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| <s><emph type="center"/>DE PROPORTIONE, <lb/>QVA GRAVIA DECIDENTIA <lb/>ACCELERANTVR.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/>DE PROPORTIONE, <lb/>QVA GRAVIA DECIDENTIA <lb/>ACCELERANTVR.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/>EPISTOLA PRIMA.<emph.end type="center"/><lb/><gap desc="hr tag"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="center"/>EPISTOLA PRIMA.<emph.end type="center"/><lb/> <!-- KEEP S--></s></p><p type="main"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <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 reciprocè <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 xlink:href="028/01/068.jpg" 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></p><p type="main"> | <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 reciprocè <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 xlink:href="028/01/068.jpg" 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 tertio bis, à &longs;ecundo ter, à primo quater, &c. </s></p><p type="main"> |
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| <s>XVII. <!-- KEEP S--></s> | <s>XVII. <!-- KEEP S--></s> |
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| <s>XVIII. <!-- KEEP S--></s> | <s>XVIII. <!-- KEEP S--></s> |
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| <s>Id prætereo, quod &longs;ubiicis, ex a&longs;cen&longs;u <lb/>globi ad eandem altitudinem, non &longs;atis rectè colli­<lb/>gi impetus æqualitatem; quoniam id aduer&longs;aretur <lb/>recitandæ tuæ rationi, atque experientiæ: vti & dum <lb/>cau&longs;&longs;am petis ex eo, <emph type="italics"/>quòd, quò circulus minor e&longs;t, èo<emph.end type="italics"/><pb xlink:href="028/01/070.jpg" pagenum="30"/><emph type="italics"/>de&longs;cen&longs;us procliuior, faciliorque, & a&longs;cen&longs;us difficilior vi­<lb/>deatur:<emph.end type="italics"/> id repugnaret tum compen&longs;ationi, aduer&longs;us <lb/>quam nihil obiicis, inter breuitatem, & decliu<gap/>ta­<lb/>tem &longs;patij; tum familiari experientiæ de rebus deor­<lb/>sùm impactis, quæ impetu pari deicctæ tantò emer­<lb/>gunt altiùs, quantò incidentia e&longs;t magis perpendi­<lb/>cularis. </s> | <s>Id prætereo, quod &longs;ubiicis, ex a&longs;cen&longs;u <lb/>globi ad eandem altitudinem, non &longs;atis rectè colli­<lb/>gi impetus æqualitatem; quoniam id aduer&longs;aretur <lb/>recitandæ tuæ rationi, atque experientiæ: vti & dum <lb/>cau&longs;&longs;am petis ex eo, <emph type="italics"/>quòd, quò circulus minor e&longs;t, èo<emph.end type="italics"/><pb xlink:href="028/01/070.jpg" pagenum="30"/><emph type="italics"/>de&longs;cen&longs;us procliuior, faciliorque, & a&longs;cen&longs;us difficilior vi­<lb/>deatur:<emph.end type="italics"/> id repugnaret tum compen&longs;ationi, aduer&longs;us <lb/>quam nihil obiicis, inter breuitatem, & decliuita­<lb/>tem &longs;patij; tum familiari experientiæ de rebus deor­<lb/>sùm impactis, quæ impetu pari deiectæ tantò emer­<lb/>gunt altiùs, quantò incidentia e&longs;t magis perpendi­<lb/>cularis. </s> |
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| <s>Attingo ergo potiùs id, quod &longs;upere&longs;t, <lb/>dum id &longs;ugillas, quod Galileus &longs;e e&longs;&longs;e &longs;æpiùs exper­<lb/>tum ait, <emph type="italics"/>tum globum ferreum per aërem cadentem, tum <lb/>globum æneum per excauatum in longiore tigillo alueolum, <lb/>in quacumque tigilli &longs;upra horizontem eleuatione de&longs;cenden­<lb/>tem, perpetuò tantum præcisè temporis in de&longs;cen&longs;u per pri­<lb/>mum totius percurrendi spatij quadrantem, quantum in <lb/>trium reliquorum decur&longs;u in&longs;ump&longs;i&longs;&longs;e: ex quo &longs;ine dubio con­<lb/>&longs;equens e&longs;&longs;et, &longs;patia æqualibus temporibus decur&longs;a in ea <lb/>e&longs;&longs;e ratione, quæ reperitur inter numeros impareis ab vnita­<lb/>te procedenteis.<emph.end type="italics"/></s><s> Nimirùm, vt o&longs;tendas ea, quæ ex i&longs;tis <lb/>qua&longs;i principiis con&longs;equuntur, aut inferuntur, e&longs;&longs;e ip­<lb/>&longs;is certiora, aut cuidentiora non po&longs;&longs;e: <emph type="italics"/>Id,<emph.end type="italics"/> inquis, <emph type="italics"/>tot <lb/>erroribus obnoxium e&longs;t, & exploratu adcò difficile, vt nihil <lb/>inde certi concludi po&longs;&longs;e videatur.<emph.end type="italics"/></s><s> Enimverò, vtcum­<lb/>que experiundi modus difficilis &longs;it, obnoxiu&longs;que er­<lb/>roribus; non idcircò tamen experimentum conuin­<lb/>citur fal&longs;um. </s> | <s>Attingo ergo potiùs id, quod &longs;upere&longs;t, <lb/>dum id &longs;ugillas, quod Galileus &longs;e e&longs;&longs;e &longs;æpiùs exper­<lb/>tum ait, <emph type="italics"/>tum globum ferreum per aërem cadentem, tum <lb/>globum æneum per excauatum in longiore tigillo alueolum, <lb/>in quacumque tigilli &longs;upra horizontem eleuatione de&longs;cenden­<lb/>tem, perpetuò tantum præcisè temporis in de&longs;cen&longs;u per pri­<lb/>mum totius percurrendi spatij quadrantem, quantum in <lb/>trium reliquorum decur&longs;u in&longs;ump&longs;i&longs;&longs;e: ex quo &longs;ine dubio con­<lb/>&longs;equens e&longs;&longs;et, &longs;patia æqualibus temporibus decur&longs;a in ea <lb/>e&longs;&longs;e ratione, quæ reperitur inter numeros impareis ab vnita­<lb/>te procedenteis.<emph.end type="italics"/></s><s> Nimirùm, vt o&longs;tendas ea, quæ ex i&longs;tis <lb/>qua&longs;i principiis con&longs;equuntur, aut inferuntur, e&longs;&longs;e ip­<lb/>&longs;is certiora, aut cuidentiora non po&longs;&longs;e: <emph type="italics"/>Id,<emph.end type="italics"/> inquis, <emph type="italics"/>tot <lb/>erroribus obnoxium e&longs;t, & exploratu adcò difficile, vt nihil <lb/>inde certi concludi po&longs;&longs;e videatur.<emph.end type="italics"/></s><s> Enimverò, vtcum­<lb/>que experiundi modus difficilis &longs;it, obnoxiu&longs;que er­<lb/>roribus; non idcircò tamen experimentum conuin­<lb/>citur fal&longs;um. </s> |
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| <s>Et adnitere <lb/>facere per&longs;pectum, quidnam acceleratio &longs;it, nulla men­<lb/>tione temporis; ac perno&longs;ces rem impo&longs;&longs;ibilem factu <lb/>e&longs;&longs;e. </s> | <s>Et adnitere <lb/>facere per&longs;pectum, quidnam acceleratio &longs;it, nulla men­<lb/>tione temporis; ac perno&longs;ces rem impo&longs;&longs;ibilem factu <lb/>e&longs;&longs;e. </s> |
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| <s>Vtcumque enim plureis, plurei&longs;que &longs;patij par­<lb/>teis memores<gap/> ni&longs;i tamen adiicias voces <emph type="italics"/>deinceps, con&longs;e­<lb/>quenter, &longs;ucceßiuè,<emph.end type="italics"/> aut &longs;imileis alias, quæ ad tempus at­<lb/>tineant, non magis accelerationem, quàm &longs;implicem <lb/>celeritatem, aut potiu&longs;-quam motum &longs;impliciter &longs;pe­<lb/>ctatum de&longs;cribes. </s> | <s>Vtcumque enim plureis, plurei&longs;que &longs;patij par­<lb/>teis memore: ni&longs;i tamen adiicias voces <emph type="italics"/>deinceps, con&longs;e­<lb/>quenter, &longs;ucceßiuè,<emph.end type="italics"/> aut &longs;imileis alias, quæ ad tempus at­<lb/>tineant, non magis accelerationem, quàm &longs;implicem <lb/>celeritatem, aut potiu&longs;-quam motum &longs;impliciter &longs;pe­<lb/>ctatum de&longs;cribes. </s> |
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| <s>Quanquam nihil e&longs;t opus id vr­<lb/>geam, cùm tu pro confe&longs;&longs;o iam habeas; profe&longs;&longs;us <lb/>nempe <emph type="italics"/>celeritatem in naturali de&longs;cen&longs;u grauium non modò <lb/>ad locum, &longs;ed ad tempus quoque re&longs;pectum includere:<emph.end type="italics"/> ac <lb/>mirari &longs;olùm quis po&longs;&longs;it, agno&longs;cere te in celeritate <lb/>duplicem re&longs;pectum, & velle tamen alterum, ip&longs;um­<lb/>que præcipuum in tradenda definitione accelerati mo­<lb/>tus exclu&longs;um; ac inuehi in Galileum, qui inclu&longs;um <lb/>voluerit. </s> | <s>Quanquam nihil e&longs;t opus id vr­<lb/>geam, cùm tu pro confe&longs;&longs;o iam habeas; profe&longs;&longs;us <lb/>nempe <emph type="italics"/>celeritatem in naturali de&longs;cen&longs;u grauium non modò <lb/>ad locum, &longs;ed ad tempus quoque re&longs;pectum includere:<emph.end type="italics"/> ac <lb/>mirari &longs;olùm quis po&longs;&longs;it, agno&longs;cere te in celeritate <lb/>duplicem re&longs;pectum, & velle tamen alterum, ip&longs;um­<lb/>que præcipuum in tradenda definitione accelerati mo­<lb/>tus exclu&longs;um; ac inuehi in Galileum, qui inclu&longs;um <lb/>voluerit. </s> |
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| <s>Nam & licet, veluti tu re&longs;pectum ad tem­<lb/>pus prætermi&longs;&longs;um fers, &longs;ic ille re&longs;pectum ad locum <lb/>prætermitti po&longs;&longs;e cen&longs;uerit: excu&longs;ari pote&longs;t, quòd qui <lb/>motum dicit, locum etiam dicat, quemadmodum <lb/>mox attigi; & cùm foret &longs;olùm de celeritate &longs;uperue­<lb/>niento quæ&longs;tio, ideò nugationem deuitans, illam per <lb/>re&longs;pectum ad tempus, &longs;ine quo intelligi nequeat, pu­<lb/><gap/>rit e&longs;&longs;e de&longs;iniendam. </s></p><pb xlink:href="028/01/097.jpg" pagenum="57"/><p type="main"> | <s>Nam & licet, veluti tu re&longs;pectum ad tem­<lb/>pus prætermi&longs;&longs;um fers, &longs;ic ille re&longs;pectum ad locum <lb/>prætermitti po&longs;&longs;e cen&longs;uerit: excu&longs;ari pote&longs;t, quòd qui <lb/>motum dicit, locum etiam dicat, quemadmodum <lb/>mox attigi; & cùm foret &longs;olùm de celeritate &longs;uperue­<lb/>niento quæ&longs;tio, ideò nugationem deuitans, illam per <lb/>re&longs;pectum ad tempus, &longs;ine quo intelligi nequeat, pu­<lb/>tâtit e&longs;&longs;e de&longs;iniendam. </s></p><pb xlink:href="028/01/097.jpg" pagenum="57"/><p type="main"> |
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| <s>XXXI. <!-- KEEP S--></s> | <s>XXXI. <!-- KEEP S--></s> |
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| <s>Subdis con&longs;equenter; <emph type="italics"/>Quod vt certiùs <lb/>fiat, primùm occurrendum est errori, qui facilè obrepere <lb/>potest, &longs;i quæ de cele itatis augmento in &longs;patiis æqualibus <lb/>antè demonstrata &longs;unt, minùs accuratè perpendantur. </s> | <s>Subdis con&longs;equenter; <emph type="italics"/>Quod vt certiùs <lb/>fiat, primùm occurrendum est errori, qui facilè obrepere <lb/>potest, &longs;i quæ de cele itatis augmento in &longs;patiis æqualibus <lb/>antè demonstrata &longs;unt, minùs accuratè perpendantur. </s> |
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| <s>Cùm <lb/>enim ex &longs;uperioribus iam euidenter con&longs;tet, in naturali gra­<lb/>uium de&longs;cen&longs;u, &longs;emper ex dupla di&longs;tantia, celeritatem ha­<lb/>beri duplam; & ex tripla distantia, triplam; atque ita <lb/>deinceps, eadem ratione celeritatem augeri: nihil procliuius <lb/>e&longs;&longs;e potest, quàm vt quis exi&longs;timet, accelerationem <gap/><lb/>fieri per &longs;ubdiui&longs;ionem primi cuiu&longs;libet temporis, in paricis <lb/>&longs;emper minores, pro multitudine, & ratione &longs;patiorum æqua­<lb/>lium, quæ motu decurruntur; ita videlicet, vt pars &longs;ecunda <lb/>spatij, ab&longs;oluatur dimidia parte temporis, quo prima pars <lb/>decur&longs;a est; & tertia pars &longs;patij, tertia parte eiu&longs;dem primi <lb/>temporis percurratur, & ita de cæteris: maximè cùm in hac <lb/>etiam hypothe&longs;i, &longs;patia & velocitates in eadem e&longs;&longs;e ratione, <lb/>& quod con&longs;equens e&longs;t, ex impeta quoque decidentium corpo­<lb/>rum hac ratione inuariato, iidem omnes, quos experientia <lb/>docet effectus haberi, primo a&longs;pectu videantur.<emph.end type="italics"/></s><s> Heic pro­<lb/>fectò rur&longs;us mirari tuam &longs;agacitatem par e&longs;t, qua­<lb/>tenus eam non fugit error qui ex po&longs;itione à te a&longs;­<lb/>&longs;erta con&longs;equitur; tamet&longs;i ip&longs;e non con&longs;equi ex iis, <lb/>quæ &longs;ubiicis, contendas. </s> | <s>Cùm <lb/>enim ex &longs;uperioribus iam euidenter con&longs;tet, in naturali gra­<lb/>uium de&longs;cen&longs;u, &longs;emper ex dupla di&longs;tantia, celeritatem ha­<lb/>beri duplam; & ex tripla distantia, triplam; atque ita <lb/>deinceps, eadem ratione celeritatem augeri: nihil procliuius <lb/>e&longs;&longs;e potest, quàm vt quis exi&longs;timet, accelerationem illam <lb/>fieri per &longs;ubdiui&longs;ionem primi cuiu&longs;libet temporis, in parteis <lb/>&longs;emper minores, pro multitudine, & ratione &longs;patiorum æqua­<lb/>lium, quæ motu decurruntur; ita videlicet, vt pars &longs;ecunda <lb/>spatij, ab&longs;oluatur dimidia parte temporis, quo prima pars <lb/>decur&longs;a est; & tertia pars &longs;patij, tertia parte eiu&longs;dem primi <lb/>temporis percurratur, & ita de cæteris: maximè cùm in hac <lb/>etiam hypothe&longs;i, &longs;patia & velocitates in eadem e&longs;&longs;e ratione, <lb/>& quod con&longs;equens e&longs;t, ex impeta quoque decidentium corpo­<lb/>rum hac ratione inuariato, iidem omnes, quos experientia <lb/>docet effectus haberi, primo a&longs;pectu videantur.<emph.end type="italics"/></s><s> Heic pro­<lb/>fectò rur&longs;us mirari tuam &longs;agacitatem par e&longs;t, qua­<lb/>tenus eam non fugit error qui ex po&longs;itione à te a&longs;­<lb/>&longs;erta con&longs;equitur; tamet&longs;i ip&longs;e non con&longs;equi ex iis, <lb/>quæ &longs;ubiicis, contendas. </s> |
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| <s>Me quod attinet, is e&longs;t <lb/>ip&longs;emet, quem deduxi aliàs aduer&longs;us Michaelem <lb/>Varronem, qui primus, quod &longs;ciam, eandem po&longs;itio­<lb/>nem ante annos plus minùs &longs;exaginta defendit; de­<lb/>clarando ex ea id incommodi inter cætera con&longs;equi, <lb/>vt, quemadmodum antè in&longs;inuaui, &longs;patia acqui&longs;ita <lb/>in &longs;ine æqualis cuiu&longs;libet temporis numeranda &longs;int, <lb/>vt difformiter, &longs;ic in plu&longs;quàm tripla ratione. </s> | <s>Me quod attinet, is e&longs;t <lb/>ip&longs;emet, quem deduxi aliàs aduer&longs;us Michaelem <lb/>Varronem, qui primus, quod &longs;ciam, eandem po&longs;itio­<lb/>nem ante annos plus minùs &longs;exaginta defendit; de­<lb/>clarando ex ea id incommodi inter cætera con&longs;equi, <lb/>vt, quemadmodum antè in&longs;inuaui, &longs;patia acqui&longs;ita <lb/>in &longs;ine æqualis cuiu&longs;libet temporis numeranda &longs;int, <lb/>vt difformiter, &longs;ic in plu&longs;quàm tripla ratione. </s> |
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