics"/><emph.end type="center"/></s>

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<s>Nam Primò, &longs;it vas cylindricum <lb/>erectum, & continens aquam ad certam altitudi<lb/>nem, exempli cau&longs;sâ vnius pedis: Certum e&longs;t aquam <pb pagenum="36"/>in fundo &longs;ub&longs;tantem vrgeri, ac premi à &longs;uper ex&longs;tan<lb/>te (& ab ip&longs;a quidem &longs;uperficie) vt per&longs;picuum fit vel <lb/>ex vehementia, qua ex&longs;ilire deprehenditur, forami<lb/>ne ad ba&longs;in aperto. </s>

<s>Aperiatur ergo foramen, & &longs;u<lb/>perfusâ leniter aquâ, ita vt contineatur &longs;emper ad <lb/>eandem altitudinem, excipiatur aqua, quæ interim <lb/>effluet, dato tempore, v. </s>

<s>Aperiatur ergo foramen, & &longs;u<lb/>perfusâ leniter aquâ, ita vt contineatur &longs;emper ad <lb/>eandem altitudinem, excipiatur aqua, quæ interim <lb/>effluet, dato tempore, v. c. &longs;extantis minuti, ac &longs;it <lb/>illius men&longs;ura certa, exempli gratiâ, congius. </s>

<s>&longs;extantis minuti, ac &longs;it <lb/>illius men&longs;ura certa, exempli gratiâ, congius. </s>

<s>Vt <lb/>deinde tempore eodem, & per idem foramen ex&longs;i<lb/>liant duo congij, & aqua proinde &longs;it duplò compre&longs;<lb/>&longs;ior, ad quam nam v&longs;que altitudinem adaugendus <lb/>erit, complendu&longs;ve cylindrus? </s>

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<s>Quin <lb/>poterit etiam aliunde res facillimo negotio notari, &longs;i <lb/>repleto &longs;iue ad labium, &longs;iue ad certam v&longs;que altitudi<lb/>nem cylindro, & aperto foramine, totáque aqua vno <lb/>tenore, nullamque refundendo effluente, notentur in <lb/>va&longs;e aquæ decrementa æqualibus temporibus facta. <lb/></s>

<s>Quippe &longs;i interuallum vltimi decrementi fuerit vnius <lb/>v. </s>

<s>Quippe &longs;i interuallum vltimi decrementi fuerit vnius <lb/>v. c. pedis, erit interuallum penultimi trium, ante<lb/>penultimi quinque, antecedentis &longs;eptem, ac ita &longs;em<lb/>per procedendo per &longs;uccedenteis impareis: vnde & &longs;i <lb/>primi temporis initio fuerit altitudo pedum &longs;exde<lb/>cim, erit initio &longs;ecundi nouem, tertij quatuor, quar<lb/>ti vnius. </s>

<s>pedis, erit interuallum penultimi trium, ante<lb/>penultimi quinque, antecedentis &longs;eptem, ac ita &longs;em<lb/>per procedendo per &longs;uccedenteis impareis: vnde & &longs;i <lb/>primi temporis initio fuerit altitudo pedum &longs;exde<lb/>cim, erit initio &longs;ecundi nouem, tertij quatuor, quar<lb/>ti vnius. </s>

<s>Cùm ex&longs;ilitio verò aquæ continenter fiat <lb/>ex continente impetu, quo à &longs;uper&longs;tante vigetur, & <lb/>impetus i&longs;te nihil differat à continente velocitate, <pb pagenum="37"/>qua aqua &longs;uper&longs;tans continenter incumbit, ac premit; <lb/>An-non planum e&longs;t intelligere impetum, ac velocita<lb/>tem duplò maiorem fieri non ex altitudine dupla, <lb/>&longs;ed penitùs ex quadrupla; triplo non ex tripla, &longs;ed ex <lb/>nonupla, & ita deinceps? </s>

<s>Secundò, &longs;i alligatus vno <lb/>&longs;ui extremo ad parietem funis prælongus, altero ex<lb/>tremo dependeat ex fulcro, ac appen&longs;o pondere certo, <lb/>v. </s>

<s>Secundò, &longs;i alligatus vno <lb/>&longs;ui extremo ad parietem funis prælongus, altero ex<lb/>tremo dependeat ex fulcro, ac appen&longs;o pondere certo, <lb/>v. c. vnius libræ, ten&longs;ione &longs;it leni inter ip&longs;a extrema: <lb/>verò digitis verò, ita abducatur, vt vltro citróque horizon<lb/>taliter vibretur, &longs;eu eat, ac redeat certo tempore (erunt <lb/>autem itus, reditu&longs;que omnes æqui-temporanei, &longs;eu <lb/>tam primi, quam vltimi, tam longi, quàm breues <lb/>eiu&longs;dem prorsù, durationis) &longs;itque tempus tantum, <lb/>quantum inter&longs;titium ab vna artenæ pul&longs;atione ad <lb/>aliam Vt fiat funis duplò inten&longs;ior, & itus, reditu&longs;<lb/>que ip&longs;ius euadant duplò velociores, hoc e&longs;t æquali <lb/>tempore duo; quantum, putas, erit ponderis adden<lb/>dum? </s>

<s>vnius libræ, ten&longs;ione &longs;it leni inter ip&longs;a extrema: <lb/>verò digitis verò, ita abducatur, vt vltro citróque horizon<lb/>taliter vibretur, &longs;eu eat, ac redeat certo tempore (erunt <lb/>autem itus, reditu&longs;que omnes æqui-temporanei, &longs;eu <lb/>tam primi, quam vltimi, tam longi, quàm breues <lb/>eiu&longs;dem prorsù, durationis) &longs;itque tempus tantum, <lb/>quantum inter&longs;titium ab vna artenæ pul&longs;atione ad <lb/>aliam Vt fiat funis duplò inten&longs;ior, & itus, reditu&longs;<lb/>que ip&longs;ius euadant duplò velociores, hoc e&longs;t æquali <lb/>tempore duo; quantum, putas, erit ponderis adden<lb/>dum? </s>

<s>An duplum? </s>

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<s>E&longs;t etiam Tertiò heic repetendum, quod <lb/>iam antè dixi de globis ad fila appen&longs;is, & liberè ire, <lb/>redireque permi&longs;&longs;is. </s>

<s>Videlicet globus appen&longs;us ex <lb/>vno v. </s>

<s>Videlicet globus appen&longs;us ex <lb/>vno v. c. pede, dup ò quidem plureis vibrationes per<lb/>agit, quam appen&longs;us ad quatuor, triplo, quàm ap<lb/>pen&longs;us ad nouem, quadruplo, quàm appen&longs;us ad &longs;ex<lb/>decim; &longs;ed interim tamen &longs;ecundus &longs;patium conficit <lb/>dup ò maius, quàm primus, tertius triplò, quartus <lb/>quadruplò eodem tempore; ac velocitas interim ac<lb/>qui&longs;ita, impetu&longs;que ad perpendiculum expre&longs;&longs;us, non <lb/>vt &longs;patium pertran&longs;itum, &longs;ed vt tempus elap&longs;um &longs;e <lb/><figure id="fig13"/><lb/>habet. </s>

<s>pede, dup ò quidem plureis vibrationes per<lb/>agit, quam appen&longs;us ad quatuor, triplo, quàm ap<lb/>pen&longs;us ad nouem, quadruplo, quàm appen&longs;us ad &longs;ex<lb/>decim; &longs;ed interim tamen &longs;ecundus &longs;patium conficit <lb/>dup ò maius, quàm primus, tertius triplò, quartus <lb/>quadruplò eodem tempore; ac velocitas interim ac<lb/>qui&longs;ita, impetu&longs;que ad perpendiculum expre&longs;&longs;us, non <lb/>vt &longs;patium pertran&longs;itum, &longs;ed vt tempus elap&longs;um &longs;e <lb/><figure id="fig13"/><lb/>habet. </s>

<s>Ego certè rem &longs;ic intelligo. </s>

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<s>Siquidem tamet&longs;i <pb pagenum="39"/>inter experiundum applicari diuer&longs;is &longs;eor&longs;im lineis <lb/>debeant, ne inter mouendum &longs;e&longs;e interturbent: om<lb/>neis tamen &longs;chemate vno repræ&longs;entari nihil prohibet. <lb/></s>

<s>Ducantur heinc inde duæ lineæ angulum &longs;tatuentes <lb/>in A, qui à perpendiculo bi&longs;ecctur, &longs;intque v. </s>

<s>Ducantur heinc inde duæ lineæ angulum &longs;tatuentes <lb/>in A, qui à perpendiculo bi&longs;ecctur, &longs;intque v. c. IA, <lb/>KA; & centro A; agantur inter illas arcus CD ad <expan abbr="pri-m&utilde;">pri<lb/>mum</expan> pedem, EF ad quartum, GH ad nonum IK ad <lb/>&longs;extum-decimum; qui &longs;imiles proinde erunt, pares <lb/>videlicet portiones &longs;uotum cuiu&longs;que circulorum eo<lb/>dem angulo men&longs;uratæ. </s>

<s>IA, <lb/>KA; & centro A; agantur inter illas arcus CD ad <expan abbr="pri-m&utilde;">pri<lb/>mum</expan> pedem, EF ad quartum, GH ad nonum IK ad <lb/>&longs;extum-decimum; qui &longs;imiles proinde erunt, pares <lb/>videlicet portiones &longs;uotum cuiu&longs;que circulorum eo<lb/>dem angulo men&longs;uratæ. </s>

<s>Ducantur & &longs;ubten&longs;æ ar<lb/>cuum; & adnotentur qua&longs;i &longs;agittæ, &longs;eu appellati &longs;inus <lb/>ver&longs;i, lineæ nimirùm LM, NO, PQ, RB; cùm <lb/>&longs;int altitudines, quibus globi delabuntur ex linea AI <lb/>(vbi ad illam abducti, ex ea dimittuntur) in ip&longs;um <lb/>perpendiculum; primus putà ex C in M, &longs;ecundus <lb/>ex E in O, tertius ex G in Q, quartus ex I in B. <lb/></s>

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<s>Deducitur <lb/>prætereà ex incre&longs;cente numero diametrorum, & de<lb/>cre&longs;cente numero additorum ponderum, perueniri <lb/>demùm ad æqualitatem; ita &longs;cilicet, vt &longs;it diametro<lb/>rum, ponderumque numerus par, quo &longs;uperato &longs;it <lb/>deinceps minor ponderum, maior diametrorum. </s>

<s>Et <lb/>quia talis numerus incipiendo v. </s>

<s>Et <lb/>quia talis numerus incipiendo v. c. à duodecima v&longs;<lb/>que parte diametri, è qua fuere duæ vnciæ eleuatæ, <lb/>reperitur e&longs;&longs;e proximè quinquaginta; & incipiendo à <lb/>diametro integra, è qua eleuari vi&longs;æ &longs;unt vnciæ &longs;ep<lb/>tem cum quadrante, reperitur e&longs;&longs;e itidem quinqua<lb/>ginta: idcircò videmur po&longs;&longs;e dicere, &longs;i dimittatur <lb/>globus vnam pendens vnciam, ex altitudine diame<lb/>trorum &longs;uarum quinquaginta, fore vt parem nume<lb/>rum vnciarum attollat; tamet&longs;i citra hunc numerum, <lb/>&longs;it diametrorum numerus minor, vltrà maior nu<lb/>mero vnciarum. </s>

<s>à duodecima v&longs;<lb/>que parte diametri, è qua fuere duæ vnciæ eleuatæ, <lb/>reperitur e&longs;&longs;e proximè quinquaginta; & incipiendo à <lb/>diametro integra, è qua eleuari vi&longs;æ &longs;unt vnciæ &longs;ep<lb/>tem cum quadrante, reperitur e&longs;&longs;e itidem quinqua<lb/>ginta: idcircò videmur po&longs;&longs;e dicere, &longs;i dimittatur <lb/>globus vnam pendens vnciam, ex altitudine diame<lb/>trorum &longs;uarum quinquaginta, fore vt parem nume<lb/>rum vnciarum attollat; tamet&longs;i citra hunc numerum, <lb/>&longs;it diametrorum numerus minor, vltrà maior nu<lb/>mero vnciarum. </s>

<s>Vides igitur contingere po&longs;&longs;e, vt <lb/>aliquo ca&longs;u diametrorum numerus ponderum nume<lb/>ro exæquetur; neque licere tamen inferre e&longs;&longs;e vbi<lb/>que diametrorum numerum numero ponderum <lb/>æqualem. </s>

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<s>Vnde licet aduertere, fore vt &longs;patia ea ratione incre&longs;<lb/>cant, quæ a&longs;&longs;umptis quibu&longs;libet æqualibus tempori<lb/>bus deprehendatur excedere, & difformiter quidem, <lb/>&longs;eu inæquabiliter, triplam; quippe procedendo per <lb/>hos numeros, vnum, quatuor, vndecim, triginta <expan abbr="vn&utilde;">vnum</expan>, <lb/>octoginta quatuor, &c. </s>

<s>&longs;icque lapide decidente pri<lb/>mo momento per vnam v. </s>

<s>&longs;icque lapide decidente pri<lb/>mo momento per vnam v. c. orgyiam, fore vt &longs;ecun<lb/>do æquali momento decidendo per treis, in tertio <lb/>per &longs;eptem, in quarto per viginti, in quinto per quin<lb/>quaginta duas, deciderit in fine quinti, orgyiis octo<lb/>ginta quatuor, ac breui res &longs;it abitura in immen&longs;um, <lb/>&longs;ecu&longs;que quàm docet ip&longs;a experientia, iuxta quam <lb/>orgyiiæ in fine quinti momenti &longs;uperatæ, colliguntur <lb/>plures e&longs;&longs;e non debere, quàm viginti quinque. </s>

<s>orgyiam, fore vt &longs;ecun<lb/>do æquali momento decidendo per treis, in tertio <lb/>per &longs;eptem, in quarto per viginti, in quinto per quin<lb/>quaginta duas, deciderit in fine quinti, orgyiis octo<lb/>ginta quatuor, ac breui res &longs;it abitura in immen&longs;um, <lb/>&longs;ecu&longs;que quàm docet ip&longs;a experientia, iuxta quam <lb/>orgyiiæ in fine quinti momenti &longs;uperatæ, colliguntur <lb/>plures e&longs;&longs;e non debere, quàm viginti quinque. </s>

<s>XXXII. </s>

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<s>Sumpto enim puncto quocumque inter D, & E, <lb/>ex empli gratiâ T, diui&longs;oque bifariam interuallo AT, &longs;ectio <lb/>nece&longs;&longs;ario cadet inter D, &<emph.end type="italics"/> S, <emph type="italics"/>puta in V. </s>

<s>Et quia erit <lb/>AT dupla ip&longs;ius AV, erit etiam velocitas in T dupla ve<lb/>locitatis in V, & ita in cæteris punctis, quæ de&longs;ignari po&longs;&longs;unt <lb/>inter D, & E. </s>

<s>Et quia erit <lb/>AT dupla ip&longs;ius AV, erit etiam velocitas in T dupla ve<lb/>locitatis in V, & ita in cæteris punctis, quæ de&longs;ignari po&longs;&longs;unt <lb/>inter D, & E. </s>

<s>Quare per totum interuallum DE velocitas <lb/>erit dupla velocitatis per totum spatium<emph.end type="italics"/> SD, <emph type="italics"/>&longs;icut interual<lb/>lum DE duplum e&longs;t interualli<emph.end type="italics"/> SD. <emph type="italics"/>Ambo igitur hæc in<lb/>terualla nempe<emph.end type="italics"/> SD, <emph type="italics"/>& DE æquali tempore percurruntur.<emph.end type="italics"/><lb/>Quo loco admitto imprimis, vt nouum incommo<lb/>dum, eandem partem DE, quæ probata e&longs;t primùm <lb/>percurri debere ex tuo principio minutis tribus, ac <lb/>deinde minutis duobus cum triente, probari iam per<lb/>curri debere minutis duobus. </s>

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<s>Nam &longs;i, v.c. </s>

<s>AS bifa<lb/>riam &longs;ecetur in P, conficietur eodem tuo ratiocinio, <lb/>vt PS percurratur eodem tempore, quo SD, atque <pb pagenum="63"/>idcirco eodem, quo DE. </s>

<s>AS bifa<lb/>riam &longs;ecetur in P, conficietur eodem tuo ratiocinio, <lb/>vt PS percurratur eodem tempore, quo SD, atque <pb pagenum="63"/>idcirco eodem, quo DE. </s>

<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>

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<s>Verùm priu&longs;quàm gradus ad <lb/>cæteras fiat, con&longs;i&longs;tendum e&longs;t in hac prima; cùm <pb pagenum="65"/>non &longs;it nequicquam, quod de ip&longs;a admonui. </s>

<s>O&longs;ten<lb/>&longs;um e&longs;&longs;e ais tempus, quo percurritur CD, æquale e&longs;&longs;e <lb/>tempori, quo decur&longs;um fuerit HC: &longs;eu, ne confun<lb/>damus, & rem explicemus, qua&longs;i repetendam ex &longs;u<lb/>periore &longs;chemate, o&longs;ten&longs;um e&longs;&longs;e ais id tempus, quo <lb/>percurritur DE, æquale e&longs;&longs;e tempori, quo de<lb/><figure id="fig18"/><lb/>cur&longs;um fuerit SD. </s>

<s>At primò, in&longs;inuatum iam <lb/>e&longs;t id e&longs;&longs;e impo&longs;&longs;ibile; cùm quo iure ip&longs;e bi<lb/>&longs;ecui&longs;ti primam partem AD in S, liceat bi<lb/>&longs;ecare primum dimidium AS in P; & rursùs <lb/>primum horum dimidiorum in duo alia, & <lb/>primum i&longs;torum in duo, & ita porrò quoties <lb/>libuerit: Iuxta tuum verò ratiocinium, &longs;e qua<lb/>tur tempus, quo percurritur SD, e&longs;&longs;e æqua<lb/>le tempori, quo decur&longs;um fuerit PS, quate<lb/>nus, vt velocitas per totam DE e&longs;t dupla ve<lb/>locitatis per totam SD, quemadmodum in<lb/>teruallum duplum e&longs;t; ita velocitas per totam <lb/>SD dupla e&longs;t velocitatis per totam PS, &longs;icut <lb/>interuallum e&longs;t itidem duplum; Hoc autem <lb/>po&longs;ito, vlteriùs &longs;equatur tempus per SD, atque <lb/>idcircò per DE ip&longs;i æquale, e&longs;&longs;e non iam minuto<lb/>rum duorum, vt o&longs;tendi&longs;ti, &longs;ed minuti vnius cum <lb/>triente; vt pote coæquatum tempori per PS, quod <lb/>tam e&longs;&longs;e debet triens quatuor minutorum (quibus <lb/><gap/>is AS percurri) quàm tempus per SD &longs;tatuitur à <lb/>te triens minutorum &longs;ex (quibus percurritur AD) <lb/>cùm id tamen factuimpo&longs;&longs;ibile &longs;it, repugnantia putà <lb/>inuoluens, ac tantò magis, quantò ex vlterioribus <lb/>&longs;ubdiui&longs;ionibus probari pote&longs;t eandem DE percurri <pb pagenum="66"/>rursùs non vno minuto, ac triente, &longs;ed &longs;ecundis &longs;olùm <lb/>proximè quinquaginta tribus; & rursùs proximè <lb/>octodecim, & rursùs &longs;ex, &c. </s>

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<s>XXXVI. </s>

<s>Attamen &longs;upponatur etiam tua huiu&longs;-<pb pagenum="67"/>modi de mon&longs;tratio; Sequitur ecce rursùs, vt tempus, <lb/>quo percurritur DE &longs;e&longs;quialterum &longs;it, non verò æqua<lb/>le illi tempori, quo percurritur SD. </s>

<s>Cum velocita<lb/>tes enim &longs;int per te, vt &longs;patia; ac aliunde &longs;it manife<lb/>&longs;tum, vbi e&longs;t duplum velocitatis, ibi dimidium e&longs;&longs;e <lb/>temporis, vbi triplum trientem, atque ita&longs;emper in ra<lb/>tione &longs;ubmultipla; &longs;i &longs;it primò vt AE ad AD, ita <lb/>AD ad AS; erit igitur diuidendo vt AS ad SD, ita <lb/>AD, ad DE; ac deinde, &longs;i &longs;it AS tempus minuto<lb/>rum quatuor, & SD minutorum duorum; Erit igitur <lb/>tempus AD quidem minutorum &longs;ex, & DE minuto<lb/>rum trium, atque adeò &longs;e&longs;qui-alterum, non æquale <lb/>tempori SD. </s>

<s>Sequitur iterùm, vt non &longs;ecùs, quàm <lb/>Galileus ratiocineris, dum Paralogi&longs;mi illum arguis. <lb/></s>

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<s>Quippe & tamet&longs;i partes &longs;int incompara<lb/>biliter plures in &longs;emidiametro Mundi, quàm in &longs;pa<lb/>tiolo DE, &longs;unt tamen gradus velocitatis incompara<lb/>biliter etiam plures, ac proportione totidem; vt tem<lb/>pora &longs;ubmultipla illis &longs;uperandis &longs;ufficere valeant. </s>

<s>Vt <lb/>breue faciam, erroris origo ex eo profluxi&longs;&longs;e videtur, <lb/>quòd merè gratis con&longs;titeris in parte AD, eiu&longs;que <lb/>dimidio inferiore SD; & rem perinde habueris, ac &longs;i <lb/>dimidium &longs;uperius AS diuidi perinde non po&longs;&longs;et, ne<lb/>que haberet &longs;peciatim dimidium eadem ratione, qua <lb/>habet AD. </s>

<s>Proptereà enim accepi&longs;ti &longs;olùm omnia <lb/>de&longs;ignabilia punctaper totam DE, in quibus veloci<lb/>tas e&longs;&longs;et dupla velocitatis in totidem punctis per to<lb/>tam SD; neque reputa&longs;ti pergendum, vt haberes <lb/>eodem tenore puncta de&longs;ignabilia per totam SD, in <lb/>quibus velocitas e&longs;&longs;et dupla velocitatis in totidem <lb/>punctis de&longs;ignabilibus per totam PS, atque ita in in<lb/>finitum; vt prorsùs nece&longs;&longs;arium e&longs;t ex tua ip&longs;ius &longs;up<lb/>po&longs;itione. </s>

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<s>iam <lb/>osten&longs;um est partem &longs;ecundam<emph.end type="italics"/> CD, <emph type="italics"/>& primæ par<lb/>tis dimidiam partem inferiorem<emph.end type="italics"/> NC <emph type="italics"/>æquali tempore <lb/>percurri; & ob eam quidem cau&longs;&longs;am, quòd, vt pars<emph.end type="italics"/><lb/>CD <emph type="italics"/>dupla e&longs;t partis<emph.end type="italics"/> NC, <emph type="italics"/>ita velocitas quoque per <lb/>totam<emph.end type="italics"/> CD <emph type="italics"/>dupla &longs;it velocitatis per totam<emph.end type="italics"/> NC. <emph type="italics"/>At <lb/>&longs;imili ratione etiam efficitur, velocitatem per totam<emph.end type="italics"/><lb/>DF <emph type="italics"/>duplam e&longs;&longs;e velocitatis eius, quæ habetur per <lb/>totam<emph.end type="italics"/> CD; <emph type="italics"/>&longs;icut tota<emph.end type="italics"/> DF <emph type="italics"/>dupla e&longs;t ip&longs;ius<emph.end type="italics"/> CD. <lb/>Æ<emph type="italics"/>quali igitur tempore<emph.end type="italics"/> CD, <emph type="italics"/>&<emph.end type="italics"/> DF <emph type="italics"/>decurruntur; <lb/>eademque omninò ratio e&longs;t ip&longs;arum<emph.end type="italics"/> DF, <emph type="italics"/>&<emph.end type="italics"/> FK, <lb/><emph type="italics"/>cæterarumque omnium &longs;e pariter in ratione dupla &longs;u <lb/>perantium; vt &longs;atis manife&longs;tum e&longs;t.<emph.end type="italics"/> S<emph type="italics"/>patia igitur <lb/>æqualibus temporibus emen&longs;a, & velocitates ii&longs;dem <lb/>temporibus æqualibus acqui&longs;itæ &longs;emper augentur in <lb/>continua ratione dupla.<emph.end type="italics"/></s>

<s>XL. Cæterùm, cùm i&longs;te habeatur qua&longs;i <lb/>prouentus quidam eximius totius tuæ Di&longs;&longs;ertationis; <pb pagenum="74"/>Patietur tua bonitas adm rari imprimis me, quid e&longs;&longs;e <lb/>agendum cogitaueris de primo dimidio AN. </s>

<s>Vide<lb/>licet rationem duplam, progre&longs;&longs;ionemque à puncto <lb/>N ita inchoas, vt &longs;i motus inciperer, ac vniformiter <lb/>quidem, non à puncto A, &longs;ed à puncto N. </s>

<s>Vide<lb/>licet rationem duplam, progre&longs;&longs;ionemque à puncto <lb/>N ita inchoas, vt &longs;i motus inciperer, ac vniformiter <lb/>quidem, non à puncto A, &longs;ed à puncto N. </s>

<s>An dices <lb/>fortè po&longs;&longs;e AN ita bi&longs;ecari, vt motus, & ratio, pro<lb/>gre&longs;&longs;ioque illius incipiat à puncto inter A, & N me<lb/>dio? </s>

<s>Sed bi&longs;eca, vt voles, eadem erit ruina. </s>

<s>Bi&longs;eca <lb/>rursùs, iterumque, & porrò v&longs;que in infinitum; atta<lb/>men &longs;emper &longs;upererit pars, à cuius medio, non autem <lb/>ab A fieri inc&oelig;ptio cogitetur; adeò vt prorsùs perinde <lb/>&longs;it con&longs;i&longs;tere in dimidio AN. </s>

<s>Cùm autem dicturus <lb/>prætereà non &longs;is fieri &longs;olùm quoddam qua&longs;i tyroci<lb/>nium, &longs;eu præludium ex A in N, ac motum deinde, <lb/>& rationem, progre&longs;&longs;ionemque incipere &longs;eriò ab N; <lb/>cùm non &longs;is, in quam, id dicturus, vt pote, qui motum <lb/>admittas à primo v&longs;que &longs;ui momento accelerari vni<lb/>formiter; ac &longs;upponas etiam, vbi tempus per AC mi<lb/>nutorum &longs;ex fuerit, tempus per AN futurum minuto<lb/>rum quatuor; quæ&longs;o te, ecquis modus e&longs;t progre&longs;&longs;io<lb/>nis ex A in N? </s>

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<s>dicere autem perinde non <lb/>liceat, vt AC ad CE, ita CE ad EI, & EI ad &longs;ui du<lb/>plam? </s>

<s>Dicere certè accipiendum e&longs;&longs;e po&longs;terius pri<lb/>mæ partis dimidium, quòd contineatur in eo men<lb/>&longs;ura cæterarum partium con&longs;equentium, videtur e&longs;&longs;e <lb/>dicere gratis, ip&longs;amque petere quæ&longs;tionem; ac aliunde <pb pagenum="76"/>agitur &longs;olùm de progre&longs;&longs;ione Geometrica, quam ge<lb/>neralem cùm &longs;tatuas, incipere vndelibet licet, & nullo <lb/>quidem ex puncto magis &longs;ecundum naturam, quàm <lb/>ex puncto A. </s>

<s>Dic enim, amabò, &longs;i qui&longs;piam perno&longs;&longs;e <lb/>rationem exoptet, qua decidens graue progrediatur <lb/>ab A in B, & tu o&longs;ten&longs;urus ita exordiaris, Vt NC ad <lb/>CD, ita CD ad DF, &c. </s>

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<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>

<s>E&longs;to v. </s>

<s>E&longs;to v. c. tempus per <lb/>AC triginta &longs;ex, vt triens, &longs;eu tempus, quod tribuis <lb/>po&longs;teriori dimidio, quodque primum facis, &longs;it duode<lb/>cim; cùm &longs;ubinde &longs;patium æquale dimidio, cui d<gap/>bi<lb/>tum &longs;it tempus 6. ideò duplices, vt pro &longs;ecundo &longs;patio <pb pagenum="77"/>habeas iterum duodecim; compone deinde in vnum <lb/>duo tempora duorum &longs;equentium interuallorum, vi<lb/>delicet trientem 4, & quadrantem 3, ac habebis non <lb/>duodecim, hoc e&longs;t tempus æquale primo, &longs;ed &longs;eptem <lb/>illius duodecimas dumtaxat; aut &longs;i duplices, etiam duo<lb/>decimas quatuordecim. </s>

<s>tempus per <lb/>AC triginta &longs;ex, vt triens, &longs;eu tempus, quod tribuis <lb/>po&longs;teriori dimidio, quodque primum facis, &longs;it duode<lb/>cim; cùm &longs;ubinde &longs;patium æquale dimidio, cui d<gap/>bi<lb/>tum &longs;it tempus 6. ideò duplices, vt pro &longs;ecundo &longs;patio <pb pagenum="77"/>habeas iterum duodecim; compone deinde in vnum <lb/>duo tempora duorum &longs;equentium interuallorum, vi<lb/>delicet trientem 4, & quadrantem 3, ac habebis non <lb/>duodecim, hoc e&longs;t tempus æquale primo, &longs;ed &longs;eptem <lb/>illius duodecimas dumtaxat; aut &longs;i duplices, etiam duo<lb/>decimas quatuordecim. </s>

<s>Adde pari modo quatuor <lb/>tempora quatuor aliorum interuallorum, hoc e&longs;t par<lb/>teis 5, 6, 7, 8, & habebis iterùm non duodecim, &longs;ed <lb/>vix ampliùs quàm duodecimas &longs;eptem, cum &longs;emi&longs;&longs;e; <lb/>aut &longs;i duplices, etiam quidpiam amplius, quàm duode<lb/>cimas quin lecim. </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"/></s><s> Adeò vt, &longs;i inter AB pri<lb/>mam partem, & AC aggregatum primæ cum <lb/><figure id="fig21"/><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>

<s>Ex quo fiet, vt cùm AB <lb/>&longs;upponas e&longs;&longs;e &longs;ex minutorum, AC compobetur mi<lb/>nutorum octo, & 29. &longs;ecundorum proximè; ac proin<lb/>de tempus per BC &longs;it minutorum duorum, & viginti <lb/>nouem proximè &longs;ecundorum. </s>

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<s>Sic certe habe, fore me &longs;emper com<lb/>parati&longs;&longs;imum a&longs;&longs;entiendo, &longs;i quandò maior mihi ex <lb/>te &longs;imilitudo veri affulgeat, qui &longs;um interim, &longs;i quis <lb/>alius, comparati&longs;&longs;imus ob&longs;equendo. </s>

<s>Vale, Pari&longs;ijs, <lb/>Eidib. </s>

<s>Vale, Pari&longs;ijs, <lb/>Eidib. Mart. M. DC. XLV. <lb/><figure id="fig22"/></s>

<s><emph type="center"/>DE PROPORTIONE,<emph.end type="center"/></s>

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<s><emph type="center"/>accelerantur.<emph.end type="center"/></s>

<s><emph type="center"/>EPISTOLA SECVNDA.<emph.end type="center"/><lb/><gap desc="hr tag"/></s>

<s><emph type="center"/>EPISTOLA SECVNDA.<emph.end type="center"/><lb/><gap desc="hr tag"/></s>

<s><emph type="center"/><emph type="italics"/>EIDEM.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>EIDEM.<emph.end type="italics"/><emph.end type="center"/></s>

<s>QVOD non improbâris, oprimè CASRÆE, <lb/>mandari typis meam Re&longs;pon&longs;ionem, &longs;eu <lb/>qualecumque Iudicium de tua illa Demon<lb/>&longs;tratione, circa accelerationem grauium <lb/>decidentium, cuius autographum ad te mi&longs;i, &longs;i modo <lb/>Vindicias, quas intercedente eodem nobili Senatore, <lb/>& amico &longs;ingulari, Franci&longs;co Luillerio, dedi&longs;ti ad me, <lb/>iuberem attexi: Ecce non alia conditione Typogra<lb/>pho annui, dum meam opellam exigeret, quàm vt <lb/>tuam &longs;imul accipiens, tuo de&longs;iderio faceret &longs;atis. </s>

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<s>Sed ecce demùm tuas Vindicias, cum ne minimo qui<lb/>dem vllo &longs;en&longs;us, vocumque detrimento; vtcum que &longs;e<lb/>ponerem volens ho&longs;ce titulos, quibus me exornas, <pb pagenum="92"/>quo&longs;que non promereri me, quemadmodum &longs;entio, <lb/>&longs;ic ingenuè profiteor. </s>

<s><emph type="center"/><emph type="italics"/>VINDICI<emph.end type="italics"/>Æ <emph type="italics"/>DEM<emph.end type="italics"/>O<emph type="italics"/>NSTRATI<emph.end type="italics"/>O<emph type="italics"/>NIS<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>PHYSICÆ.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>PHYSICÆ.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>De Proportione, qua grauia decidentia accelerantur.<emph.end type="italics"/><emph.end type="center"/></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"/></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>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>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>

<s>Et ecce ea tamen futura e&longs;t continens; <lb/>ac ip&longs;i gradus velocitatis repræ&longs;entati iuxta te paralle<lb/>lis ED, GF, IH, LK, cum interceptis omnibus, ha<lb/>bituri &longs;unt inter &longs;e, eandem rationem, quam ip&longs;æ par<lb/>tes &longs;pati, repræ entatæ iuxta te partibus lineæ AC. <lb/></s>

<s>Quòd &longs;i id reputes ab&longs;urdum; ab&longs;urdum quoque vi<lb/>deri debet metiri accelerationem, ac vniformem po<lb/>ti&longs;&longs;imùm, penes &longs;patium, non penes tempus: atque <lb/>idcircò lineam AC comparatam ad eas parallelas pro <lb/>velocitatibus habitas, non pro tempore, &longs;ed pro &longs;patio <lb/>habere. </s>

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<s>An per<gap/>i&longs;&longs;e illum dicemus? <lb/></s>

<s>Non &longs;ane: quoniam alioquin mobili perueniente ex <lb/>A in G non reperiretur acqui&longs;itus in G, ni&longs;i vnus velo<lb/>citatis gradus; quatenus etiam per te, &longs;eu ex vulgari de<lb/>finitione, additamenta ex E in G æqualia &longs;unt addita<lb/>mentis ex A in E, nec pote&longs;t proinde ab v&longs;que E ac<lb/>qui&longs;itus e&longs;&longs;e, ni&longs;i gradus vnus, v. </s>

<s>FP æqualis ip&longs;i DE <pb pagenum="102"/>acqui&longs;ito ab v&longs;que A. </s>

<s>Et quamvis tu &longs;is inferiùs di<lb/>cturus velocitatem acqui&longs;itam ex E in G duplam e&longs;&longs;e <lb/>acqui&longs;itæ in E (nempe dum &longs;tatuis primum gradum <lb/>acquiri à &longs;olo medio ip&longs;ius AE) & &longs;ic velle debeas <lb/>gradum acqui&longs;itum in E, &longs;eu DE perire; quoniam re<lb/>periri in G, ni&longs;i duos gradus non vis: cùm &longs;i acqui&longs;itus <lb/>in E remaneret, futuri e&longs;&longs;ent tres: vide nihilominùs <lb/>quid hoc loco &longs;equatur. </s>

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<s>Quo ca&longs;u neque mobile æquabiliter moue<lb/>retur; neque peruenienti in G &longs;upere&longs;&longs;et ampliùs vlla <lb/>velocitas: neque proinde, &longs;i velocitate hac decre&longs;cente <lb/>intelligamus acquiri velocitatem &longs;ecundum triangu<lb/>lum DFP, acqui&longs;ita erit in G velocitas alia, quàm FP <lb/>ip&longs;ius DE æqualis, non dupla. </s>

<s>Igitur mobile percur<lb/>rens EG velocitate &longs;ola DE percurreret ip&longs;um tem<lb/>pore breuiore, quàm percurri&longs;&longs;et AE. </s>

<s>Igitur mobile percur<lb/>rens EG velocitate &longs;ola DE percurreret ip&longs;um tem<lb/>pore breuiore, quàm percurri&longs;&longs;et AE. </s>

<s>Quanto igitur? <lb/></s>

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<s>Sanètriente. </s>

<s>Nam vt <lb/>velocitas &longs;ecundum quadrangulum DG, dupla ve<lb/>locitatis &longs;ecundum triangulum ADE diminuit tem<lb/>pus ad dimidium; ita velocitas &longs;ecundum trapezion <lb/>DFGE, triplum eiu&longs;dem trianguli, diminuit ad v&longs;<lb/>que trientem: Adeò vt, &longs;i tempus, quo decur&longs;um <lb/>fuerit AE, &longs;upponatur, vt à te fit, minutorum v. </s>

<s>&longs;ex, <lb/>tempus, quo decurretur EG, futurum &longs;it minutorum <lb/>duorum. </s>

<s>Cæterùm præter iam obiecta alibi incom<lb/>moda, tum illud quoque heinc &longs;equitur, Quòd &longs;i <lb/>EG &longs;ecunda pars &longs;patij percurratur triente eius tem<lb/>poris, quo decur&longs;a fuerit prima AE, futurum &longs;it, vt <lb/>tempore &longs;ecundo percurrantur partes non modò &longs;e<lb/>cunda, &longs;ed etiam tertia, quarta, quinta, &longs;exta, &longs;eptima, <lb/>& penè octaua; quandò qua ratione &longs;ecundum &longs;pa<lb/>tium percurritur triente, eadem tertium percurretur <lb/>quinta eiu&longs;dem temporis parte; quartum &longs;eptima, <lb/>quintum nona, &longs;extum vndecima, &longs;eptimum decima<lb/>tertia, octauum quintadecima, & hæc fragmenta &longs;i<lb/>mùl iuncta vnum integrum proximè conficient. <lb/></s>

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<s>Vides ergo quantum repugnet po&longs;itio huiu&longs;modi; <lb/>ac peruidere &longs;imul potes, quantum inter&longs;it di&longs;eriminis <lb/>inter hypothe&longs;in vtramque. </s>

<s>Nam in ea quidem, <lb/>quam &longs;equor, cùm partes lineæ AC, fiant partes <lb/>temporis, linea DE optimè repræ&longs;entat velocitatem <lb/>aqui&longs;itam in fi<gap/>e primi, & &longs;imul triangulum ADE op<lb/>timè repræ&longs;entat vnum &longs;patium, dum ea acquiritur, <lb/>tran&longs;actum: FG verò optimè repræ&longs;entat velocita<lb/>tem acqui&longs;itam in fine &longs;ecundi; & &longs;imul trapezion <lb/>DFGE optimè repræ&longs;entat tribus triangulis tria &longs;pa<lb/>tia peracta, quorum vnum debeatur gradui FP, prout <lb/>interim acquifito, & alij duo gradui PG, prout per<lb/>&longs;eueranti ab v&longs;que puncto E. </s>

<s>At in ea, quam tu &longs;e<lb/>queris, neque habes, quò referas tempus, cuius etiam <lb/>tua definitio non meminit<gap/> neque cùm plures &longs;patij <lb/>partes æquali tempore percurrantur, illarum di&longs;tin<lb/>ctionem habes, vt ad eas referas gradus inæqualeis ve<lb/>locitatis. </s>

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<s>Ad hæc, Quem<lb/>admodum proinde æqualibus temporibus æqualia <lb/>fiant additamenta, &longs;eu æquales gradus velocitatis ac<lb/>quirantur, & interim tamen decur&longs;us &longs;patiorum &longs;ecun<lb/>dum &longs;eriem numerorum ab vnitate inc&oelig;ptorum <lb/>fiat. </s>

<s><emph type="italics"/>Adde quòd ad vniformen motus accelerationem minimè <lb/>nece&longs;&longs;arium e&longs;t, vt acqui&longs;ita æqualibus temporibus velocitatis <lb/>incrementa æqualia &longs;int (vt paßim &longs;upponere videris) &longs;ed <lb/>&longs;atis e&longs;t, &longs;i continuò maiora in quacumque ratione<emph.end type="italics"/> G<emph type="italics"/>eome<lb/>trica acquirantur: cùm notum &longs;it omnibus progreßiones <lb/>Geometricas non minùs vniformeis e&longs;&longs;e, quàm Arithmeticas. <lb/></s>

<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>

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<s>Heic idem dicendum, quod & paulò antè, quate<lb/>nus parteis lineæ AB contendis habendas pro parti<lb/>bus &longs;patij, quæ comparentur cum parallelis habitis <lb/>pro gradibus velocitatis, nulla habita temporis ratio<lb/>ne. </s>

<s>Quod autem quæris, <emph type="italics"/>Cur hoc loco celeritatis aug<lb/>menta triangulis in &longs;uperiore autem figura lineis metienda <lb/>edixerim?<emph.end type="italics"/> Cau&longs;&longs;am ex eo potes intelligere, quòd cùm <lb/>tu duos gradus NM, & MD, v. c. æqualeis facias, <lb/>qua&longs;i acqui&longs;itos ex L, & C, &longs;ecundum duos triangulos <lb/>LNM, & CMD (tamet&longs;i inæquales &longs;int, & MD ex <lb/>LC manente factus, duobus æquiualeat) ideò quem <lb/>defectum exprimere non licuit lineâ ND, exprimere <lb/>placuerit trapezio LD. Nimirùm, cùm velocitas <lb/>ND creetur partim ex LC, promota in MD &longs;ecun<lb/>dum quadrangulum, partim ex additamentis ip&longs;i fa<lb/>ctis &longs;ecundum triangulum LNM; tu ex velocitate hac <lb/>detrahis integrum triangulum LMC: &longs;icque ex tri<lb/>bus &longs;uper&longs;unt tantum partes velocitatis duæ, quas vt <lb/>&longs;imul iunct is repræ&longs;entarem, triangulum à te factum <lb/><expan abbr="vacu&utilde;">vacuum</expan> &longs;upplcui, tran&longs;lato LNM in MCL: cópo&longs;itoque <lb/>inde quadrangulo, locum ip&longs;um trianguli tran&longs;lati re<lb/>liqui inanem. </s>

<s>æqualeis facias, <lb/>qua&longs;i acqui&longs;itos ex L, & C, &longs;ecundum duos triangulos <lb/>LNM, & CMD (tamet&longs;i inæquales &longs;int, & MD ex <lb/>LC manente factus, duobus æquiualeat) ideò quem <lb/>defectum exprimere non licuit lineâ ND, exprimere <lb/>placuerit trapezio LD. Nimirùm, cùm velocitas <lb/>ND creetur partim ex LC, promota in MD &longs;ecun<lb/>dum quadrangulum, partim ex additamentis ip&longs;i fa<lb/>ctis &longs;ecundum triangulum LNM; tu ex velocitate hac <lb/>detrahis integrum triangulum LMC: &longs;icque ex tri<lb/>bus &longs;uper&longs;unt tantum partes velocitatis duæ, quas vt <lb/>&longs;imul iunct is repræ&longs;entarem, triangulum à te factum <lb/><expan abbr="vacu&utilde;">vacuum</expan> &longs;upplcui, tran&longs;lato LNM in MCL: cópo&longs;itoque <lb/>inde quadrangulo, locum ip&longs;um trianguli tran&longs;lati re<lb/>liqui inanem. </s>

<s>Fandem autem ob cau&longs;&longs;am relicti &longs;unt <lb/>duo trianguli manes ad ordinem tertium tres ad quar<lb/>tum, &c. </s>

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<s>Intelligatur <lb/>AC, diui&longs;a in duodecim parteis æqualeis, ac proinde <lb/>eius dimidium AB, &longs;eu ip&longs;i æqualeis DE in <gap/>x; &longs;int<lb/>que primùm duo mobilia, quorum vnum de&longs;cendat <pb pagenum="113"/>ex A, ver&longs;us C, eodem momento, quo aliud ex D, <lb/>ver&longs;us E; notum e&longs;t, &longs;i vtrumque quidem fer<lb/><figure id="fig27"/><lb/>retur non accelerato, &longs;ed æquabili motu, <lb/>euenturum e&longs;&longs;e, vt velocitate illius ex&longs;i&longs;tente <lb/>dupla ad velocitatem i&longs;tius, illud perueniret <lb/>in C, eodem momento, quo i&longs;tud in E; <lb/>quoniam &longs;patium ab illo &longs;uperatum foret <lb/>vbique ad &longs;patium ab i&longs;to &longs;uperatum, du<lb/>plum; hoc e&longs;t, forent ab illo &longs;uperatæ duæ <lb/>partes, cùm ab i&longs;to vna: ab illo quatuor, cùm ab hoc <lb/>duæ, &c. </s>

<s>quatenus &longs;patia &longs;e haberent vbique, vt velo<lb/>citates; hoc e&longs;t, velocitas per totam AC, e&longs;&longs;et vbique <lb/>dupla velocitatis per totam DE. </s>

<s>quatenus &longs;patia &longs;e haberent vbique, vt velo<lb/>citates; hoc e&longs;t, velocitas per totam AC, e&longs;&longs;et vbique <lb/>dupla velocitatis per totam DE. </s>

<s>At verò, quoniam <lb/>heic agitur de motu non æquabili, &longs;ed continenter <lb/>accelerato; ita di&longs;cedant rursùs mobilia eodem tem<lb/>pore, vnum ab A, aliud à D, vt &longs;uccre&longs;centibus conti<lb/>nuò velocitatis gradibus, illud perueniendo in C, ac<lb/>qui&longs;ierit duodecim, hoc perueniendo in E, &longs;ex: <emph type="italics"/>Tum <lb/>interrogas,<emph.end type="italics"/> Quid impediat, quò minùs illud perueniat <lb/>in C, eodem tempore, quo i&longs;tud in E? <emph type="italics"/>Ego verò re&longs;<lb/>pondeo, nihil certè impedire, &longs;i tales e&longs;&longs;ent, quales de&longs;cribis <lb/>velocitate: taleis autem &longs;ine dubio de&longs;cribis, qualeis in prima <lb/>illa<emph.end type="italics"/> G<emph type="italics"/>alilei propo&longs;itione &longs;ignificari putas. </s>

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<s>Iam cùm &longs;it A&longs;<lb/>&longs;umptio hypothetica, & duas proinde parteis <expan abbr="cõtineat">contineat</expan>. <pb pagenum="118"/><expan abbr="quar&utilde;">quarum</expan> altera Antecedens, altera Con&longs;equens dicatur, <lb/>tu &longs;ic vtramque à conditione (vt Dialectici loquuntur) <lb/>ab&longs;oluis, vt priorem &longs;en&longs;um antecedenti tribuas, & <lb/>po&longs;ter orem con&longs;equenti; ac po&longs;tquàm antecedens ex<lb/>pre&longs;&longs;i&longs;ti in linea (expre&longs;&longs;um priùs in triangulo, dum ex<lb/>plicares priorem &longs;en&longs;um) arguas non inferri ex eo legi<lb/>timè con&longs;equens, expre&longs;&longs;um iuxta po&longs;teriorem. </s>

<s>Tu <lb/>igitur tale facis Antecedens. </s>

<s>Tu <lb/>igitur tale facis Antecedens. </s>

<s><emph type="italics"/>Acceleratio velocitatis in de&longs;cen&longs;u grauium per<emph.end type="italics"/><lb/><figure id="fig28"/><lb/><emph type="italics"/>totam AC, ita continua &longs;ucceßione cre&longs;cit, vt pri<lb/>mùm in B acqui&longs;itus &longs;upponatur vnus aliquis ve<lb/>locitatis gradus, & vlteriùs procedente motu, & <lb/>continuò incre&longs;cente celeritate duo iam in C velo<lb/>citatis gradus habeantur.<emph.end type="italics"/></s>

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<s>Hi&longs;ce præmi&longs;&longs;is, videndum e&longs;t, quo iure tu&longs;eque<lb/>lam neges, & mon&longs;tres con&longs;equens non rectè, ac para<lb/>logi&longs;ticè inferri ex antecedente. </s>

<s>Nam nece&longs;&longs;itas qui<lb/>dem inferendi ex eo manife&longs;ta e&longs;t, quod Acceleratio <lb/>fieri, aut velocitas cre&longs;cere non po&longs;&longs;it æquabiliter per <lb/>totam AC, neque &longs;imiliter per totam AB, quin &longs;i ve<lb/>locitas in C dupla &longs;it velocitatis in B, quælibet partes <lb/>analogæ acceptæ per totam AC, duplæ &longs;int ad analo<lb/>gas per totam AB: atque ita, quin velocitas mobilis <lb/>de&longs;cendentis per AC &longs;it perpetuò dupla velocitatis <lb/>eiu&longs;dem mobilis de&longs;cendentis per AB. </s>

<s>Quod &longs;anè <lb/>adeò e&longs;t manife&longs;tum, vt neip&longs;e quidem negare id po<lb/>tueris, po&longs;tquàm ob&longs;erua&longs;ti comparatam primùm à <lb/>me lineam AC diui&longs;am in duodecim parteis cum <lb/>linea AC diui&longs;a in &longs;ex, tanquam cum &longs;eparata, exi&longs;ten<lb/>teque, intelligentiæ cau&longs;sâ DE, ac &longs;ubinde intellexi<lb/>&longs;ti e&longs;&longs;e omninò nece&longs;&longs;arium, vt idem mobile, &longs;i velo<lb/>eitatem in B, &longs;implam, in C verò duplam acquirat, <lb/>reperiatur &longs;imul in fine primæ, & in fine &longs;ecundæ <lb/>duodenarum partium; in fine tertiæ, & in fine &longs;extæ; <lb/>in fine &longs;extæ, & in fine duodecimæ; propter analogiam <lb/>&longs;implicium partium lineæ AB, & duplicium lineæ AC. <lb/>Ecquid-nam ergo iuris iam habes, vt perneges con&longs;e<lb/>quutionem? </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"/></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>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><emph type="italics"/>Si velocitatis incrementa tempori bus æqua<lb/>libus acqui&longs;ita eam inter &longs;e rationem ob&longs;erua<lb/>rent, quam tempora, nece&longs;&longs;ariò ip&longs;æ quoque <lb/>velocitates perpetuò e&longs;&longs;ent inter &longs;e, vt tempora, <lb/>e&longs;&longs;etque, exempli gratiâ, velocitas duobus temporibus æquali<lb/>bus acqui&longs;ita velocitatis primo tempore acqui&longs;itæ dupla.<emph.end type="italics"/></s>

<s>Scilicet i&longs;ta tibi e&longs;t hypothetica Propo&longs;itio. </s>

<s>Scilicet i&longs;ta tibi e&longs;t hypothetica Propo&longs;itio. </s>

<s>A&longs;&longs;um<lb/>tio &longs;equitur. </s>

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<s>Tunc autem addo e&longs;&longs;e nece&longs;&longs;e, vt percurratur &longs;pa<lb/>tium non modo duplum, &longs;ed & quadruplum primi: &longs;i <lb/>velocitas quidem acqui&longs;ita æquabiliter fuerit (qualis <lb/>illa e&longs;t, qua de agimus) quatenus dum &longs;ecundus veloci<lb/>tatis gradus tempore &longs;ecundo acquiritur, & per ip&longs;um <lb/>par &longs;patium illi, quod decur&longs;um fuit tempore primo, <lb/>percurritur, percurruntur &longs;imùl duo alia per gradum <lb/>velocitatis primo tempore acqui&longs;itum, ac in vigore <lb/>per&longs;euerantem, veluti iam antè declaratum e&longs;t. </s>

<s>Sed <lb/>ecce Sub&longs;umis. </s>

<s>Sed <lb/>ecce Sub&longs;umis. </s>

<s><emph type="italics"/>Si igitur primo tempore AD, spatium PM percurra<lb/>tur à velocitate &longs;ubdupla primo illo toto tempore acqui&longs;ita, <lb/>eodem tempore &longs;imul percurretur &longs;patium PN &longs;patii PM <lb/>duplum à velocitate dupla toto tempore AE acqui&longs;ita.<emph.end type="italics"/></s><pb pagenum="127"/>

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<s>tan<lb/>quam con&longs;equens ex tuo decreto cum hac propo&longs;i<lb/>tione congruo, de &longs;patiis emen&longs;is, temporibus æqua<lb/>libus, in ratione continuò dupla. </s>

<s>Priu&longs;quam hæc de Paralogi&longs;mo, quem Galileo ob<lb/>ieci&longs;ti, dimi<gap/>am, memini&longs;&longs;e iuuatobie ci&longs;&longs;e me tibi arti<lb/>culis XXXVI, & XXXVIII. fui&longs;&longs;e tenon &longs;ecus ratiocina-<pb pagenum="135"/>tum, quàm Galileum: atque idcircò &longs;i ille quidem Pa<lb/>ralogi&longs;mum admi&longs;erit, incidi&longs;&longs;e te, recidi&longs;&longs;eque <lb/><figure id="fig36"/><lb/>in cundem: ac o&longs;tendere vel ex ea &longs;ola ratiocina<lb/>tione tua, quæ relata e&longs;t articulo XXXIII. quemad<lb/>modum ex tuis principiis demon&longs;trare liceat, <emph type="italics"/>&longs;i <lb/>velocitates &longs;icut &longs;patia &longs;int,<emph.end type="italics"/> fore <emph type="italics"/>vt totum, & pars <lb/>eodem, aut æquali tempore percurrantur.<emph.end type="italics"/> A&longs;&longs;umptâ <lb/>ergo, quæ illeic, lineâ, ideò probas <emph type="italics"/>&longs;patium<emph.end type="italics"/> DE, <lb/><emph type="italics"/>eodem tempore tran&longs;curri, quo<emph.end type="italics"/> SD; quia <emph type="italics"/>cùm<emph.end type="italics"/> AD <lb/><emph type="italics"/>dupla &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, <emph type="italics"/>nece&longs;&longs;e &longs;it ve<lb/>locitatem in<emph.end type="italics"/> D <emph type="italics"/>duplam e&longs;&longs;e velocitatis in<emph.end type="italics"/> S, <emph type="italics"/>& veloci<lb/>tatem in<emph.end type="italics"/> E <emph type="italics"/>velocitatis in<emph.end type="italics"/> D. </s>

<s>Cùm & aliunde, <emph type="italics"/>velo<lb/>citas per totam<emph.end type="italics"/> DE <emph type="italics"/>dupla &longs;it velocitatis per totam<emph.end type="italics"/><lb/>SD; quatenus <emph type="italics"/>quodlibet &longs;patium inc&oelig;ptum ab<emph.end type="italics"/> A, <lb/><emph type="italics"/>& terminatum inter<emph.end type="italics"/> D, <emph type="italics"/>&<emph.end type="italics"/> E, <emph type="italics"/>duplum e&longs;t alterius <lb/>&longs;patii, quod &longs;it item inc&oelig;ptum ab<emph.end type="italics"/> A, <emph type="italics"/>& terminatum <lb/>inter<emph.end type="italics"/> S, <emph type="italics"/>&<emph.end type="italics"/> D; Dico aut te inde nihil conclude<lb/>re, aut &longs;ic licere argumentari. </s>

<s><emph type="italics"/>Si<emph.end type="italics"/> DE, <emph type="italics"/>&<emph.end type="italics"/> SD, <emph type="italics"/>eodem tempore percurruntur, quia veloci<lb/>tas à<emph.end type="italics"/> D <emph type="italics"/>in<emph.end type="italics"/> E, <emph type="italics"/>dupla e&longs;t velocitatis ab<emph.end type="italics"/> S <emph type="italics"/>in<emph.end type="italics"/> D. </s>

<s>Igitur, <emph type="italics"/>AD, & A<emph.end type="italics"/>S, <emph type="italics"/>eodem tempore percurrentur, quia <lb/>velocitas, ab A in D dupla e&longs;t velocitatis ab A in<emph.end type="italics"/> S. </s>

<s>Et &longs;imiliter, <emph type="italics"/>AE, & AD eodem tempore percurrentur; <lb/>quia velocitas ab<emph.end type="italics"/> A <emph type="italics"/>in<emph.end type="italics"/> E, <emph type="italics"/>dupla e&longs;t velocitatis ab<emph.end type="italics"/> A <emph type="italics"/>in<emph.end type="italics"/> D. </s>

<s>Ac rur&longs;us, quia vt velocitas per totam DE dupla <lb/>e&longs;t velocitatis per totam SD, ita velocitas per totam <lb/>SD debet e&longs;&longs;e dupla velocitatis per totam PS, & ve<lb/>locitas per totam PS, velocitatis per aliud vlterius di<lb/>midium, acita porrò, quantum licebit &longs;ubdiuidere ad <lb/>v&longs;que punctum A, &longs;icque demum velocitas per totam <pb pagenum="136"/>AE repenetur dupla velocitatis per totam AD, & ve<lb/>locitas per totam AD velocitatis per totam AS; Dico <lb/>aut te nihil concludere, aut &longs;ic licere ratiocinari. </s>

<s>Si <emph type="italics"/>DE, &<emph.end type="italics"/> SD <emph type="italics"/>eodem tempore percurruntur, quia velo<lb/>citas per totam<emph.end type="italics"/> DE, <emph type="italics"/>dupla e&longs;t velocitatis per totam<emph.end type="italics"/> SD. </s>

<s>Igitur, <emph type="italics"/>AD, &<emph.end type="italics"/> AS <emph type="italics"/>eodem tempore percurrentur, quia <lb/>velocitas per totam<emph.end type="italics"/> AD <emph type="italics"/>dupla e&longs;t velocitatis per totam<emph.end type="italics"/> AS. </s>

<s>Et &longs;imiliter, AE <emph type="italics"/>&<emph.end type="italics"/> DA <emph type="italics"/>eodem tempore percurrentur, <lb/>qui velocitas per totam<emph.end type="italics"/> AE, <emph type="italics"/>dupla e&longs;t veloci tatis per to<lb/>tam<emph.end type="italics"/> AD. </s>

<s>Quo, & non aliomodo Galileus, & ego ratiocina<lb/>ti &longs;umus. </s>

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<s>Quanquam & &longs;i per&longs;tes putare detrahendum <lb/>e&longs;&longs;e <expan abbr="æquilibri&utilde;">æquilibrium</expan>, nihil erit quamobrem repugnem, aut <lb/>quamobrem ip&longs;e proptereà lucratus aliquid videaris, <lb/>cùm eo detracto tam ex primo, quàm cæteris ponderi<lb/>bus, quæ pondera &longs;uperfutura, &longs;unt pari progre&longs;&longs;ione <lb/>&longs;int con&longs;equutura. </s>

<s>Nam in exemplo quidem tuo, v g. <lb/></s>

<s>Nam in exemplo quidem tuo, v g. <lb/>&longs;eu numeros 5.2, 10.4, 15.6, 21, 26.2, detracto æqui<lb/>librio, &longs;eu comprehen&longs;o habeas (quod tibi forta&longs;&longs;is <pb pagenum="153"/>exprimendum fuit) eadem continuò erit progre&longs;&longs;io <lb/>quinarii numeri cum quadrante, &longs;eu dr. </s>

<s>&longs;eu numeros 5.2, 10.4, 15.6, 21, 26.2, detracto æqui<lb/>librio, &longs;eu comprehen&longs;o habeas (quod tibi forta&longs;&longs;is <pb pagenum="153"/>exprimendum fuit) eadem continuò erit progre&longs;&longs;io <lb/>quinarii numeri cum quadrante, &longs;eu dr. </s>

<s>2; vt putà, &longs;eu <lb/>dicas 4.2, 9.4, 14.6, 20, 25.2: &longs;eu 6.2, 11.4, 16.6, 22, 27.2. <lb/>Sed res e&longs;t per &longs;e &longs;atis manife&longs;ta. </s>

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<s><emph type="italics"/>Atque in primis, eandem iterùm mihi Propo&longs;itio<lb/>nem affingis, quam iam &longs;upra numero<emph.end type="italics"/> 7. <emph type="italics"/>indicaui, <lb/>& in hunc locum examinandam reieci. </s>

<s>Vis enim, <lb/>& &longs;iue demon&longs;tratione,s&s&longs;ine vlla vel probabili ratione <lb/>ais, & qua&longs;i pro tuo iure &longs;upponis,<emph.end type="italics"/> graue de&longs;cen<lb/>dens per &longs;patium AB in parteis quotlibet <lb/>æqualeis diui&longs;um, percurrere partem &longs;ecundam <lb/>DE, in dimidio eius temporis, quo percurritur <lb/>prior pars AD, <emph type="italics"/>& quod idem est,<emph.end type="italics"/> partem DE per<lb/>curri velocitate dupla eius velocitatis, qua tran&longs;<lb/>curritur AD. </s>

<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"/></s><s> Sequitur. </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"/></s><s> 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>Non &longs;anè mutatio con&longs;ilij <lb/>in me; &longs;ed quæ fal&longs;orum principiorum, incommodo<lb/>rumque ex iis deductorum variatio in te ob&longs;eruatur. <lb/></s>

<s>Nam quòd velis quidem velocitatem acqui&longs;itam in E <lb/>e&longs;&longs;e duplam velocitatis acqui&longs;itæ in D, vt &longs;patium AE, <lb/>&longs;patij AD duplum e&longs;t: contendo iam velocitatem, qua <lb/>percurritur DE, e&longs;&longs;e duplam eius, qua tran&longs;curritur AD, <lb/>&longs;eu, quæ acquiritur per AD: &, quòd tu contendas ab <lb/>A, v&longs;que ad E, augeri æquabiliter, idcircò &longs;um argu-<pb pagenum="162"/>mentatus articulo illo velocitatem per totam AE, du<lb/>plam e&longs;&longs;e velocitatis per totam AD. </s>

<s>Cùm hoc autem <lb/>&longs;uo iam loco demon&longs;tratum abundè &longs;it: ideò illud &longs;o<lb/>lùm, quod tu huius loci facis proprium, e&longs;t attenden<lb/>dum. </s>

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<s>Si velis; igitur perip&longs;am DE &longs;unt duo gradus, vnus <lb/>nempe manens, & alius, qui interim acquiritur. </s>

<s>Si no<lb/>lis; igitur oportet duos gradus, qui &longs;unt in E, acqui&longs;i<lb/>tos e&longs;&longs;e per &longs;olam DE. An-non ergo vtrovis modo <lb/>nece&longs;&longs;e e&longs;t velocitatem per &longs;olam DE, duplam e&longs;&longs;e <lb/>eius, quæ acquiritur per AD? </s>

<s>Dilemma e&longs;t, neutrum<lb/>que e&longs;t membrum, circa quod liceat tergiuer&longs;ari. </s>

<s>Nam <lb/>circa &longs;ecundum quidem, dicere nihil potes: cùm id <lb/>&longs;it tamen reuerâ tuum; quatenus, vt &longs;uperiùs quoque <lb/>adnotatum e&longs;t, vis velocitatem acqui&longs;itam per totam <lb/>DE, e&longs;&longs;e duplam acqui&longs;itæ in D, & acqui&longs;itam in D <lb/>perire: nam alioquin in E velocitas iam e&longs;&longs;et tripla, &longs;i<lb/>ue in E tres gradus e&longs;&longs;ent: cùm e&longs;&longs;e tu velis &longs;olùm duos, <lb/>& acqui&longs;itos quidem per &longs;olam DE. </s>

<s>Circa primum <lb/>autem &longs;i forta&longs;&longs;is dicas manere quidem primum gra<lb/>dum, &longs;ed nihil agere; &longs;equetur &longs;olo &longs;ecundo gradu, qui <lb/>per DE acquiretur, agente, partem DE tempore ni<lb/>hilo breuiore tran&longs;curri, quàm ip&longs;am AD: cùm etiam <lb/>per te percurratur minùs, quam dimidio. </s>

<s>Et, &longs;i dicas <lb/>agere: Aut ob &longs;ui con&longs;tantiam duplò aget ampliùs, <lb/>quàm per AD, vt &longs;uperiùs deduximus; & tunc incom<lb/>modum &longs;equetur, quod &longs;uprà quoque o&longs;ten&longs;um e&longs;t; <pb pagenum="163"/>quatenus DE percurretur præcisè triente primi tem<lb/>poris; & &longs;ecundum tempus integrum non effluet, ni&longs;i <lb/>&longs;ub partem &longs;patij octauam, quod tu vis effluere cum <lb/>ip&longs;a &longs;ecunda: Aut certè tantumdem; & tunc, quia etiam <lb/>tantumdem aget, qui gradus acquiretur per ip&longs;am <lb/>DE: recurret idip&longs;um, quod tu refugis; nempe partem <lb/>DE percurri velocitate dupla illius, qua decur&longs;a fuerit <lb/>AD. </s>

<s><emph type="italics"/>Sed neutram Propo&longs;itionem probas, aut ex &longs;tatutis à me <lb/>principiis vlla ratione deducis: & vt priorem iam &longs;uprà fal<lb/>&longs;am euici; ita nunc i&longs;tam e&longs;&longs;e impoßibilem, hac ratione cui<lb/>denter demon&longs;tro.<emph.end type="italics"/></s>

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<s>Sed <lb/>tuum e&longs;to principium; quid inde? </s>

<s><emph type="italics"/>At hoc dato, nece&longs;&longs;arium etiam e&longs;t, vt quanto tempore gra<lb/>ue de&longs;cendens percurrit &longs;ecundam partem DE, tantò præcisè <lb/>spatium duplò minus antè percurrerit; nempe SD, quod <lb/>&longs;upponitur dimidium &longs;uperioris spatij AD.<emph.end type="italics"/></s>

<s>An-non agno&longs;cis circulum? </s>

<s>Neque enim alia ratio<lb/>ne probas &longs;patia continuò percurri in ratione dupla, <lb/>quàm quia &longs;upponis tanquam principium, partem DE <lb/>percurri tanto tempore, quantò dimidium SD. </s>

<s>Sed <lb/>& hoc e&longs;to. </s>

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<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>

<s>Quartò te rursùs eâ implicari, <lb/>quòd cùm huc v&longs;que volueris acqui&longs;itos e&longs;&longs;e ab A in <lb/>E duos gradus, qui &longs;imùl iuncti &longs;int duplum illius, qui <lb/>acqui&longs;itus e&longs;t ex A in D; velis iam eo&longs;dem duos gra<lb/>dus e&longs;&longs;e duplum illius, qui &longs;olummodò &longs;it acqui&longs;itus <lb/>ex S in D. </s>

<s>Quintò te idcircò omnia perturbare; qua<lb/>tenus quicquid hactenus dixi&longs;ti de &longs;patio in parteis <lb/>æqualeis diui&longs;o, & incipiendo quidem ab A, vt proba<lb/>res velocitates acqui&longs;itas e&longs;&longs;e vt &longs;patia; de &longs;patiis iam, <lb/>ac velocitatibus ita loqueris, vt &longs;i incipiendum &longs;it ab S, <lb/>neglecto pror&longs;us dimidio AS. Sextò, non re&longs;ponde<lb/>re te quæ&longs;tioni; quoniam quæ&longs;tio e&longs;t, non an veloci<lb/>tas per &longs;olam DE &longs;it dupla velocitatis per AD; &longs;ed an <pb pagenum="166"/>e&longs;&longs;e duplam &longs;equatur ex tuis principiis, veluti præmo<lb/>nitum e&longs;t. </s>

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<s>Concipe in triangulo AB<emph.end type="italics"/>C, <emph type="italics"/>& <lb/>in eius latere AC parteis æqualeis non iam<emph.end type="italics"/><lb/><figure id="fig39"/><lb/><emph type="italics"/>&longs;patij, &longs;ed temporis<emph.end type="italics"/> AD, DE, EF, <emph type="italics"/>&c. <lb/></s>

<s>& in<emph.end type="italics"/> D <emph type="italics"/>acqui&longs;itum quem volueris gra<lb/>dum velocitatis, expre&longs;&longs;um linea<emph.end type="italics"/> DG; <emph type="italics"/>erit <lb/>ex tuis, &<emph.end type="italics"/> G<emph type="italics"/>alilei principiis acqui&longs;itus in<emph.end type="italics"/><lb/>E <emph type="italics"/>gradus &longs;ecundus expre&longs;&longs;us linea<emph.end type="italics"/> EH, <emph type="italics"/>&longs;ic<lb/>que velocitas in<emph.end type="italics"/> E, <emph type="italics"/>dupla erit velocitatis in <lb/>D.<emph.end type="italics"/></s>

<s>Quamobrem igitur aggre&longs;&longs;us ar<lb/>gumentari ad hominem, & demon<lb/>&longs;trare tanta volens aduer&longs;us Galileum, <lb/>ac me, in ip&longs;o limineaberras? </s>

<s>Scilicet neque Galilei, <pb pagenum="172"/>neque mea &longs;ententia e&longs;t, <emph type="italics"/>acqui&longs;itum in E gradum &longs;ecun<lb/>dum exprimi lineâ EH,<emph.end type="italics"/> &longs;ed huius lineæ dimidio &longs;o<lb/>lum: &longs;iquidem tota linea EH non &longs;ecundum modò <lb/>gradum exprimit, acqui&longs;itum abv&longs;que D, verùm etiam <lb/>primum acqui&longs;itam ab v&longs;que A, ip&longs;umque iunctum <lb/>cum &longs;ecundo. </s>

<s><emph type="italics"/>Conclude&longs; ne igitur velocitatem tempore<emph.end type="italics"/> DE <emph type="italics"/>acqui&longs;i<lb/>tam duplam e&longs;&longs;e velocitatis acqui&longs;itæ toto tempore AD?<emph.end type="italics"/></s>

<s>Non; &longs;ed acqui&longs;itam toto tempore AE: ita vt tem<lb/>pore AD acquiratur vnus velocitatis gradus, & illo <lb/>per&longs;euerante, æquiualentéque duobus, quantum ad <lb/>&longs;patia &longs;uperanda tempore æquali attinet, acquiratur <lb/>interim alius &longs;uccedente tempore DE, qui cum eo <lb/>iunctus fiat aggregatum, quod &longs;it ip&longs;ius duplum, vt <lb/>deductum &longs;uperiùs e&longs;t. </s>

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<s>Concedo, inquam, quatenus hæ omnes <lb/>velocitates ab A incipiunt, & eandem inter &longs;e ratio<lb/>nem, quam ip&longs;a tempora ob&longs;eruant. </s>

<s><emph type="italics"/>Ex quo nece&longs;&longs;ariò con&longs;equens e&longs;t, vt tota velocitas acqui&longs;i<lb/>ta toto tempore<emph.end type="italics"/> DE, <emph type="italics"/>præcisè, & exactè dupla &longs;it velocitatis <lb/>acqui&longs;itæ toto tempore<emph.end type="italics"/> SD. </s>

<s>Tamet&longs;i punctum, à quo incipiunt velocitates, iam <lb/>varies: concedo nihilominus, & neque id modò, &longs;ed <lb/>etiam velocitatem acqui&longs;itam tempore DE duplam <lb/>e&longs;&longs;e acqui&longs;itæ tempore AS, & tempore DK, & tem<lb/>pore KE. </s>

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<s>Hoc autem cùm æquale &longs;it acqui&longs;itæ ab A in S, <lb/>à D in K, à K in E: ideò acqui&longs;ita à D in E, pari modo <lb/>e&longs;t earum omnium dupla. </s>

<s><emph type="italics"/>Non autem totius acqui&longs;itæ tempore<emph.end type="italics"/> AD. </s>

<s><emph type="italics"/>Non autem totius acqui&longs;itæ tempore<emph.end type="italics"/> AD. </s>

<s>Et quis, cui hoc dixit, acqui&longs;itam tempore DE, du<lb/>plam e&longs;&longs;e acqui&longs;itæ tempore AD, ni&longs;i ip&longs;e tibi? </s>

<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"/></s><s> Nam <lb/>in mea quidem, & Galilei &longs;ententia &longs;umendo has <lb/>parteis DE, AD, SD pro partibus <lb/><figure id="fig40"/><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>Nempe hoc placet ex abundanti: vide ergo perpe<lb/>tuum aduer&longs;us nos paralogi&longs;mum. </s>

<s>Nam vt hactenùs <lb/>falsò &longs;uppo&longs;ui&longs;ti velle nos totam velocitatem EH, quæ <lb/>dupla e&longs;t velocitatis DG, acqui&longs;itam e&longs;&longs;e &longs;olo tempo<lb/>re DE, quam acqui&longs;itam tamen facimus toto tempore <lb/>AE, cùm ratiocinatio no&longs;tra con&longs;tans &longs;it, vt AD, ad <lb/>DG, ita AE ad EH; non autem vnquam, vt AD ad <lb/>DG, ita DE ad EH: vt hactenus, inquam, id falsò <lb/>&longs;uppo&longs;ui&longs;ti; &longs;ic falsò iam &longs;upponis velle nos totam ve<lb/>locitatem FI, quæ tripla e&longs;t eiu&longs;dem velocitatis DG, <lb/>acqui&longs;itam e&longs;&longs;e &longs;olo tempore EF, quam acqui&longs;itam &longs;ta<lb/>tuimus toto tempore AF: cùm con&longs;tanter dicamus, vt <lb/>AD, ad DG, ita AF ad FI; neque tu o&longs;tendere po&longs;<lb/>&longs;is dixi&longs;&longs;e vnquam nos, vt AD ad DG, ita EF ad FI. </s>

<s><emph type="italics"/>De&longs;ignata enim ex<emph.end type="italics"/> D <emph type="italics"/>ver&longs;us<emph.end type="italics"/> A <emph type="italics"/>tertia parte totius<emph.end type="italics"/> AD, <lb/><emph type="italics"/>quæ &longs;it<emph.end type="italics"/> DY, <emph type="italics"/>&longs;umptaque ip&longs;i æquali<emph.end type="italics"/> DZ, <emph type="italics"/>erit totum tempus<emph.end type="italics"/><pb pagenum="177"/>AE <emph type="italics"/>treis in parteis &ecedil;qualeis diui&longs;um, ob <expan abbr="eãque">eanque</expan> cau&longs;&longs;am velocitas <lb/>in<emph.end type="italics"/> E, <emph type="italics"/>tripla erit velocitatis acqui&longs;itæ in<emph.end type="italics"/> Y. <emph type="italics"/>Sed eadem etiam <lb/>ratione velocitas in<emph.end type="italics"/> F <emph type="italics"/>tripla e&longs;t velocitatis acqui&longs;itæ in<emph.end type="italics"/> D, <emph type="italics"/>& <lb/>alia quælibet velocitas de&longs;ignabilis inter<emph.end type="italics"/> E, <emph type="italics"/>&<emph.end type="italics"/> F <emph type="italics"/>tripla &longs;em<lb/>per e&longs;t velocitatis alterius inter<emph.end type="italics"/> Y, <emph type="italics"/>&<emph.end type="italics"/> D <emph type="italics"/>acqui&longs;itæ. </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"/><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>ac prima parte bi&longs;ecti in S, <lb/><figure id="fig41"/><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>

<s>Quomodo <lb/>ergo nece&longs;&longs;itatem huius con&longs;equutionis pro<lb/>bas? </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"/></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. c. duorum, idem &longs;patium SD, <lb/>percurreretur &longs;imùl minuto vno cum triente, &longs;iue &longs;e<lb/>cundis 80: ac rur&longs;us &longs;ecundis 53, ac iterum 18, iterumque <lb/>6, &c. </s>

<s>duorum, idem &longs;patium SD, <lb/>percurreretur &longs;imùl minuto vno cum triente, &longs;iue &longs;e<lb/>cundis 80: ac rur&longs;us &longs;ecundis 53, ac iterum 18, iterumque <lb/>6, &c. </s>

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<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>

<s><emph type="italics"/>Certè hanc ip&longs;am fal&longs;am hypothe&longs;in, eodem numero &longs;ta<lb/>tim expreßè a&longs;&longs;umis; ideóque nihil inde concludis: fru&longs;traque <lb/>in&longs;uper laboras, vt originem erroris inquiras, qui nullus e&longs;t, <lb/>ni&longs;i in fal&longs;is &longs;uppo&longs;itionibus tuis.<emph.end type="italics"/></s>

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<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>

<s>Neque enim in <lb/>compingendo v. </s>

<s>Neque enim in <lb/>compingendo v. g. animalculo acari no&longs;trum &longs;en&longs;um <lb/>con&longs;ulit, qui ip&longs;um habet qua&longs;i punctum, &longs;iue rem vi&longs;u <lb/>minimam; &longs;ed &longs;eip&longs;am potiùs, prout illud texit ex <lb/>innumeris myriadibus partium infra omnem &longs;en&longs;us <lb/>acutiem ex&longs;i&longs;tentium, & nece&longs;&longs;ariarum tamen, vt rem <lb/>faciat per&longs;e mobilem, ac vegetationis, &longs;en&longs;us, appeti<lb/>tus capacem. </s>

<s>animalculo acari no&longs;trum &longs;en&longs;um <lb/>con&longs;ulit, qui ip&longs;um habet qua&longs;i punctum, &longs;iue rem vi&longs;u <lb/>minimam; &longs;ed &longs;eip&longs;am potiùs, prout illud texit ex <lb/>innumeris myriadibus partium infra omnem &longs;en&longs;us <lb/>acutiem ex&longs;i&longs;tentium, & nece&longs;&longs;ariarum tamen, vt rem <lb/>faciat per&longs;e mobilem, ac vegetationis, &longs;en&longs;us, appeti<lb/>tus capacem. </s>

<s>Vt præteream &longs;en&longs;um haberi regulam <lb/>plu&longs;quàm Le&longs;biam, propter diuer&longs;itatem &longs;en&longs;uum acu-<pb pagenum="195"/>tiorum, hebetiorumque, & adiumentorum, quibus <lb/>po&longs;&longs;unt &longs;ubtiliora omnibus rebus antè perceptis per<lb/>cipere; & &longs;ine &longs;pe tamen, vt vnquam naturæ &longs;ubtilita<lb/>tem a&longs;&longs;equantur. </s>

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<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>

<s>An aliquot pauculas, <lb/>v. </s>

<s>An aliquot pauculas, <lb/>v. c. &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>&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"/></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>

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<s>Vide igitur per quot parteis, & per quot <lb/>momenta temporis di&longs;tincta inefficacem facias cau&longs;<lb/>&longs;am Phy&longs;icam, quam aduocas &longs;tatim. </s>

<s>Videlicet <emph type="italics"/>cau&longs;<lb/>&longs;am accelerationis<emph.end type="italics"/> decernis <emph type="italics"/>e&longs;&longs;e &longs;olum medium, v. </s>

<s>Videlicet <emph type="italics"/>cau&longs;<lb/>&longs;am accelerationis<emph.end type="italics"/> decernis <emph type="italics"/>e&longs;&longs;e &longs;olum medium, v. c. 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>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> 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>Tandem, quatenus <lb/>etiam iuxta progre&longs;&longs;ionem in ratione dupla, quam &longs;o<lb/>lam vis e&longs;&longs;e continuam, repugnes tibi nece&longs;&longs;e e&longs;t, cùm <lb/>indefinite aiens <emph type="italics"/>æqualibus temporibus spatia decurri ma<lb/>iora &longs;emper, ac maiora in ratione dupla,<emph.end type="italics"/> nece&longs;&longs;e &longs;it eandem <lb/>rationem euertas, quotie&longs;cumque a&longs;&longs;ump&longs;eris tempo<lb/>ra a&longs;&longs;umptis maiora, & ip&longs;a tamen inter &longs;e æqualia. <lb/></s>

<s>Quippe cùm in tuo, v. </s>

<s>Quippe cùm in tuo, v. c. de ca&longs;u ex Luna exem<lb/>plo a&longs;&longs;ump&longs;eris primo tempore decurri pedes 100, &longs;e<lb/>cundo 200, tertio 400, quarto 800, quinto 1600, <lb/>&longs;exto 3200, &c. </s>

<s>de ca&longs;u ex Luna exem<lb/>plo a&longs;&longs;ump&longs;eris primo tempore decurri pedes 100, &longs;e<lb/>cundo 200, tertio 400, quarto 800, quinto 1600, <lb/>&longs;exto 3200, &c. </s>

<s>con&longs;tat&longs;i deinceps duo tempora pri<lb/>ma pro vno a&longs;&longs;umas, duo &longs;equentia pro alio, duo <lb/>item &longs;equentia pro alio: aut &longs;i tria quidem prima pro <lb/>vno, tria &longs;uccedentia pro alio, &c. </s>

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<s>De quodam <lb/>lap&longs;u emendando circa cau&longs;&longs;am Phy&longs;icam <lb/>accelerati grauium Motus.<emph.end type="center"/></s>

<s>Cum nihil habeas circa alios, qui heinc ad con<lb/>e&longs;u&longs;ionem v&longs;que inter&longs;eruntur, articulos, & ego in ip<lb/>&longs;is, occa&longs;ione Phy&longs;icæ cau&longs;&longs;æ, de qua te dicturum alio <lb/>loco, temporéque receperas, in&longs;inuâtim lap&longs;um, à quo <lb/>non &longs;atis caueram, in priore Epi&longs;tolatum de Motu im<lb/>pre&longs;&longs;o à motore tran&longs;lato (imò & in Epi&longs;tola ante duos <lb/>annos ad te data) eam ob rem heic locus erit opportu<lb/>nus, vt rem paulò fu&longs;iùs deducam, ac memetip&longs;um cor<lb/>rigam, dicturus &longs;imùl de Phy&longs;ica cau&longs;&longs;a, quam tu pla<lb/>cere tibi dixi&longs;ti in articulum XXXV. Itaque, cùm ego <lb/>demirarer illam accelerati motus progre&longs;&longs;ionem &longs;e<lb/>cundum &longs;eriem numerorum ab vnitate imparium, Ra<lb/>tiocinatus &longs;um imprimis, lapidem v.g. non habere ex <lb/>&longs;e huiu&longs;modi motum; quoniam &longs;i &longs;olus lapis non ex<lb/>&longs;i&longs;tente Mundo foret, aut aliàs in vacuo &longs;ic con&longs;titue<lb/>retur, vt nihil cum Mundo communicaret; non e&longs;&longs;et <lb/>prorsùs, quamobrem eò, quò iam mouetur tenderet; <lb/>vnde & conclu&longs;i cau&longs;&longs;am huiu&longs;modi motus e&longs;&longs;e debe<lb/>re extrin&longs;ecam, ip&longs;amque aut impellentem, aut attra-<pb pagenum="210"/>hentem, aut vtramque &longs;imùl. </s>

<s>non habere ex <lb/>&longs;e huiu&longs;modi motum; quoniam &longs;i &longs;olus lapis non ex<lb/>&longs;i&longs;tente Mundo foret, aut aliàs in vacuo &longs;ic con&longs;titue<lb/>retur, vt nihil cum Mundo communicaret; non e&longs;&longs;et <lb/>prorsùs, quamobrem eò, quò iam mouetur tenderet; <lb/>vnde & conclu&longs;i cau&longs;&longs;am huiu&longs;modi motus e&longs;&longs;e debe<lb/>re extrin&longs;ecam, ip&longs;amque aut impellentem, aut attra-<pb pagenum="210"/>hentem, aut vtramque &longs;imùl. </s>

<s>Secundò, vi&longs;um mihi <lb/>e&longs;t a&longs;&longs;umi po&longs;&longs;e aërem, qui infernè pre&longs;&longs;us, re&longs;ilien&longs;<lb/>que ad latera, in locum po&longs;terum &longs;uccederet, &longs;uperné<lb/>que in&longs;taret, pro cau&longs;&longs;a impellente; & magneticam Ter<lb/>ræ vim, quæ hamulorum, catenularumque in&longs;tar, in<lb/>fernè pelliceret, pro cau&longs;&longs;a trahente. </s>

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<s>Itaque motus à grauitate &longs;ola non &longs;ic elicietur, vt &longs;it <lb/>&longs;emper &longs;ui &longs;imilis, atque vniformis; neque grauitas <lb/>&longs;emper eadem, &longs;imili&longs;que &longs;ui, & inalterata (hoc e&longs;t, quæ <lb/>à me &longs;implex dicta e&longs;t, &longs;ine appellata adiectitia) per<lb/>&longs;euerabit. </s>

<s><emph type="center"/>IN RESPONSIONIS CONCLVSIONEM.<emph.end type="center"/></s>

<s><emph type="center"/>IN RESPONSIONIS CONCLVSIONEM.<emph.end type="center"/></s>

<s><emph type="italics"/>Et hæc, Clarißime<emph.end type="italics"/> G<emph type="italics"/>a&longs;&longs;ende, præcipua &longs;unt, quæ tibi <lb/>nece&longs;&longs;ariò pro me, & pro veritate re&longs;cribenda putaui; tum <lb/>vt, &longs;i fieri pote&longs;t, eam tibi, quam ignotam acrius impugnas, <lb/>veritatem, maiore luce illu&longs;tratam aperiam: tum vt, ne &longs;al<lb/>tem apud eos, qui Respon&longs;ionem tuam vi&longs;uri &longs;unt, adeò de<lb/>formis, & ab&longs;urdus appaream, quàm me deformem, & ab-<emph.end type="italics"/><pb pagenum="221"/><emph type="italics"/>&longs;urdum effingis. </s>

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<s>Ac non requiro <lb/>quidem, quæ &longs;int illa ob&longs;curiora, magi&longs;que incerta, in <lb/>quibus ais tua decreta tantam tueri con&longs;tantiam; quan<lb/>dò videor tibi ne in huius quidem longè clarioris, <lb/>certiori&longs;que de Motu controuer&longs;iæ ingre&longs;&longs;us penetra<lb/>lia; te&longs;tor tamen me longè e&longs;&longs;e, vt in illa vnquam in<lb/>quiram, qui etiam, i&longs;ta quod attinet, &longs;i forte præmo<lb/>nui&longs;&longs;es me, quid rei tibi cordi foret, non adulatus <pb pagenum="226"/>&longs;anè fui&longs;&longs;em, ne aduer&longs;us meam mentem loqueter: &longs;ed <lb/>neque quicquam re&longs;crip &longs;i&longs;&longs;em, ne videri po&longs;&longs;em quam <lb/>tu heic appellas f&oelig;dam di&longs;&longs;en&longs;ionem (qua&longs;i diceres <lb/>Camarinam) mouere. </s>

<s><emph type="italics"/>Cæterùm quantalibet aut decretorum meorum inter &longs;e, <lb/>aut pro veritate inter nos pugna, & contentio interce&longs;&longs;erit, <lb/>&longs;umma tamen, vt spero, per&longs;euerabit &longs;emper animorum <lb/>con&longs;en&longs;io, nec minùs vnquam futurus &longs;um Tuus ad omnia<emph.end type="italics"/><lb/>PETRVS CAZRÆVS. <emph type="italics"/>Metis,<emph.end type="italics"/> 6. <emph type="italics"/>Eid. </s>

<s>April.<emph.end type="italics"/><lb/>M. DC. XLV. </s>

<s>Ego verò &longs;anctè affirmo, nihil me vnquam remi&longs;<lb/>&longs;urum neque de &longs;umma veneratione, qua te pro&longs;e<lb/>quor, neque de &longs;incero affectu, quo toto ex corde &longs;um <lb/>Tuus. </s>

<s>Pari&longs;ijs, Non. </s>

<s>Pari&longs;ijs, Non. Maij, M. DC. XLV. <lb/><figure id="fig46"/></s>

<s>EPISTOLA TERTIA, <lb/>QVAM, TAMETSI TEMPORE <lb/>primam, vi&longs;um e&longs;t tamen po&longs;t-ponere, quòd <lb/>præter argumentum cum &longs;uperioribus com<lb/>mune, contineat etiam explicationem plu<lb/>rium aliarum difficultatum, quæ fuerant in <lb/>Epi&longs;tolas, <emph type="italics"/>De Motu impre&longs;&longs;o a Motore tran&longs;<lb/>lato,<emph.end type="italics"/> objectæ. <lb/><gap desc="hr tag"/></s>

<s><emph type="italics"/>AD MODVM REVERENDO, <lb/>& Religiv&longs;ißimo, Doctißimóque Viro,<emph.end type="italics"/> P. <lb/>PETRO CAZRÆO, <emph type="italics"/>Societatis<emph.end type="italics"/> IESV, <lb/><emph type="italics"/>Diuionen&longs;is Collegij Rectori &longs;apient ißimo.<emph.end type="italics"/></s>

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

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

<s>EXIMIA profectò humanitas tua, vt im<lb/>perâris tibi patientiam percurrendi, co<lb/>gno&longs;cendique quicquid illud fuit mearum <lb/>ineptiarum; méque &longs;imul adeò &longs;olerti, ele<lb/>gantique di&longs;qui&longs;itione cohone&longs;tandum cen&longs;ueris. </s>

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<s>Poti&longs;&longs;imæ fuere, cùm <lb/>rem præ&longs;titi, adnotatis &longs;patiis, tam in prolixiore &longs;ex<lb/>decim orgyis pariete, quàm in tubo vitreo inclinato <lb/>prolixiore duabus; ac &longs;ociis &longs;imul adhibitis, quorum <lb/>&longs;inguli ad &longs;ingula &longs;patia, eorumque notas attenderent, <lb/>vt tam decidente globo <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> parietem, quàm dela<lb/>bente per tubum, dicere po&longs;&longs;ent, ecquo momento ex <lb/>numeratis (& alta voce pronunciatis) æqualibus, glo<lb/>bus pertran&longs;iret vnamquamque notam. </s>

<s>Nempe ex<lb/>inde con&longs;titit, quale &longs;patium fui&longs;&longs;et primo momento <lb/>&longs;uperatum vnum, talia deinceps &longs;uperata fui&longs;&longs;e &longs;ecundo <lb/>momento tria, tertio quinque, quarto &longs;eptem: adeò vt <lb/>illa aggregando reperirentur &longs;uperata in fine primi <lb/>momenti vnum, in fine &longs;ecundi quatuor, in fine tertij <pb pagenum="230"/>nouem, in fine quarti &longs;exdecim & c. </s>

<s>&longs;icque aggregata <lb/>&longs;patiorum &longs;e vt temporum quadrata haberent. </s>

<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>

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<s>Dices <lb/>quidem fortè, illud e&longs;&longs;e formam, quæ vt &longs;eipsâ vnitur <lb/>materiæ, ita &longs;eipsâ, ab&longs;que vllo intercedente organo <lb/>mouere po&longs;&longs;it materiam; vnde & totius ma&longs;&longs;æ, &longs;eu Fer<lb/>ri con&longs;equatur motus: verùm vtcumque heinc explice<lb/>tur motus Ferri, quà graue e&longs;t, & deor&longs;um tendit; illi <lb/>tamen motus, flexu&longs;que in quamcumque partem fuerit <lb/>Magnes appo&longs;itus, non videntur po&longs;&longs;e intelligi ex &longs;ola <lb/>applicatione formæ ad materiam, ni&longs;i & illa anima &longs;it, <lb/>& tum vireis, tum articulos flexanimcis habeat, vt quæ<lb/>dam variorum motuum organa; quæ nulla tamen de<lb/>prehenduntur. </s>

<s>Sed hæc vt præteream; cùm videamus <lb/>Ferrum non ex quacumque di&longs;tantia in amplexum <lb/>Magnetis accurrere, &longs;ed accurrere &longs;olum, v. </s>

<s>Sed hæc vt præteream; cùm videamus <lb/>Ferrum non ex quacumque di&longs;tantia in amplexum <lb/>Magnetis accurrere, &longs;ed accurrere &longs;olum, v. c. ab vno <lb/>palmo; quo modo vis intelligamus incitari ferrum <lb/>&longs;ponte naturæ in di&longs;tantia palmi, non in di&longs;tantia cubi<lb/>ti? </s>

<s>ab vno <lb/>palmo; quo modo vis intelligamus incitari ferrum <lb/>&longs;ponte naturæ in di&longs;tantia palmi, non in di&longs;tantia cubi<lb/>ti? </s>

<s>An in di&longs;tantia cubiti &longs;uæ &longs;pontis non e&longs;t? </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"/></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>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>Cùm enim Phi<lb/>lo&longs;ophia quam plurima doceat, quæ vera habentur, & <lb/>ab omnibus viris piis, atque Chri&longs;t anis admittuntur; <lb/>tamet&longs;i ip&longs;is refragari &longs;acræ Literæ apertè videan<lb/>tur; par e&longs;t profectò Literas &longs;acras eam pati interpreta<lb/>tionem, vt o&longs;tendi po&longs;&longs;it eas, cùm veræ &longs;int, veritati <lb/>non repugnare. </s>

<s>Id autem D. </s>

<s>Id autem D. </s>

<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>

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<s>Deinde <pb pagenum="282"/>&longs;ubuereor, ne illi re&longs;pon&longs;uri ad tuas huiu&longs;cemodi con&longs;e<lb/>quutiones fuerint, ablegandam igitur e&longs;&longs;e vniuer&longs;am <lb/>Phy&longs;icam, quatenusnullum e&longs;t placitum, ex quo dicere <lb/>non po&longs;&longs;imus, deduci po&longs;&longs;e ab aliquibus incommoda <lb/>non ab&longs;imilia. </s>

<s>Ponatur enim, exempli cau&longs;&longs;a, <emph type="italics"/>E&longs;&longs;e <lb/>Terram sphæricam:<emph.end type="italics"/> Concludetur, e&longs;&longs;e eam ergo habita<lb/>bilem circumquáque; & procliue fore credere Antipo<lb/>das. </s>

<s>Inferetur, eos non potui&longs;&longs;e ab Adamo propagari; <lb/>atque idcircò Chri&longs;tum Dominum non e&longs;&longs;e eorum <lb/>Redemptorem. </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"/></s><s> 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>Et tamet&longs;i dicam vi&longs;um iri tan<lb/>tum, quantum Orbem magnum, in&longs;ignemve portio<lb/>nem regionis Planetariæ; cau&longs;&longs;a e&longs;t, quia ex eadem <lb/>di&longs;tantia totus Orbis magnus non maiore appareret <lb/>amplitudine, quàm heinc appareat vna Stellarum cum <lb/>circumfu&longs;is corpu&longs;culo radiis. </s>

<s>Tu verò &longs;ic interrogas, <lb/>vt &longs;i cen&longs;erem ex ea di&longs;tantia tum magnum Orbem <lb/>appariturum eiu&longs;dem, qua propè amplitudinis; tum <lb/>Solem non modò maiorem, quàm heinc con&longs;piciatur; <lb/>&longs;ed etiam quantus Orbis magnus ex Marte, v. </s>

<s>aut <lb/>Ioue con&longs;piceretur, appariturum. </s>

<s>Quòd verò &longs;ic in<lb/>terrogas, eo permotus argumento, <emph type="italics"/>quòd con&longs;tet Lu<lb/>nam, ac Martem, ip&longs;umque etiam Solem quò propiùs acce<lb/>dunt ad nos, eò maiores con&longs;pici; quò longiùs ab&longs;cedunt,<emph.end type="italics"/><pb pagenum="306"/><emph type="italics"/>minores:<emph.end type="italics"/> vides rem e&longs;&longs;e incohærentem. </s>

<s>Etenim agitur <lb/>hoc loco de incremento in lucidis facto non ratione <lb/>di&longs;tantiæ, &longs;ed ratione ob&longs;curitatis. </s>

<s>Neque enim re<lb/>quiritur, cur Mars v. </s>

<s>Neque enim re<lb/>quiritur, cur Mars v. g. dum e&longs;t perigeius, terri&longs;ve pro<lb/>pinquior, appareat maior, quàm apogeius, &longs;eu à terris <lb/>remotior, & in eodem quidem tenebrarum gradu: &longs;ed <lb/>cur in eadem propinquitate, aut in eadem remotione <lb/>maior, & minor appareat, prout in variis gradibus ob<lb/>&longs;curitatis con&longs;picitur; vt claro adhûc crepu&longs;culo, & no<lb/>cte iam facta profunda. </s>

<s>dum e&longs;t perigeius, terri&longs;ve pro<lb/>pinquior, appareat maior, quàm apogeius, &longs;eu à terris <lb/>remotior, & in eodem quidem tenebrarum gradu: &longs;ed <lb/>cur in eadem propinquitate, aut in eadem remotione <lb/>maior, & minor appareat, prout in variis gradibus ob<lb/>&longs;curitatis con&longs;picitur; vt claro adhûc crepu&longs;culo, & no<lb/>cte iam facta profunda. </s>

<s>Quare & ad hoc non ad il<lb/>lud &longs;imilitudo candelæ facit; & ad hoc, non verò ad <lb/>illud, quam cau&longs;&longs;am e&longs;&longs;e prætermittendam cen&longs;ui&longs;ti, <lb/>referenda fuit. </s>

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<s>Et quia propter <lb/>hanc communionem efficitur, vt motus diurnus non <lb/>&longs;it integer accipiendus, ni&longs;i po&longs;tquàm non modò Ter<lb/>ra ex meridiano quopiam digre&longs;&longs;a ad eundem meridia<lb/>num redit, &longs;ed po&longs;tquàm ip&longs;a etiam Luna meridianum <lb/>eundem repetit: inde e&longs;t, cur Luna illum dietim repe<lb/>tente, vnâ prope hora, &longs;eu quatuor quintis horæ tar<lb/>diùs; cur, inquam, alteratio illa, atque adeò æ&longs;tus con<lb/>tingat dietim tanto tempore: quatuor &longs;cilicet horæ <lb/>quintis tardiùs. </s>

<s>Prætereo autem, cùm Luna ad datum <lb/>meridianum eádem diei hora, ni&longs;i po&longs;t men&longs;em non <lb/>redeat, excur&longs;us tamen, & recur&longs;us maris eadem hora <lb/>po&longs;t dies quindecim in&longs;taurari; quòd ij geminentur <lb/>in dies &longs;ingulos, ac eadem hora eueniant, non <lb/>modò cùm Luna e&longs;t nobis in mendiano &longs;upra horizon<lb/>tem, &longs;ed etiam cùm infià, in meridiano Antipodum. <lb/></s>

<s>Adeò proinde, vt dici po&longs;&longs;it, quemadmodum Luna <lb/>intra men&longs;em apparet reuolui circa Terram vna vice <lb/>minùs, quàm Sol; ita Mare affluere, & refluere duabus <lb/>vicibus minùs, quàm afflueret, ac reflueret, ab&longs;que illa <pb pagenum="317"/>retar datione. </s>

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<s>Tu intereà rogatus <lb/>perge, quod vltrò c&oelig;pi&longs;ti; hoc e&longs;t, ama me, & bene, <lb/>imò optimè Vale. </s>

<s>Pari&longs;iis, VI. Eid. </s>

<s>Pari&longs;iis, VI. Eid. Decembris. <lb/></s>

<s>Decembris. <lb/></s>

<s><emph type="center"/>FINIS.<emph.end type="center"/><lb/><figure id="fig47"/><pb pagenum="319"/><gap desc="hr tag"/></s>

<s><emph type="center"/>VIRO Nobili&longs;&longs;imo PHILIBERTO DE LA MARE <lb/>Senatori Diuionen&longs;i, <emph type="italics"/>P.GASSENDVS S.<emph.end type="italics"/><emph.end type="center"/></s>

<s>SErò Re&longs;pondeo; nam eccemen&longs;is, ex quo tuæ li<lb/>teræ datæ: &longs;ed in cau&longs;&longs;a fuit tum inualetudo, tum <lb/>prolixa Re&longs;pon&longs;io, cui hoc adtextum &longs;chediolum ha<lb/>bes. </s>

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<s>Pari&longs;iis, VI. Eid. </s>

<s>Pari&longs;iis, VI. Eid. Decemb. M. DC. XLII. <lb/><gap desc="hr tag"/></s>

<s>Decemb. </s>

<s><emph type="center"/><emph type="italics"/>SVMMA PRIVILEGII.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>SVMMA PRIVILEGII.<emph.end type="italics"/><emph.end type="center"/></s>

<s>IVxta Priuilegium à Rege Chri&longs;tiani&longs;&longs;imo conce&longs;<lb/>&longs;um, cautum e&longs;t, ne quistoto Regnoimprimat, alibi<lb/>ve impre&longs;&longs;as diuendat PETRI GASSENDI <emph type="italics"/>De <lb/>Proportione, qua grauia decidentia accelerantur, Epi&longs;tolas <lb/>treis,<emph.end type="italics"/> præter LVD. DE HEVQVEVILLE, Bibliopolam <lb/>Pari&longs;ien&longs;em, idque in decennium, &longs;ub &longs;olitis p&oelig;nis. <lb/></s>

<s>Datum Pari&longs;iis 8. April. </s>

<s>Datum Pari&longs;iis 8. April. </s>

<s>1642. Signatum CEBERET. </s> </chap> </body> <back/> </text></archimedes>

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